Stochastic block model

The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized by being connected with one another with particular edge densities. For example, edges may be more common within communities than between communities. Its mathematical formulation was first introduced in 1983 in the field of social network analysis by Paul W. Holland et al. The stochastic block model is important in statistics, machine learning, and network science, where it serves as a useful benchmark for the task of recovering community structure in graph data. == Definition == The stochastic block model takes the following parameters: The number n {\displaystyle n} of vertices; a partition of the vertex set { 1 , … , n } {\displaystyle \{1,\ldots ,n\}} into disjoint subsets C 1 , … , C r {\displaystyle C_{1},\ldots ,C_{r}} , called communities; a symmetric r × r {\displaystyle r\times r} matrix P {\displaystyle P} of edge probabilities. The edge set is then sampled at random as follows: any two vertices u ∈ C i {\displaystyle u\in C_{i}} and v ∈ C j {\displaystyle v\in C_{j}} are connected by an edge with probability P i j {\displaystyle P_{ij}} . An example problem is: given a graph with n {\displaystyle n} vertices, where the edges are sampled as described, recover the groups C 1 , … , C r {\displaystyle C_{1},\ldots ,C_{r}} . == Special cases == If the probability matrix is a constant, in the sense that P i j = p {\displaystyle P_{ij}=p} for all i , j {\displaystyle i,j} , then the result is the Erdős–Rényi model G ( n , p ) {\displaystyle G(n,p)} . This case is degenerate—the partition into communities becomes irrelevant—but it illustrates a close relationship to the Erdős–Rényi model. The planted partition model is the special case that the values of the probability matrix P {\displaystyle P} are a constant p {\displaystyle p} on the diagonal and another constant q {\displaystyle q} off the diagonal. Thus two vertices within the same community share an edge with probability p {\displaystyle p} , while two vertices in different communities share an edge with probability q {\displaystyle q} . Sometimes it is this restricted model that is called the stochastic block model. The case where p > q {\displaystyle p>q} is called an assortative model, while the case p < q {\displaystyle p P j k {\displaystyle P_{ii}>P_{jk}} whenever j ≠ k {\displaystyle j\neq k} : all diagonal entries dominate all off-diagonal entries. A model is called weakly assortative if P i i > P i j {\displaystyle P_{ii}>P_{ij}} whenever i ≠ j {\displaystyle i\neq j} : each diagonal entry is only required to dominate the rest of its own row and column. Disassortative forms of this terminology exist, by reversing all inequalities. For some algorithms, recovery might be easier for block models with assortative or disassortative conditions of this form. == Typical statistical tasks == Much of the literature on algorithmic community detection addresses three statistical tasks: detection, partial recovery, and exact recovery. === Detection === The goal of detection algorithms is simply to determine, given a sampled graph, whether the graph has latent community structure. More precisely, a graph might be generated, with some known prior probability, from a known stochastic block model, and otherwise from a similar Erdos-Renyi model. The algorithmic task is to correctly identify which of these two underlying models generated the graph. === Partial recovery === In partial recovery, the goal is to approximately determine the latent partition into communities, in the sense of finding a partition that is correlated with the true partition significantly better than a random guess. === Exact recovery === In exact recovery, the goal is to recover the latent partition into communities exactly. The community sizes and probability matrix may be known or unknown. == Statistical lower bounds and threshold behavior == Stochastic block models exhibit a sharp threshold effect reminiscent of percolation thresholds. Suppose that we allow the size n {\displaystyle n} of the graph to grow, keeping the community sizes in fixed proportions. If the probability matrix remains fixed, tasks such as partial and exact