AI Chat Free No Limit — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.
Picture Prowler was an early piece of photo management software developed around and meant to show off Xing Technology's JPEG image decompression library during the early 1990s. Little known today, it featured thumbnail based picture management, printing, etc. The primary developer was Ray Bunnage from compression / decompression libraries developed by Howard Gordon and Chris Eddy.
Read more →
Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a manifold is correctly unfolded, all of the tangent hyperplanes to the manifold will become aligned. It begins by computing the k-nearest neighbors of every point. It computes the tangent space at every point by computing the d-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by data samples, and thus can not be used for classification directly.
Read more →
In statistics, a latent class model (LCM) is a model for clustering multivariate discrete data. It assumes that the data arise from a mixture of discrete distributions, within each of which the variables are independent. It is called a latent class model because the class to which each data point belongs is unobserved (or latent). Latent class analysis (LCA) is a subset of structural equation modeling used to find groups or subtypes of cases in multivariate categorical data. These groups or subtypes of cases are called "latent classes". When faced with the following situation, a researcher might opt to use LCA to better understand the data: Symptoms a, b, c, and d have been recorded in a variety of patients diagnosed with diseases X, Y, and Z. Disease X is associated with symptoms a, b, and c; disease Y is linked to symptoms b, c, and d; and disease Z is connected to symptoms a, c, and d. In this context, the LCA would attempt to detect the presence of latent classes (i.e., the disease entities), thus creating patterns of association in the symptoms. As in factor analysis, LCA can also be used to classify cases according to their maximum likelihood class membership probability. The key criterion for resolving the LCA is identifying latent classes in which the observed symptom associations are effectively rendered null. This is because within each class, the diseases responsible for the symptoms create a structure of dependencies. As a result, the symptoms become conditionally independent, meaning that, given the class a case belongs to, the symptoms are no longer related to one another. == Model == Within each latent class, the observed variables are statistically independent—an essential aspect of latent class modeling. Usually, the observed variables are statistically dependent. By introducing the latent variable, independence is restored in the sense that within classes, variables are independent (local independence). Therefore, the association between the observed variables is explained by the classes of the latent variable (McCutcheon, 1987). In one form, the LCM is written as p i 1 , i 2 , … , i N ≈ ∑ t T p t ∏ n N p i n , t n , {\displaystyle p_{i_{1},i_{2},\ldots ,i_{N}}\approx \sum _{t}^{T}p_{t}\,\prod _{n}^{N}p_{i_{n},t}^{n},} where T {\displaystyle T} is the number of latent classes and p t {\displaystyle p_{t}} are the so-called recruitment or unconditional probabilities that should sum to one. p i n , t n {\displaystyle p_{i_{n},t}^{n}} are the marginal or conditional probabilities. For a two-way latent class model, the form is p i j ≈ ∑ t T p t p i t p j t . {\displaystyle p_{ij}\approx \sum _{t}^{T}p_{t}\,p_{it}\,p_{jt}.} This two-way model is related to probabilistic latent semantic analysis and non-negative matrix factorization. The probability model used in LCA is closely related to the Naive Bayes classifier. The main difference is that in LCA, the class membership of an individual is a latent variable, whereas in Naive Bayes classifiers, the class membership is an observed label. == Related methods == There are a number of methods with distinct names and uses that share a common relationship. Cluster analysis is, like LCA, used to discover taxon-like groups of cases in data. Multivariate mixture estimation (MME) is applicable to continuous data and assumes that such data arise from a mixture of distributions, such as a set of heights arising from a mixture of men and women. If a multivariate mixture estimation is constrained so that measures must be uncorrelated within each distribution, it is termed latent profile analysis. Modified to handle discrete data, this constrained analysis is known as LCA. Discrete latent trait models further constrain the classes to form from segments of a single dimension, allocating members to classes based on that dimension. An example would be assigning cases to social classes based on ability or merit. In a practical instance, the variables could be multiple choice items of a political questionnaire. In this case, the data consists of an N-way contingency table with answers to the items for a number of respondents. In this example, the latent variable refers to political opinion, and the latent classes to political groups. Given group membership, the conditional probabilities specify the chance that certain answers are chosen. == Application == LCA may be used in many fields, such as: collaborative filtering, Behavior Genetics and Evaluation of diagnostic tests.
Read more →
In machine learning, a variational autoencoder (VAE) is an artificial neural network architecture introduced by Diederik P. Kingma and Max Welling in 2013. It is part of the families of probabilistic graphical models and variational Bayesian methods. In addition to being seen as an autoencoder neural network architecture, variational autoencoders can also be studied within the mathematical formulation of variational Bayesian methods, connecting a neural encoder network to its decoder through a probabilistic latent space (for example, as a multivariate Gaussian distribution) that corresponds to the parameters of a variational distribution. Thus, the encoder maps each point (such as an image) from a large complex dataset into a distribution within the latent space, rather than to a single point in that space. The decoder has the opposite function, which is to map from the latent space to the input space, again according to a distribution (although in practice, noise is rarely added during the decoding stage). By mapping a point to a distribution instead of a single point, the network can avoid overfitting the training data. Both networks are typically trained together with the usage of the reparameterization trick, although the variance of the noise model can be learned separately. Although this type of model was initially designed for unsupervised learning, its effectiveness has been proven for semi-supervised learning and supervised learning. == Overview of architecture and operation == A variational autoencoder is a generative model with a prior and noise distribution respectively. Usually such models are trained using the expectation-maximization meta-algorithm (e.g. probabilistic PCA, (spike & slab) sparse coding). Such a scheme optimizes a lower bound of the data likelihood, which is usually computationally intractable, and in doing so requires the discovery of q-distributions, or variational posteriors. These q-distributions are normally parameterized for each individual data point in a separate optimization process. However, variational autoencoders use a neural network as an amortized approach to jointly optimize across data points. In that way, the same parameters are reused for multiple data points, which can result in massive memory savings. The first neural network takes as input the data points themselves, and outputs parameters for the variational distribution. As it maps from a known input space to the low-dimensional latent space, it is called the encoder. The decoder is the second neural network of this model. It is a function that maps from the latent space to the input space, e.g. as the means of the noise distribution. It is possible to use another neural network that maps to the variance, however this can be omitted for simplicity. In such a case, the variance can be optimized with gradient descent. To optimize this model, one needs to know two terms: the "reconstruction error", and the Kullback–Leibler divergence (KL-D). Both terms are derived from the free energy expression of the probabilistic model, and therefore differ depending on the noise distribution and the assumed prior of the data, here referred to as p-distribution. For example, a standard VAE task such as IMAGENET is typically assumed to have a gaussianly distributed noise; however, tasks such as binarized MNIST require a Bernoulli noise. The KL-D from the free energy expression maximizes the probability mass of the q-distribution that overlaps with the p-distribution, which unfortunately can result in mode-seeking behaviour. The "reconstruction" term is the remainder of the free energy expression, and requires a sampling approximation to compute its expectation value. More recent approaches replace Kullback–Leibler divergence (KL-D) with various statistical distances, see "Statistical distance VAE variants" below. == Formulation == From the point of view of probabilistic modeling, one wants to maximize the likelihood of the data x {\displaystyle x} by their chosen parameterized probability distribution p θ ( x ) = p ( x | θ ) {\displaystyle p_{\theta }(x)=p(x|\theta )} . This distribution is usually chosen to be a Gaussian N ( x | μ , σ ) {\displaystyle N(x|\mu ,\sigma )} which is parameterized by μ {\displaystyle \mu } and σ {\displaystyle \sigma } respectively, and as a member of the exponential family it is easy to work with as a noise distribution. Simple distributions are easy enough to maximize, however distributions where a prior is assumed over the latents z {\displaystyle z} results in intractable integrals. Let us find p θ ( x ) {\displaystyle p_{\theta }(x)} via marginalizing over z {\displaystyle z} . p θ ( x ) = ∫ z p θ ( x , z ) d z , {\displaystyle p_{\theta }(x)=\int _{z}p_{\theta }({x,z})\,dz,} where p θ ( x , z ) {\displaystyle p_{\theta }({x,z})} represents the joint distribution under p θ {\displaystyle p_{\theta }} of the observable data x {\displaystyle x} and its latent representation or encoding z {\displaystyle z} . According to the chain rule, the equation can be rewritten as p θ ( x ) = ∫ z p θ ( x | z ) p θ ( z ) d z {\displaystyle p_{\theta }(x)=\int _{z}p_{\theta }({x|z})p_{\theta }(z)\,dz} In the vanilla variational autoencoder, z {\displaystyle z} is usually taken to be a finite-dimensional vector of real numbers, and p θ ( x | z ) {\displaystyle p_{\theta }({x|z})} to be a Gaussian distribution. Then p θ ( x ) {\displaystyle p_{\theta }(x)} is a mixture of Gaussian distributions. It is now possible to define the set of the relationships between the input data and its latent representation as Prior p θ ( z ) {\displaystyle p_{\theta }(z)} Likelihood p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} Posterior p θ ( z | x ) {\displaystyle p_{\theta }(z|x)} Unfortunately, the computation of p θ ( z | x ) {\displaystyle p_{\theta }(z|x)} is expensive and in most cases intractable. To speed up the calculus to make it feasible, it is necessary to introduce a further function to approximate the posterior distribution as q ϕ ( z | x ) ≈ p θ ( z | x ) {\displaystyle q_{\phi }({z|x})\approx p_{\theta }({z|x})} with ϕ {\displaystyle \phi } defined as the set of real values that parametrize q {\displaystyle q} . This is sometimes called amortized inference, since by "investing" in finding a good q ϕ {\displaystyle q_{\phi }} , one can later infer z {\displaystyle z} from x {\displaystyle x} quickly without doing any integrals. In this way, the problem is to find a good probabilistic autoencoder, in which the conditional likelihood distribution p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} is computed by the probabilistic decoder, and the approximated posterior distribution q ϕ ( z | x ) {\displaystyle q_{\phi }(z|x)} is computed by the probabilistic encoder. Parametrize the encoder as E ϕ {\displaystyle E_{\phi }} , and the decoder as D θ {\displaystyle D_{\theta }} . == Evidence lower bound (ELBO) == Like many deep learning approaches that use gradient-based optimization, VAEs require a differentiable loss function to update the network weights through backpropagation. For variational autoencoders, the idea is to jointly optimize the generative model parameters θ {\displaystyle \theta } to reduce the reconstruction error between the input and the output, and ϕ {\displaystyle \phi } to make q ϕ ( z | x ) {\displaystyle q_{\phi }({z|x})} as close as possible to p θ ( z | x ) {\displaystyle p_{\theta }(z|x)} . As reconstruction loss, mean squared error and cross entropy are often used. The Kullback–Leibler divergence D K L ( q ϕ ( z | x ) ∥ p θ ( z | x ) ) {\displaystyle D_{KL}(q_{\phi }({z|x})\parallel p_{\theta }({z|x}))} can be used as a loss function to squeeze q ϕ ( z | x ) {\displaystyle q_{\phi }({z|x})} under p θ ( z | x ) {\displaystyle p_{\theta }(z|x)} . This divergence loss expands to D K L ( q ϕ ( z | x ) ∥ p θ ( z | x ) ) = E z ∼ q ϕ ( ⋅ | x ) [ ln q ϕ ( z | x ) p θ ( z | x ) ] = E z ∼ q ϕ ( ⋅ | x ) [ ln q ϕ ( z | x ) p θ ( x ) p θ ( x , z ) ] = ln p θ ( x ) + E z ∼ q ϕ ( ⋅ | x ) [ ln q ϕ ( z | x ) p θ ( x , z ) ] . {\displaystyle {\begin{aligned}D_{KL}(q_{\phi }({z|x})\parallel p_{\theta }({z|x}))&=\mathbb {E} _{z\sim q_{\phi }(\cdot |x)}\left[\ln {\frac {q_{\phi }(z|x)}{p_{\theta }(z|x)}}\right]\\&=\mathbb {E} _{z\sim q_{\phi }(\cdot |x)}\left[\ln {\frac {q_{\phi }({z|x})p_{\theta }(x)}{p_{\theta }(x,z)}}\right]\\&=\ln p_{\theta }(x)+\mathbb {E} _{z\sim q_{\phi }(\cdot |x)}\left[\ln {\frac {q_{\phi }({z|x})}{p_{\theta }(x,z)}}\right].\end{aligned}}} Now, define the evidence lower bound (ELBO): L θ , ϕ ( x ) := E z ∼ q ϕ ( ⋅ | x ) [ ln p θ ( x , z ) q ϕ ( z | x ) ] = ln p θ ( x ) − D K L ( q ϕ ( ⋅ | x ) ∥ p θ ( ⋅ | x ) ) {\displaystyle L_{\theta ,\phi }(x):=\mathbb {E} _{z\sim q_{\phi }(\cdot |x)}\left[\ln {\frac {p_{\theta }(x,z)}{q_{\phi }({z|x})}}\right]=\ln p_{\theta }(x)-D_{KL}(q_{\phi }({\cdot |x})\parallel p_{\theta }({\cdot |x}))} Maximizing the ELBO θ ∗ , ϕ ∗ = argmax θ , ϕ L θ , ϕ ( x ) {\dis
Read more →
AirFair was a mobile travel application that checks flights, and shows whether a traveler is owed compensation. == History == AirFair was developed in 2016 by Allay Logic Ltd; a Newcastle-based tech-company. == Services == AirFair offered a free flight check to see if compensation is owed. The app could indicate how much the person is owed within minutes whether the flight was delayed, cancelled or the traveler is refused boarding.
Read more →
Triplet loss is a machine learning loss function widely used in one-shot learning, a setting where models are trained to generalize effectively from limited examples. It was conceived by Google researchers for their prominent FaceNet algorithm for face detection. Triplet loss is designed to support metric learning. Namely, to assist training models to learn an embedding (mapping to a feature space) where similar data points are closer together and dissimilar ones are farther apart, enabling robust discrimination across varied conditions. In the context of face detection, data points correspond to images. == Definition == The loss function is defined using triplets of training points of the form ( A , P , N ) {\displaystyle (A,P,N)} . In each triplet, A {\displaystyle A} (called an "anchor point") denotes a reference point of a particular identity, P {\displaystyle P} (called a "positive point") denotes another point of the same identity in point A {\displaystyle A} , and N {\displaystyle N} (called a "negative point") denotes a point of an identity different from the identity in point A {\displaystyle A} and P {\displaystyle P} . Let x {\displaystyle x} be some point and let f ( x ) {\displaystyle f(x)} be the embedding of x {\displaystyle x} in the finite-dimensional Euclidean space. It shall be assumed that the L2-norm of f ( x ) {\displaystyle f(x)} is unity (the L2 norm of a vector X {\displaystyle X} in a finite dimensional Euclidean space is denoted by ‖ X ‖ {\displaystyle \Vert X\Vert } .) We assemble m {\displaystyle m} triplets of points from the training dataset. The goal of training here is to ensure that, after learning, the following condition (called the "triplet constraint") is satisfied by all triplets ( A ( i ) , P ( i ) , N ( i ) ) {\displaystyle (A^{(i)},P^{(i)},N^{(i)})} in the training data set: ‖ f ( A ( i ) ) − f ( P ( i ) ) ‖ 2 2 + α < ‖ f ( A ( i ) ) − f ( N ( i ) ) ‖ 2 2 {\displaystyle \Vert f(A^{(i)})-f(P^{(i)})\Vert _{2}^{2}+\alpha <\Vert f(A^{(i)})-f(N^{(i)})\Vert _{2}^{2}} The variable α {\displaystyle \alpha } is a hyperparameter called the margin, and its value must be set manually. In the FaceNet system, its value was set as 0.2. Thus, the full form of the function to be minimized is the following: L = ∑ i = 1 m max ( ‖ f ( A ( i ) ) − f ( P ( i ) ) ‖ 2 2 − ‖ f ( A ( i ) ) − f ( N ( i ) ) ‖ 2 2 + α , 0 ) {\displaystyle L=\sum _{i=1}^{m}\max {\Big (}\Vert f(A^{(i)})-f(P^{(i)})\Vert _{2}^{2}-\Vert f(A^{(i)})-f(N^{(i)})\Vert _{2}^{2}+\alpha ,0{\Big )}} == Intuition == A baseline for understanding the effectiveness of triplet loss is the contrastive loss, which operates on pairs of samples (rather than triplets). Training with the contrastive loss pulls embeddings of similar pairs closer together, and pushes dissimilar pairs apart. Its pairwise approach is greedy, as it considers each pair in isolation. Triplet loss innovates by considering relative distances. Its goal is that the embedding of an anchor (query) point be closer to positive points than to negative points (also accounting for the margin). It does not try to further optimize the distances once this requirement is met. This is approximated by simultaneously considering two pairs (anchor-positive and anchor-negative), rather than each pair in isolation. == Triplet "mining" == One crucial implementation detail when training with triplet loss is triplet "mining", which focuses on the smart selection of triplets for optimization. This process adds an additional layer of complexity compared to contrastive loss. A naive approach to preparing training data for the triplet loss involves randomly selecting triplets from the dataset. In general, the set of valid triplets of the form ( A ( i ) , P ( i ) , N ( i ) ) {\displaystyle (A^{(i)},P^{(i)},N^{(i)})} is very large. To speed-up training convergence, it is essential to focus on challenging triplets. In the FaceNet paper, several options were explored, eventually arriving at the following. For each anchor-positive pair, the algorithm considers only semi-hard negatives. These are negatives that violate the triplet requirement (i.e, are "hard"), but lie farther from the anchor than the positive (not too hard). Restated, for each A ( i ) {\displaystyle A^{(i)}} and P ( i ) {\displaystyle P^{(i)}} , they seek N ( i ) {\displaystyle N^{(i)}} such that: The rationale for this design choice is heuristic. It may appear puzzling that the mining process neglects "very hard" negatives (i.e., closer to the anchor than the positive). Experiments conducted by the FaceNet designers found that this often leads to a convergence to degenerate local minima. Triplet mining is performed at each training step, from within the sample points contained in the training batch (this is known as online mining), after embeddings were computed for all points in the batch. While ideally the entire dataset could be used, this is impractical in general. To support a large search space for triplets, the FaceNet authors used very large batches (1800 samples). Batches are constructed by selecting a large number of same-category sample points (40), and randomly selected negatives for them. == Extensions == Triplet loss has been extended to simultaneously maintain a series of distance orders by optimizing a continuous relevance degree with a chain (i.e., ladder) of distance inequalities. This leads to the Ladder Loss, which has been demonstrated to offer performance enhancements of visual-semantic embedding in learning to rank tasks. In Natural Language Processing, triplet loss is one of the loss functions considered for BERT fine-tuning in the SBERT architecture. Other extensions involve specifying multiple negatives (multiple negatives ranking loss).
