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Voyages: The Trans-Atlantic Slave Trade Database

Voyages: The Trans-Atlantic Slave Trade Database is a database hosted at Rice University that aims to present all documentary material pertaining to the transatlantic slave trade. It is a sister project to African Origins. The database breaks down the kingdoms and countries that engaged in the Atlantic trade. By 2008, the project had gathered data on nearly 35,000 transatlantic slave voyages from 1501 to 1867. For each voyage they sought to establish dates, owners, vessels, captains, African visits, American destinations, numbers of slaves embarked, and numbers landed. They have been able to find much of this material for an estimated 80 percent of the entire transatlantic African slave trade. With corrections for missing voyages, the Project has estimated the entire size of the transatlantic slave trade with more comprehension, precision, and accuracy than before. They reckon that in 366 years, slaving vessels embarked about 12.5 million captives in Africa, and landed 10.7 million in the New World. A horrific discovery is a careful estimate that the Middle Passage took a toll of more than 1.8 million African lives. In this quantitative database, the numbers are enslaved people.
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Supervised learning

In machine learning, supervised learning (SL) is a type of machine learning paradigm where an algorithm learns to map input data to a specific output based on example input-output pairs. This process involves training a statistical model using labeled data, meaning each piece of input data is provided with the correct output. The term "supervised" refers to the role of a teacher or supervisor who provides this training data, guiding the algorithm towards correct predictions. For instance, if you want a model to identify cats in images, supervised learning would involve feeding it many images of cats (inputs) that are explicitly labeled "cat" (outputs). The goal of supervised learning is for the trained model to accurately predict the output for new, unseen data. This requires the algorithm to effectively generalize from the training examples, a quality measured by its generalization error. Supervised learning is commonly used for tasks like classification (predicting a category, e.g., spam or not spam) and regression (predicting a continuous value, e.g., house prices). == Steps to follow == To solve a given problem of supervised learning, the following steps must be performed: Determine the type of training samples. Before doing anything else, the user should decide what kind of data is to be used as a training set. In the case of handwriting analysis, for example, this might be a single handwritten character, an entire handwritten word, an entire sentence of handwriting, or a full paragraph of handwriting. Gather a training set. The training set needs to be representative of the real-world use of the function. Thus, a set of input objects is gathered together with corresponding outputs, either from human experts or from measurements. Determine the input feature representation of the learned function. The accuracy of the learned function depends strongly on how the input object is represented. Typically, the input object is transformed into a feature vector, which contains a number of features that are descriptive of the object. The number of features should not be too large, because of the curse of dimensionality; but should contain enough information to accurately predict the output. Determine the structure of the learned function and corresponding learning algorithm. For example, one may choose to use support-vector machines or decision trees. Complete the design. Run the learning algorithm on the gathered training set. Some supervised learning algorithms require the user to determine certain control parameters. These parameters may be adjusted by optimizing performance on a subset (called a validation set) of the training set, or via cross-validation. Evaluate the accuracy of the learned function. After parameter adjustment and learning, the performance of the resulting function should be measured on a test set that is separate from the training set. == Algorithm choice == A wide range of supervised learning algorithms are available, each with its strengths and weaknesses. There is no single learning algorithm that works best on all supervised learning problems (see the No free lunch theorem). There are four major issues to consider in supervised learning: === Bias–variance tradeoff === A first issue is the tradeoff between bias and variance. Imagine that we have available several different, but equally good, training data sets. A learning algorithm is biased for a particular input x {\displaystyle x} if, when trained on each of these data sets, it is systematically incorrect when predicting the correct output for x {\displaystyle x} . A learning algorithm has high variance for a particular input x {\displaystyle x} if it predicts different output values when trained on different training sets. The prediction error of a learned classifier is related to the sum of the bias and the variance of the learning algorithm. Generally, there is a tradeoff between bias and variance. A learning algorithm with low bias must be "flexible" so that it can fit the data well. But if the learning algorithm is too flexible, it will fit each training data set differently, and hence have high variance. A key aspect of many supervised learning methods is that they are able to adjust this tradeoff between bias and variance (either automatically or by providing a bias/variance parameter that the user can adjust). === Function complexity and amount of training data === The second issue is of the amount of training data available relative to the complexity of the "true" function (classifier or regression function). If the true function is simple, then an "inflexible" learning algorithm with high bias and low variance will be able to learn it from a small amount of data. But if the true function is highly complex (e.g., because it involves complex interactions among many different input features and behaves differently in different parts of the input space), then the function will only be able to learn with a large amount of training data paired with a "flexible" learning algorithm with low bias and high variance. === Dimensionality of the input space === A third issue is the dimensionality of the input space. If the input feature vectors have large dimensions, learning the function can be difficult even if the true function only depends on a small number of those features. This is because the many "extra" dimensions can confuse the learning algorithm and cause it to have high variance. Hence, input data of large dimensions typically requires tuning the classifier to have low variance and high bias. In practice, if the engineer can manually remove irrelevant features from the input data, it will likely improve the accuracy of the learned function. In addition, there are many algorithms for feature selection that seek to identify the relevant features and discard the irrelevant ones. This is an instance of the more general strategy of dimensionality reduction, which seeks to map the input data into a lower-dimensional space prior to running the supervised learning algorithm. === Noise in the output values === A fourth issue is the degree of noise in the desired output values (the supervisory target variables). If the desired output values are often incorrect (because of human error or sensor errors), then the learning algorithm should not attempt to find a function that exactly matches the training examples. Attempting to fit the data too carefully leads to overfitting. You can overfit even when there are no measurement errors (stochastic noise) if the function you are trying to learn is too complex for your learning model. In such a situation, the part of the target function that cannot be modeled "corrupts" your training data – this phenomenon has been called deterministic