AI Builder Pricing

AI Builder Pricing — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Gerrit (software)

  Gerrit ( GERR-it) is a free, web-based team code collaboration tool. Software developers in a team can review each other's modifications on their source code using a Web browser and approve or reject those changes. It integrates closely with Git, a distributed version control system. Gerrit is a fork of Rietveld, a code review tool for Subversion. Both are named after Dutch designer Gerrit Rietveld. == History == Originally written in Python like Rietveld, it is now written in Java (Java EE Servlet) with SQL since version 2 and a custom-made Git-based database (NoteDb) since version 3. In versions 2.0–2.16 Gerrit used Google Web Toolkit for its browser-based front-end. After being developed and used in parallel with GWT for versions 2.14–2.16, a new Polymer web UI replaced the GWT UI in version 3.0.

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  Linguamatics

  Linguamatics, headquartered in Cambridge, England, with offices in the United States and UK, is a provider of text mining systems through software licensing and services, primarily for pharmaceutical and healthcare applications. Founded in 2001, the company was purchased by IQVIA in January 2019. == Technology == The company develops enterprise search tools for the life sciences sector. The core natural language processing engine (I2E) uses a federated architecture to incorporate data from 3rd party resources. Initially developed to be used interactively through a graphic user interface, the core software also has an application programming interface that can be used to automate searches. LabKey, Penn Medicine, Atrius Health and Mercy all use Linguamatics software to extract electronic health record data into data warehouses. Linguamatics software is used by 17 of the top 20 global pharmaceutical companies, the US Food and Drug Administration, as well as healthcare providers. == Software community == The core software, "I2E", is used by a number of companies to either extend their own software or to publish their data. Copyright Clearance Center uses I2E to produce searchable indexes of material that would otherwise be unsearchable due to copyright. Thomson Reuters produces Cortellis Informatics Clinical Text Analytics, which depends on I2E to make clinical data accessible and searchable. Pipeline Pilot can integrate I2E as part of a workflow. ChemAxon can be used alongside I2E to allow named entity recognition of chemicals within unstructured data. Data sources include MEDLINE, ClinicalTrials.gov, FDA Drug Labels, PubMed Central, and Patent Abstracts.

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  Autoencoder

  An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data (unsupervised learning). An autoencoder learns two functions: an encoding function that transforms the input data, and a decoding function that recreates the input data from the encoded representation. The autoencoder learns an efficient representation (encoding) for a set of data, typically for dimensionality reduction, to generate lower-dimensional embeddings for subsequent use by other machine learning algorithms. Variants exist which aim to make the learned representations assume useful properties. Examples are regularized autoencoders (sparse, denoising and contractive autoencoders), which are effective in learning representations for subsequent classification tasks, and variational autoencoders, which can be used as generative models. Autoencoders are applied to many problems, including facial recognition, feature detection, anomaly detection, and learning the meaning of words. In terms of data synthesis, autoencoders can also be used to randomly generate new data that is similar to the input (training) data. == Mathematical principles == === Definition === An autoencoder is defined by the following components: Two sets: the space of encoded messages Z {\displaystyle {\mathcal {Z}}} ; the space of decoded messages X {\displaystyle {\mathcal {X}}} . Typically X {\displaystyle {\mathcal {X}}} and Z {\displaystyle {\mathcal {Z}}} are Euclidean spaces, that is, X = R m , Z = R n {\displaystyle {\mathcal {X}}=\mathbb {R} ^{m},{\mathcal {Z}}=\mathbb {R} ^{n}} with m > n . {\displaystyle m>n.} Two parametrized families of functions: the encoder family E ϕ : X → Z {\displaystyle E_{\phi }:{\mathcal {X}}\rightarrow {\mathcal {Z}}} , parametrized by ϕ {\displaystyle \phi } ; the decoder family D θ : Z → X {\displaystyle D_{\theta }:{\mathcal {Z}}\rightarrow {\mathcal {X}}} , parametrized by θ {\displaystyle \theta } .For any x ∈ X {\displaystyle x\in {\mathcal {X}}} , we usually write z = E ϕ ( x ) {\displaystyle z=E_{\phi }(x)} , and refer to it as the code, the latent variable, latent representation, latent vector, etc. Conversely, for any z ∈ Z {\displaystyle z\in {\mathcal {Z}}} , we usually write x ′ = D θ ( z ) {\displaystyle x'=D_{\theta }(z)} , and refer to it as the (decoded) message. Usually, both the encoder and the decoder are defined as multilayer perceptrons (MLPs). For example, a one-layer-MLP encoder E ϕ {\displaystyle E_{\phi }} is: E ϕ ( x ) = σ ( W x + b ) {\displaystyle E_{\phi }(\mathbf {x} )=\sigma (Wx+b)} where σ {\displaystyle \sigma } is an element-wise activation function, W {\displaystyle W} is a "weight" matrix, and b {\displaystyle b} is a "bias" vector. === Training an autoencoder === An autoencoder, by itself, is simply a tuple of two functions. To judge its quality, we need a task. A task is defined by a reference probability distribution μ r e f {\displaystyle \mu _{ref}} over X {\displaystyle {\mathcal {X}}} , and a "reconstruction quality" function d : X × X → [ 0 , ∞ ] {\displaystyle d:{\mathcal {X}}\times {\mathcal {X}}\to [0,\infty ]} , such that d ( x , x ′ ) {\displaystyle d(x,x')} measures how much x ′ {\displaystyle x'} differs from x {\displaystyle x} . With those, we can define the loss function for the autoencoder as L ( θ , ϕ ) := E x ∼ μ r e f [ d ( x , D θ ( E ϕ ( x ) ) ) ] {\displaystyle L(\theta ,\phi ):=\mathbb {\mathbb {E} } _{x\sim \mu _{ref}}[d(x,D_{\theta }(E_{\phi }(x)))]} The optimal autoencoder for the given task ( μ r e f , d ) {\displaystyle (\mu _{ref},d)} is then arg ⁡ min θ , ϕ L ( θ , ϕ ) {\displaystyle \arg \min _{\theta ,\phi }L(\theta ,\phi )} . The search for the optimal autoencoder can be accomplished by any mathematical optimization technique, but usually by gradient descent. This search process is referred to as "training the autoencoder". In most situations, the reference distribution is just the empirical distribution given by a dataset { x 1 , . . . , x N } ⊂ X {\displaystyle \{x_{1},...,x_{N}\}\subset {\mathcal {X}}} , so that μ r e f = 1 N ∑ i = 1 N δ x i {\displaystyle \mu _{ref}={\frac {1}{N}}\sum _{i=1}^{N}\delta _{x_{i}}} where δ x i {\displaystyle \delta _{x_{i}}} is the Dirac measure, the quality function is just L 2 {\displaystyle L^{2}} loss: d ( x , x ′ ) = ‖ x − x ′ ‖ 2 2 {\displaystyle d(x,x')=\|x-x'\|_{2}^{2}} , and ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} is the Euclidean norm. Then the problem of searching for the optimal autoencoder is just a least-squares optimization: min θ , ϕ L ( θ , ϕ ) , where L ( θ , ϕ ) = 1 N ∑ i = 1 N ‖ x i − D θ ( E ϕ ( x i ) ) ‖ 2 2 {\displaystyle \min _{\theta ,\phi }L(\theta ,\phi ),\qquad {\text{where }}L(\theta ,\phi )={\frac {1}{N}}\sum _{i=1}^{N}\|x_{i}-D_{\theta }(E_{\phi }(x_{i}))\|_{2}^{2}} === Interpretation === An autoencoder has two main parts: an encoder that maps the message to a code, and a decoder that reconstructs the message from the code. An optimal autoencoder would perform as close to perfect reconstruction as possible, with "close to perfect" defined by the reconstruction quality function d {\displaystyle d} . The simplest way to perform the copying task perfectly would be to duplicate the signal. To suppress this behavior, the code space Z {\displaystyle {\mathcal {Z}}} usually has fewer dimensions than the message space X {\displaystyle {\mathcal {X}}} . Such an autoencoder is called undercomplete. It can be interpreted as compressing the message, or reducing its dimensionality. At the limit of an ideal undercomplete autoencoder, every possible code z {\displaystyle z} in the code space is used to encode a message x {\displaystyle x} that really appears in the distribution μ r e f {\displaystyle \mu _{ref}} , and the decoder is also perfect: D θ ( E ϕ ( x ) ) = x {\displaystyle D_{\theta }(E_{\phi }(x))=x} . This ideal autoencoder can then be used to generate messages indistinguishable from real messages, by feeding its decoder arbitrary code z {\displaystyle z} and obtaining D θ ( z ) {\displaystyle D_{\theta }(z)} , which is a message that really appears in the distribution μ r e f {\displaystyle \mu _{ref}} . If the code space Z {\displaystyle {\mathcal {Z}}} has dimension larger than (overcomplete), or equal to, the message space X {\displaystyle {\mathcal {X}}} , or the hidden units are given enough capacity, an autoencoder can learn the identity function and become useless. However, experimental results found that overcomplete autoencoders might still learn useful features. In the ideal setting, the code dimension and the model capacity could be set on the basis of the complexity of the data distribution to be modeled. A standard way to do so is to add modifications to the basic autoencoder, to be detailed below. == Variations == === Variational autoencoder (VAE) === Variational autoencoders (VAEs) belong to the families of variational Bayesian methods. Despite the architectural similarities with basic autoencoders, VAEs are architected with different goals and have a different mathematical formulation. The latent space is, in this case, composed of a mixture of distributions instead of fixed vectors. Given an input dataset x {\displaystyle x} characterized by an unknown probability function P ( x ) {\displaystyle P(x)} and a multivariate latent encoding vector z {\displaystyle z} , the objective is to model the data as a distribution p θ ( x ) {\displaystyle p_{\theta }(x)} , with θ {\displaystyle \theta } defined as the set of the network parameters so that p θ ( x ) = ∫ z p θ ( x , z ) d z {\displaystyle p_{\theta }(x)=\int _{z}p_{\theta }(x,z)dz} . === Sparse autoencoder (SAE) === Inspired by the sparse coding hypothesis in neuroscience, sparse autoencoders (SAE) are variants of autoencoders, such that the codes E ϕ ( x ) {\displaystyle E_{\phi }(x)} for messages tend to be sparse codes, that is, E ϕ ( x ) {\displaystyle E_{\phi }(x)} is close to zero in most entries. Sparse autoencoders may include more (rather than fewer) hidden units than inputs, but only a small number of the hidden units are allowed to be active at the same time. Encouraging sparsity improves performance on classification tasks. There are two main ways to enforce sparsity. One way is to simply clamp all but the highest-k activations of the latent code to zero. This is the k-sparse autoencoder. The k-sparse autoencoder inserts the following "k-sparse function" in the latent layer of a standard autoencoder: f k ( x 1 , . . . , x n ) = ( x 1 b 1 , . . . , x n b n ) {\displaystyle f_{k}(x_{1},...,x_{n})=(x_{1}b_{1},...,x_{n}b_{n})} where b i = 1 {\displaystyle b_{i}=1} if | x i | {\displaystyle |x_{i}|} ranks in the top k, and 0 otherwise. Backpropagating through f k {\displaystyle f_{k}} is simple: set gradient to 0 for b i = 0 {\displaystyle b_{i}=0} entries, and keep gradient for b i = 1 {\displaystyle b_{i}=1} entries. This is essentially a generalized ReLU function. The other way is a relaxed version of the k-