Read more →
In the United States, prescription monitoring programs (PMPs) or prescription drug monitoring programs (PDMPs) are state-run programs which collect and distribute data about the prescription and dispensation of federally controlled substances and, depending on state requirements, other potentially abusable prescription drugs. PMPs are meant to help prevent adverse drug-related events such as opioid overdoses, drug diversion, and substance abuse by decreasing the amount and/or frequency of opioid prescribing, and by identifying those patients who are obtaining prescriptions from multiple providers (i.e., "doctor shopping") or those physicians overprescribing opioids. Most US health care workers support the idea of PMPs, which intend to assist physicians, physician assistants, nurse practitioners, dentists and other prescribers, the pharmacists, chemists and support staff of dispensing establishments. The database, whose use is required by State law, typically requires prescribers and pharmacies dispensing controlled substances to register with their respective state PMPs and (for pharmacies and providers who dispense from their offices) to report the dispensation of such prescriptions to an electronic online database. The majority of PMPs are authorized to notify law enforcement agencies or licensing boards or physicians when a prescriber, or patients receiving prescriptions, exceed thresholds established by the state or prescription recipient exceeds thresholds established by the State. All states have implemented PDMPs, although evidence for the effectiveness of these programs is mixed. While prescription of opioids has decreased with PMP use, overdose deaths in many states have actually increased, with those states sharing data with neighboring jurisdictions or requiring reporting of more drugs experiencing highest increases in deaths. This may be because those declined opioid prescriptions turn to street drugs, whose potency and contaminants carry greater overdose risk. == History == Prescription drug monitoring programs, or PDMPs, are an example of one initiative proposed to alleviate effects of the opioid crisis. The programs are designed to restrict prescription drug abuse by limiting a patient's ability to obtain similar prescriptions from multiple providers (i.e. “doctor shopping”) and reducing diversion of controlled substances. This is meant to reduce risk of fatal overdose caused by high doses of opioids or interactions between opioids and benzodiazepenes, and to enable better decision making on the part of healthcare providers who may be unaware of a patient's prescription drug use, history or other prescriptions. PDMPs have been implemented in state legislations since 1939 in California, a time before electronic medical records, though implementation rose alongside increased awareness of overprescribing of opioids and overdose. A later New York state program was struck down by the U.S. Supreme Court in Whalen v. Roe. But, by 2019, 49 states, the District of Columbia, and Guam had enacted PDMP legislation. In 2021 Missouri, the last State to not use a PMP, adopted legislation to create one. PMPs are constantly being updated to increase speed of data collection, sharing of data across States, and ease of interpretation. This is being done by integrating PDMP reports with other health information technologies such as health information exchanges (HIE), electronic health record (EHR) systems, and/ or pharmacy dispensing software systems. One program that has been implemented in nine states is called the PDMP Electronic Health Records Integration and Interoperability Expansion, also known as PEHRIIE. Another software, marketed by Bamboo Health and integrated with PMPs in 43 states, uses an algorithm to track factors thought to increase risk of diversion, abuse or overdose, and assigns patients a three digit score based on presumed indicators of risk. While some studies have suggested that PDMP-HIT integration and sharing of interstate data brings benefits such as reduced opioid-related inpatient morbidity, others have found no or negative impact on mortality compared to states without PMP data sharing. Patient and media reports suggest need for testing and evaluation of algorithmic software used to score risk, with some patients reporting denial of prescriptions without c explanation or clarity of data. == Goals == Most health care workers support PMPs which intend to assist physicians, physician assistants, nurse practitioners, dentists and other prescribers, the pharmacists, chemists and support staff of dispensing establishments, as well as law-enforcement agencies. The collaboration supports the legitimate medical use of controlled substances while limiting their abuse and diversion. Pharmacies dispensing controlled substances and prescribers typically must register with their respective state PMPs and (for pharmacies and providers who dispense controlled substances from their offices) report the dispensation to an electronic online database. Some pharmacy software can submit these reports automatically to multiple states. == Usage == === List of programs by state === === Software systems === NarxCare is a prescription drug monitoring program (PDMP) run by Bamboo Health. Bamboo Health was formerly known as Appriss. It is widely used across the United States by pharmacies including Rite Aid as well as those at Walmart and Sam’s Club. The NarxCare software allows doctors to view data about a patient, combining data from the prescription registries of various U.S. states to make the registries interoperable nationally. It also uses machine learning to generate an "Overdose Risk Score" that potentially includes EMS and criminal justice data; these scores have been criticized by researchers and patient advocates for the lack of transparency in the process as well as the potential for disparate treatment of women and minority groups. Advertised as an "analytics tool and care management platform", the NarxCare software allows doctors to view data about a patient including how many pharmacies they have visited and the combinations of medication they are prescribed. It combines data from the prescription registries of various U.S. states, making the registries interoperable nationally. It additionally uses machine learning to generate various three-digit "risk scores" and an overall "Overdose Risk Score", collectively referred to as Narx Scores, in a process that potentially includes EMS and criminal justice data as well as court records. == Controversy == Many doctors and researchers support the idea of PDMPs as a tool in combatting the opioid epidemic. Opioid prescribing, opioid diversion and supply, opioid misuse, and opioid-related morbidity and mortality are common elements in data entered into PDMPs. Prescription Monitoring Programs are purported to offer economic benefits for the states who implement them by decreasing overall health care costs, lost productivity, and investigation times. However, there are many studies that conclude the impact of PDMPs is unclear. While use of PMPs has been accompanied by decrease in opioid prescribing, few analyses consider corresponding use of street opioids, extramedical use, or diversion, which might provide a more holistic method for evaluation of PMP intent and efficacy. Evidence for PDMP impact on fatal overdoses is decidedly mixed, with multiple studies finding increased overdose rates in some states, decreases in others, or no clear impact. Interestingly, an increase in heroin overdoses after PDMP implementation has been commonly reported, presumably as denial of prescription opioids sends patients in search of street drugs. Narx Scores have been criticized by researchers and patient advocates for the lack of transparency in the generation process as well as the potential for disparate treatment of women and minority groups. Writing in Duke Law Journal, Jennifer Oliva stated that "black-box algorithms" are used to generate the scores.
