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\
Word error rate
Word error rate (WER) is a common metric of the performance of a speech recognition or machine translation system. The WER metric typically ranges from 0 to 1, where 0 indicates that the compared pieces of text are exactly identical, and 1 (or larger) indicates that they are completely different with no similarity. This way, a WER of 0.8 means that there is an 80% error rate for compared sentences. The general difficulty of measuring performance lies in the fact that the recognized word sequence can have a different length from the reference word sequence (supposedly the correct one). The WER is derived from the Levenshtein distance, working at the word level instead of the phoneme level. The WER is a valuable tool for comparing different systems as well as for evaluating improvements within one system. This kind of measurement, however, provides no details on the nature of translation errors and further work is therefore required to identify the main source(s) of error and to focus any research effort. This problem is solved by first aligning the recognized word sequence with the reference (spoken) word sequence using dynamic string alignment. Examination of this issue is seen through a theory called the power law that states the correlation between perplexity and word error rate. Word error rate can then be computed as: W E R = S + D + I N = S + D + I S + D + C {\displaystyle {\mathit {WER}}={\frac {S+D+I}{N}}={\frac {S+D+I}{S+D+C}}} where S is the number of substitutions, D is the number of deletions, I is the number of insertions, C is the number of correct words, N is the number of words in the reference (N=S+D+C) The intuition behind 'deletion' and 'insertion' is how to get from the reference to the hypothesis. So if we have the reference "This is wikipedia" and hypothesis "This _ wikipedia", we call it a deletion. Note that since N is the number of words in the reference, the word error rate can be larger than 1.0, namely if the number of insertions I is larger than the number of correct words C. When reporting the performance of a speech recognition system, sometimes word accuracy (WAcc) is used instead: W A c c = 1 − W E R = N − S − D − I N = C − I N {\displaystyle {\mathit {WAcc}}=1-{\mathit {WER}}={\frac {N-S-D-I}{N}}={\frac {C-I}{N}}} Since the WER can be larger than 1.0, the word accuracy can be smaller than 0.0. == Experiments == It is commonly believed that a lower word error rate shows superior accuracy in recognition of speech, compared with a higher word error rate. However, at least one study has shown that this may not be true. In a Microsoft Research experiment, it was shown that, if people were trained under "that matches the optimization objective for understanding", (Wang, Acero and Chelba, 2003) they would show a higher accuracy in understanding of language than other people who demonstrated a lower word error rate, showing that true understanding of spoken language relies on more than just high word recognition accuracy. == Other metrics == One problem with using a generic formula such as the one above, however, is that no account is taken of the effect that different types of error may have on the likelihood of successful outcome, e.g. some errors may be more disruptive than others and some may be corrected more easily than others. These factors are likely to be specific to the syntax being tested. A further problem is that, even with the best alignment, the formula cannot distinguish a substitution error from a combined deletion plus insertion error. Hunt (1990) has proposed the use of a weighted measure of performance accuracy where errors of substitution are weighted at unity but errors of deletion and insertion are both weighted only at 0.5, thus: W E R = S + 0.5 D + 0.5 I N {\displaystyle {\mathit {WER}}={\frac {S+0.5D+0.5I}{N}}} There is some debate, however, as to whether Hunt's formula may properly be used to assess the performance of a single system, as it was developed as a means of comparing more fairly competing candidate systems. A further complication is added by whether a given syntax allows for error correction and, if it does, how easy that process is for the user. There is thus some merit to the argument that performance metrics should be developed to suit the particular system being measured. Whichever metric is used, however, one major theoretical problem in assessing the performance of a system is deciding whether a word has been “mis-pronounced,” i.e. does the fault lie with the user or with the recogniser. This may be particularly relevant in a system which is designed to cope with non-native speakers of a given language or with strong regional accents. The pace at which words should be spoken during the measurement process is also a source of variability between subjects, as is the need for subjects to rest or take a breath. All such factors may need to be controlled in some way. For text dictation it is generally agreed that performance accuracy at a rate below 95% is not acceptable, but this again may be syntax and/or domain specific, e.g. whether there is time pressure on users to complete the task, whether there are alternative methods of completion, and so on. The term "Single Word Error Rate" is sometimes referred to as the percentage of incorrect recognitions for each different word in the system vocabulary. == Edit distance == The word error rate may also be referred to as the length normalized edit distance. The normalized edit distance between X and Y, d( X, Y ) is defined as the minimum of W( P ) / L ( P ), where P is an editing path between X and Y, W ( P ) is the sum of the weights of the elementary edit operations of P, and L(P) is the number of these operations (length of P).