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  Rule-based machine learning

  Rule-based machine learning (RBML) is a term in computer science intended to encompass any machine learning method that identifies, learns, or evolves 'rules' to store, manipulate or apply. The defining characteristic of a rule-based machine learner is the identification and utilization of a set of relational rules that collectively represent the knowledge captured by the system. Rule-based machine learning approaches include learning classifier systems, association rule learning, artificial immune systems, and any other method that relies on a set of rules, each covering contextual knowledge. While rule-based machine learning is conceptually a type of rule-based system, it is distinct from traditional rule-based systems, which are often hand-crafted, and other rule-based decision makers. This is because rule-based machine learning applies some form of learning algorithm such as Rough sets theory to identify and minimise the set of features and to automatically identify useful rules, rather than a human needing to apply prior domain knowledge to manually construct rules and curate a rule set. == Rules == Rules typically take the form of an '{IF:THEN} expression', (e.g. {IF 'condition' THEN 'result'}, or as a more specific example, {IF 'red' AND 'octagon' THEN 'stop-sign}). An individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Therefore rule-based machine learning methods typically comprise a set of rules, or knowledge base, that collectively make up the prediction model usually known as decision algorithm. Rules can also be interpreted in various ways depending on the domain knowledge, data types(discrete or continuous) and in combinations. == RIPPER == Repeated incremental pruning to produce error reduction (RIPPER) is a propositional rule learner proposed by William W. Cohen as an optimized version of IREP.

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  Once (dating platform)

  Once is an online dating platform founded in 2015. The platform offers users one selected match per day for more meaningful connections. == History == Once was established in 2015, the founders included dating industry entrepreneur Jean Meyer, who became a CEO of the company, as well as Guillaume Sempe and Guilhem Duche. It focused on providing a single daily match to its users. On its early stages Once secured a $3.5 million seed round from Partech Ventures and some private investors. The same year, it opened offices in Paris, and London. By 2016, it reached 1 million users. In 2020, the company was acquired by Dating Group for $18 million. Following the acquisition, Once underwent rebranding. Alexandra Beaumont took over leadership of the brand in 2021, driving growth, rebranding, and innovation. == Overview == Once provides an online dating service with a focus on thoughtful connections. Users receive one selected match per day, which encourages meaningful interactions. The platform operates primarily in the United States, the United Kingdom, Canada, France, and Spain. The platform is supported by Android, iOS, and Apple Watch OS.

