AI Image Generators

Explore the best AI Image Generators — independent reviews, comparisons, pricing and step-by-step how-to guides, curated by Aizhi.

  • Avid Free DV

    Avid Free DV

    Avid Free DV is a non-linear editing video editing software application developed by Avid Technology. Avid introduced Free DV in January 2003 at the 2003 MacWorld Expo; the company discontinued it in September 2007. Free DV was intended to give editors a sample of the Avid interface to use in deciding whether or not to purchase Avid software, so when compared with other Avid products its features were relatively minimal. When it was available it was not limited by time or watermarking, so it could be used as a non-linear editor for as long as desired. == Comparisons == When compared with other consumer-end non-linear editors such as iMovie and Windows Movie Maker, it sported more powerful video processing tools, but lacked the ease-of-use and shallow learning curve emphasized in similar programs because it had the full interface of the professional Avid system. However, Avid did offer a number of flash-based tutorials to help new users learn how to use the program for capturing, editing, clipping, processing, and outputting audio/video, among other things. == Limitations == The limitations of Avid Free DV included that it allowed only two video and audio tracks, had fewer editing tools than other Avid products, had few import and export formats, and allowed capture and output of standard-definition DV only, via FireWire. Avid Free DV projects and media were not compatible with other Avid systems. As the name implied, Avid Free DV was available as a free download, although users were required to complete a short survey on the Avid website before they were given a download link and key. In addition to using Free DV to evaluate Avid prior to purchase, it could also act as a stepping stone for people wishing to learn to use Avid's other editing products, such as Xpress Pro, Media Composer and Symphony. While additional skills and techniques are necessary to use these professionally geared systems, the basic operation remains the same. == Operating systems == Avid Free DV was available for Windows XP and Mac OS X. The officially supported Mac OS X versions were Panther versions up to 10.3.5, and Tiger versions up to 10.4.3 only. == Supported formats == Avid Free DV supported QuickTime (MOV) and DV AVIs. == Reception == John P. Mello Jr. of The Boston Globe gave Free DV a negative review, finding the user interface obfuscatory and the process of ingesting video error-prone. He summarized: "Professional video editors who use an Avid competitor may jump at the chance to take a free look at how Avid does things. But for the merely curious, this software is a nightmare". Video Systems's Steve Mullen opined that its lack of interoperability with Avid's professional editing software contracted Avid's stated goal to entice budding video editors into buying into the company's software ecosystem.

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  • The Best Free AI Paraphrasing Tool for Beginners

    The Best Free AI Paraphrasing Tool for Beginners

    Trying to pick the best AI paraphrasing tool? An AI paraphrasing tool 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 paraphrasing tool 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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  • Is an AI Code Generator Worth It in 2026?

    Is an AI Code Generator Worth It in 2026?

    Comparing the best AI code generator? An AI code generator is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI code generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  • Barbara Di Eugenio

    Barbara Di Eugenio

    Barbara Di Eugenio is an Italian-American computer scientist, the Collegiate Warren S. McCulloch Professor of Computer Science at the University of Illinois Chicago. Her research focuses on natural language processing and its applications to human–computer interaction, educational technology, and artificial intelligence in healthcare. == Education and career == Di Eugenio is originally from Turin. After an undergraduate education in Italy, she completed her Ph.D. in computer and information science in 1993 at the University of Pennsylvania. Her dissertation, Understanding Natural Language Instructions: A Computational Approach to Purpose Clauses, was supervised by Bonnie Webber. She became a faculty member at the University of Illinois Chicago in 1999, and at that time was the only woman faculty member in the Department of Electrical Engineering and Computer Science. == Recognition == In 2022, Di Eugenio received the Zenith Award of the Association for Women in Science. She was named as a Fellow of the Association for Computational Linguistics in 2023, "for outstanding contributions to natural language generation; intelligent tutoring systems; discourse; intercoder agreement; and applying multimodal interactive systems to health".