noise. When either type of noise is present, it is better to go with a higher bias, lower variance estimator. In practice, there are several approaches to alleviate noise in the output values such as early stopping to prevent overfitting as well as detecting and removing the noisy training examples prior to training the supervised learning algorithm. There are several algorithms that identify noisy training examples and removing the suspected noisy training examples prior to training has decreased generalization error with statistical significance. === Other factors to consider === Other factors to consider when choosing and applying a learning algorithm include the following: Heterogeneity of the data. If the feature vectors include features of many different kinds (discrete, discrete ordered, counts, continuous values), some algorithms are easier to apply than others. Many algorithms, including support-vector machines, linear regression, logistic regression, neural networks, and nearest neighbor methods, require that the input features be numerical and scaled to similar ranges (e.g., to the [-1,1] interval). Methods that employ a distance function, such as nearest neighbor methods and support-vector machines with Gaussian kernels, are particularly sensitive to this. An advantage of decision trees is that they easily handle heterogeneous data. Redundancy in the data. If the input features contain redundant information (e.g., highly correlated features), some learning algorithms (e.g., linear regression, logistic regression, and distance-based methods) will perform poorly because of numerical instabilities. These problems can often be solved by imposing some form of regularization. Presence of interactions and non-linearities. If each of the features makes an independent contribution to the output, then algorithms based on linear functions (e.g., linear regression, logistic regression, support-vector machines, naive Bayes) and distance functions (e.g., nearest neighbor methods, support-vector machines with Gaussian kernels) generally perform well. However, if there are complex interactions among features, then algorithms such as decision trees and neural networks work better, becaus
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Eric Brill

Eric Brill is a computer scientist specializing in natural language processing. He created the Brill tagger, a supervised part of speech tagger. Another research paper of Brill introduced a machine learning technique now known as transformation-based learning. == Biography == Brill earned a BA in mathematics from the University of Chicago in 1987 and a MS in Computer Science from UT Austin in 1989. In 1994, he completed his PhD at the University of Pennsylvania. He was an assistant professor at Johns Hopkins University from 1994 to 1999. In 1999, he left JHU for Microsoft Research, he developed a system called "Ask MSR" that answered search engine queries written as questions in English, and was quoted in 2004 as predicting the shift of Google's web-page based search to information based search. In 2009 he moved to eBay to head their research laboratories.
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AI Subtitle Generators Reviews: What Actually Works in 2026

Trying to pick the best AI subtitle generator? An AI subtitle generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI subtitle generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Clubdjpro

ClubDJPro (often referred to as ClubDJ) is a DJ console and video mixing tool developed by Cube Software Solutions Inc. software. It was released in June 2005. == User interface == ClubDJPro has a GUI that was designed to allow aesthetic revisions via Skins. The skin engine that ClubDJPro uses allows for the ability to expand the software to take up the entire screen. As of 4.4.3.3 there are 3 user changeable skins included in the program which are changeable in the preferences tab. They are called 'AquaLung', 'Eleanor', and 'Grabber'. == Editions == ClubDJPro is available in two different editions, with separate features depending upon their target consumer group. DJ Edition - Can play audio files only. VJ Edition - Contains all of the features of the DJ Edition, in addition to support for video, karaoke, and visualizations. == Supported MIDI Controllers == Supported since version 2.0: Hercules Console Hercules Console MK2 Hercules Control MP3 PCDJ DAC-2 Controller == History == The initial "final release" of ClubDJPro was released on June 24, 2005. On June 26, 2009, the 4th iteration of the ClubDJPro software was released. The development of the software and website appears to have halted. As of March 2018 the website continues to show a new version "Coming Spring 2016".
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Max Welling

Max Welling (born 1968) is a Dutch computer scientist in machine learning at the University of Amsterdam. In August 2017, the university spin-off Scyfer BV, co-founded by Welling, was acquired by Qualcomm. He has since then served as a Vice President of Technology at Qualcomm Netherlands. He is also a Distinguished Scientist at Microsoft Research AI4Science, based in Amsterdam. Welling received his PhD in physics with a thesis on quantum gravity under the supervision of Nobel laureate Gerard 't Hooft (1998) at the Utrecht University. He has published over 250 peer-reviewed articles in machine learning, computer vision, statistics and physics, and has most notably invented variational autoencoders (VAEs), together with Diederik P Kingma. In 2025 Welling was elected member of the Royal Netherlands Academy of Arts and Sciences.
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Kunihiko Fukushima

Kunihiko Fukushima (Japanese: 福島邦彦, born 16 March 1936) is a Japanese computer scientist, most noted for his work on artificial neural networks and deep learning. He is currently working part-time as a senior research scientist at the Fuzzy Logic Systems Institute in Fukuoka, Japan. == Notable scientific achievements == In 1980, Fukushima published the neocognitron, the original deep convolutional neural network (CNN) architecture. Fukushima proposed several supervised and unsupervised learning algorithms to train the parameters of a deep neocognitron such that it could learn internal representations of incoming data. Today, however, the CNN architecture is usually trained through backpropagation. This approach is now heavily used in computer vision. In 1969 Fukushima introduced the ReLU (Rectifier Linear Unit) activation function in the context of visual feature extraction in hierarchical neural networks, which he called "analog threshold element". (Though the ReLU was first used by Alston Householder in 1941 as a mathematical abstraction of biological neural networks.) As of 2017 it is the most popular activation function for deep neural networks. == Education and career == In 1958, Fukushima received his Bachelor of Engineering in electronics from Kyoto University. He became a senior research scientist at the NHK Science & Technology Research Laboratories. In 1989, he joined the faculty of Osaka University. In 1999, he joined the faculty of the University of Electro-Communications. In 2001, he joined the faculty of Tokyo University of Technology. From 2006 to 2010, he was a visiting professor at Kansai University. Fukushima acted as founding president of the Japanese Neural Network Society (JNNS). He also was a founding member on the board of governors of the International Neural Network Society (INNS), and president of the Asia-Pacific Neural Network Assembly (APNNA). He was one of the board of governors of the International Neural Network Society (INNS) in 1989-1990 and 1993-2005. == Awards == In 2020, Fukushima received the Bower Award and Prize for Achievement in Science. In 2022, Fukushima became a laureate of the Asian Scientist 100 by the Asian Scientist. He also received the IEICE Achievement Award and Excellent Paper Awards, the IEEE Neural Networks Pioneer Award, the APNNA Outstanding Achievement Award, the JNNS Excellent Paper Award and the INNS Helmholtz Award.