Aarogya Setu
Aarogya Setu (lit. 'The bridge to health') is an Indian COVID-19 "contact tracing, syndromic mapping and self-assessment" digital service, primarily a mobile app, developed by the National Informatics Centre under the Ministry of Electronics and Information Technology (MeitY). The app reached more than 100 million installs in 40 days. On 26 May, amid growing privacy and security concerns, the source code of the app was made public. == Full view == The stated purpose of this app is to spread awareness of COVID-19 and to connect essential COVID-19-related health services to the people of India. This app augments the initiatives of the Department of Health to contain COVID-19 and shares best practices and advisories. It is a tracking app which uses the smartphone's GPS and Bluetooth features to track COVID-19 cases. The app is available for Android and iOS mobile operating systems. With Bluetooth, it tries to determine the risk if one has been near (within six feet of) a COVID-19-infected person, by scanning through a database of known cases across India. Using location information, it determines whether the location one is in belongs to one of the infected areas based on the data available. This app is an updated version of an earlier app called Corona Kavach (now discontinued) which was released earlier by the Government of India. == Features and tools == Aarogya Setu has four sections: User Status (tells the risk of getting COVID-19 for the user) Self Assess (helps the users identify COVID-19 symptoms and their risk profile) COVID-19 Updates (gives updates on local and national COVID-19 cases) E-pass integration (if applied for E-pass, it will be available) See Recent Contacts option (allows the users to assess the risk level of their Bluetooth contacts) It tells how many COVID-19 positive cases are likely in a radius of 500 m, 1 km, 2 km, 5 km and 10 km from the user. The app is built on a platform that can provide an application programming interface (API) so that other computer programs, mobile applications, and web services can make use of the features and data available in Aarogya Setu. == Response == Aarogya Setu crossed five million downloads within three days of its launch, making it one of the most popular government apps in India. It became the world's fastest-growing mobile app, beating Pokémon Go, with more than 50 million installs 13 days after launching in India on 2 April 2020. It reached 100 million installs by 13 May 2020, that is in 40 days since its launch. In an order on 29 April 2020 the central government made it mandatory for all employees to download the app and use it – "Before starting for office, they must review their status on Aarogya Setu and commute only when the app shows safe or low risk". The Union Home Ministry also said that the application is mandatory for all living in the COVID-19 containment zone. The government gave the announcement along with the nationwide lockdown extension by two weeks from the 4 May with certain relaxations. On 21 May 2020, the Airport Authority of India issued a Standard Operating Procedure (SOP) stating that all departing passengers must compulsorily be registered with the Aarogya Setu app. It added that the app would not be mandatory for children below 14 years. However, the next day, Civil Aviation Minister Hardeep Singh Puri clarified that the app would not be mandatory for any passengers. On 26 May 2020, the Aarogya Setu app code was made open to developers across the globe to help other countries manage contact tracing in their fight against COVID-19 pandemic. In March 2021, Co-WIN portal was integrated with the app. This allowed users to schedule an appointment through the app for COVID-19 vaccine by registering their phone number and providing relevant documents. == Effectiveness == NITI Aayog CEO revealed that "the app has been able to identify more than 3,000 hotspots in 3–17 days ahead of time." However, users and experts in India and around the world say the app raises huge data security concerns. The app collects name, number, gender, travel history, and uses a phone's Bluetooth and location data to let users know if they have been near a person with COVID-19 by scanning a database of known cases of infection, and also share it with the government simultaneously. This is the major area of concern as the app's constant access to a phone's Bluetooth imposes a form of security threat. But it stood to clarify itself that the informations received are not going to be made public. Amidst all these, the app hits a record of about one-hundred million downloads. == Reception == Rahul Gandhi, leader of the Congress party, termed the Aarogya Setu application a "sophisticated surveillance system" after the government announced that downloading the app would be mandatory for both government and private employees. Following this, others raised the same concerns about the Aarogya Setu app. The Ministry of Electronics and Information Technology (MeitY) responded to these concerns by asserting that Gandhi's claims were false, and that the app was being appreciated internationally. On 5 May, French ethical hacker Robert Baptiste, who goes by the name Elliot Alderson on Twitter, claimed that there were security issues with the app. The Indian government, as well as the app developers, responded to this claim by thanking the hacker for his