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  • Box blur

    Box blur

    A box blur (also known as a box linear filter) is a spatial domain linear filter in which each pixel in the resulting image has a value equal to the average value of its neighboring pixels in the input image. It is a form of low-pass ("blurring") filter. A 3 by 3 box blur ("radius 1") can be written as matrix 1 9 [ 1 1 1 1 1 1 1 1 1 ] . {\displaystyle {\frac {1}{9}}{\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}.} Due to its property of using equal weights, it can be implemented using a much simpler accumulation algorithm, which is significantly faster than using a sliding-window algorithm. Box blurs are frequently used to approximate a Gaussian blur. By the central limit theorem, repeated application of a box blur will approximate a Gaussian blur. In the frequency domain, a box blur has zeros and negative components. That is, a sine wave with a period equal to the size of the box will be blurred away entirely, and wavelengths shorter than the size of the box may be phase-reversed, as seen when two bokeh circles touch to form a bright spot where there would be a dark spot between two bright spots in the original image. == Extensions == Gwosdek, et al. has extended Box blur to take a fractional radius: the edges of the 1-D filter are expanded with a fraction. It makes slightly better gaussian approximation possible due to the elimination of integer-rounding error. Mario Klingemann has a "stack blur" that tries to better emulate gaussian's look in one pass by stacking weights: 1 9 [ 1 2 3 2 1 ] {\displaystyle {\frac {1}{9}}{\begin{bmatrix}1&2&3&2&1\end{bmatrix}}} The triangular impulse response it forms decomposes to two rounds of box blur. Stacked Integral Image by Bhatia et al. takes the weighted average of a few box blurs to fit the gaussian response curve. == Implementation == The following pseudocode implements a 3x3 box blur. The example does not handle the edges of the image, which would not fit inside the kernel, so that these areas remain unblurred. In practice, the issue is better handled by: Introducing an alpha channel to represent the absence of colors; Extending the boundary by filling in values, ranked by quality: Fill in a mirrored image at the border Fill in a constant color extending from the last pixel Pad in a fixed color A number of optimizations can be applied when implementing the box blur of a radius r and N pixels: The box blur is a separable filter, so that only two 1D passes of averaging 2 r + 1 pixels will be needed, one horizontal and one vertical, for each pixel. This lowers the complexity from O(Nr2) to O(Nr). In digital signal processing terminology, each pass is a moving-average filter. Accumulation. Instead of discarding the sum for each pixel, the algorithm re-uses the previous sum, and updates it by subtracting away the old pixel and adding the new pixel in the blurring range. A summed-area table can be used similarly. This lowers the complexity from O(Nr) to O(N). When being used in multiple passes to approximate a Gaussian blur, the cascaded integrator–comb filter construction allows for doing the equivalent operation in a single pass.

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  • European Association for Machine Translation

    European Association for Machine Translation

    The European Association for Machine Translation is the European branch of the International Association for Machine Translation Archived 2010-06-24 at the Wayback Machine. It is a non-profit organisation and organises conferences and workshops on the subject of machine translation. It was registered in 1991 in Switzerland and is the only organisation of its type in Europe.