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Brendan Frey

Brendan John Frey FRSC (born 29 August 1968) is a Canadian computer scientist, entrepreneur, and engineer. He is Founder and CEO of Deep Genomics, Cofounder of the Vector Institute for Artificial Intelligence and Professor of Engineering and Medicine at the University of Toronto. Frey is a pioneer in the development of machine learning and artificial intelligence methods, their use in accurately determining the consequences of genetic mutations, and in designing medications that can slow, stop or reverse the progression of disease. As far back as 1995, Frey co-invented one of the first deep learning methods, called the wake-sleep algorithm, the affinity propagation algorithm for clustering and data summarization, and the factor graph notation for probability models. In the late 1990s, Frey was a leading researcher in the areas of computer vision, speech recognition, and digital communications. == Education == Frey studied computer engineering and physics at the University of Calgary (BSc 1990) and the University of Manitoba (MSc 1993), and then studied neural networks and graphical models as a doctoral candidate at the University of Toronto under the supervision of Geoffrey Hinton (PhD 1997). He was an invited participant of the Machine Learning program at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK (1997) and was a Beckman Fellow at the University of Illinois at Urbana Champaign (1999). == Career == Following his undergraduate studies, Frey worked as a junior research scientist at Bell-Northern Research from 1990 to 1991. After completing his postdoctoral studies at the University of Illinois at Urbana-Champaign, Frey was an assistant professor in the Department of Computer Science at the University of Waterloo, from 1999 to 2001. In 2001, Frey joined the Department of Electrical and Computer Engineering at the University of Toronto and was cross-appointed to the Department of Computer Science, the Banting and Best Department of Medical Research and the Terrence Donnelly Centre for Cellular and Biomolecular Research. From 2008 to 2009, he was a visiting researcher at Microsoft Research (Cambridge, UK) and a visiting professor in the Cavendish Laboratories and Darwin College at Cambridge University. Between 2001 and 2014, Frey consulted for several groups at Microsoft Research and acted as a member of its Technical Advisory Board. In 2002, a personal crisis led Frey to face the fact that there was a tragic gap between our ability to measure a patient's mutations and our ability to understand and treat the consequences. Recognizing that biology is too complex for humans to understand, that in the decades to come there would be an exponential growth in biology data, and that machine learning is the best technology we have for discovering relationships in large datasets, Frey set out to build machine learning systems that could accurately predict genome and cell biology. Frey’s group pioneered much of the early work in the field and over the next 15 years published more papers in leading-edge journals than any other academic or industrial research lab. In 2015, Frey founded Deep Genomics, with the goal of building a company that can produce effective and safe genetic medicines more rapidly and with a higher rate of success than was previously possible. The company has received 240 million dollars in funding to date from leading Bay Area investors, including the backers of SpaceX and Tesla.
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Integreat

Integreat (former project name: Refguide+) is an open source mobile app that provides local information and services tailored to refugees and migrants coming to Germany. The content is maintained by local organizations, such as local governments or integration officers, and made available in locally relevant languages. It was developed by Tür an Tür - Digitalfabrik gGmbH (formerly Tür an Tür - Digital Factory gGmbH) in Augsburg together with a team of researchers and students from the Technical University of Munich. == History == In 1997, the Augsburg association "Tür an Tür", which has been working for refugees since 1992, published the brochure "First Steps", which answers local everyday questions. Since addresses and contact persons change quickly, some information is already outdated after a few weeks. Students of business informatics at the Technical University of Munich therefore developed the app Integreat within eight months together with the association and the social department of the city of Augsburg. The app was then also used by other cities and districts within months. As of February 3, 2022, information is available at 72 locations, including Munich, Dortmund, Nuremberg and Augsburg. == Mode of action == Refugees need information on areas such as registration, contact persons, health care, education, family, work and everyday life. Integreat seeks to provide refugees with this information by allowing them to select their geographic location and receive locally relevant information. This information is available offline once the app is opened so it can be used without an internet connection. In addition, the content is translated into the native languages of refugees and migrants to facilitate access. The content is licensed with a CC BY 4.0 license to facilitate collaboration and translation between content creators and dissemination of the content. Integreat is now being used for a broader migrant audience and says it can also support professionals, volunteers, and counseling centers. == Comparable mobile apps == Other mobile apps that are likewise intended to provide initial orientation for refugees include the app Ankommen, a joint project of the Federal Office for Migration and Refugees, the Goethe-Institut, the Federal Employment Agency and the Bavarian Broadcasting Corporation, which is intended as a companion for the first few weeks in Germany, and the Welcome App, a company-sponsored non-profit initiative for information about Germany and asylum procedures with a regional focus, and a book by the Konrad Adenauer Foundation (KAS) and Verlag Herder with a corresponding app Deutschland - Erste Informationen für Flüchtlinge (Germany - First Information for Refugees) as a companion for Arabic-speaking refugees in Germany.