recovery become feasible for all non-degenerate parameter settings. However, if we scale down the probability matrix at a suitable rate as n {\displaystyle n} increases, we observe a sharp phase transition: for certain settings of the parameters, it will become possible to achieve recovery with probability tending to 1, whereas on the opposite side of the parameter threshold, the probability of recovery tends to 0 no matter what algorithm is used. For partial recovery, the appropriate scaling is to take P i j = P ~ i j / n {\displaystyle P_{ij}={\tilde {P}}_{ij}/n} for fixed P ~ {\displaystyle {\tilde {P}}} , resulting in graphs of constant average degree. In the case of two equal-sized communities, in the assortative planted partition model with probability matrix P = ( p ~ / n q ~ / n q ~ / n p ~ / n ) , {\displaystyle P=\left({\begin{array}{cc}{\tilde {p}}/n&{\tilde {q}}/n\\{\tilde {q}}/n&{\tilde {p}}/n\end{array}}\right),} partial recovery is feasible with probability 1 − o ( 1 ) {\displaystyle 1-o(1)} whenever ( p ~ − q ~ ) 2 > 2 ( p ~ + q ~ ) {\displaystyle ({\tilde {p}}-{\tilde {q}})^{2}>2({\tilde {p}}+{\tilde {q}})} , whereas any estimator fails partial recovery with probability 1 − o ( 1 ) {\displaystyle 1-o(1)} whenever ( p ~ − q ~ ) 2 < 2 ( p ~ + q ~ ) {\displaystyle ({\tilde {p}}-{\tilde {q}})^{2}<2({\tilde {p}}+{\tilde {q}})} . For exact recovery, the appropriate scaling is to take P i j = P ~ i j log ⁡ n / n {\displaystyle P_{ij}={\tilde {P}}_{ij}\log n/n} , resulting in graphs of logarithmic average degree. Here a similar threshold exists: for the assortative planted partition model with r {\displaystyle r} equal-sized communities, the threshold lies at p ~ − q ~ = r {\displaystyle {\sqrt {\tilde {p}}}-{\sqrt {\tilde {q}}}={\sqrt {r}}} . In fact, the exact recovery threshold is known for the fully general stochastic block model. == Algorithms == In principle, exact recovery can be solved in its feasible range using maximum likelihood, but this amounts to solving a constrained or regularized cut problem such as minimum bisection that is typically NP-complete. Hence, no known efficient algorithms will correctly compute the maximum-likelihood estimate in the worst case. However, a wide variety of algorithms perform well in the average case, and many high-probability performance guarantees have been proven for algorithms in both the partial and exact recovery settings. Successful algorithms include spectral clustering of the vertices, semidefinite programming, forms of belief propagation, and community detection among others. == Variants == Several variants of the model exist. One minor tweak allocates vertices to communities randomly, according to a categorical distribution, rather than in a fixed partition. More significant variants include the degree-corrected stochastic block model, the hierarchical stochastic block model, the geometric block model, censored block model and the mixed-membership block model. == Topic models == Stochastic block model have been recognised to be a topic model on bipartite networks. In a network of documents and words, Stochastic block model can identify topics: group of words with a similar meaning. == Extensions to signed graphs == Signed graphs allow for both favorable and adverse relationships and serve as a common model choice for various data analysis applications, e.g., correlation clustering. The stochastic block model can be trivially extended to signed graphs by assigning both positive and negative edge weights or equivalently using a difference of adjacency matrices of two stochastic block models. == DARPA/MIT/AWS Graph Challenge: streaming stochastic block partition == GraphChallenge encourages community approaches to developing new solutions for analyzing graphs and sparse data derived from social media, sensor feeds, and scientific data to enable relationships between events to be discovered as they unfold in the field. Streaming stochastic block partition is one of the challenges since 2017. Spectral clustering has demonstrated outstanding performance compared to the original and even improved base algorithm, matching its quality of clusters while being multiple orders of magnitude faster.