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  • Thomas G. Dietterich

    Thomas G. Dietterich

    Thomas G. Dietterich is emeritus professor of computer science at Oregon State University. He is one of the pioneers of the field of machine learning. He served as executive editor of Machine Learning (journal) (1992–98) and helped co-found the Journal of Machine Learning Research. In response to the media's attention on the dangers of artificial intelligence, Dietterich has been quoted for an academic perspective to a broad range of media outlets including National Public Radio, Business Insider, Microsoft Research, CNET, and The Wall Street Journal. Among his research contributions were the invention of error-correcting output coding to multi-class classification, the formalization of the multiple-instance problem, the MAXQ framework for hierarchical reinforcement learning, and the development of methods for integrating non-parametric regression trees into probabilistic graphical models. == Biography and education == Thomas Dietterich was born in South Weymouth, Massachusetts, in 1954. His family later moved to New Jersey and then again to Illinois, where Tom graduated from Naperville Central High School. Dietterich then entered Oberlin College and began his undergraduate studies. In 1977, Dietterich graduated from Oberlin with a degree in mathematics, focusing on probability and statistics. Dietterich spent the following two years at the University of Illinois, Urbana-Champaign. After those two years, he began his doctoral studies in the Department of Computer Science at Stanford University. Dietterich received his Ph.D. in 1984 and moved to Corvallis, Oregon, where he was hired as an assistant professor in computer science. in 2013, he was named "Distinguished Professor". In 2016, Dietterich retired from his position at Oregon State University. Throughout his career, Dietterich has worked to promote scientific publication and conference presentations. For many years, he was the editor of the MIT Press series on Adaptive Computation and Machine Learning. He also held the position of co-editor of the Morgan Claypool Synthesis Series on Artificial Intelligence and Machine Learning. He has organized several conferences and workshops including serving as Technical Program Co-Chair of the National Conference on Artificial Intelligence (AAAI-90), Technical Program Chair of the Neural Information Processing Systems (NIPS-2000) and General Chair of NIPS-2001. He served as founding President of the International Machine Learning Society and he has been a member of the IMLS Board since its founding. He is currently also a member of the Steering Committee of the Asian Conference on Machine Learning. == Research interests == Professor Dietterich is interested in all aspects of machine learning. There are three major strands of his research. First, he is interested in the fundamental questions of artificial intelligence and how machine learning can provide the basis for building integrated intelligent systems. Second, he is interested in ways that people and computers can collaborate to solve challenging problems. And third, he is interested in applying machine learning to problems in the ecological sciences and ecosystem management as part of the emerging field of computational sustainability. Over his career, he has worked on a wide variety of problems ranging from drug design to user interfaces to computer security. His current focus is on ways that computer science methods can help advance ecological science and improve our management of the Earth's ecosystems. This passion has led to several projects including research in wildfire management, invasive vegetation and understanding the distribution and migration of birds. For example, Dietterich's research is helping scientists at the Cornell Lab of Ornithology answer questions like: How do birds decide to migrate north? How do they know when to land and stopover for a few days? How do they choose where to make a nest? Tens of thousands of volunteer birdwatchers (citizen scientists) all over the world contribute data to the study by submitting their bird sightings to the eBird website. The amount of data is overwhelming – in March 2012 they had over 3.1 million bird observations. Machine learning can uncover patterns in data to model the migration of species. But there are many other applications for the same techniques which will allow organizations to better manage our forests, oceans, and endangered species, as well