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  Mixture model

  In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population. However, while problems associated with "mixture distributions" relate to deriving the properties of the overall population from those of the sub-populations, "mixture models" are used to make statistical inferences about the properties of the sub-populations given only observations on the pooled population, without sub-population identity information. Mixture models are used for clustering, under the name model-based clustering, and also for density estimation. Mixture models should not be confused with models for compositional data, i.e., data whose components are constrained to sum to a constant value (1, 100%, etc.). However, compositional models can be thought of as mixture models, where members of the population are sampled at random. Conversely, mixture models can be thought of as compositional models, where the total size reading population has been normalized to 1. == Structure == === General mixture model === A typical finite-dimensional mixture model is a hierarchical model consisting of the following components: N random variables that are observed, each distributed according to a mixture of K components, with the components belonging to the same parametric family of distributions (e.g., all normal, all Zipfian, etc.) but with different parameters. However, it is also possible to have a finite mixture model where each component belongs to a different parametric family of distributions, for example, a mixture of a multivariate normal distribution and a generalized hyperbolic distribution. N random latent variables specifying the identity of the mixture component of each observation, each distributed according to a K-dimensional categorical distribution A set of K mixture weights, which are probabilities that sum to 1. A set of K parameters, each specifying the parameter of the corresponding mixture component. In many cases, each "parameter" is actually a set of parameters. For example, if the mixture components are Gaussian distributions, there will be a mean and variance for each component. If the mixture components are categorical distributions (e.g., when each observation is a token from a finite alphabet of size V), there will be a vector of V probabilities summing to 1. In addition, in a Bayesian setting, the mixture weights and parameters will themselves be random variables, and prior distributions will be placed over the variables. In such a case, the weights are typically viewed as a K-dimensional random vector drawn from a Dirichlet distribution (the conjugate prior of the categorical distribution), and the parameters will be distributed according to their respective conjugate priors. Mathematically, a basic parametric mixture model can be described as follows: K = number of mixture components N = number of observations θ i = 1 … K = parameter of distribution of observation associated with component i ϕ i = 1 … K = mixture weight, i.e., prior probability of a particular component i ϕ = K -dimensional vector composed of all the individual ϕ 1 … K ; must sum to 1 z i = 1 … N = component of observation i x i = 1 … N = observation i F ( x | θ ) = probability distribution of an observation, parametrized on θ z i = 1 … N ∼ Categorical ⁡ ( ϕ ) x i = 1 … N | z i = 1 … N ∼ F ( θ z i ) {\displaystyle {\begin{array}{lcl}K&=&{\text{number of mixture components}}\\N&=&{\text{number of observations}}\\\theta _{i=1\dots K}&=&{\text{parameter of distribution of observation associated with component }}i\\\phi _{i=1\dots K}&=&{\text{mixture weight, i.e., prior probability of a particular component }}i\\{\boldsymbol {\phi }}&=&K{\text{-dimensional vector composed of all the individual }}\phi _{1\dots K}{\text{; must sum to 1}}\\z_{i=1\dots N}&=&{\text{component of observation }}i\\x_{i=1\dots N}&=&{\text{observation }}i\\F(x|\theta )&=&{\text{probability distribution of an observation, parametrized on }}\theta \\z_{i=1\dots N}&\sim &\operatorname {Categorical} ({\boldsymbol {\phi }})\\x_{i=1\dots N}|z_{i=1\dots N}&\sim &F(\theta _{z_{i}})\end{array}}} In a Bayesian setting, all parameters are associated with random variables, as follows: K , N = as above θ i = 1 … K , ϕ i = 1 … K , ϕ = as above z i = 1 … N , x i = 1 … N , F ( x | θ ) = as above α = shared hyperparameter for component parameters β = shared hyperparameter for mixture weights H ( θ | α ) = prior probability distribution of component parameters, parametrized on α θ i = 1 … K ∼ H ( θ | α ) ϕ ∼ S y m m e t r i c - D i r i c h l e t K ⁡ ( β ) z i = 1 … N | ϕ ∼ Categorical ⁡ ( ϕ ) x i = 1 … N | z i = 1 … N , θ i = 1 … K ∼ F ( θ z i ) {\displaystyle {\begin{array}{lcl}K,N&=&{\text{as above}}\\\theta _{i=1\dots K},\phi _{i=1\dots K},{\boldsymbol {\phi }}&=&{\text{as above}}\\z_{i=1\dots N},x_{i=1\dots N},F(x|\theta )&=&{\text{as above}}\\\alpha &=&{\text{shared hyperparameter for component parameters}}\\\beta &=&{\text{shared hyperparameter for mixture weights}}\\H(\theta |\alpha )&=&{\text{prior probability distribution of component parameters, parametrized on }}\alpha \\\theta _{i=1\dots K}&\sim &H(\theta |\alpha )\\{\boldsymbol {\phi }}&\sim &\operatorname {Symmetric-Dirichlet} _{K}(\beta )\\z_{i=1\dots N}|{\boldsymbol {\phi }}&\sim &\operatorname {Categorical} ({\boldsymbol {\phi }})\\x_{i=1\dots N}|z_{i=1\dots N},\theta _{i=1\dots K}&\sim &F(\theta _{z_{i}})\end{array}}} This characterization uses F and H to describe arbitrary distributions over observations and parameters, respectively. Typically H will be the conjugate prior of F. The two most common choices of F are Gaussian aka "normal" (for real-valued observations) and categorical (for discrete observations). Other common possibilities for the distribution of the mixture components are: Binomial distribution, for the number of "positive occurrences" (e.g., successes, yes votes, etc.) given a fixed number of total occurrences Multinomial distribution, similar to the binomial distribution, but for counts of multi-way occurrences (e.g., yes/no/maybe in a survey) Negative binomial distribution, for binomial-type observations but where the quantity of interest is the number of failures before a given number of successes occurs Poisson distribution, for the number of occurrences of an event in a given period of time, for an event that is characterized by a fixed rate of occurrence Exponential distribution, for the time before the next event occurs, for an event that is characterized by a fixed rate of occurrence Log-normal distribution, for positive real numbers that are assumed to grow exponentially, such as incomes or prices Multivariate normal distribution (aka multivariate Gaussian distribution), for vectors of correlated outcomes that are individually Gaussian-distributed Multivariate Student's t-distribution, for vectors of heavy-tailed correlated outcomes A vector of Bernoulli-distributed values, corresponding, e.g., to a black-and-white image, with each value representing a pixel; see the handwriting-recognition example below === Specific examples === ==== Gaussian mixture model ==== A typical non-Bayesian Gaussian mixture model looks like this: K , N = as above ϕ i = 1 … K , ϕ = as above z i = 1 … N , x i = 1 … N = as above θ i = 1 … K = { μ i = 1 … K , σ i = 1 … K 2 } μ i = 1 … K = mean of component i σ i = 1 … K 2 = variance of component i z i = 1 … N ∼ Categorical ⁡ ( ϕ ) x i = 1 … N ∼ N ( μ z i , σ z i 2 ) {\displaystyle {\begin{array}{lcl}K,N&=&{\text{as above}}\\\phi _{i=1\dots K},{\boldsymbol {\phi }}&=&{\text{as above}}\\z_{i=1\dots N},x_{i=1\dots N}&=&{\text{as above}}\\\theta _{i=1\dots K}&=&\{\mu _{i=1\dots K},\sigma _{i=1\dots K}^{2}\}\\\mu _{i=1\dots K}&=&{\text{mean of component }}i\\\sigma _{i=1\dots K}^{2}&=&{\text{variance of component }}i\\z_{i=1\dots N}&\sim &\operatorname {Categorical} ({\boldsymbol {\phi }})\\x_{i=1\dots N}&\sim &{\mathcal {N}}(\mu _{z_{i}},\sigma _{z_{i}}^{2})\end{array}}} A Bayesian version of a Gaussian mixture model is as follows: K , N = as above ϕ i = 1 … K , ϕ = as above z i = 1 … N , x i = 1 … N = as above θ i = 1 … K = { μ i = 1 … K , σ i = 1 … K 2 } μ i = 1 … K = mean of component i σ i = 1 … K 2 = variance of component i μ 0 , λ , ν , σ 0 2 = shared hyperparameters μ i = 1 … K ∼ N ( μ 0 , λ σ i 2 ) σ i = 1 … K 2 ∼ I n v e r s e - G a m m a ⁡ ( ν , σ 0 2 ) ϕ ∼ S y m m e t r i c - D i r i c h l e t K ⁡ ( β ) z i = 1 … N ∼ Categorical ⁡ ( ϕ ) x i = 1 … N ∼ N ( μ z i , σ z i 2 ) {\displaystyle {\begin{array}{lcl}K,N&=&{\text{as above}}\\\phi _{i=1\dots K},{\boldsymbol {\phi }}&=&{\text{as above}}\\z_{i=1\dots N},x_{i=1\dots N}&=&{\text{as above}}\\\theta _{i=1\

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  World Programming System

  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.

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  European Conference on Computer Vision

  The European Conference on Computer Vision (ECCV) is a biennial research conference with the proceedings published by Springer Science+Business Media. Similar to ICCV in scope and quality, it is held those years which ICCV is not. It is considered to be one of the top conferences in computer vision, alongside CVPR and ICCV, with an 'A' rating from the Australian Ranking of ICT Conferences and an 'A1' rating from the Brazilian ministry of education. The acceptance rate for ECCV 2010 was 24.4% for posters and 3.3% for oral presentations. Like other top computer vision conferences, ECCV has tutorial talks, technical sessions, and poster sessions. The conference is usually spread over five to six days with the main technical program occupying three days in the middle, and tutorial and workshops, focused on specific topics, being held in the beginning and at the end. The ECCV presents the Koenderink Prize annually to recognize fundamental contributions in computer vision. == Location == The conference is usually held in autumn in Europe.

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  EditDV

  EditDV was a video editing software released by Radius, Inc. in late 1997 as an evolution of their earlier Radius Edit product. EditDV was one of the first products providing professional-quality editing of the then new DV format at a relatively affordable cost ($999 including Radius FireWire capture card) and was named "The Best Video Tool of 1998". Originally EditDV was available for Macintosh only but in February 2000 EditDV 2.0 for Windows was released. With version 3.0 EditDV's name was changed to CineStream. == Features == Originally bundled with a FireWire card, EditDV 1.5 got updated into a less expensive software only package for use with the newer PowerMac G3 that came with a FireWire interface. Later, a scaled down version named EditDV 1.6.1 Unplugged was released as a freeware version next to EditDV 2.0. Unlike many other applications at the time which transcoded video to M-JPEG for editing, EditDV provided lossless native editing of the DV format. Only transitions (such as dissolves or wipes), effects (such as rotating or scaling the video, adjusting the audio level, or adding titles) and filters (such as changing the brightness or color balance) needed to be rendered. This also had the disadvantage to not work with analogue video capture. EditDV was built on top of QuickTime and supported QuickTime filters as well as its own built-in effects and transitions. Effects could be animated using keyframes. EditDV 2.0 worked natively with Quicktime MOV format. For Microsoft Windows users, where the standard was AVI, this required the use of a provided external conversion tool afterwards when AVI was wanted. The user interface had a Project window for organising clips into bins, a Sequence window with a multi-track timeline for arranging clips into a program using three-point editing, and Source and Program monitor windows. A finished program could either be exported as a QuickTime movie or written back to DV tape using the "print to video" command. Version 3.0, then renamed CineStream, shifted towards web designers who wanted to add video streaming interactivity to a website. The new feature called EventStream allowed setting clickable hot spots to link to another location, either to another page with a URL or to another video. This feature distinguished CineStream from the rest of the competition. == Products == The EditDV product family included a number of related products, all sharing a similar name: EditDV Video editing software (Mac and Windows) SoftDV A QuickTime software codec for playing DV media, included as part of EditDV (Mac and Windows) MotoDV PCI-based FireWire interface with DV capture software (Mac and Windows) PhotoDV Software to capture high-quality stills from a DV tape using MotoDV hardware (Mac and Windows) RotoDV Software for rotoscoping (painting over video), released in Sept 1999 (Macintosh only) == Name changes and eventual demise == In 1999, the company Radius Inc. changed its name to Digital Origin. In 2000, Digital Origin Inc (and EditDV) was bought by Media 100. In early 2001, Media 100 released an updated version of EditDV under the new name CineStream 3.0. Later that year (October 2001) Media 100 was bought by Autodesk's Discreet Division. CineStream for Macintosh required classic Mac OS. It was never ported to Mac OS X and faced increasing competition on that platform from Apple's own Final Cut Pro application. Development of EditDV/Cinestream was officially discontinued in 2002.