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Chris Callison-Burch

Chris Callison-Burch is an American computer scientist and professor of computer and information science at the University of Pennsylvania (Penn), specializing in natural language processing (NLP), artificial intelligence (AI), and crowdsourcing. He is recognised for his contributions to machine translation, paraphrase generation, and the application of large language models (LLMs) to AI challenges, with over 200 publications cited more than 33,000 times. Callison-Burch has influenced public policy on AI and copyright, testifying before the U.S. Congress in 2023 on generative AI’s implications. He serves as the faculty director for Penn’s Online Master of Science in Engineering in AI program. == Education == Callison-Burch earned his PhD in Computer Science from the University of Edinburgh in 2008, focusing on machine translation and paraphrasing techniques. His doctoral research developed statistical methods for generating paraphrases in machine translation systems, laying the foundation for his later NLP work. Prior to his PhD, he studied at Stanford University, where he developed an interest in computational linguistics. == Career == After his PhD, Callison-Burch joined the Centre for Language and Speech Processing at Johns Hopkins University as a research faculty member from 2008 to 2013, working on NLP projects, including machine translation and crowdsourcing for creating training data. In 2013, he joined the University of Pennsylvania as an assistant professor in the Department of Computer and Information Science and was promoted to associate professor in 2017, and to full professor in 2024. At Penn, Callison-Burch teaches courses on AI and NLP, including CIS 5300 (Natural Language Processing) and CIS 5210 (Artificial Intelligence), which attract over 500 students annually. He directs Penn’s Online Master of Science in Engineering in AI program, launched in 2025. He teaches AI and NLP courses on Coursera, reaching thousands of global learners. Callison-Burch was a part-time visiting researcher at Google in 2019 and 2020, where he collaborated on applying Google's LLM to Dungeons & Dragons dialogues. In 2023, he took a sabbatical at the Allen Institute for AI (AI2), where he contributed to vision-language models. == Research == Callison-Burch’s research focuses on NLP, AI, and crowdsourcing, with significant contributions to machine translation, paraphrase generation, and LLMs for tasks like text simplification and bias detection. His early work developed crowdsourcing methods for machine translation, leveraging non-expert annotators for paraphrase-based evaluation, influencing platforms like Amazon Mechanical Turk. Recent projects have included several notable works. Molmo and PixMo (2025) are open-weight vision-language models developed with AI2, achieving state-of-the-art multimodal performance and earning a Best Paper Honourable Mention at CVPR 2025. Also in 2025, his work on Calibrating Large Language Models with Sample Consistency improves LLM reliability via sample-based calibration, presented at NAACL 2025. The Media Bias Detector (2025) is a real-time tool analysing selection and framing bias in news, using LLMs to detect persuasive language differences (e.g., Russian vs. English Wikipedia). Holodeck (2024) is a language-guided system for generating 3D embodied AI environments, presented at CVPR 2024. BORDIRLINES (2024) is a dataset for cross-lingual retrieval-augmented generation, focusing on culturally sensitive tasks. He has co-authored over 200 publications, featured at conferences like ACL, EMNLP, and CVPR. == Awards and recognition == Callison-Burch has received numerous awards: Best Paper Honourable Mention at CVPR 2025 for "Molmo and PixMo". Best Paper Award at the Workshop on Cognitive Modelling and Computational Linguistics (CMCL) 2024 for "Evaluating Vision-Language Models on Bistable Images". Best Paper Award at STARSEM 2016 for "So-Called Non-Subsective Adjectives". Best Paper Award at the Workshop on Sense, Concept and Entity Representations 2017 for "Word Sense Filtering Improves Embedding-Based Lexical Substitution". Honourable Mention Award at CHI 2018 for "A Data-Driven Analysis of Workers’ Earnings on Amazon Mechanical Turk". Google Faculty Research Award (2013) for crowdsourcing in NLP. Sloan Research Fellowship (2014). He has received research funding from Google, Microsoft, Amazon, Facebook, Roblox, DARPA, IARPA, and NSF. His h-index is 72, with over 33,000 citations. He served as General Chair of ACL 2017 and as the Program Co-Chair EMNLP 2015. == Public policy and testimony == On May 17, 2023, Callison-Burch testified before the U.S. House Subcommittee on Courts, Intellectual Property, and the Internet on AI and copyright law. His testimony emphasised generative AI’s role in creative industries and the need for balanced copyright frameworks. He has appeared on Fox News to discuss AI’s societal impact, and discussed its impact with other print news sources. He contributes to AI ethics discussions, including workshops on AI’s effects on writing and creative professions.