attention, but dismissed his concerns. The developers of the app stated that the fetching of location data is a documented feature of the app, rather than a flaw, since the app is designed to track the distribution of the virus-infected population. They also asserted that no personal information of any user has been proven to be at risk. On 6 May, Robert Baptiste tweeted that security vulnerabilities in Aarogya Setu allowed hackers to "know who is infected, unwell, [or] made a self assessment in the area of his choice". He also gave details of how many people were unwell and infected at the Prime Minister's Office, the Indian Parliament and the Home Office. The Economic Times pointed out that a clause in the app's Terms and Conditions stated that the user "agrees and acknowledges that the Government of India will not be liable for ... any unauthorised access to your information or modification thereof". In response, several software developers called for the source code to be made public. On 12 May, former Supreme Court Judge Justice B.N. Srikrishna termed the government's push mandating the use of Aarogya Setu app "utterly illegal". He said so far it is not backed by any law and questioned "under what law, government is mandating it on anyone". MIT Technology Review gave 2 out of 5 stars to Aarogya Setu app after analyzing the COVID contact tracing apps launched in 25 countries. The app got stars only for the policy which suggests that data collected is deleted after a period of time and that the data collection, as far as user inputs go, is minimal. It also highlighted that India is the only democracy making its app mandatory for millions of people. The rating was further downgraded from 2 to 1 for collecting more information than the app needs to function. Following this, the MeitY made the source code of the Android app public on GitHub on 26 May, which will be followed by iOS and API documentation. Further, the Government has also launched a "bug bounty program". This was done to "promote transparency and ensure security and integrity of the app". However, experts stated that the server-side code had not yet been publicly released, which meant that public opinion on security and privacy was yet to be completely assuaged. Following this, ZDNet noted that the source code seemed to confirm the government's claim that user location data, if collected, would be anonymised and would be deleted after 45 days, or 60 days for high-risk individuals.
Aseprite
Aseprite ( ace-prite) is a proprietary, source-available image editor designed primarily for pixel art drawing and animation. It runs on Windows, macOS, and Linux, and features different tools for image and animation editing such as layers, frames, tilemap support, command-line interface, Lua scripting, among others. It is developed by Igara Studio S.A. and led by the developers David, Gaspar, and Martín Capello. Aseprite can be downloaded as freeware, (albeit it does not have the ability to save sprites) or purchased on Steam or Itch.io. Aseprite source code and binaries are distributed under EULA, educational, and Steam proprietary licenses. == History == Aseprite, formerly known as Allegro Sprite Editor, had its first release in 2001 as a free software project under the GPLv2 license. This license was kept until August 2016 with version v1.1.8, when the developers switched to a EULA, thus making the software proprietary. On the 1st of September 2016, the main developer, David Capello, wrote a post on the Aseprite Devblog explaining this change. The EULA permits others to download the Aseprite source code, compile it, and use it for personal purposes, but forbids its redistribution to third parties. After the license change, LibreSprite, a free and open source version of it, was created. Both before and after the license change, Aseprite was sold online, on Steam, itch.io, and the project's website. The project's code repository was hosted on Google Code until August 2014, when it was migrated to GitHub, where it remains hosted to date. As of October 2022, its repository has had 68 contributors and around 19 thousand stars. From 2014 to 2021, Aseprite had 66 different releases. Aseprite was used in the development of several notable games such as TowerFall (2013), Celeste (2018), Minit (2018), Wargroove (2019), Loop Hero (2021), Eastward (2021), Unpacking (2021), Haiku the Robot (2022) and Pizza Tower (2023). == Design and features == The main design purpose of Aseprite is to create animated 2D pixel-art sprites. Some of its features include: Layers and frames, with layer grouping and animation tagging Pixel-art specific transformations and tools (pixel-perfect modes, custom brushes, etc.) Animation real-time preview and onion skinning Tilemap and tileset modes Color palette managing, including 65 default palettes Color profiles and modes (RGBA, indexed and grayscale) Non-square pixels Command line interface (CLI) and Lua scripting Aseprite uses its own binary file type to store data, which is typically saved with .ase or .aseprite extensions. Different third-party projects were developed to support parsing of .ase files in programming languages including C#, Python and JavaScript, and in game engines such as Unity and Godot. Images and animations can be exported to different file formats including PNG, GIF, FLC, FLI, JPEG, PCX, TGA, ICO, SVG, and bitmap (BMP).