LCD crosstalk

LCD crosstalk is a visual defect in an LCD screen which occurs because of interference between adjacent pixels. Owing to the way rows and columns in the display are addressed, and charge is pushed around, the data on one part of the display has the potential to influence what is displayed elsewhere. This is generally known as crosstalk, and in matrix displays typically occurs in the horizontal and vertical directions. Crosstalk used to be a serious problem in the old passive-matrix (STN) displays, but is rarely discernable in modern active-matrix (TFT) displays. A fortunate side effect of inversion (see above) is that, for most display material, what little crosstalk there is largely cancelled out. For most practical purposes, the level of crosstalk in modern LCDs is negligible. Certain patterns, particularly those involving fine dots, can interact with the inversion and reveal visible crosstalk. If you try moving a small Window in front of the inversion pattern (above) which makes your screen flicker the most, you may well see crosstalk in the surrounding pattern. Different patterns are required to reveal crosstalk on different displays (depending on their inversion scheme).

Alexander Gammerman

Alexander Gammerman (born 2 November 1944) is a British computer scientist, and professor at Royal Holloway University of London. He is the co-inventor of conformal prediction. He is the founding director of the Centre for Machine Learning at Royal Holloway, University of London, and a Fellow of the Royal Statistical Society. == Career == Gammerman's academic career has been pursued in the Soviet Union and the United Kingdom. He started working as a Research Fellow in the Agrophysical Research Institute, St. Petersburg. In 1983, he emigrated to the United Kingdom and was appointed as a lecturer in the Computer Science Department at Heriot-Watt University, Edinburgh. Together with Roger Thatcher, Gammerman published several articles on Bayesian inference. In 1993, he was appointed to the established chair in Computer Science at University of London tenable at Royal Holloway and Bedford New College, where he served as the Head of Computer Science department from 1995 to 2005. In 1998, the Centre for Reliable Machine Learning was established, and Gammerman became the first director of the centre. Gammerman has written 7 books. == Honours and awards == In 1996, Gammerman received the P.W. Allen Award from the Forensic Science Society. In 2006, he became an Honorary Professor, at University College London. In 2009, he became a Distinguished Professor at Complutense University of Madrid, Spain. In 2019, he received a research grant funded by the energy company Centrica about predicting the time to the next failure of equipment. In 2020, he received the Amazon Research Award for the project titled Conformal Martingales for Change-Point Detection == Selected books == Measures of Complexity (2016), Springer, ISBN 3319357786. Algorithmic Learning in a Random World (2005), Springer, ISBN 0387001522. Causal Models and Intelligent Data Management (1999), Springer, ISBN 978-3-642-58648-4. Probabilistic Reasoning and Bayesian Belief Networks (1998), Nelson Thornes Ltd, ISBN 1872474268. Computational Learning and Probabilistic Reasoning (1996), Wiley, ISBN 0471962791.

EuroMatrixPlus

The EuroMatrixPlus is a project that ran from March 2009 to February 2012. EuroMatrixPlus succeeded a project called EuroMatrix (September 2006 to February 2009) and continued in further development and improvement of machine translation (MT) systems for languages of the European Union (EU). == Project objectives == EuroMatrixPlus focused on achieving several goals: To continue advance of MT technology (create MT systems for all official EU languages and provide other MT researchers with existing data and infrastructure). To continually expand and investigate different MT approaches and techniques; to stay open to novel combinations of methods of MT. To bring MT to the users. Users post-edit output of statistical models and the system learns from the feedback and improves itself. Two groups of users were aimed at: Professional translators and translation agencies Users who voluntarily translate texts into their native language To contribute to MT research in Europe. To produce sample application for automatic translation of news and web pages and make that application freely accessible. == Outcome == EuroMatrixPlus contributed to MT field in several ways. It continued in development of an open source statistical MT engine Moses. The project worked on research in hybrid approaches to MT (combination of rule-based and statistical techniques). Several “MT Marathons” and annual evaluation campaigns were organized by the project. The project also resulted in releasing of 196 scientific publications. The results of the work were arranged into ten work packages: WP1: Rich Tree-Based Statistical Translation WP2: Hybrid Machine Translation WP3: Advanced Learning Methods for MT WP4: Open Source Tools and Data WP5: "WikiTrans" Translation Environments WP6: Integrated Localisation Workflow WP7: Evaluation Campaign WP8: Project Management and Dissemination WP9: Integrating Slovak Language Resources WP10: HPSG-based Statistical Translation === Software and data === Here is a list of software and data that were released by the project: Appraise – an open source tool for manual evaluation of MT output BURGER – Bulgarian Resource BulTreeBank – Treebank of Bulgarian CSLM toolkit – free tool for training continuous space language models (CSLM) to large tasks Caitra – tool for post-editing MT results Europarl – European Parliament parallel corpus IRSTLM toolkit – tool for training language models Joshua – an open-source statistical machine translation decoder for hierarchical and syntax-based MT MT Server Land – an open-source architecture for MT Moses – statistical MT MultiUN Corpora – parallel corpus extracted from the United Nations Website PCEDT 2.0 – Prague Czech-English Dependency Treebank PEDT 2.0 – English part of the Prague Czech-English Dependency Treebank Slovak corpora – English-Slovak and Czech-Slovak as well as a Slovak-English and a Slovak-Czech parallel corpus Slovak treebank – A dependency treebank TermEx – RBMT-Suited Statistical Terminology Extraction Tool Treex, TectoMT == Funding == The EuroMatrixPlus project was sponsored by EU Information Society Technology program. Total cost of the project was 5 942 121 €, from which the European Union contributed 4 266 896 €. == Project members == To ensure advance in MT, several organizations that are experts in various disciplines (linguistics, computer science, mathematics, translation) were brought together to cooperate on EuroMatrixPlus. The consortium consisted of academic as well as commercial partners. Academic partners were the University of Edinburgh (United Kingdom), DFKI – German Research Centre for Artificial Intelligence (Germany), Charles University (Czech Republic), Johns Hopkins University (United States), University of Le Mans (France), Fondazione Bruno Kessler (Italy), Dublin City University (Ireland). Two institutions joined about one year into the project. These were the L'udovít Štúr Institute of Linguistics (Slovak Republic) and IICT – Institute of Information and Communication Technologies at the Bulgarian Academy of Sciences (Bulgaria). Commercial partners included Lucy Software and Services GmbH (Germany) and CEET s.r.o. (Czech Republic). Coordination of the project was in hands of DFKI with its Language Technology Lab in Saarbrücken. The principal investigator and scientific coordinator was Hans Uszkoreit, a professor of Computational Linguistics at Saarland University.