Read more →
The World Programming System, also known as WPS Analytics or WPS, is a software product developed by a company called World Programming (acquired by Altair Engineering). WPS Analytics supports users of mixed ability to access and process data and to perform data science tasks. It has interactive visual programming tools using data workflows, and it has coding tools supporting the use of the SAS language mixed with Python, R and SQL. == About == WPS can use programs written in the language of SAS without the need for translating them into any other language. In this regard WPS is compatible with the SAS system. WPS has a built-in language interpreter able to process the language of SAS and produce similar results. WPS is available to run on z/OS, Windows, macOS, Linux (x86, Armv8 64-bit, IBM Power LE, IBM Z), and AIX. On all supported platforms, programs written in the language of SAS can be executed from a WPS command line interface, often referred to as running in batch mode. WPS can also be used from a graphical user interface known as the WPS Workbench for managing, editing and running programs written in the language of SAS. The WPS Workbench user interface is based on Eclipse. WPS version 4 (released in March 2018) introduced a drag-and-drop workflow canvas providing interactive blocks for data retrieval, blending and preparation, data discovery and profiling, predictive modelling powered by machine learning algorithms, model performance validation and scorecards. WPS version 3 (released in February 2012) provided a new client/server architecture that allows the WPS Workbench GUI to execute SAS programs on remote server installations of WPS in a network or cloud. The resulting output, data sets, logs, etc., can then all be viewed and manipulated from inside the Workbench as if the workloads had been executed locally. SAS programs do not require any special language statements to use this feature. == Summary of main features == Runs on Windows, macOS, z/OS, Linux (x86, Armv8 64-bit, IBM Power LE, IBM Z), and AIX An integrated development environment based on Eclipse for Linux, macOS and Windows. Support for language of SAS elements. Support for the language of SAS Macros. Matrix Programming support using PROC IML. Support for generating band plots, bar charts, box plots, bubble plots, contour plots, dendrogram plots, ellipse plots, fringe plots, heat maps, high-low plots, histograms, loess plots, needle plots, pie charts, penalised b-spline, radar charts, reference lines, scatter plots, series plots, step plots, regression plots and vector plots. Support for statistical procedures ACECLUS, ASSOCRULES, ANOVA, BIN, BOXPLOT, CANCORR, CANDISC, CLUSTER, CORRESP, DISCRIM, DISTANCE, FACTOR, FASTCLUS, FREQ, GAM, GANNO, GENMOD, GLIMMIX, GLM, GLMMOD, GLMSELECT, ICLIFETEST, KDE, LIFEREG, LIFETEST, LOESS, LOGISTIC, MDS, MEANS, MI, MIANALYSE, MIXED, MODECLUS, NESTED, NLIN, NPAR1WAY, PHREG, PLAN, PLS, POWER, PRINCOMP, PROBIT, QUANTREG, RBF, REG, ROBUSTREG, RSREG, SCORE, SEGMENT, SIMNORMAL, STANDARD, STDSIZE, STDRATE, STEPDISC, SUMMARY, SURVEYMEANS, SURVEYSELECT, TPSPLINE, TRANSREG, TREE, TTEST, UNIVARIATE, VARCLUS, VARCOMP Support for time series procedures ARIMA, AUTOREG, ESM, EXPAND, FORECAST, LOAN, SEVERITY, SPECTRA, TIMESERIES, X12 Support for machine learning procedures DECISIONFOREST, DECISIONTREE, GMM, MLP, OPTIMALBIN, SEGMENT, SVM Support for ODS. Reads and writes SAS datasets (compressed or uncompressed). Access: Actian Matrix (previously known as ParAccel), DASD, DB2, Excel, Greenplum, Hadoop, Informix, Kognitio Archived 2012-08-24 at the Wayback Machine, MariaDB, MySQL, Netezza, ODBC, OLEDB, Oracle, PostgreSQL, SAND, Snowflake, SPSS/PSPP, SQL Server, Sybase, Sybase IQ, Teradata, VSAM, Vertica and XML. Support for SAS Tape Format. Direct output of reports to CSV, PDF and HTML. Support to connect WPS systems programmatically, remote submit parts of a program to execute on connected remote servers, upload and download data between the connected systems. Support for Hadoop Support for R Support for Python == Industry recognition == Gartner recognized World Programming in their Cool Vendors in Data Science, 2014 Report. == Lawsuit == In 2010 World Programming defended its use of the language of SAS in the High Court of England and Wales in SAS Institute Inc. v World Programming Ltd. The software was the subject of a lawsuit by SAS Institute. The EU Court of Justice ruled in favor of World Programming, stating that the copyright protection does not extend to the software functionality, the programming language used and the format of the data files used by the program. It stated that there is no copyright infringement when a company which does not have access to the source code of a program studies, observes and tests that program to create another program with the same functionality.
Read more →
A pedagogical agent is a concept borrowed from computer science and artificial intelligence and applied to education, usually as part of an intelligent tutoring system (ITS). It is a simulated human-like interface between the learner and the content, in an educational environment. A pedagogical agent is designed to model the type of interactions between a student and another person. Mabanza and de Wet define it as "a character enacted by a computer that interacts with the user in a socially engaging manner". A pedagogical agent can be assigned different roles in the learning environment, such as tutor or co-learner, depending on the desired purpose of the agent. "A tutor agent plays the role of a teacher, while a co-learner agent plays the role of a learning companion". == History == The history of Pedagogical Agents is closely aligned with the history of computer animation. As computer animation progressed, it was adopted by educators to enhance computerized learning by including a lifelike interface between the program and the learner. The first versions of a pedagogical agent were more cartoon than person, like Microsoft's Clippy which helped users of Microsoft Office load and use the program's features in 1997. However, with developments in computer animation, pedagogical agents can now look lifelike. By 2006 there was a call to develop modular, reusable agents to decrease the time and expertise required to create a pedagogical agent. There was also a call in 2009 to enact agent standards. The standardization and re-usability of pedagogical agents is less of an issue since the decrease in cost and widespread availability of animation tools. Individualized pedagogical agents can be found across disciplines including medicine, math, law, language learning, automotive, and armed forces. They are used in applications directed to every age, from preschool to adult. == Learning theories related to pedagogical agent design == === Distributed cognition theory === Distributed cognition theory is the method in which cognition progresses in the context of collaboration with others. Pedagogical agents can be designed to assist the cognitive transfer to the learner, operating as artifacts or partners with collaborative role in learning. To support the performance of an action by the user, the pedagogical agent can act as a cognitive tool as long as the agent is equipped with the knowledge that the user lacks. The interactions between the user and the pedagogical agent can facilitate a social relationship. The pedagogical agent may fulfill the role of a working partner. === Socio-cultural learning theory === Socio-cultural learning theory is how the user develops when they are involved in learning activities in which there is interaction with other agents. A pedagogical agent can: intervene when the user requests, provide support for tasks that the user cannot address, and potentially extend the learners cognitive reach. Interaction with the pedagogical agent may elicit a variety of emotions from the learner. The learner may become excited, confused, frustrated, and/or discouraged. These emotions affect the learners' motivation. === Extraneous Cognitive Load === Extraneous cognitive load is the extra effort being exerted by an individual's working memory due to the way information is being presented. A pedagogical agent can increase the user's cognitive load by distracting them and becoming the focus of their attention, causing split attention between the instructional material and the agent. Agents can reduce the perceived cognitive load by providing narration and personalization that can also promote a user's interest and motivation. While research on the reduction of cognitive load from pedagogical agents is minimal, more studies have shown that agents do not increase it. == Effectiveness == It has been suggested by researchers that pedagogical agents may take on different roles in the learning environment. Examples of these roles are: supplanting, scaffolding, coaching, testing, or demonstrating or modelling a procedure. A pedagogical agent as a tutor has not been demonstrated to add any benefit to an educational strategy in equivalent lessons with and without a pedagogical agent. According to Richard Mayer, there is some support in research for pedagogical agent increasing learning, but only as a presenter of social cues. A co-learner pedagogical agent is believed to increase the student's self-efficacy. By pointing out important features of instructional content, a pedagogical agent can fulfill the signaling function, which research on multimedia learning has shown to enhance learning. Research has demonstrated that human-human interaction may not be completely replaced by pedagogical agents, but learners may prefer the agents to non-agent multimedia systems. This finding is supported by social agency theory. Much like the varying effectiveness of the pedagogical agent roles in the learning environment, agents that take into account the user's affect have had mixed results. Research has shown pedagogical agents that make use of the users’ affect have been found to increase user knowledge retention, motivation, and perceived self-efficacy. However, with such a broad range of modalities in affective expressions, it is often difficult to utilize them. Additionally, having agents detect a user's affective state with precision remains challenging, as displays of affect are different across individuals. == Design == === Attractiveness === The appearance of a pedagogical agent can be manipulated to meet the learning requirements. The attractiveness of a pedagogical agent can enhance student's learning when the users were the opposite gender of the pedagogical agent. Male students prefer a sexy appearance of a female pedagogical agents and dislike the sexy appearance of male agents. Female students were not attracted by the sexy appearance of either male or female pedagogical agents. === Affective Response === Pedagogical agents have reached a point where they can convey and elicit emotion, but also reason about and respond to it. These agents are often designed to elicit and respond to affective actions from users through various modalities such as speech, facial expressions, and body gestures. They respond to the affective state of the given user, and make use of these modalities using a wide array of sensors incorporated into the design of the agent. Specifically in education and training applications, pedagogical agents are often designed to increasingly recognize when users or learners exhibit frustration, boredom, confusion, and states of flow. The added recognition in these agents is a step toward making them more emotionally intelligent, comforting and motivating the users as they interact. === Digital Representation === The design of a pedagogical agent often begins with its digital representation, whether it will be 2D or 3D and static or animated. Several studies have developed pedagogical agents that were both static and animated, then evaluated the relative benefits. Similar to other design considerations, the improved learning from static or animated agents remains questionable. One study showed that the appearance of an agent portrayed using a static image can impact a user's recall, based on the visual appearance. Other research found results that suggest static agent images improve learning outcomes. However, several other studies found user's learned more when the pedagogical agent was animated rather than static. Recently a meta-analysis of such research found a negligible improvement in learning via pedagogical agents, suggesting more work needs to be done in the area to support any claims.