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Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it, i.e. the Markov chain's equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Markov chain Monte Carlo methods are used to study probability distributions that are too complex or too high dimensional to study with analytic techniques alone. Various algorithms exist for constructing such Markov chains, including the Metropolis–Hastings algorithm. == General explanation == Markov chain Monte Carlo methods create samples from a continuous random variable, with probability density proportional to a known function. These samples can be used to evaluate an integral over that variable, as its expected value or variance. Practically, an ensemble of chains is generally developed, starting from a set of points arbitrarily chosen and sufficiently distant from each other. These chains are stochastic processes of "walkers" which move around randomly according to an algorithm that looks for places with a reasonably high contribution to the integral to move into next, assigning them higher probabilities. Random walk Monte Carlo methods are a kind of random simulation or Monte Carlo method. However, whereas the random samples of the integrand used in a conventional Monte Carlo integration are statistically independent, those used in MCMC are autocorrelated. Correlations of samples introduces the need to use the Markov chain central limit theorem when estimating the error of mean values. These algorithms create Markov chains such that they have an equilibrium distribution which is proportional to the function given. == History == The development of MCMC methods is deeply rooted in the early exploration of Monte Carlo (MC) techniques in the mid-20th century, particularly in physics. These developments were marked by the Metropolis algorithm proposed by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall Rosenbluth, Augusta H. Teller, and Edward Teller in 1953, which was designed to tackle high-dimensional integration problems using early computers. Then in 1970, W. K. Hastings generalized this algorithm and inadvertently introduced the component-wise updating idea, later known as Gibbs sampling. Simultaneously, the theoretical foundations for Gibbs sampling were being developed, such as the Hammersley–Clifford theorem from Julian Besag's 1974 paper. Although the seeds of MCMC were sown earlier, including the formal naming of Gibbs sampling in image processing by Stuart Geman and Donald Geman (1984) and the data augmentation method by Martin A. Tanner and Wing Hung Wong (1987), its "revolution" in mainstream statistics largely followed demonstrations of the universality and ease of implementation of sampling methods (especially Gibbs sampling) for complex statistical (particularly Bayesian) problems, spurred by increasing computational power and software like BUGS. This transformation was accompanied by significant theoretical advancements, such as Luke Tierney's (1994) rigorous treatment of MCMC convergence, and Jun S. Liu, Wong, and Augustine Kong's (1994, 1995) analysis of Gibbs sampler structure. Subsequent developments further expanded the MCMC toolkit, including particle filters (Sequential Monte Carlo) for sequential problems, Perfect sampling aiming for exact simulation (Jim Propp and David B. Wilson, 1996), RJMCMC (Peter J. Green, 1995) for handling variable-dimension models, and deeper investigations into convergence diagnostics and the central limit theorem. Overall, the evolution of MCMC represents a paradigm shift in statistical computation, enabling the analysis of numerous previously intractable complex models and continually expanding the scope and impact of statistics. == Mathematical setting == Suppose (Xn) is a Markov Chain in the general state space X {\displaystyle {\mathcal {X}}} with specific properties. We are interested in the limiting behavior of the partial sums: S n ( h ) = 1 n ∑ i = 1 n h ( X i ) {\displaystyle S_{n}(h)={\dfrac {1}{n}}\sum _{i=1}^{n}h(X_{i})} as n goes to infinity. Particularly, we hope to establish the Law of Large Numbers and the Central Limit Theorem for MCMC. In the following, we state some definitions and theorems necessary for the important convergence results. In short, we need the existence of invariant measure and Harris recurrent to establish the Law of Large Numbers of MCMC (Ergodic Theorem). And we need aperiodicity, irreducibility and extra conditions such as reversibility to ensure the Central Limit Theorem holds in MCMC. === Irreducibility and aperiodicity === Recall that in the discrete setting, a Markov chain is said to be irreducible if it is possible to reach any state from any other state in a finite number of steps with positive probability. However, in the continuous setting, point-to-point transitions have zero probability. In this case, φ-irreducibility generalizes irreducibility by using a reference measure φ on the measurable space ( X , B ( X ) ) {\displaystyle ({\mathcal {X}},{\mathcal {B}}({\mathcal {X}}))} . Definition (φ-irreducibility) Given a measure φ {\displaystyle \varphi } defined on ( X , B ( X ) ) {\displaystyle ({\mathcal {X}},{\mathcal {B}}({\mathcal {X}}))} , the Markov chain ( X n ) {\displaystyle (X_{n})} with transition kernel K ( x , y ) {\displaystyle K(x,y)} is φ-irreducible if, for every A ∈ B ( X ) {\displaystyle A\in {\mathcal {B}}({\mathcal {X}})} with φ ( A ) > 0 {\displaystyle \varphi (A)>0} , there exists n {\displaystyle n} such that K n ( x , A ) > 0 {\displaystyle K^{n}(x,A)>0} for all x ∈ X {\displaystyle x\in {\mathcal {X}}} (Equivalently, P x ( τ A < ∞ ) > 0 {\displaystyle P_{x}(\tau _{A}<\infty )>0} , here τ A = inf { n ≥ 1 ; X n ∈ A } {\displaystyle \tau _{A}=\inf\{n\geq 1;X_{n}\in A\}} is the first n {\displaystyle n} for which the chain enters the set A {\displaystyle A} ). This is a more general definition for irreducibility of a Markov chain in non-discrete state space. In the discrete case, an irreducible Markov chain is said to be aperiodic if it has period 1. Formally, the period of a state ω ∈ X {\displaystyle \omega \in {\mathcal {X}}} is defined as: d ( ω ) := g c d { m ≥ 1 ; K m ( ω , ω ) > 0 } {\displaystyle d(\omega ):=\mathrm {gcd} \{m\geq 1\,;\,K^{m}(\omega ,\omega )>0\}} For the general (non-discrete) case, we define aperiodicity in terms of small sets: Definition (Cycle length and small sets) A φ-irreducible Markov chain ( X n ) {\displaystyle (X_{n})} has a cycle of length d if there exists a small set C {\displaystyle C} , an associated integer M {\displaystyle M} , and a probability distribution ν M {\displaystyle \nu _{M}} such that d is the greatest common divisor of: { m ≥ 1 ; ∃ δ m > 0 such that C is small for ν m ≥ δ m ν M } . {\displaystyle \{m\geq 1\,;\,\exists \,\delta _{m}>0{\text{ such that }}C{\text{ is small for }}\nu _{m}\geq \delta _{m}\nu _{M}\}.