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  Fitness function

  A fitness function is a particular type of objective or cost function that is used to summarize, as a single figure of merit, how close a given candidate solution is to achieving the set aims. It is an important component of evolutionary algorithms (EA), such as genetic programming, evolution strategies or genetic algorithms. An EA is a metaheuristic that reproduces the basic principles of biological evolution as a computer algorithm in order to solve challenging optimization or planning tasks, at least approximately. For this purpose, many candidate solutions are generated, which are evaluated using a fitness function in order to guide the evolutionary development towards the desired goal. Similar quality functions are also used in other metaheuristics, such as ant colony optimization or particle swarm optimization. In the field of EAs, each candidate solution, also called an individual, is commonly represented as a string of numbers (referred to as a chromosome). After each round of testing or simulation the idea is to delete the n worst individuals, and to breed n new ones from the best solutions. Each individual must therefore to be assigned a quality number indicating how close it has come to the overall specification, and this is generated by applying the fitness function to the test or simulation results obtained from that candidate solution. Two main classes of fitness functions exist: one where the fitness function does not change, as in optimizing a fixed function or testing with a fixed set of test cases; and one where the fitness function is mutable, as in niche differentiation or co-evolving the set of test cases. Another way of looking at fitness functions is in terms of a fitness landscape, which shows the fitness for each possible chromosome. In the following, it is assumed that the fitness is determined based on an evaluation that remains unchanged during an optimization run. A fitness function does not necessarily have to be able to calculate an absolute value, as it is sometimes sufficient to compare candidates in order to select the better one. A relative indication of fitness (candidate a is better than b) is sufficient in some cases, such as tournament selection or Pareto optimization. == Requirements of evaluation and fitness function == The quality of the evaluation and calculation of a fitness function is fundamental to the success of an EA optimisation. It implements Darwin's principle of "survival of the fittest". Without fitness-based selection mechanisms for mate selection and offspring acceptance, EA search would be blind and hardly distinguishable from the Monte Carlo method. When setting up a fitness function, one must always be aware that it is about more than just describing the desired target state. Rather, the evolutionary search on the way to the optimum should also be supported as much as possible (see also section on auxiliary objectives), if and insofar as this is not already done by the fitness function alone. If the fitness function is designed badly, the algorithm will either converge on an inappropriate solution, or will have difficulty converging at all. Definition of the fitness function is not straightforward in many cases and often is performed iteratively if the fittest solutions produced by an EA is not what is desired. Interactive genetic algorithms address this difficulty by outsourcing evaluation to external agents which are normally humans. == Computational efficiency == The fitness function should not only closely align with the designer's goal, but also be computationally efficient. Execution speed is crucial, as a typical evolutionary algorithm must be iterated many times in order to produce a usable result for a non-trivial problem. Fitness approximation may be appropriate, especially in the following cases: Fitness computation time of a single solution is extremely high Precise model for fitness computation is missing The fitness function is uncertain or noisy. Alternatively or also in addition to the fitness approximation, the fitness calculations can also be distributed to a parallel computer in order to reduce the execution times. Depending on the population model of the EA used, both the EA itself and the fitness calculations of all offspring of one generation can be executed in parallel. == Multi-objective optimization == Practical applications usually aim at optimizing multiple and at least partially conflicting objectives. Two fundamentally different approaches are often used for this purpose, Pareto optimization and optimization based on fitness calculated using the weighted sum. === Weighted sum and penalty functions === When optimizing with the weighted sum, the single values of the O {\displaystyle O} objectives are first normalized so that they can be compared. This can be done with the help of costs or by specifying target values and determining the current value as the degree of fulfillment. Costs or degrees of fulfillment can then be compared with each other and, if required, can also be mapped to a uniform fitness scale. Without loss of generality, fitness is assumed to represent a value to be maximized. Each objective o i {\displaystyle o_{i}} is assigned a weight w i {\displaystyle w_{i}} in the form of a percentage value so that the overall raw fitness f r a w {\displaystyle f_{raw}} can be calculated as a weighted sum: f r a w = ∑ i = 1 O o i ⋅ w i w i t h ∑ i = 1 O w i = 1 {\displaystyle f_{raw}=\sum _{i=1}^{O}{o_{i}\cdot w_{i}}\quad {\mathsf {with}}\quad \sum _{i=1}^{O}{w_{i}}=1} A violation of R {\displaystyle R} restrictions r j {\displaystyle r_{j}} can be included in the fitness determined in this way in the form of penalty functions. For this purpose, a function p f j ( r j ) {\displaystyle pf_{j}(r_{j})} can be defined for each restriction which returns a value between 0 {\displaystyle 0} and 1 {\displaystyle 1} depending on the degree of violation, with the result being 1 {\displaystyle 1} if there is no violation. The previously determined raw fitness is multiplied by the penalty function(s) and the result is then the final fitness f f i n a l {\displaystyle f_{final}} : f f i n a l = f r a w ⋅ ∏ j = 1 R p f j ( r j ) = ∑ i = 1 O ( o i ⋅ w i ) ⋅ ∏ j = 1 R p f j ( r j ) {\displaystyle f_{final}=f_{raw}\cdot \prod _{j=1}^{R}{pf_{j}(r_{j})}=\sum _{i=1}^{O}{(o_{i}\cdot w_{i})}\cdot \prod _{j=1}^{R}{pf_{j}(r_{j})}} This approach is simple and has the advantage of being able to combine any number of objectives and restrictions. The disadvantage is that different objectives can compensate each other and that the weights have to be defined before the optimization. This means that the compromise lines must be defined before optimization, which is why optimization with the weighted sum is also referred to as the a priori method. In addition, certain solutions may not be obtained, see the section on the comparison of both types of optimization. === Pareto optimization === A solution is called Pareto-optimal if the improvement of one objective is only possible with a deterioration of at least one other objective. The set of all Pareto-optimal solutions, also called Pareto set, represents the set of all optimal compromises between the objectives. The figure below on the right shows an example of the Pareto set of two objectives f 1 {\displaystyle f_{1}} and f 2 {\displaystyle f_{2}} to be maximized. The elements of the set form the Pareto front (green line). From this set, a human decision maker must subsequently select the desired compromise solution. Constraints are included in Pareto optimization in that solutions without constraint violations are per se better than those with violations. If two solutions to be compared each have constraint violations, the respective extent of the violations decides. It was recognized early on that EAs with their simultaneously considered solution set are well suited to finding solutions in one run that cover the Pareto front sufficiently well. They are therefore well suited as a-posteriori methods for multi-objective optimization, in which the final decision is made by a human decision maker after optimization and determination of the Pareto front. Besides the SPEA2, the NSGA-II and NSGA-III have established themselves as standard methods. The advantage of Pareto optimization is that, in contrast to the weighted sum, it provides all alternatives that are equivalent in terms of the objectives as an overall solution. The disadvantage is that a visualization of the alternatives becomes problematic or even impossible from four objectives on. Furthermore, the effort increases exponentially with the number of objectives. If there are more than three or four objectives, some have to be combined using the weighted sum or other aggregation methods. === Comparison of both types of assessment === With the help of the weighted sum, the total Pareto front can be obtained by a suitable choice of weights, provided that it is convex