Read more →
Proximal policy optimization (PPO) is a reinforcement learning (RL) algorithm for training an intelligent agent. Specifically, it is a policy gradient method, often used for deep RL when the policy network is very large. == History == The predecessor to PPO, Trust Region Policy Optimization (TRPO), was published in 2015. It addressed the instability issue of another algorithm, the Deep Q-Network (DQN), by using the trust region method to limit the KL divergence between the old and new policies. However, TRPO uses the Hessian matrix (a matrix of second derivatives) to enforce the trust region, but the Hessian is inefficient for large-scale problems. PPO was published in 2017. It was essentially an approximation of TRPO that does not require computing the Hessian. The KL divergence constraint was approximated by simply clipping the policy gradient. Since 2018, PPO was the default RL algorithm at OpenAI. PPO has been applied to many areas, such as controlling a robotic arm, beating professional players at Dota 2 (OpenAI Five), and playing Atari games. == TRPO == TRPO, the predecessor of PPO, is an on-policy algorithm. It can be used for environments with either discrete or continuous action spaces. The pseudocode is as follows: Input: initial policy parameters θ 0 {\textstyle \theta _{0}} , initial value function parameters ϕ 0 {\textstyle \phi _{0}} Hyperparameters: KL-divergence limit δ {\textstyle \delta } , backtracking coefficient α {\textstyle \alpha } , maximum number of backtracking steps K {\textstyle K} for k = 0 , 1 , 2 , … {\textstyle k=0,1,2,\ldots } do Collect set of trajectories D k = { τ i } {\textstyle {\mathcal {D}}_{k}=\left\{\tau _{i}\right\}} by running policy π k = π ( θ k ) {\textstyle \pi _{k}=\pi \left(\theta _{k}\right)} in the environment. Compute rewards-to-go R ^ t {\textstyle {\hat {R}}_{t}} . Compute advantage estimates, A ^ t {\textstyle {\hat {A}}_{t}} (using any method of advantage estimation) based on the current value function V ϕ k {\textstyle V_{\phi _{k}}} . Estimate policy gradient as g ^ k = 1 | D k | ∑ τ ∈ D k ∑ t = 0 T ∇ θ log π θ ( a t ∣ s t ) | θ k A ^ t {\displaystyle {\hat {g}}_{k}=\left.{\frac {1}{\left|{\mathcal {D}}_{k}\right|}}\sum _{\tau \in {\mathcal {D}}_{k}}\sum _{t=0}^{T}\nabla _{\theta }\log \pi _{\theta }\left(a_{t}\mid s_{t}\right)\right|_{\theta _{k}}{\hat {A}}_{t}} Use the conjugate gradient algorithm to compute x ^ k ≈ H ^ k − 1 g ^ k {\displaystyle {\hat {x}}_{k}\approx {\hat {H}}_{k}^{-1}{\hat {g}}_{k}} where H ^ k {\textstyle {\hat {H}}_{k}} is the Hessian of the sample average KL-divergence. Update the policy by backtracking line search with θ k + 1 = θ k + α j 2 δ x ^ k T H ^ k x ^ k x ^ k {\displaystyle \theta _{k+1}=\theta _{k}+\alpha ^{j}{\sqrt {\frac {2\delta }{{\hat {x}}_{k}^{T}{\hat {H}}_{k}{\hat {x}}_{k}}}}{\hat {x}}_{k}} where j ∈ { 0 , 1 , 2 , … K } {\textstyle j\in \{0,1,2,\ldots K\}} is the smallest value which improves the sample loss and satisfies the sample KL-divergence constraint. Fit value function by regression on mean-squared error: ϕ k + 1 = arg min ϕ 1 | D k | T ∑ τ ∈ D k ∑ t = 0 T ( V ϕ ( s t ) − R ^ t ) 2 {\displaystyle \phi _{k+1}=\arg \min _{\phi }{\frac {1}{\left|{\mathcal {D}}_{k}\right|T}}\sum _{\tau \in {\mathcal {D}}_{k}}\sum _{t=0}^{T}\left(V_{\phi }\left(s_{t}\right)-{\hat {R}}_{t}\right)^{2}} typically via some gradient descent algorithm. == PPO == The pseudocode is as follows: Input: initial policy parameters θ 0 {\textstyle \theta _{0}} , initial value function parameters ϕ 0 {\textstyle \phi _{0}} for k = 0 , 1 , 2 , … {\textstyle k=0,1,2,\ldots } do Collect set of trajectories D k = { τ i } {\textstyle {\mathcal {D}}_{k}=\left\{\tau _{i}\right\}} by running policy π k = π ( θ k ) {\textstyle \pi _{k}=\pi \left(\theta _{k}\right)} in the environment. Compute rewards-to-go R ^ t {\textstyle {\hat {R}}_{t}} . Compute advantage estimates, A ^ t {\textstyle {\hat {A}}_{t}} (using any method of advantage estimation) based on the current value function V ϕ k {\textstyle V_{\phi _{k}}} . Update the policy by maximizing the PPO-Clip objective: θ k + 1 = arg max θ 1 | D k | T ∑ τ ∈ D k ∑ t = 0 T min ( π θ ( a t ∣ s t ) π θ k ( a t ∣ s t ) A π θ k ( s t , a t ) , g ( ϵ , A π θ k ( s t , a t ) ) ) {\displaystyle \theta _{k+1}=\arg \max _{\theta }{\frac {1}{\left|{\mathcal {D}}_{k}\right|T}}\sum _{\tau \in {\mathcal {D}}_{k}}\sum _{t=0}^{T}\min \left({\frac {\pi _{\theta }\left(a_{t}\mid s_{t}\right)}{\pi _{\theta _{k}}\left(a_{t}\mid s_{t}\right)}}A^{\pi _{\theta _{k}}}\left(s_{t},a_{t}\right),\quad g\left(\epsilon ,A^{\pi _{\theta _{k}}}\left(s_{t},a_{t}\right)\right)\right)} typically via stochastic gradient ascent with Adam. Fit value function by regression on mean-squared error: ϕ k + 1 = arg min ϕ 1 | D k | T ∑ τ ∈ D k ∑ t = 0 T ( V ϕ ( s t ) − R ^ t ) 2 {\displaystyle \phi _{k+1}=\arg \min _{\phi }{\frac {1}{\left|{\mathcal {D}}_{k}\right|T}}\sum _{\tau \in {\mathcal {D}}_{k}}\sum _{t=0}^{T}\left(V_{\phi }\left(s_{t}\right)-{\hat {R}}_{t}\right)^{2}} typically via some gradient descent algorithm. Like all policy gradient methods, PPO is used for training an RL agent whose actions are determined by a differentiable policy function by gradient ascent. Intuitively, a policy gradient method takes small policy update steps, so the agent can reach higher and higher rewards in expectation. Policy gradient methods may be unstable: A step size that is too big may direct the policy in a suboptimal direction, thus having little possibility of recovery; a step size that is too small lowers the overall efficiency. To solve the instability, PPO implements a clip function that constrains the policy update of an agent from being too large, so that larger step sizes may be used without negatively affecting the gradient ascent process. === Basic concepts === To begin the PPO training process, the agent is set in an environment to perform actions based on its current input. In the early phase of training, the agent can freely explore solutions and keep track of the result. Later, with a certain amount of transition samples and policy updates, the agent will select an action to take by randomly sampling from the probability distribution P ( A | S ) {\displaystyle P(A|S)} generated by the policy network. The actions that are most likely to be beneficial will have the highest probability of being selected from the random sample. After an agent arrives at a different scenario (a new state) by acting, it is rewarded with a positive reward or a negative reward. The objective of an agent is to maximize the cumulative reward signal across sequences of states, known as episodes. === Policy gradient laws: the advantage function === The advantage function (denoted as A {\displaystyle A} ) is central to PPO, as it tries to answer the question of whether a specific action of the agent is better or worse than some other possible action in a given state. By definition, the advantage function is an estimate of the relative value for a selected action. If the output of this function is positive, it means that the action in question is better than the average return, so the possibilities of selecting that specific action will increase. The opposite is true for a negative advantage output. The advantage function can be defined as A = Q − V {\displaystyle A=Q-V} , where Q {\displaystyle Q} is the discounted sum of rewards (the total weighted reward for the completion of an episode) and V {\displaystyle V} is the baseline estimate. Since the advantage function is calculated after the completion of an episode, the program records the outcome of the episode. Therefore, calculating advantage is essentially an unsupervised learning problem. The baseline estimate comes from the value function that outputs the expected discounted sum of an episode starting from the current state. In the PPO algorithm, the baseline estimate will be noisy (with some variance), as it also uses a neural network, like the policy function itself. With Q {\displaystyle Q} and V {\displaystyle V} computed, the advantage function is calculated by subtracting the baseline estimate from the actual discounted return. If A > 0 {\displaystyle A>0} , the actual return of the action is better than the expected return from experience; if A < 0 {\displaystyle A<0} , the actual return is worse. === Ratio function === In PPO, the ratio function ( r t {\displaystyle r_{t}} ) calculates the probability of selecting action a {\displaystyle a} in state s {\displaystyle s} given the current policy network, divided by the previous probability under the old policy. In other words: If r t ( θ ) > 1 {\displaystyle r_{t}(\theta )>1} , where θ {\displaystyle \theta } are the policy network parameters, then selecting action a {\displaystyle a} in state s {\displaystyle s} is more likely based on the current policy than the previous policy. If 0 ≤ r t ( θ ) < 1 {\displaystyle 0\leq r_{t}(\theta )<1} , then selecting actio
Read more →
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.). Multinomial logistic regression is known by a variety of other names, including polytomous LR, multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model. == Background == Multinomial logistic regression is used when the dependent variable in question is nominal (equivalently categorical, meaning that it falls into any one of a set of categories that cannot be ordered in any meaningful way) and for which there are more than two categories. Some examples would be: Which major will a college student choose, given their grades, stated likes and dislikes, etc.? Which blood type does a person have, given the results of various diagnostic tests? In a hands-free mobile phone dialing application, which person's name was spoken, given various properties of the speech signal? Which candidate will a person vote for, given particular demographic characteristics? Which country will a firm locate an office in, given the characteristics of the firm and of the various candidate countries? These are all statistical classification problems. They all have in common a dependent variable to be predicted that comes from one of a limited set of items that cannot be meaningfully ordered, as well as a set of independent variables (also known as features, explanators, etc.), which are used to predict the dependent variable. Multinomial logistic regression is a particular solution to classification problems that use a linear combination of the observed features and some problem-specific parameters to estimate the probability of each particular value of the dependent variable. The best values of the parameters for a given problem are usually determined from some training data (e.g. some people for whom both the diagnostic test results and blood types are known, or some examples of known words being spoken). == Assumptions == The multinomial logistic model assumes that data are case-specific; that is, each independent variable has a single value for each case. As with other types of regression, there is no need for the independent variables to be statistically independent from each other (unlike, for example, in a naive Bayes classifier); however, collinearity is assumed to be relatively