as improve traffic flow, water systems, the electrical power grid, and more. I realized I wanted to have an impact on something that really mattered – and certainly the whole Earth's ecosystem, of which we are a part, is under threat in so many ways. And so if there's some way that I can use my technical skills to improve both the science base and the tools needed for policy and management decisions, then I would like to do that. I am passionate about that. == Dangers of AI: an academic perspective == Dietterich has argued that the most realistic risks about the dangers of artificial intelligence are basic mistakes, breakdowns and cyberattacks, and the fact that it simply may not always work, rather than machines that become super powerful or destroy the human race. Dietterich considers machines becoming self-aware and trying to exterminate humans to be more science fiction than scientific fact. But to the extent that computer systems are given increasingly dangerous tasks, and asked to learn from and interpret their experiences, he said they may simply make mistakes. Instead, much of the work done in the AI safety community does indeed focus around accidents and design flaws. == Positions held == 2014–2016: President, Association for the Advancement of Artificial Intelligence (AAAI). 2013–present: Distinguished Professor of computer science, Oregon State University. 2011–present: Chief Scientist, BigML, Corvallis, OR. 2005–present: Director of Intelligent Systems Research, School of Electrical Engineering and Computer Science, Oregon State University. 2006–2008: Chief Scientist, Smart Desktop, Inc., Seattle, WA. 2004–2005: Chief Scientist, MyStrands, Inc., Corvallis, OR. 1995-2013: Professor of computer science, Oregon State University. 1998–1999: Visiting Senior Scientist, Institute for the Investigation of Artificial Intelligence, Barcelona, Spain. (Sabbatical leave position) 1988–1995: Associate Professor of computer science, Oregon State University. 1991–1993: Senior Scientist, Arris Pharmaceutical Corporation, S. San Francisco, CA. 1985–1988: Assistant Professor of computer science, Oregon State University. 1979–1984: Research Assistant, Heuristic Programming Project, Department of Computer Science, Stanford University. 1979 (Summer): Member of Technical Staff, Bell Telephone Laboratories, Naperville, Illinois. Computer-to-computer file transfer and micro-code distribution to remote switching systems. 1977 (Summer): Assistant to the Director of Planning and Research, Oberlin College, Oberlin, Ohio. Developed institutional planning database. == Awards and honors == Thomas Dietterich was honored by Oregon State University in the spring of 2013 as a "Distinguished Professor" for his work as a pioneer in the field of machine learning and being one of the mostly highly cited scientists in his field. He has also earned exclusive "Fellow" status in the Association for the Advancement of Artificial Intelligence, the American Association for the Advancement of Science and the Association for Computing Machinery. Over his career, he obtained more than $30 million in research grants, helped build a world-class research group at Oregon State, and created three software companies. He also co-founded two of the field's leading journals and was elected first president of the International Machine Learning Society. His other awards and honors include: ACM Distinguished Lecturer, 2012-2013 Fellow, American Association for the Advancement of Science, 2007 Oregon State University, College of Engineering Collaboration Award, 2004 Winner, JAIR Award for Best Paper in Previous Five Years, 2003 Fellow, Association for Computing Machinery, elected 2003 Oregon State University, College of Engineering Research Award, 1998 Fellow, Association for the Advancement of Artificial Intelligence, elected 1994 NSF Presidential Young Investigator, 1987-92 Nominated for Carter Award for Graduate Teaching, 1987, 1988 IBM Graduate Fellow, 1982, 1983 Upsilon Pi Epsilon, 1996 Sigma Xi, 1979–present State Farm Companies Foundation Fellowship, 1978 Member, Board of Trustees, Oberlin College, 1977-1980 Graduation with Honors in Mathematics, Oberlin College, 1977 Phi Beta Kappa, 1977 National Merit Scholar, 1973 == Selected publications == Liping Liu, Thomas G. Dietterich, Nan Li, Zhi-Hua Zhou (2016). Transductive Optimization of Top k Precision. International Joint Conference on Artificial Intelligence (IJCAI-2016). pp. 1781–1787. New York, NY Md. Amran Siddiqui, Alan Fern, Thomas G. Dietterich, Shubhomoy Da