} A set C {\displaystyle C} is called small if there exists m ∈ N ∗ {\displaystyle m\in \mathbb {N} ^{}} and a nonzero measure ν m {\displaystyle \nu _{m}} such that: K m ( x , A ) ≥ ν m ( A ) , ∀ x ∈ C , ∀ A ∈ B ( X ) . {\displaystyle K^{m}(x,A)\geq \nu _{m}(A),\quad \forall x\in C,\,\forall A\in {\mathcal {B}}({\mathcal {X}}).} === Harris recurrent === Definition (Harris recurrence) A set A {\displaystyle A} is Harris recurrent if P x ( η A = ∞ ) = 1 {\displaystyle P_{x}(\eta _{A}=\infty )=1} for all x ∈ A {\displaystyle x\in A} , where η A = ∑ n = 1 ∞ I A ( X n ) {\displaystyle \eta _{A}=\sum _{n=1}^{\infty }\mathbb {I} _{A}(X_{n})} is the number of visits of the chain ( X n ) {\displaystyle (X_{n})} to the set A {\displaystyle A} . The chain ( X n ) {\displaystyle (X_{n})} is said to be Harris recurrent if there exists a measure ψ {\displaystyle \psi } such that the chain is ψ {\displaystyle \psi } -irreducible and every measurable set A {\displaystyle A} with ψ ( A ) > 0 {\displaystyle \psi (A)>0} is Harris recurrent. A useful criterion for verifying Harris recurrence is the following: Proposition If for every A ∈ B ( X ) {\displaystyle A\in {\mathcal {B}}({\mathcal {X}})} , we have P x ( τ A < ∞ ) = 1 {\displaystyle P_{x}(\tau _{A}<\infty )=1} for every x ∈ A {\displaystyle x\in A} , then P x ( η A = ∞ ) = 1 {\displaystyle P_{x}(\eta _{A}=\infty )=1} for all x ∈ X {\displaystyle x\in {\mathcal {X}}} , and the chain ( X n ) {\displaystyle (X_{n})} is Harris recurrent. This definition is only needed when the state space X {\displaystyle {\mathcal {X}}} is uncountable. In the countable case, recurrence corresponds to E x [ η x ] = ∞ {\displaystyle \mathbb {E} _{x}[\eta _{x}]=\infty } , which is equivalent to P x ( τ x < ∞ ) = 1 {\displaystyle P_{x}(\tau _{x}<\infty )=1} for all x ∈ X {\displaystyle x\i
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Jerome H. Friedman

Jerome Harold Friedman (born December 29, 1939) is an American statistician, consultant and Professor of Statistics at Stanford University, known for his contributions in the field of statistics and data mining. == Biography == Friedman studied at Chico State College for two years before transferring to the University of California, Berkeley in 1959, where he received his AB in Physics in 1962, and his PhD in High Energy Particle Physics in 1967. In 1968 he started his academic career as research physicist at the Lawrence Berkeley National Laboratory. In 1972 he started at Stanford University as leader of the Computation Research Group at the Stanford Linear Accelerator Center, where he would participate until 2003. In the year 1976–77 he was a visiting scientist at CERN in Geneva. From 1981 to 1984 he was visiting professor at the University of California, Berkeley. In 1982 he was appointed Professor of Statistics at Stanford University. In 1984 he was elected as a Fellow of the American Statistical Association. In 2002 he was awarded the SIGKDD Innovation Award by the Association for Computing Machinery (ACM). In 2010 he was elected as a member of the National Academy of Sciences (Applied mathematical sciences). == Publications == Friedman has authored and co-authored many publications in the field of data-mining including "nearest neighbor classification, logistical regressions, and high dimensional data analysis. His primary research interest is in the area of machine learning." A selection: Friedman, Jerome H. & Tukey, John W. (1974). "A projection pursuit algorithm for exploratory data analysis". IEEE Transactions on Computers. 23 (9): 881–890. doi:10.1109/T-C.1974.224051. OSTI 1442925. S2CID 7997450. Friedman, Jerome H. & Stuetzle, Werner (1981). "Projection pursuit regression". Journal of the American Statistical Association. 76 (376): 817–823. doi:10.1080/01621459.1981.10477729. OSTI 1445517. Friedman, Jerome H. (1991). "Multivariate adaptive regression splines". Annals of Statistics. 19 (1): 1–67. CiteSeerX 10.1.1.382.970. doi:10.1214/aos/1176347963. JSTOR 2241837. Friedman, Jerome H. (2001). "Greedy function approximation: a gradient boosting machine". Annals of Statistics. 29 (5): 1189–1232. doi:10.1214/aos/1013203451. JSTOR 2699986.
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Feed forward (control)

A feed forward (sometimes written feedforward) is an element or pathway within a control system that passes a controlling signal from a source in its external environment to a load elsewhere in its external environment. This is often a command signal from an external operator. In control engineering, a feedforward control system is a control system that uses sensors to detect disturbances affecting the system and then applies an additional input to minimize the effect of the disturbance. This requires a mathematical model of the system so that the effect of disturbances can be properly predicted. A control system which has only feed-forward behavior responds to its control signal in a pre-defined way without responding to the way the system reacts; it is in contrast with a system that also has feedback, which adjusts the input to take account of how it affects the system, and how the system itself may vary unpredictably. In a feed-forward system, the control variable adjustment is not error-based. Instead it is based on knowledge about the process in the form of a mathematical model of the process and knowledge about, or measurements of, the process disturbances. Some prerequisites are needed for control scheme to be reliable by pure feed-forward without feedback: the external command or controlling signal must be available, and the effect of the output of the system on the load should be known (that usually means that the load must be predictably unchanging with time). Sometimes pure feed-forward control without feedback is called 'ballistic', because once a control signal has been sent, it cannot be further adjusted; any corrective adjustment must be by way of a new control signal. In contrast, 'cruise control' adjusts the output in response to the load that it encounters, by a feedback mechanism. These systems could relate to control theory, physiology, or computing. == Overview == With feed-forward or feedforward control, the disturbances are measured and accounted for before they have time to affect the system. In the house example, a feed-forward system may measure the fact that the door is opened and automatically turn on the heater before the house can get too cold. The difficulty with feed-forward control is that the effects of the disturbances on the system must be accurately predicted, and there must not be any unmeasured disturbances. For instance, if a window was opened that was not being measured, the