low, as it becomes difficult to differentiate between the impact of several variables if this is not the case. If the multinomial logit is used to model choices, it relies on the assumption of independence of irrelevant alternatives (IIA), which is not always desirable. This assumption states that the odds of preferring one class over another do not depend on the presence or absence of other "irrelevant" alternatives. For example, the relative probabilities of taking a car or bus to work do not change if a bicycle is added as an additional possibility. This allows the choice of K alternatives to be modeled as a set of K − 1 independent binary choices, in which one alternative is chosen as a "pivot" and the other K − 1 compared against it, one at a time. The IIA hypothesis is a core hypothesis in rational choice theory; however numerous studies in psychology show that individuals often violate this assumption when making choices. An example of a problem case arises if choices include a car and a blue bus. Suppose the odds ratio between the two is 1 : 1. Now if the option of a red bus is introduced, a person may be indifferent between a red and a blue bus, and hence may exhibit a car : blue bus : red bus odds ratio of 1 : 0.5 : 0.5, thus maintaining a 1 : 1 ratio of car : any bus while adopting a changed car : blue bus ratio of 1 : 0.5. Here the red bus option was not in fact irrelevant, because a red bus was a perfect substitute for a blue bus. If the multinomial logit is used to model choices, it may in some situations impose too much constraint on the relative preferences between the different alternatives. It is especially important to take into account if the analysis aims to predict how choices would change if one alternative were to disappear (for instance if one political candidate withdraws from a three candidate race). Other models like the nested logit or the multinomial probit may be used in such cases as they allow for violation of the IIA. == Model == === Introduction === There are multiple equivalent ways to describe the mathematical model underlying multinomial logistic regression. This can make it difficult to compare different treatments of the subject in different texts. The article on logistic regression presents a number of equivalent formulations of simple logistic regression, and many of these have analogues in the multinomial logit model. The idea behind all of them, as in many other statistical classification techniques, is to construct a linear predictor function that constructs a score from a set of weights that are linearly combined with the explanatory variables (features) of a given observation using a dot product: score ( X i , k ) = β k ⋅ X i , {\displaystyle \operatorname {score} (\mathbf {X} _{i},k)={\boldsymbol {\beta }}_{k}\cdot \mathbf {X} _{i},} where Xi is the vector of explanatory variables describing observation i, βk is a vector of weights (or regression coefficients) corresponding to outcome k, and score(Xi, k) is the score associated with assigning observation i to category k. In discrete choice theory, where observations represent people and outcomes represent choices, the score is considered the utility associated with person i choosing outcome k. The predicted outcome is the one with the highest score. The difference between the multinomial logit model and numerous other methods, models, algorithms, etc. with the same basic setup (the perceptron algorithm, support vector machines, linear discriminant analysis, etc.) is the procedure for determining (training) the optimal weights/coefficients and the way that the score is interpreted. In particular, in the multinomial logit model, the score can directly be converted to a probability value, indicating the probability of observation i choosing outcome k given the measured characteristics of the observation. This provides a principled way of incorporating the prediction of a particular multinomial logit model into a larger procedure that may involve multiple such predictions, each with a possibility of error. Without such means of combining predictions, errors tend to multiply. For example, imagine a large predictive model that is broken down into a series of submodels where the prediction of a given submodel is used as the input of another submodel, and that prediction is in turn used as the input into a third submodel, etc. If each submodel has 90% accuracy in its predictions, and there are five submodels in series, then the overall model has only 0.95 = 59% accuracy. If each submodel has 80% accuracy, then overall accuracy drops to 0.85 = 33% accuracy. This issue is known as error propagation and is a serious problem in real-world predictive models, which are usually composed of numerous parts. Predicting probabilities of each possible outcome, rather than simply making a single optimal prediction, is one means of alleviating this issue. === Setup === The basic setup is the same as in logistic regression, the only difference being that the dependent variables are categorical rather than binary, i.e. there are K possible outcomes rather than just two. The following description is somewhat shortened; for more details, consult the logistic regression article. ==== Data points ==== Specifically, it is assumed that we have a series of N observed data points. Each data point i (ranging from 1 to N) consists of a set of M explanatory variables x1,i ... xM,i (also known as independent variables, predictor variables, features, etc.), and an associated categorical outcome Yi (also known as dependent variable, response variable), which can take on one of K possible values. These possible values represent logically separate categories (e.g. different political parties, blood types, etc.), and are often described mathematically by arbitrarily assigning each a number from 1 to K. The explanatory variables and outcome represent observed properties of the data points, and are often thought of as originating in the observations of N "experiments" — although an "experiment" may consist of nothing more than gathering data. The goal of multinomial logistic regression is to construct a model that explains the relationship between the explanatory variables and the outcome, so tha
Read more →
The Ni1000 is an artificial neural network chip developed by Nestor Corporation and Intel, developed in the 1990s. It is Intel's second-generation neural network chip, but the first all-digital chip. The chip is aimed at image analysis applications– containing more than 3 million transistors – and can analyze 40,000 patterns per second. Prototypes running Nestor's OCR software in 1994 were capable of recognizing around 100 handwritten characters per second. The development was funded with money from DARPA and Office of Naval Research.
Read more →
The LENA Foundation is an American nonprofit organisation which provides tools for measuring children's language acquisition and exposure. Specifically, the LENA system consists of a digital language processor which is worn by a child and records and analyses their auditory environment, using propriety software. It then presents a summary of child-adult conversation, such as conversation turns and word counts. The purpose of the LENA system is to encourage interactive talk between children (between the age of two to forty-eight months) and their caretakers. The LENA system is also used for research; while useful for researchers who wish to save transcription costs or observe the child in its natural state, the accuracy of this system, while often quite high, varies between contexts, for example notably in the case of hard of hearing children. Because of this, several researchers recommend caution in using only the LENA system on its own for the purposes of scientific research. == History == The LENA Foundation was established in 2009 by Terrance and Judith Paul, founders of Renaissance Learning, Inc., with the purpose of aiding children with disabilities and assisting with early learning. They were inspired by the book "Meaningful Differences in the Everyday Experience of American Children" by Dr. Betty Hart and Dr. Todd Risley. A pilot version of the LENA system was launched in February 2006. The LENA Research Foundation was registered as a tax-exempt 501(c)(3) nonprofit in September 2010. The organisation was renamed simply LENA in 2018 and adopted the tagline "Building brains through early talk." LENA has been used for parental feedback, linguistics or paediatrics research, and for specific clinical cases. == Scientific background == In 2018, research using the LENA system showed that there was a link between children's conversational turns and activation of Broca's area (a part of the brain responsible, although not necessarily essential, for language processing). The LENA foundation cites research by its own employees as evidence for the scientific basis of its technology. Said research claims that verbal interaction with young children has an effect on language acquisition, including verbal comprehension skills during adolescence. == LENA System == The LENA software analyses a child's natural language environment, such as verbal exposure, and provides several metrics, such as adult and child speech time, television/recorded audio time, word count, or conversation turn count. The LENA hardware is a recorder that is usually placed into a child's specially-designed vest. The software was trained on over 65,000 hours of manually annotated American English audio recordings. It splits the audio into segments which are categorised as "key child", "other child", "male adult", "noise", etc. The advantages of LENA as opposed to manual transcription are its speed and ease of use; the disadvantages are its potential inaccuracies and lack of transcription capability (which LENA does not profess to attempt). The LENA system has also been criticised for prioritising quantity of speaking over quality (i.e., mastery of the language, as opposed to babble). == Product lines == === LENA Start === LENA Start is a program for parents that utilises feedback from the LENA System in conjunction with weekly group sessions in order to address the home language environment. It was introduced in 2015 and implemented across several U.S. states. In October 2020, during the restrictions of the COVID-19 pandemic, Read Aloud Delaware began a virtual LENA Start program with families statewide, where parents received feedback and participated in one-hour Zoom workshops each week during the 10-week program. === LENA Grow === LENA Grow is a professional development program for teachers in early childhood classrooms. Before launching at sites around the country, the program was first piloted in Escambia County, Florida. === LENA Home === LENA Home is a supplement to existing parent coaching curricula. Typically, home visitors facilitate the use of the LENA System to help parents track their progress towards increasing interactive talk in their homes. === Developmental Snapshot === The LENA Developmental Snapshot, based on a 52-question parent survey, assesses both expressive and receptive language skills and provides an estimate of a child's developmental age from 2 months to 36 months.