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  Neural cryptography

  Neural cryptography is a branch of cryptography dedicated to analyzing the application of stochastic algorithms, especially artificial neural network algorithms, for use in encryption and cryptanalysis. == Definition == Artificial neural networks are well known for their ability to selectively explore the solution space of a given problem. This feature finds a natural niche of application in the field of cryptanalysis. At the same time, neural networks offer a new approach to attack ciphering algorithms based on the principle that any function could be reproduced by a neural network, which is a powerful proven computational tool that can be used to find the inverse-function of any cryptographic algorithm. The ideas of mutual learning, self learning, and stochastic behavior of neural networks and similar algorithms can be used for different aspects of cryptography, like public-key cryptography, solving the key distribution problem using neural network mutual synchronization, hashing or generation of pseudo-random numbers. Another idea is the ability of a neural network to separate space in non-linear pieces using "bias". It gives different probabilities of activating the neural network or not. This is very useful in the case of Cryptanalysis. Two names are used to design the same domain of research: Neuro-Cryptography and Neural Cryptography. The first work that it is known on this topic can be traced back to 1995 in an IT Master Thesis. == Applications == In 1995, Sebastien Dourlens applied neural networks to cryptanalyze DES by allowing the networks to learn how to invert the S-tables of the DES. The bias in DES studied through Differential Cryptanalysis by Adi Shamir is highlighted. The experiment shows about 50% of the key bits can be found, allowing the complete key to be found in a short time. Hardware application with multi micro-controllers have been proposed due to the easy implementation of multilayer neural networks in hardware. One example of a public-key protocol is given by Khalil Shihab . He describes the decryption scheme and the public key creation that are based on a backpropagation neural network. The encryption scheme and the private key creation process are based on Boolean algebra. This technique has the advantage of small time and memory complexities. A disadvantage is the property of backpropagation algorithms: because of huge training sets, the learning phase of a neural network is very long. Therefore, the use of this protocol is only theoretical so far. == Neural key exchange protocol == The most used protocol for key exchange between two parties A and B in the practice is Diffie–Hellman key exchange protocol. Neural key exchange, which is based on the synchronization of two tree parity machines, should be a secure replacement for this method. Synchronizing these two machines is similar to synchronizing two chaotic oscillators in chaos communications. === Tree parity machine === The tree parity machine is a special type of multi-layer feedforward neural network. It consists of one output neuron, K hidden neurons and K×N input neurons. Inputs to the network take three values: x i j ∈ { − 1 , 0 , + 1 } {\displaystyle x_{ij}\in \left\{-1,0,+1\right\}} The weights between input and hidden neurons take the values: w i j ∈ { − L , . . . , 0 , . . . , + L } {\displaystyle w_{ij}\in \left\{-L,...,0,...,+L\right\}} Output value of each hidden neuron is calculated as a sum of all multiplications of input neurons and these weights: σ i = sgn ⁡ ( ∑ j = 1 N w i j x i j ) {\displaystyle \sigma _{i}=\operatorname {sgn}(\sum _{j=1}^{N}w_{ij}x_{ij})} Signum is a simple function, which returns −1,0 or 1: sgn ⁡ ( x ) = { − 1 if x < 0 , 0 if x = 0 , 1 if x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1&{\text{if }}x<0,\\0&{\text{if }}x=0,\\1&{\text{if }}x>0.\end{cases}}} If the scalar product is 0, the output of the hidden neuron is mapped to −1 in order to ensure a binary output value. The output of neural network is then computed as the multiplication of all values produced by hidden elements: τ = ∏ i = 1 K σ i {\displaystyle \tau =\prod _{i=1}^{K}\sigma _{i}} Output of the tree parity machine is binary. === Protocol === Each party (A and B) uses its own tree parity machine. Synchronization of the tree parity machines is achieved in these steps Initialize random weight values Execute these steps until the full synchronization is achieved Generate random input vector X Compute the values of the hidden neurons Compute the value of the output neuron Compare the values of both tree parity machines Outputs are the same: one of the suitable learning rules is applied to the weights Outputs are different: go to 2.1 After the full synchronization is achieved (the weights wij of both tree parity machines are same), A and B can use their weights as keys. This method is known as a bidirectional learning. One of the following learning rules can be used for the synchronization: Hebbian learning rule: w i + = g ( w i + σ i x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}+\sigma _{i}x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Anti-Hebbian learning rule: w i + = g ( w i − σ i x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}-\sigma _{i}x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Random walk: w i + = g ( w i + x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}+x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Where: Θ ( a , b ) = 0 {\displaystyle \Theta (a,b)=0} if a ≠ b {\displaystyle a\neq b} otherwise Θ ( a , b ) = 1 {\displaystyle \Theta (a,b)=1} And: g ( x ) {\displaystyle g(x)} is a function that keeps the w i {\displaystyle w_{i}} in the range { − L , − L + 1 , . . . , 0 , . . . , L − 1 , L } {\displaystyle \{-L,-L+1,...,0,...,L-1,L\}} === Attacks and security of this protocol === In every attack it is considered, that the attacker E can eavesdrop messages between the parties A and B, but does not have an opportunity to change them. ==== Brute force ==== To provide a brute force attack, an attacker has to test all possible keys (all possible values of weights wij). By K hidden neurons, K×N input neurons and boundary of weights L, this gives (2L+1)KN possibilities. For example, the configuration K = 3, L = 3 and N = 100 gives us 310253 key possibilities, making the attack impossible with today's computer power. ==== Learning with own tree parity machine ==== One of the basic attacks can be provided by an attacker, who owns the same tree parity machine as the parties A and B. He wants to synchronize his tree parity machine with these two parties. In each step there are three situations possible: Output(A) ≠ Output(B): None of the parties updates its weights. Output(A) = Output(B) = Output(E): All the three parties update weights in their tree parity machines. Output(A) = Output(B) ≠ Output(E): Parties A and B update their tree parity machines, but the attacker can not do that. Because of this situation his learning is slower than the synchronization of parties A and B. It has been proven, that the synchronization of two parties is faster than learning of an attacker. It can be improved by increasing of the synaptic depth L of the neural network. That gives this protocol enough security and an attacker can find out the key only with small probability. ==== Other attacks ==== For conventional cryptographic systems, we can improve the security of the protocol by increasing of the key length. In the case of neural cryptography, we improve it by increasing of the synaptic depth L of the neural networks. Changing this parameter increases the cost of a successful attack exponentially, while the effort for the users grows polynomially. Therefore, breaking the security of neural key exchange belongs to the complexity class NP. Alexander Klimov, Anton Mityaguine, and Adi Shamir say that the original neural synchronization scheme can be broken by at least three different attacks—geometric, probabilistic analysis, and using genetic algorithms. Even though this particular implementation is insecure, the ideas behind chaotic synchronization could potentially lead to a secure implementation. === Permutation parity machine === The permutation parity machine is a binary variant of the tree parity machine. It consists of one input layer, one hidden layer and one output layer. The number of neurons in the output layer depends on the number of hidden units K. Each hidden neuron has N binary input neurons: x i j ∈ { 0 , 1 } {\displaystyle x_{ij}\in \left\{0,1\right\}} The weights between input and hidden neurons are also binary: w i j ∈ { 0 , 1 } {\displaystyle w_{ij}\in \left\{0,1\right\}} Output value of each hidden neuron is calculated as a sum of all exclusive disjunctions (exclusive or) of input neurons and these weights: σ i = θ N ( ∑ j = 1 N w i j ⊕ x i j ) {\displaystyle \sigma _{i}=\theta _{N}(\sum _{j=1}^{N}w_{ij}\oplus x_{ij})} (⊕ means XOR). Th