feed-forward-controlled thermostat might let the house cool down. The term has specific meaning within the field of CPU-based automatic control. The discipline of feedforward control as it relates to modern, CPU based automatic controls is widely discussed, but is seldom practiced due to the difficulty and expense of developing or providing for the mathematical model required to facilitate this type of control. Open-loop control and feedback control, often based on canned PID control algorithms, are much more widely used. There are three types of control systems: open-loop, feed-forward, and feedback. An example of a pure open-loop control system is manual non-power-assisted steering of a motor car; the steering system does not have access to an auxiliary power source and does not respond to varying resistance to turning of the direction wheels; the driver must make that response without help from the steering system. In comparison, power steering has access to a controlled auxiliary power source, which depends on the engine speed. When the steering wheel is turned, a valve is opened which allows fluid under pressure to turn the wheels. A sensor monitors that pressure so that the valve only opens enough to cause the correct pressure to reach the wheel turning mechanism. This is feed-forward control where the output of the system, the change in direction of travel of the vehicle, plays no part in the system. See Model predictive control. If the driver is included in the system, then they do provide a feedback path by observing the direction of travel and compensating for errors by turning the steering wheel. In that case you have a feedback system, and the block labeled System in Figure(c) is a feed-forward system. In other words, systems of different types can be nested, and the overall system regarded as a black-box. Feedforward control is distinctly different from open-loop control and teleoperator systems. Feedforward control requires a mathematical model of the plant (process and/or machine being controlled) and the plant's relationship to any inputs or feedback the system might receive. Neither open-loop control nor teleoperator systems require the sophistication of a mathematical model of the physical system or plant being controlled. Control based on operator input without integral processing and interpretation through a mathematical model of the system is a teleoperator system and is not considered feedforward control. == History == Historically, the use of the term feedforward is found in works by Harold S. Black in US patent 1686792 (invented 17 March 1923) and D. M. MacKay as early as 1956. While MacKay's work is in the field of biological control theory, he speaks only of feedforward systems. MacKay does not mention feedforward control or allude to the discipline of feedforward controls. MacKay and other early writers who use the term feedforward are generally writing about theories of how human or animal brains work. Black also has US patent 2102671 invented 2 August 1927 on the technique of feedback applied to electronic systems. The discipline of feedforward controls was largely developed by professors and graduate students at Georgia Tech, MIT, Stanford and Carnegie Mellon. Feedforward is not typically hyphenated in scholarly publications. Meckl and Seering of MIT and Book and Dickerson of Georgia Tech began the development of the concepts of Feedforward Control in the mid-1970s. The discipline of Feedforward Controls was well defined in many scholarly papers, articles and books by the late 1980s. == Benefits == The benefits of feedforward control are significant and can often justify the extra cost, time and effort required to implement the technology. Control accuracy can often be improved by as much as an order of magnitude if the mathematical model is of sufficient quality and implementation of the feedforward control law is well thought out. Energy consumption by the feedforward control system and its driver is typically substantially lower than with other controls. Stability is enhanced such that the controlled device can be built of lower cost, lighter weight, springier materials while still being highly accurate and able to operate at high speeds. Other benefits of feedforward control include reduced wear and tear on equipment, lower maintenance costs, higher reliability and a substantial reduction in hysteresis. Feedforward control is often combined with feedback control to optimize performance. == Model == The mathematical model of the plant (machine, process or organism) used by the feedforward control system may be created and input by a control engineer or it may be learned by the control system. Control systems capable of learning and/or adapting their mathematical model have become more practical as microprocessor speeds have increased. The discipline of modern feedforward control was itself made possible by the invention of microprocessors. Feedforward control requires integration of the mathematical model into the control algorithm such that it is used to determine the control actions based on what is known about the state of the system being controlled. In the case of control for a lightweight, flexible robotic arm, this could be as simple as compensating between when the robot arm is carrying a payload and when it is not. The target joint angles are adjusted to place the payload in the desired position based on knowing the deflections in the arm from the mathematical model's interpretation of the disturbance caused by the payload. Systems that plan actions and then pass the plan to a different system for execution do not satisfy the above definition of feedforward control. Unless the system includes a means to detect a disturbance or receive an input and process that input through the mathematical model to determine the required modification to the control action, it is not true feedforward control. === Open system === In control theory, an open system is a feed forward system that does not have any feedback loop to control its output. In contrast, a closed system uses on a feedback loop to control the operation of the system. In an open system, the output of the system is not fed back into the input to the system for control or operation. == Applications == === Physiological feed-forward system === In physiology, feed-forward control is exemplified by the normal anticipatory regulation of heartbeat in advance of actual physical exertion by the central autonomic network. Feed-forward
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Jun'ichi Tsujii