Read more →
abess (Adaptive Best Subset Selection, also ABESS) is a machine learning method designed to address the problem of best subset selection. It aims to determine which features or variables are crucial for optimal model performance when provided with a dataset and a prediction task. abess was introduced by Zhu in 2020 and it dynamically selects the appropriate model size adaptively, eliminating the need for selecting regularization parameters. abess is applicable in various statistical and machine learning tasks, including linear regression, the Single-index model, and other common predictive models. abess can also be applied in biostatistics. == Basic Form == The basic form of abess is employed to address the optimal subset selection problem in general linear regression. abess is an l 0 {\displaystyle l_{0}} method, it is characterized by its polynomial time complexity and the property of providing both unbiased and consistent estimates. In the context of linear regression, assuming we have knowledge of n {\displaystyle n} independent samples ( x i , y i ) , i = 1 , … , n {\displaystyle (x_{i},y_{i}),i=1,\ldots ,n} , where x i ∈ R p × 1 {\displaystyle x_{i}\in \mathbb {R} ^{p\times 1}} and y i ∈ R {\displaystyle y_{i}\in \mathbb {R} } , we define X = ( x 1 , … , x n ) ⊤ {\displaystyle X=(x_{1},\ldots ,x_{n})^{\top }} and y = ( y 1 , … , y n ) ⊤ {\displaystyle y=(y_{1},\ldots ,y_{n})^{\top }} . The following equation represents the general linear regression model: y = X β + ε . {\displaystyle y=X\beta +\varepsilon .} To obtain appropriate parameters β {\displaystyle \beta } , one can consider the loss function for linear regression: L n LR ( β ; X , y ) = 1 2 n ‖ y − X β ‖ 2 2 . {\displaystyle {\mathcal {L}}_{n}^{\text{LR}}(\beta ;X,y)={\frac {1}{2n}}\|y-X\beta \|_{2}^{2}.} In abess, the initial focus is on optimizing the loss function under the l 0 {\displaystyle l_{0}} constraint. That is, we consider the following problem: min β ∈ R p × 1 L n LR ( β ; X , y ) , subject to ‖ β ‖ 0 ≤ s , {\displaystyle \min _{\beta \in \mathbb {R} ^{p\times 1}}{\mathcal {L}}_{n}^{\text{LR}}(\beta ;X,y),{\text{ subject to }}\|\beta \|_{0}\leq s,} where s {\displaystyle s} represents the desired size of the support set, and ‖ β ‖ 0 = ∑ i = 1 p I ( β i ≠ 0 ) {\displaystyle \|\beta \|_{0}=\sum _{i=1}^{p}{\mathcal {I}}_{(\beta _{i}\neq 0)}} is the l 0 {\displaystyle l_{0}} norm of the vector. To address the optimization problem described above, abess iteratively exchanges an equal number of variables between the active set and the inactive set. In each iteration, the concept of sacrifice is introduced as follows: For j in the active set ( j ∈ A ^ {\displaystyle j\in {\hat {\mathcal {A}}}} ): ξ j = L n LR ( β ^ A ∖ { j } ) − L n LR ( β ^ A ) = X j ⊤ X j 2 n ( β ^ j ) 2 {\displaystyle \xi _{j}={\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{{\mathcal {A}}\backslash \{j\}}\right)-{\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{\mathcal {A}}\right)={\frac {{\boldsymbol {X}}_{j}^{\top }{\boldsymbol {X}}_{j}}{2n}}\left({\hat {\beta }}_{j}\right)^{2}} For j in the inactive set ( j ∉ A ^ {\displaystyle j\notin {\hat {\mathcal {A}}}} ): ξ j = L n LR ( β ^ A ) − L n LR ( β ^ A + t ^ { j } ) = X j ⊤ X j 2 n ( d ^ j X j ⊤ X j / n ) 2 {\displaystyle \xi _{j}={\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{\mathcal {A}}\right)-{\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{\mathcal {A}}+{\hat {\boldsymbol {t}}}^{\{j\}}\right)={\frac {{\boldsymbol {X}}_{j}^{\top }{\boldsymbol {X}}_{j}}{2n}}\left({\frac {{\hat {\mathrm {d} }}_{j}}{{\boldsymbol {X}}_{j}^{\top }{\boldsymbol {X}}_{j}/n}}\right)^{2}} Here are the key elements in the above equations: β ^ A {\displaystyle {\hat {\beta }}^{\mathcal {A}}} : This represents the estimate of β {\displaystyle \beta } obtained in the previous iteration. A ^ {\displaystyle {\hat {\mathcal {A}}}} : It denotes the estimated active set from the previous iteration. β ^ A ∖ { j } {\displaystyle {\hat {\boldsymbol {\beta }}}^{{\mathcal {A}}\backslash \{j\}}} : This is a vector where the j-th element is set to 0, while the other elements are the same as β ^ A {\displaystyle {\hat {\beta }}^{\mathcal {A}}} . t ^ { j } = arg min t L n LR ( β ^ A + t { j } ) {\displaystyle {\hat {\boldsymbol {t}}}^{\{j\}}=\arg \min _{t}{\mathcal {L}}_{n}^{\text{LR}}\left({\hat {\boldsymbol {\beta }}}^{\mathcal {A}}+{\boldsymbol {t}}^{\{j\}}\right)} : Here, t { j } {\displaystyle t^{\{j\}}} represents a vector where all elements are 0 except the j-th element. d ^ j = X j ⊤ ( y − X β ^ ) / n {\displaystyle {\hat {d}}_{j}={\boldsymbol {X}}_{j}^{\top }({\boldsymbol {y}}-{\boldsymbol {X}}{\hat {\boldsymbol {\beta }}})/n} : This is calculated based on the equation mentioned. The iterative process involves exchanging variables, with the aim of minimizing the sacrifices in the active set while maximizing the sacrifices in the inactive set during each iteration. This approach allows abess to efficiently search for the optimal feature subset. In abess, select an appropriate s max {\displaystyle s_{\max }} and optimize the above problem for active sets size s = 1 , … , s max {\displaystyle s=1,\ldots ,s_{\max }} using the information criterion GIC = n log L n LR + s log p log log n , {\displaystyle {\text{GIC}}=n\log {\mathcal {L}}_{n}^{\text{LR}}+s\log p\log \log n,} to adaptively choose the appropriate active set size s {\displaystyle s} and obtain its corresponding abess estimator. == Generalizations == The splicing algorithm in abess can be employed for subset selection in other models. === Distribution-Free Location-Scale Regression === In 2023, Siegfried extends abess to the case of Distribution-Free and Location-Scale. Specifically, it considers the optimization problem max ϑ ∈ R P , β ∈ R J , γ ∈ R J ∑ i = 1 N ℓ i ( ϑ , x i ⊤ β , exp ( x i ⊤ γ ) − 1 ) , {\displaystyle \max _{{\boldsymbol {\vartheta }}\in \mathbb {R} ^{P},{\boldsymbol {\beta }}\in \mathbb {R} ^{J},{\boldsymbol {\gamma }}\in \mathbb {R} ^{J}}\sum _{i=1}^{N}\ell _{i}\left({\boldsymbol {\vartheta }},{\boldsymbol {x}}_{i}^{\top }{\boldsymbol {\beta }},{\sqrt {\exp \left({\boldsymbol {x}}_{i}^{\top }{\boldsymbol {\gamma }}\right)}}^{-1}\right),} subject to ‖ ( β ⊤ , γ ⊤ ) ⊤ ‖ 0 ≤ s , {\displaystyle \left\|\left({\boldsymbol {\beta }}^{\top },{\boldsymbol {\gamma }}^{\top }\right)^{\top }\right\|_{0}\leq s,} where ℓ i {\displaystyle \ell _{i}} is a loss function, ϑ {\displaystyle {\boldsymbol {\vartheta }}} is a parameter vector, β {\displaystyle {\boldsymbol {\beta }}} and γ {\displaystyle {\boldsymbol {\gamma }}} are vectors, and x i {\displaystyle {\boldsymbol {x}}_{i}} is a data vector. This approach, demonstrated across various applications, enables parsimonious regression modeling for arbitrary outcomes while maintaining interpretability through innovative subset selection procedures. === Groups Selection === In 2023, Zhang applied the splicing algorithm to group selection, optimizing the following model: min β ∈ R p L n LR ( β ; X , y ) subject to ∑ j = 1 J I ( ‖ β G j ‖ 2 ≠ 0 ) ≤ s {\displaystyle \min _{{\boldsymbol {\beta }}\in \mathbb {R} ^{p}}{\mathcal {L}}_{n}^{\text{LR}}(\beta ;X,y){\text{ subject to }}\sum _{j=1}^{J}I\left(\|{\boldsymbol {\beta }}_{G_{j}}\|_{2}\neq 0\right)\leq s} Here are the symbols involved: J {\displaystyle J} : Total number of feature groups, representing the existence of J {\displaystyle J} non-overlapping feature groups in the dataset. G j {\displaystyle G_{j}} : Index set for the j {\displaystyle j} -th feature group, where j {\displaystyle j} ranges from 1 to J {\displaystyle J} , representing the feature grouping structure in the data. s {\displaystyle s} : Model size, a positive integer determined from the data, limiting the number of selected feature groups. === Regression with Corrupted Data === Zhang applied the splicing algorithm to handle corrupted data. Corrupted data refers to information that has been disrupted or contains errors during the data collection or recording process. This interference may include sensor inaccuracies, recording errors, communication issues, or other external disturbances, leading to inaccurate or distorted observations within the dataset. === Single Index Models === In 2023, Tang applied the splicing algorithm to optimal subset selection in the Single-index model. The form of the Single Index Model (SIM) is given by y i = g ( b ⊤ x i , e i ) , i = 1 , … , n , {\displaystyle y_{i}=g({\boldsymbol {b}}^{\top }{\boldsymbol {x}}_{i},e_{i}),\quad i=1,\ldots ,n,} where b {\displaystyle {\boldsymbol {b}}} is the parameter vector, e i {\displaystyle e_{i}} is the error term. The corresponding loss function is defined as l n ( β ) = ∑ i = 1 n ( r i n − 1 2 − x i ⊤ β ) 2 , {\displaystyle l_{n}({\boldsymbol {\beta }})=\sum _{i=1}^{n}\left({\frac {r_{i}}{n}}-{\frac {1}{2}}-{\boldsymbol {x}}_{i}^{\top }{\boldsymbol {\beta }}\right)^{2},} where r {\disp