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Ed (chatbot)

Ed was a chatbot co-developed by the Los Angeles Unified School District and AllHere Education. Described as a learning acceleration platform, it was the first personal assistant for students in the United States. Part of the district's Individual Acceleration Plan, it was able to interact with students both verbally and visually, offering support in 100 languages. The chatbot was launched on March 20, 2024, as part of the district's plan for academic recovery from the COVID-19 pandemic and to improve overall academic performance. Utilizing artificial intelligence, Ed organizes data and reports on grades, test scores, and attendance, creating individualized plans for each student. After the company behind it, AllHere, collapsed, the district shuttered operations of the chatbot on June 14, 2024. The firm is under investigation by the US Federal Bureau of Investigation. == History == On February 14, 2022, Alberto M. Carvalho became the Superintendent of the Los Angeles Unified School District, pledging to give the district a full academic recovery from the COVID-19 pandemic. In December 2022, he announced the Individual Acceleration Plan for the district, which aimed to provide each student with a unique progress report and help them determine if they were on track to graduate. The district faced criticism from disability advocates for its management of Individualized Education Programs, and in April 2022, the United States Department of Education announced that the district had failed to provide appropriate educational services to students with disabilities during the pandemic. The district had been grappling with significant absenteeism issues since the pandemic, which led to declining academic performance and disengagement among students. On February 17, 2023, the district issued a request for proposals to develop a fully integrated portal system. Later that year, they signed a $6 million, five-year contract with AllHere Education, a Boston-based company founded in 2016. The introduction of Ed follows the public launch of ChatGPT, which has been utilized by both teachers and students in educational settings. On August 4, 2023, during an annual address at the Walt Disney Concert Hall, Carvalho and the Los Angeles Unified School District announced the launch of Ed. The district invested $4 million into the chatbot, with Carvalho noting that this cost would be halved thanks to donor and grant funding. The chatbot was launched on March 20, 2024. Following its launch, a press conference was held to address security and technology concerns. Carvalho stated that the district had collaborated with security companies and incorporated filters to screen for threatening language. Months after its launch, AllHere Education furloughed most of its staff on June 14, citing their “current financial position” on its website as the reason. After learning about the furlough, the district terminated its dealings with AllHere Education. However, it stated its intention to bring the chatbot back in the future once officials determine the best course of action. Carvalho announced that he would appoint an independent task force to review what went wrong with AllHere Education and the chatbot. On February 25, 2026, the FBI served a search warrant on Carvalho’s home and office in connection with AllHere. The FBI also raided the LAUSD's headquarters. == Service == The chatbot was described as a personal assistant and a "one-stop shop for parents and students" who want to see information about a student's attendance and grades, as well as other resources from the district. Additionally, the application can function as an alarm clock, provide daily lunch menus from the school cafeteria, and offer updates on the location of school buses. The chatbot also helps students and parents who do not speak English as their first language by translating displayed information into approximately 100 different languages. The application can also help with submitting applications and give updates on progress and upcoming assignments. The district stated that the primary goal of Ed was to actively motivate students to complete homework and other tasks. == Reception == The chatbot received a mostly positive reception among parents and observers upon its launch. Some parents and teachers expressed caution about the technology, voicing concerns that the district's push for its implementation lacked public accountability. Rob Nelson from the University of Pennsylvania described the district's strategy as risky, saying that the release felt "like the beginning of a Clippy-level disaster". After the chatbot's shutdown, The 74 criticized it for misusing student data. Chris Whiteley, a former software engineer at AllHere Education, alleged that the data collected by the chatbot likely violated the district's data privacy rules.

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