Jun'ichi Tsujii (辻井潤一, Tsujii Jun'ichi; born 7 February 1949) is a Japanese computer scientist specializing in natural language processing and text mining, particularly in the field of biology and bioinformatics. == Education == Tsujii received his Bachelor of Engineering, Master of Engineering and PhD degrees in electrical engineering from Kyoto University in 1971, 1973, and 1978 respectively. He was Assistant Professor and Associate Professor at Kyoto University, before accepting a position as Professor of Computational Linguistics at the University of Manchester Institute of Science and Technology (UMIST) in 1988. He was President of the Association for Computational Linguistics (ACL) in 2006, and has been a permanent member of the International Committee on Computational Linguistics (ICCL) since 1992, and the chair of the committee since 2014. == Research == Since May 2015, Tsujii has been the director of the Artificial Intelligence Research Center at the National Institute of Advanced Industrial Science and Technology, Japan. Tsujii was previously a Principal Researcher at Microsoft Research Asia (MSRA). Before joining MSRA, he was a professor at the University of Tokyo, where he belonged to both the School of Inter-faculty Initiative on Informatics and the Graduate School of Information Science and Technology. Tsujii is also a Visiting Professor and Scientific Advisor at the National Centre for Text Mining (NaCTeM) at the University of Manchester in the United Kingdom. == Awards == On 14 May 2010, Tsujii was awarded the Medals of Honor with Purple Ribbon, one of Japan's highest awards, presented to influential contributors in the fields of art, academics or sports. In September 2014, Tsujii was awarded the FUNAI Achievement Award at the Forum on Information Technology (FIT), which took place at the University of Tsukuba. The award is presented to distinguished individuals engaged in research or related business activities in the field of Information Technology who have produced excellent achievements in the field, are still active in leading positions and have strong impact on young students and researchers. In December 2014, Tsujii was named as an ACL Fellow, in recognition of his significant contributions to MT, parsing by unification-based grammar and text mining for biology. In March 2016, Tsujii was awarded Okawa Prize for his contribution to the field of Natural Language Processing, Machine Translation and Text Mining, together with Professor Jaime Carbonnel of CMU. In August 2021, Tsujii received ACL Lifetime Achievement Award, which is considered the most prestigious award in the field of Computational Linguistics and Natural Language Processing. In May 2022, Tsujii received the Order of the Sacred Treasure, Gold Rays and Neck Ribbon, from the Japanese government. In October 2024, Tsujii was designated a Person of Cultural Merit. == Selected publications == Oiwa, Hidekazu; Tsujii, Jun'ichi (2014). Common Space Embedding of Primal-Dual Relation Semantic Spaces. COLING 2014. Dublin. pp. 1579–1590. Taura, K.; Matsuzaki, T.; Miwa, M.; Kamoshida, Y.; Yokoyama, D.; Dun, N.; Shibata, T.; Jun, C. S.; Tsujii, J. (2013). "Design and implementation of GXP make – A workflow system based on make". Future Generation Computer Systems. 29 (2): 662–672. doi:10.1016/j.future.2011.05.026. S2CID 31627886. Sun, X.; Zhang, Y.; Matsuzaki, T.; Tsuruoka, Y.; Tsujii, J. (2013). "Probabilistic Chinese word segmentation with non-local information and stochastic training". Information Processing & Management. 49 (3): 626–636. doi:10.1016/j.ipm.2012.12.003. Mu, T.; Goulermas, J. Y.; Tsujii, J.; Ananiadou, S. (2012). "Proximity-Based Frameworks for Generating Embeddings from Multi-Output Data". IEEE Transactions on Pattern Analysis and Machine Intelligence. 34 (11): 2216–2232. Bibcode:2012ITPAM..34.2216M. doi:10.1109/TPAMI.2012.20. PMID 23289130. S2CID 711467. Miwa, M.; Sætre, R.; Kim, J. D.; Tsujii, J. (2010). "Event Extraction with Complex Event Classification Using Rich Features". Journal of Bioinformatics and Computational Biology. 08 (1): 131–146. doi:10.1142/S0219720010004586. PMID 20183879. Kim, J. D.; Ohta, T.; Tsujii, J. (2008). "Corpus annotation for mining biomedical events from literature". BMC Bioinformatics. 9 10. doi:10.1186/1471-2105-9-10. PMC 2267702. PMID 18182099. Miyao, Y.; Tsujii, J. (2008). "Feature Forest Models for Probabilistic HPSG Parsing". Computational Linguistics. 34: 35–80. doi:10.1162/coli.2008.34.1.35. S2CID 885002. Sagae, Kenji; Tsujii, Jun'ichi (2007). Dependency Parsing and Domain Adaptation with LR Models and Parser Ensembles. EMNLP-CoNLL. pp. 1044–1050. Ananiadou, S; Pyysalo, S; Tsujii, J; Kell, D. B. (2010). "Event extraction for systems biology by text mining the literature". Trends in Biotechnology. 28 (7): 381–90. doi:10.1016/j.tibtech.2010.04.005. PMID 20570001. Tsuruoka, Y.; Tateishi, Y.; Kim, J. D.; Ohta, T.; McNaught, J.; Ananiadou, S.; Tsujii, J. (2005). "Developing a Robust Part-of-Speech Tagger for Biomedical Text". Advances in Informatics. Lecture Notes in Computer Science. Vol. 3746. p. 382. doi:10.1007/11573036_36. ISBN 978-3-540-29673-7. S2CID 206592413. Tsuruoka, Y.; Tsujii, J. (2005). Bidirectional inference with the easiest-first strategy for tagging sequence data. Proceedings of the conference on Human Language Technology and Empirical Methods in Natural Language Processing - HLT '05. pp. 467–474. doi:10.3115/1220575.1220634. Tsujii, J.; Ananiadou, S. (2005). "Thesaurus or Logical Ontology, Which One Do We Need for Text Mining?". Language Resources and Evaluation. 39: 77–90. doi:10.1007/s10579-005-2697-0. S2CID 3204827. Kazama, J. I.; Tsujii, J. I. (2005). "Maximum Entropy Models with Inequality Constraints: A Case Study on Text Categorization". Machine Learning. 60 (1–3): 159–194. doi:10.1007/s10994-005-0911-3. hdl:10119/3305. Matsuzaki, T.; Miyao, Y.; Tsujii, J. I. (2005). Probabilistic CFG with latent annotations. 43rd Annual Meeting on Association for Computational Linguistics - ACL '05. p. 75. doi:10.3115/1219840.1219850. Kim, J. -D.; Ohta, T.; Tateisi, Y.; Tsujii, J. (2003). "GENIA corpus--a semantically annotated corpus for bio-textmining". Bioinformatics. 19: i180–i182. doi:10.1093/bioinformatics/btg1023. PMID 12855455. Hirschman, L.; Park, J. C.; Tsujii, J.; Wong, L.; Wu, C. H. (2002). "Accomplishments and challenges in literature data mining for biology". Bioinformatics. 18 (12): 1553–1561. doi:10.1093/bioinformatics/18.12.1553. PMID 12490438. Torisawa, K.; Tsujii, J. I. (1996). Computing phrasal-signs in HPSG prior to parsing. 16th conference on Computational linguistics -. Vol. 2. p. 949. doi:10.3115/993268.993332.
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AI Photo Editors: Free vs Paid (2026)

Trying to pick the best AI photo editor? An AI photo editor is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI photo editor slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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