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  Polynomial kernel

  In machine learning, the polynomial kernel is a kernel function commonly used with support vector machines (SVMs) and other kernelized models, that represents the similarity of vectors (training samples) in a feature space over polynomials of the original variables, allowing learning of non-linear models. Intuitively, the polynomial kernel looks not only at the given features of input samples to determine their similarity, but also combinations of these. In the context of regression analysis, such combinations are known as interaction features. The (implicit) feature space of a polynomial kernel is equivalent to that of polynomial regression, but without the combinatorial blowup in the number of parameters to be learned. When the input features are binary-valued (booleans), then the features correspond to logical conjunctions of input features. == Definition == For degree-d polynomials, the polynomial kernel is defined as K ( x , y ) = ( x T y + c ) d {\displaystyle K(\mathbf {x} ,\mathbf {y} )=(\mathbf {x} ^{\mathsf {T}}\mathbf {y} +c)^{d}} where x and y are vectors of size n in the input space, i.e. vectors of features computed from training or test samples and c ≥ 0 is a free parameter trading off the influence of higher-order versus lower-order terms in the polynomial. When c = 0, the kernel is called homogeneous. (A further generalized polykernel divides xTy by a user-specified scalar parameter a.) As a kernel, K corresponds to an inner product in a feature space based on some mapping φ: K ( x , y ) = ⟨ φ ( x ) , φ ( y ) ⟩ {\displaystyle K(\mathbf {x} ,\mathbf {y} )=\langle \varphi (\mathbf {x} ),\varphi (\mathbf {y} )\rangle } The nature of φ can be seen from an example. Let d = 2, so we get the special case of the quadratic kernel. After using the multinomial theorem (twice—the outermost application is the binomial theorem) and regrouping, K ( x , y ) = ( ∑ i = 1 n x i y i + c ) 2 = ∑ i = 1 n ( x i 2 ) ( y i 2 ) + ∑ i = 2 n ∑ j = 1 i − 1 ( 2 x i x j ) ( 2 y i y j ) + ∑ i = 1 n ( 2 c x i ) ( 2 c y i ) + c 2 {\displaystyle K(\mathbf {x} ,\mathbf {y} )=\left(\sum _{i=1}^{n}x_{i}y_{i}+c\right)^{2}=\sum _{i=1}^{n}\left(x_{i}^{2}\right)\left(y_{i}^{2}\right)+\sum _{i=2}^{n}\sum _{j=1}^{i-1}\left({\sqrt {2}}x_{i}x_{j}\right)\left({\sqrt {2}}y_{i}y_{j}\right)+\sum _{i=1}^{n}\left({\sqrt {2c}}x_{i}\right)\left({\sqrt {2c}}y_{i}\right)+c^{2}} From this it follows that the feature map is given by: φ ( x ) = ( x n 2 , … , x 1 2 , 2 x n x n − 1 , … , 2 x n x 1 , 2 x n − 1 x n − 2 , … , 2 x n − 1 x 1 , … , 2 x 2 x 1 , 2 c x n , … , 2 c x 1 , c ) {\displaystyle \varphi (x)=\left(x_{n}^{2},\ldots ,x_{1}^{2},{\sqrt {2}}x_{n}x_{n-1},\ldots ,{\sqrt {2}}x_{n}x_{1},{\sqrt {2}}x_{n-1}x_{n-2},\ldots ,{\sqrt {2}}x_{n-1}x_{1},\ldots ,{\sqrt {2}}x_{2}x_{1},{\sqrt {2c}}x_{n},\ldots ,{\sqrt {2c}}x_{1},c\right)} generalizing for ( x T y + c ) d {\displaystyle \left(\mathbf {x} ^{T}\mathbf {y} +c\right)^{d}} , where x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} , y ∈ R n {\displaystyle \mathbf {y} \in \mathbb {R} ^{n}} and applying the multinomial theorem: ( x T y + c ) d = ∑ j 1 + j 2 + ⋯ + j n + 1 = d d ! j 1 ! ⋯ j n ! j n + 1 ! x 1 j 1 ⋯ x n j n c j n + 1 d ! j 1 ! ⋯ j n ! j n + 1 ! y 1 j 1 ⋯ y n j n c j n + 1 = φ ( x ) T φ ( y ) {\displaystyle {\begin{alignedat}{2}\left(\mathbf {x} ^{T}\mathbf {y} +c\right)^{d}&=\sum _{j_{1}+j_{2}+\dots +j_{n+1}=d}{\frac {\sqrt {d!}}{\sqrt {j_{1}!\cdots j_{n}!j_{n+1}!}}}x_{1}^{j_{1}}\cdots x_{n}^{j_{n}}{\sqrt {c}}^{j_{n+1}}{\frac {\sqrt {d!}}{\sqrt {j_{1}!\cdots j_{n}!j_{n+1}!}}}y_{1}^{j_{1}}\cdots y_{n}^{j_{n}}{\sqrt {c}}^{j_{n+1}}\\&=\varphi (\mathbf {x} )^{T}\varphi (\mathbf {y} )\end{alignedat}}} The last summation has l d = ( n + d d ) {\displaystyle l_{d}={\tbinom {n+d}{d}}} elements, so that: φ ( x ) = ( a 1 , … , a l , … , a l d ) {\displaystyle \varphi (\mathbf {x} )=\left(a_{1},\dots ,a_{l},\dots ,a_{l_{d}}\right)} where l = ( j 1 , j 2 , . . . , j n , j n + 1 ) {\displaystyle l=(j_{1},j_{2},...,j_{n},j_{n+1})} and a l = d ! j 1 ! ⋯ j n ! j n + 1 ! x 1 j 1 ⋯ x n j n c j n + 1 | j 1 + j 2 + ⋯ + j n + j n + 1 = d {\displaystyle a_{l}={\frac {\sqrt {d!}}{\sqrt {j_{1}!\cdots j_{n}!j_{n+1}!}}}x_{1}^{j_{1}}\cdots x_{n}^{j_{n}}{\sqrt {c}}^{j_{n+1}}\quad |\quad j_{1}+j_{2}+\dots +j_{n}+j_{n+1}=d} == Practical use == Although the RBF kernel is more popular in SVM classification than the polynomial kernel, the latter is quite popular in natural language processing (NLP). The most common degree is d = 2 (quadratic), since larger degrees tend to overfit on NLP problems. Various ways of computing the polynomial kernel (both exact and approximate) have been devised as alternatives to the usual non-linear SVM training algorithms, including: full expansion of the kernel prior to training/testing with a linear SVM, i.e. full computation of the mapping φ as in polynomial regression; basket mining (using a variant of the apriori algorithm) for the most commonly occurring feature conjunctions in a training set to produce an approximate expansion; inverted indexing of support vectors. One problem with the polynomial kernel is that it may suffer from numerical instability: when xTy + c < 1, K(x, y) = (xTy + c)d tends to zero with increasing d, whereas when xTy + c > 1, K(x, y) tends to infinity.

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  Roposo

  Roposo is an Indian video-sharing social media service, owned by Glance, a subsidiary of InMobi. Roposo provides a space where users can share posts related to different topics like food, comedy, music, poetry, fashion and travel. It is a platform where people express visually with homemade videos and photos. The app offers a TV-like browsing experience with user-generated content on its channels. Users can also use editing tools on the platform and upload their content. == History == Established in July 2014 under Relevant E-solutions Pvt. Ltd., Roposo is the brainchild of three IIT Delhi alumni – Mayank Bhangadia, Avinash Saxena, and Kaushal Shubhank. Under Bhangadia's leadership, the company pivoted from a fashion-based network into a short-form video platform with AI-powered moderation, and its journey was featured as a Harvard Business Publishing case study. In November 2019, Roposo was acquired by InMobi's Glance Digital Experience Pvt. Ltd.(the mobile content platform and part of the InMobi Group). When the Chinese-owned video-sharing app TikTok was banned on 30 June 2020, the app saw a huge spike in users with several TikTok users registering on Roposo. == Technology == The open platform has some features such as a TV-like browsing, different channels, a chat feature that lets buyers and sellers converse directly through the platform, and creation tools such as an option to add voice-over, music and GIF stickers for videos and photos.

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  Targeted maximum likelihood estimation