Read more →
In reinforcement learning, error-driven learning is a method for adjusting a model's (intelligent agent's) parameters based on the difference between its output results and the ground truth. These models stand out as they depend on environmental feedback, rather than explicit labels or categories. They are based on the idea that language acquisition involves the minimization of the prediction error (MPSE). By leveraging these prediction errors, the models consistently refine expectations and decrease computational complexity. Typically, these algorithms are operated by the GeneRec algorithm. Error-driven learning has widespread applications in cognitive sciences and computer vision. These methods have also found successful application in natural language processing (NLP), including areas like part-of-speech tagging, parsing, named entity recognition (NER), machine translation (MT), speech recognition (SR), and dialogue systems. == Formal Definition == Error-driven learning models are ones that rely on the feedback of prediction errors to adjust the expectations or parameters of a model. The key components of error-driven learning include the following: A set S {\displaystyle S} of states representing the different situations that the learner can encounter. A set A {\displaystyle A} of actions that the learner can take in each state. A prediction function P ( s , a ) {\displaystyle P(s,a)} that gives the learner's current prediction of the outcome of taking action a {\displaystyle a} in state s {\displaystyle s} . An error function E ( o , p ) {\displaystyle E(o,p)} that compares the actual outcome o {\displaystyle o} with the prediction p {\displaystyle p} and produces an error value. An update rule U ( p , e ) {\displaystyle U(p,e)} that adjusts the prediction p {\displaystyle p} in light of the error e {\displaystyle e} . == Algorithms == Error-driven learning algorithms refer to a category of reinforcement learning algorithms that leverage the disparity between the real output and the expected output of a system to regulate the system's parameters. Typically applied in supervised learning, these algorithms are provided with a collection of input-output pairs to facilitate the process of generalization. The widely utilized error backpropagation learning algorithm is known as GeneRec, a generalized recirculation algorithm primarily employed for gene prediction in DNA sequences. Many other error-driven learning algorithms are derived from alternative versions of GeneRec. == Applications == === Cognitive science === Simpler error-driven learning models effectively capture complex human cognitive phenomena and anticipate elusive behaviors. They provide a flexible mechanism for modeling the brain's learning process, encompassing perception, attention, memory, and decision-making. By using errors as guiding signals, these algorithms adeptly adapt to changing environmental demands and objectives, capturing statistical regularities and structure. Furthermore, cognitive science has led to the creation of new error-driven learning algorithms that are both biologically acceptable and computationally efficient. These algorithms, including deep belief networks, spiking neural networks, and reservoir computing, follow the principles and constraints of the brain and nervous system. Their primary aim is to capture the emergent properties and dynamics of neural circuits and systems. === Computer vision === Computer vision is a complex task that involves understanding and interpreting visual data, such as images or videos. In the context of error-driven learning, the computer vision model learns from the mistakes it makes during the interpretation process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This repeated process of learning from errors helps improve the model's performance over time. For NLP to do well at computer vision, it employs deep learning techniques. This form of computer vision is sometimes called neural computer vision (NCV), since it makes use of neural networks. NCV therefore interprets visual data based on a statistical, trial and error approach and can deal with context and other subtleties of visual data. === Natural Language Processing === ==== Part-of-speech tagging ==== Part-of-speech (POS) tagging is a crucial component in Natural Language Processing (NLP). It helps resolve human language ambiguity at different analysis levels. In addition, its output (tagged data) can be used in various applications of NLP such as information extraction, information retrieval, question Answering, speech eecognition, text-to-speech conversion, partial parsing, and grammar correction. ==== Parsing ==== Parsing in NLP involves breaking down a text into smaller pieces (phrases) based on grammar rules. If a sentence cannot be parsed, it may contain grammatical errors. In the context of error-driven learning, the parser learns from the mistakes it makes during the parsing process. When an error is encountered, the parser updates its internal model to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the parser's performance over time. In conclusion, error-driven learning plays a crucial role in improving the accuracy and efficiency of NLP parsers by allowing them to learn from their mistakes and adapt their internal models accordingly. ==== Named entity recognition (NER) ==== NER is the task of identifying and classifying entities (such as persons, locations, organizations, etc.) in a text. Error-driven learning can help the model learn from its false positives and false negatives and improve its recall and precision on (NER). In the context of error-driven learning, the significance of NER is quite profound. Traditional sequence labeling methods identify nested entities layer by layer. If an error occurs in the recognition of an inner entity, it can lead to incorrect identification of the outer entity, leading to a problem known as error propagation of nested entities. This is where the role of NER becomes crucial in error-driven learning. By accurately recognizing and classifying entities, it can help minimize these errors and improve the overall accuracy of the learning process. Furthermore, deep learning-based NER methods have shown to be more accurate as they are capable of assembling words, enabling them to understand the semantic and syntactic relationship between various words better. ==== Machine translation ==== Machine translation is a complex task that involves converting text from one language to another. In the context of error-driven learning, the machine translation model learns from the mistakes it makes during the translation process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. ==== Speech recognition ==== Speech recognition is a complex task that involves converting spoken language into written text. In the context of error-driven learning, the speech recognition model learns from the mistakes it makes during the recognition process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. ==== Dialogue systems ==== Dialogue systems are a popular NLP task as they have promising real-life applications. They are also complicated tasks since many NLP tasks deserving study are involved. In the context of error-driven learning, the dialogue system learns from the mistakes it makes during the dialogue process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. == Advantages == Error-driven learning has several advantages over other types of machine learning algorithms: They can learn from feedback and correct their mistakes, which makes them adaptive and robust to noise and changes in the data. They can handle large and high-dimensional data sets, as they do not require explicit feature engineering or prior knowledge of the data distribution. They can achieve high accuracy and performance, as they can learn complex and nonlinear relationships between the input and the output. == Limitations == Although error driven learning has its advantages, their algorithms also have the following limitations: They can suffer from overfitting, which means that they memorize the training data and fail to generalize to new and unseen data. This can be mitigated by using regularization techniques, such as adding a penalty term to the loss function, or reducing the complexity of the model. They can be sensitive to the choice of
Read more →