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  • Best AI Bug Finders in 2026

    Best AI Bug Finders in 2026

    In search of the best AI bug finder? An AI bug finder is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI bug finder slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Just This Once

    Just This Once

    Just This Once is a 1993 romance novel written in the style of Jacqueline Susann by a Macintosh IIcx computer named "Hal" in collaboration with its programmer, Scott French. French reportedly spent $40,000 and 8 years developing an artificial intelligence program to analyze Susann's works and attempt to create a novel that Susann might have written. A legal dispute between the estate of Jacqueline Susann and the publisher resulted in a settlement to split the profits, and the book was referenced in several legal journal articles about copyright laws. The book had two small print runs totaling 35,000 copies, receiving mixed reviews. == Creation == The novel's creation spanned the fields of artificial intelligence, expert systems, and natural language processing. Scott French first scanned and analyzed portions of two books by Jacqueline Susann, Valley of the Dolls and Once Is Not Enough, to determine constituents of Susann's writing style, which French stated was the most difficult task. This analysis extracted several hundred components including frequency and type of sexual acts and sentence structure. "Once you're there, the writer's style emerges, part of her actual personality comes out, and the computer can be programmed to make a story." French also created several thousand rules to govern tone, plotting, scenes, and characters. The text generated by Hal, the computer, was intended to mimic what Susann might have written, although the output required significant editing. French credits Hal's work with "almost 100% of the plot, 100% of the theme and style." French estimates that he wrote 10% of the prose, the computer Hal wrote about 25% of the prose, and the remaining two-thirds was more of a collaboration between the two. A typical scenario to write a scene would involve Hal asking questions that French would answer (for example, Hal might ask about the "cattiness factor" involved in a meeting between two key female characters, and French would reply with a range of 1 to 10), and the computer would then generate a few sentences to which French would make minor edits. The process would repeat for the next few sentences until the scene was written. == Legal issues == Jacqueline Susann's publisher was skeptical of the legality of Just This Once, although French doubted that an author's thought processes could be copyrighted. Susann's estate reportedly threatened to sue Scott French but the parties settled out of court; the settlement involved splitting profits between the parties but the terms of the settlement were not disclosed. The publication of Just This Once raised questions in the legal profession concerning how copyright law applies to computer-generated works derived from an analysis of other copyrighted works, and whether the generation of such works infringes on copyright. The publications on this topic suggested that the copyright laws of the time were ill-equipped to deal with computer-generated creative works. == Reception == The book's publisher Steven Shragis of Carol Group said of the novel, "I'm not going to say this is a great literary work, but it's every bit as good as anything out in this field, and better than an awful lot." The novel received some positive early reviews. In USA Today, novelist Thomas Gifford compared Just This Once to another novel in the same genre, American Star by Jackie Collins. Gifford concluded: "If you do like this stuff, you'd be much, much better off with the one written by the computer." The Dead Jackie Susann Quarterly declared that Susann "would be proud. Lots of money, sleaze, disease, death, oral sex, tragedy and the good girl gone bad." Other reviews were mixed. Publishers Weekly wrote, "If the books of Jacqueline Susann and Harold Robbins seem formulaic, this debut novel of sin and success in Las Vegas outdoes them all. And that, in a way, is the point.... All novelty rests in the conceit of computer authorship, not in the story itself." Library Journal stated "French invested eight years and $50,000 in a scheme to use artificial intelligence to fulfill his authentic, if dubious, desire to generate a trashy novel a la Jacqueline Susann. Shallow, beautiful-people characters are flatly conceived and randomly accessed in a formulaic plot ... a sexy, boring morality tale. Of possible interest to computer buffs for its use of Expert Systems and the virtual promise of more worthy possibilities; others should read Susann." Kirkus Reviews wrote: "The deal here is that author French is not the author, he's just the midwife, having allegedly programmed his computer to write about our times just the way Susann would... almost perfectly capturing glamorous Jackie's turgid but E-Z reading prose style and ultrareliable mix of sex, glitz, dope 'n' despair.... One wonders, though, if French's tale spinning PC will do as well on the talkshows as Jackie did. The computer weenies have been trying to tell us for years, garbage in-garbage out."

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  • How to Choose an Conversational AI Platform

    How to Choose an Conversational AI Platform

    Trying to pick the best conversational AI platform? An conversational AI platform 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 conversational AI platform slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Markov chain