  Targeted Maximum Likelihood Estimation (TMLE) (also more accurately referred to as Targeted Minimum Loss-Based Estimation) is a general statistical estimation framework for causal inference and semiparametric models. TMLE combines ideas from maximum likelihood estimation, semiparametric efficiency theory, and machine learning. It was introduced by Mark J. van der Laan and colleagues in the mid-2000s as a method that yields asymptotically efficient plug-in estimators while allowing the use of flexible, data-adaptive algorithms such as ensemble machine learning for nuisance parameter estimation. TMLE is used in epidemiology, biostatistics, and the social sciences to estimate causal effects in observational and experimental studies. Applications of TMLE include Longitudinal TMLE (LTMLE) for time-varying treatments and confounders. Variations in how the targeting step in TMLE is carried out have resulted in various versions of TMLE such as Collaborative TMLE (CTMLE) and Adaptive TMLE for improved finite-sample performance and automated variable selection. == History == The TMLE framework was first described by van der Laan and Rubin (2006) as a general approach for the construction of efficient plug-in estimators of smooth features of the data density. It was demonstrated in the context of causal inference and missing data problems. It was developed to address limitations of traditional doubly robust methods, such as Augmented Inverse Probability Weighting (AIPW), by respecting the plug-in principle in the sense that it respects that the target parameter is a function of the data density that is an element of the statistical model. TMLE estimates the data density or relevant parts of it with machine learning and targets these machine learning fits before it is plugged in the target parameter mapping. In this manner, a TMLE always respects global knowledge and satisfies known bounds such as that the target parameter is a probability . Since its introduction, TMLE has been developed in a series of theoretical and applied papers, culminating in book-length treatments of the method and its applications to survival analysis, adaptive designs, and longitudinal data. == Methodology == At its core, TMLE is a two-step estimation procedure: Initial estimation: Machine learning methods (such as the Super Learner ensemble) are used to obtain flexible estimates of nuisance parameters, such as outcome regressions and propensity scores. Targeting step: The initial estimate is updated by solving a score equation (the efficient influence function) so that the final estimator is consistent, asymptotically normal, and efficient under mild regularity conditions. The targeted machine learning fit is then mapped into the corresponding estimator of the target parameter by simply plugging it in the target parameter mapping. This approach balances the bias–variance trade-off by combining data-adaptive estimation with semiparametric efficiency theory. TMLE is doubly robust, meaning it remains consistent if either the outcome model or the treatment model is consistently estimated. === Formula === Here we explain the TMLE of the average treatment effect of a binary treatment on an outcome adjusting for baseline covariates. Consider i.i.d. observations O i = ( W i , A i , Y i ) {\displaystyle O_{i}=(W_{i},A_{i},Y_{i})} from a distribution P 0 {\displaystyle P_{0}} , where W {\displaystyle W} are baseline covariates, A {\displaystyle A} is a binary treatment, and Y {\displaystyle Y} is an outcome. Let Q ¯ ( a , w ) = E [ Y ∣ A = a , W = w ] {\displaystyle {\bar {Q}}(a,w)=\mathbb {E} [Y\mid A=a,W=w]} represent the outcome model and g ( a ∣ w ) = P ( A = a ∣ W = w ) {\displaystyle g(a\mid w)=P(A=a\mid W=w)} represent the propensity score. The average treatment effect (ATE) is given by ψ 0 = E { Q ¯ ( 1 , W ) − Q ¯ ( 0 , W ) } . {\displaystyle \psi _{0}=\mathbb {E} \{{\bar {Q}}(1,W)-{\bar {Q}}(0,W)\}.} A basic TMLE for the ATE proceeds as follows: Step 1: Estimate initial models. Obtain estimates Q ¯ ^ ( a , w ) {\displaystyle {\hat {\bar {Q}}}(a,w)} and g ^ ( a ∣ w ) {\displaystyle {\hat {g}}(a\mid w)} , often using flexible methods such as Super Learner. Step 2: Compute the clever covariate. Define: H ( A , W ) = A g ^ ( 1 ∣ W ) − 1 − A g ^ ( 0 ∣ W ) . {\displaystyle H(A,W)={\frac {A}{{\hat {g}}(1\mid W)}}-{\frac {1-A}{{\hat {g}}(0\mid W)}}.} Step 3: Estimate the fluctuation parameter. Fit a logistic regression of Y {\displaystyle Y} on H ( A , W ) {\displaystyle H(A,W)} with logit ⁡ ( Q ¯ ^ ( A , W ) ) {\displaystyle \operatorname {logit} ({\hat {\bar {Q}}}(A,W))} as offset. This yields ε ^ {\displaystyle {\hat {\varepsilon }}} , the MLE that solves the score equation: 1 n ∑ i = 1 n H ( A i , W i ) { Y i − Q ¯ ^ ε ( A i , W i ) } = 0. {\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}H(A_{i},W_{i}){\big \{}Y_{i}-{\hat {\bar {Q}}}^{\varepsilon }(A_{i},W_{i}){\big \}}=0.} Step 4: Update the initial estimate. Apply the "blip" to obtain the targeted estimate: Q ¯ ^ ∗ ( A , W ) = expit ⁡ ( logit ⁡ ( Q ¯ ^ ( A , W ) ) + ε ^ H ( A , W ) ) . {\displaystyle {\hat {\bar {Q}}}^{}(A,W)=\operatorname {expit} {\Big (}\operatorname {logit} {\big (}{\hat {\bar {Q}}}(A,W){\big )}+{\hat {\varepsilon }}\,H(A,W){\Big )}.} Step 5: Compute the TMLE. The ATE estimate is: ψ ^ TMLE = 1 n ∑ i = 1 n [ Q ¯ ^ ∗ ( 1 , W i ) − Q ¯ ^ ∗ ( 0 , W i ) ] . {\displaystyle {\hat {\psi }}_{\text{TMLE}}={\frac {1}{n}}\sum _{i=1}^{n}{\big [}{\hat {\bar {Q}}}^{}(1,W_{i})-{\hat {\bar {Q}}}^{}(0,W_{i}){\big ]}.} Inference. The efficient influence function (EIF) for the ATE is: D ∗ ( O ) = H ( A , W ) { Y − Q ¯ ∗ ( A , W ) } + Q ¯ ∗ ( 1 , W ) − Q ¯ ∗ ( 0 , W ) − ψ . {\displaystyle D^{}(O)=H(A,W)\{Y-{\bar {Q}}^{}(A,W)\}+{\bar {Q}}^{}(1,W)-{\bar {Q}}^{}(0,W)-\psi .} The variance is estimated by σ ^ 2 = n − 1 ∑ i = 1 n ( D ∗ ( O i ) ) 2 {\displaystyle {\hat {\sigma }}^{2}=n^{-1}\sum _{i=1}^{n}{\big (}D^{}(O_{i}){\big )}^{2}} , yielding Wald-type confidence intervals ψ ^ TMLE ± z 1 − α / 2 σ ^ / n {\displaystyle {\hat {\psi }}_{\text{TMLE}}\pm z_{1-\alpha /2}\,{\hat {\sigma }}/{\sqrt {n}}} . Remark. For continuous outcomes, a linear fluctuation Q ¯ ^ ∗ = Q ¯ ^ + ε ^ H {\displaystyle {\hat {\bar {Q}}}^{}={\hat {\bar {Q}}}+{\hat {\varepsilon }}\,H} may be used instead. For bounded continuous outcomes, the logistic fluctuation (after rescaling Y {\displaystyle Y} to [ 0 , 1 ] {\displaystyle [0,1]} ) is often preferred for improved finite-sample performance. == Applications == TMLE has been applied in: Epidemiology: Estimating causal effects of exposures and interventions in observational cohort studies. Clinical trials and real-world evidence: The Targeted Learning roadmap provides a structured framework for generating and validating real-world evidence (RWE), bridging randomized trials and observational data using TMLE and related estimation techniques. This approach enables transparency, sensitivity analysis, and stronger causal inference for regulatory and clinical trial contexts. High-dimensional settings: Integration with ensemble methods for causal effect estimation. TMLE has been successfully applied in pharmacoepidemiology where a large number of covariates are automatically selected to adjust for confounding. In a study of post–myocardial infarction statin use and 1-year mortality, TMLE demonstrated robust performance relative to inverse probability weighting in scenarios with hundreds of potential confounders. == Derivatives and extensions == Longitudinal TMLE (LTMLE): A methodological extension of TMLE for longitudinal data with time-varying treatments, confounders, and censoring. It allows the estimation of dynamic treatment regimes and intervention-specific causal effects over time. This framework was originally introduced by van der Laan & Gruber (2012). Collaborative TMLE (CTMLE): Enhances finite-sample performance and variable selection by collaboratively fitting the treatment mechanism in conjunction with the target parameter. == Software == Several R packages implement TMLE and related methods: tmle: Functions for binary, categorical, and continuous outcomes. ltmle: Implementation for longitudinal data with time-varying treatments and outcomes. ctmle: Algorithms for collaborative TMLE and adaptive variable selection. SuperLearner: A theoretically grounded, cross-validated ensemble learning method that combines predictions from multiple algorithms to minimize predictive risk. Widely used in TMLE for estimating nuisance parameters. The original implementation is available as the R package SuperLearner. Recent machine learning platforms like H2O AutoML implement similar ensemble strategies, combining diverse learners in parallel and leveraging stacking and blending techniques, effectively functioning as a large-scale Super Learner.