Time-inhomogeneous hidden Bernoulli model
Time-inhomogeneous hidden Bernoulli model (TI-HBM) is an alternative to hidden Markov model (HMM) for automatic speech recognition. Contrary to HMM, the state transition process in TI-HBM is not a Markov-dependent process, rather it is a generalized Bernoulli (an independent) process. This difference leads to elimination of dynamic programming at state-level in TI-HBM decoding process. Thus, the computational complexity of TI-HBM for probability evaluation and state estimation is O ( N L ) {\displaystyle O(NL)} (instead of O ( N 2 L ) {\displaystyle O(N^{2}L)} in the HMM case, where N {\displaystyle N} and L {\displaystyle L} are number of states and observation sequence length respectively). The TI-HBM is able to model acoustic-unit duration (e.g. phone/word duration) by using a built-in parameter named survival probability. The TI-HBM is simpler and faster than HMM in a phoneme recognition task, but its performance is comparable to HMM. For details, see [1] or [2].
Vicuna LLM
Vicuna LLM is an omnibus large language model used in AI research. Its methodology is to enable the public at large to contrast and compare the accuracy of LLMs "in the wild" (an example of citizen science) and to vote on their output; a question-and-answer chat format is used. At the beginning of each round two LLM chatbots from a diverse pool of nine are presented randomly and anonymously, their identities only being revealed upon voting on their answers. The user has the option of either replaying ("regenerating") a round, or beginning an entirely fresh one with new LLMs. (The user also has the option of choosing which LLMs to do battle.) Based on Llama 2, it is an open source project, and it itself has become the subject of academic research in the burgeoning field. A non-commercial, public demo of the Vicuna-13b model is available to access using LMSYS.
DataScene
DataScene is a scientific graphing, animation, data analysis, and real-time data monitoring software package. It was developed with the Common Language Infrastructure technology and the GDI+ graphics library. With the two Common Language Runtime engines - the .Net and Mono frameworks - DataScene runs on all major operating systems. With DataScene, the user can plot 39 types 2D & 3D graphs (e.g., Area graph, Bar graph, Boxplot graph, Pie graph, Line graph, Histogram graph, Surface graph, Polar graph, Water Fall graph, etc.), manipulate, print, and export graphs to various formats (e.g., Bitmap, WMF/EMF, JPEG, PNG, GIF, TIFF, PostScript, and PDF), analyze data with different mathematical methods (fitting curves, calculating statics, FFT, etc.), create chart animations for presentations (e.g. with PowerPoint), classes, and web pages, and monitor and chart real-time data. == History == DataScene was first released (version 1.0) in March 2009 for the Windows platform and the .Net 2.0 framework. Since version 2.0, DataScene has been ported to the Mono framework 2.6 and all Linux and Unix/X11 operating systems. Cyberwit offers free licensing for the Express edition of DataScene.