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  Correlation clustering

  Clustering is the problem of partitioning data points into groups based on similarity or dissimilarity. Correlation clustering is a clustering framework in which a set of objects is partitioned into clusters based on pairwise similarity and dissimilarity information, without requiring the number of clusters to be specified in advance. == Description of the problem == In machine learning, correlation clustering (also known as cluster editing) considers settings in which pairwise similarity or dissimilarity relationships between objects are known. A standard formulation models the input as an unweighted complete graph G = ( V , E ) {\displaystyle G=(V,E)} , where each edge is labeled either + {\displaystyle +} or − {\displaystyle -} (that is, the graph is a signed graph), indicating whether the corresponding endpoints are similar or dissimilar. The goal is to find a clustering (that is, a partition of V {\displaystyle V} ) that either maximizes the number of agreements—the sum of positive edges whose endpoints lie in the same cluster and negative edges whose endpoints lie in different clusters—or minimizes the number of disagreements—the sum of positive edges whose endpoints are separated and negative edges whose endpoints lie in the same cluster. Unlike other clustering methods such as k-means, correlation clustering does not require choosing the number of clusters k {\displaystyle k} in advance. It is not always possible to find a clustering with zero disagreements. For example, consider a triangle graph containing two positive edges and one negative edge. In this case, every clustering incurs at least one disagreement. Such configurations are referred to in the literature as bad triangles. From a computational perspective, optimizing the correlation clustering objective is challenging. The (decision version of the) problem is NP-complete. A large body of subsequent work has developed approximation algorithms for correlation clustering under various assumptions, including complete or general graphs and unweighted or weighted graphs, for both minimization and maximization objectives. This problem is considered one of the fundamental combinatorial optimization problems, and many algorithmic techniques have been developed to address it. The problem has also been studied extensively across multiple disciplines. A comprehensive literature review of early correlation clustering research is provided by Wahid and Hassini. == Formal Definitions == Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph with nodes V {\displaystyle V} and edges E {\displaystyle E} . A clustering of G {\displaystyle G} is a partition of its node set Π = { π 1 , … , π k } {\displaystyle \Pi =\{\pi _{1},\dots ,\pi _{k}\}} with V = π 1 ∪ ⋯ ∪ π k {\displaystyle V=\pi _{1}\cup \dots \cup \pi _{k}} and π i ∩ π j = ∅ {\displaystyle \pi _{i}\cap \pi _{j}=\emptyset } for i ≠ j {\displaystyle i\neq j} . For a given clustering Π {\displaystyle \Pi } , let δ ( Π ) = { { u , v } ∈ E ∣ { u , v } ⊈ π ∀ π ∈ Π } {\displaystyle \delta (\Pi )=\{\{u,v\}\in E\mid \{u,v\}\not \subseteq \pi \;\forall \pi \in \Pi \}} denote the subset of edges of G {\displaystyle G} whose endpoints are in different subsets of the clustering Π {\displaystyle \Pi } . Now, let w : E → R ≥ 0 {\displaystyle w\colon E\to \mathbb {R} _{\geq 0}} be a function that assigns a non-negative weight to each edge of the graph and let E = E + ∪ E − {\displaystyle E=E^{+}\cup E^{-}} be a partition of the edges into attractive ( E + {\displaystyle E^{+}} ) and repulsive ( E − {\displaystyle E^{-}} ) edges; that is, the edges are signed. The minimum disagreement correlation clustering problem is the following optimization problem: minimize Π ∑ e ∈ E + ∩ δ ( Π ) w e + ∑ e ∈ E − ∖ δ ( Π ) w e . {\displaystyle {\begin{aligned}&{\underset {\Pi }{\operatorname {minimize} }}&&\sum _{e\in E^{+}\cap \delta (\Pi )}w_{e}+\sum _{e\in E^{-}\setminus \delta (\Pi )}w_{e}\;.\end{aligned}}} Here, the set E + ∩ δ ( Π ) {\displaystyle E^{+}\cap \delta (\Pi )} contains the attractive edges whose endpoints are in different components with respect to the clustering Π {\displaystyle \Pi } and the set E − ∖ δ ( Π ) {\displaystyle E^{-}\setminus \delta (\Pi )} contains the repulsive edges whose endpoints are in the same component with respect to the clustering Π {\displaystyle \Pi } . Together these two sets contain all edges that disagree with the clustering Π {\displaystyle \Pi } . Similarly to the minimum disagreement correlation clustering problem, the maximum agreement correlation clustering problem is defined as maximize Π ∑ e ∈ E + ∖ δ ( Π ) w e + ∑ e ∈ E − ∩ δ ( Π ) w e . {\displaystyle {\begin{aligned}&{\underset {\Pi }{\operatorname {maximize} }}&&\sum _{e\in E^{+}\setminus \delta (\Pi )}w_{e}+\sum _{e\in E^{-}\cap \delta (\Pi )}w_{e}\;.\end{aligned}}} Here, the set E + ∖ δ ( Π ) {\displaystyle E^{+}\setminus \delta (\Pi )} contains the attractive edges whose endpoints are in the same component with respect to the clustering Π {\displaystyle \Pi } and the set E − ∩ δ ( Π ) {\displaystyle E^{-}\cap \delta (\Pi )} contains the repulsive edges whose endpoints are in different components with respect to the clustering Π {\displaystyle \Pi } . Together these two sets contain all edges that agree with the clustering Π {\displaystyle \Pi } . Instead of formulating the correlation clustering problem in terms of non-negative edge weights and a partition of the edges into attractive and repulsive edges the problem is also formulated in terms of positive and negative edge costs without partitioning the set of edges explicitly. For given weights w : E → R ≥ 0 {\displaystyle w\colon E\to \mathbb {R} _{\geq 0}} and a given partition E = E + ∪ E − {\displaystyle E=E^{+}\cup E^{-}} of the edges into attractive and repulsive edges, the edge costs can be defined by c e = { w e if e ∈ E + − w e if e ∈ E − {\displaystyle {\begin{aligned}c_{e}={\begin{cases}\;\;w_{e}&{\text{if }}e\in E^{+}\\-w_{e}&{\text{if }}e\in E^{-}\end{cases}}\end{aligned}}} for all e ∈ E {\displaystyle e\in E} . An edge whose endpoints are in different clusters is said to be cut. The set δ ( Π ) {\displaystyle \delta (\Pi )} of all edges that are cut is often called a multicut of G {\displaystyle G} . The minimum cost multicut problem is the problem of finding a clustering Π {\displaystyle \Pi } of G {\displaystyle G} such that the sum of the costs of the edges whose endpoints are in different clusters is minimal: minimize Π ∑ e ∈ δ ( Π ) c e . {\displaystyle {\begin{aligned}&{\underset {\Pi }{\operatorname {minimize} }}&&\sum _{e\in \delta (\Pi )}c_{e}\;.\end{aligned}}} Similar to the minimum cost multicut problem, coalition structure generation in weighted graph games is the problem of finding a clustering such that the sum of the costs of the edges that are not cut is maximal: maximize Π ∑ e ∈ E ∖ δ ( Π ) c e . {\displaystyle {\begin{aligned}&{\underset {\Pi }{\operatorname {maximize} }}&&\sum _{e\in E\setminus \delta (\Pi )}c_{e}\;.\end{aligned}}} This formulation is also known as the clique partitioning problem. It can be shown that all four problems that are formulated above are equivalent. This means that a clustering that is optimal with respect to any of the four objectives is optimal for all of the four objectives. == Algorithms == If the graph admits a clustering with zero disagreements, then deleting all negative edges and computing the connected components of the remaining graph yields an optimal clustering. A necessary and sufficient condition for the existence of such a clustering was given by Davis: no cycle in the graph may contain exactly one negative edge. Bansal et al. discuss the NP-completeness proof and also present both a constant factor approximation algorithm and polynomial-time approximation scheme to find the clusters in this setting. Ailon et al. propose a randomized 3-approximation algorithm for the same problem. CC-Pivot(G=(V,E+,E−)) Pick random pivot i ∈ V Set C = { i } {\displaystyle C=\{i\}} , V'=Ø For all j ∈ V, j ≠ i; If (i,j) ∈ E+ then Add j to C Else (If (i,j) ∈ E−) Add j to V' Let G' be the subgraph induced by V' Return clustering C,CC-Pivot(G') The authors show that the above algorithm is a 3-approximation algorithm for correlation clustering. The best polynomial-time approximation algorithm known at the moment for this problem achieves a ~2.06 approximation by rounding a linear program, as shown by Chawla, Makarychev, Schramm, and Yaroslavtsev. Karpinski and Schudy proved existence of a polynomial time approximation scheme (PTAS) for that problem on complete graphs and fixed number of clusters. == Optimal number of clusters == In 2011, it was shown by Bagon and Galun that the optimization of the correlation clustering functional is closely related to well known discrete optimization methods. In their work they proposed a probabilistic analysis of the underlying implicit model that allows the correlation clustering functional to estimate the

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