    Markov chain

    In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes. They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, finance, information theory, physics, signal processing, and speech processing. The adjectives Markovian and Markov are used to describe something that is related to a Markov process. == Principles == === Definition === A Markov process is a stochastic process that satisfies the Markov property (sometimes characterized as "memorylessness"). In simpler terms, it is a process for which predictions can be made regarding future outcomes based solely on its present state and—most importantly—such predictions are just as good as the ones that could be made knowing the process's full history. In other words, conditional on the present state of the system, its future and past states are independent. A Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless of the nature of time), but it is also common to define a Markov chain as having discrete time in either countable or continuous state space (thus regardless of the state space). === Types of Markov chains === The system's state space and time parameter index need to be specified. The following table gives an overview of the different instances of Markov processes for different levels of state space generality for both discrete and continuous time: Note that there is no definitive agreement in the literature on the use of some of the terms that signify special cases of Markov processes. Usually the term "Markov chain" is reserved for a process with a discrete set of times, that is, a discrete-time Markov chain (DTMC), but a few authors use the term "Markov process" to refer to a continuous-time Markov chain (CTMC) without explicit mention. In addition, there are other extensions of Markov processes that are referred to as such but do not necessarily fall within any of these four categories (see Markov model). Moreover, the time index need not necessarily be real-valued; like with the state space, there are conceivable processes that move through index sets with other mathematical constructs. Notice that the general state space continuous-time Markov chain is general to such a degree that it has no designated term. While the time parameter is usually discrete, the state space of a Markov chain does not have any generally agreed-on restrictions: the term may refer to a process on an arbitrary state space. However, many applications of Markov chains employ finite or countably infinite state spaces, which have a more straightforward statistical analysis. Besides time-index and state-space parameters, there are many other variations, extensions and generalizations (see Variations). For simplicity, most of this article concentrates on the discrete-time, discrete state-space case, unless mentioned otherwise. === Transitions === The changes of state of the system are called transitions. The probabilities associated with various state changes are called transition probabilities. The process is characterized by a state space, a transition matrix describing the probabilities of particular transitions, and an initial state (or initial distribution) across the state space. By convention, we assume all possible states and transitions have been included in the definition of the process, so there is always a next state, and the process does not terminate. A discrete-time random process involves a system which is in a certain state at each step, with the state changing randomly between steps. The steps are often thought of as moments in time, but they can equally well refer to physical distance or any other discrete measurement. Formally, the steps are the integers or natural numbers, and the random process is a mapping of these to states. The Markov property states that the conditional probability distribution for the system at the next step (and in fact at all future steps) depends only on the current state of the system, and not additionally on the state of the system at previous steps. Since the system changes randomly, it is generally impossible to predict with certainty the state of a Markov chain at a given point in the future. However, the statistical properties of the system's future can be predicted. In many applications, it is these statistical properties that are important. == History == Andrey Markov studied Markov processes in the early 20th century, publishing his first paper on the topic in 1906. Markov processes in continuous time were discovered long before his work in the early 20th century in the form of the Poisson process. Markov was interested in studying an extension of independent random sequences, motivated by a disagreement with Pavel Nekrasov who claimed independence was necessary for the weak law of large numbers to hold. In his first paper on Markov chains, published in 1906, Markov showed that under certain conditions the average outcomes of the Markov chain would converge to a fixed vector of values, so proving a weak law of large numbers without the independence assumption, which had been commonly regarded as a requirement for such mathematical laws to hold. Markov later used Markov chains to study the distribution of vowels in Eugene Onegin, written by Alexander Pushkin, and proved a central limit theorem for such chains. In 1912 Henri Poincaré studied Markov chains on finite groups with an aim to study card shuffling. Other early uses of Markov chains include a diffusion model, introduced by Paul and Tatyana Ehrenfest in 1907, and a branching process, introduced by Francis Galton and Henry William Watson in 1873, preceding the work of Markov. After the work of Galton and Watson, it was later revealed that their branching process had been independently discovered and studied around three decades earlier by Irénée-Jules Bienaymé. Starting in 1928, Maurice Fréchet became interested in Markov chains, eventually resulting in him publishing in 1938 a detailed study on Markov chains. Andrey Kolmogorov developed in a 1931 paper a large part of the early theory of continuous-time Markov processes. Kolmogorov was partly inspired by Louis Bachelier's 1900 work on fluctuations in the stock market as well as Norbert Wiener's work on Einstein's model of Brownian movement. He introduced and studied a particular set of Markov processes known as diffusion processes, where he derived a set of differential equations describing the processes. Independent of Kolmogorov's work, Sydney Chapman derived in a 1928 paper an equation, now called the Chapman–Kolmogorov equation, in a less mathematically rigorous way than Kolmogorov, while studying Brownian movement. The differential equations are now called the Kolmogorov equations or the Kolmogorov–Chapman equations. Other mathematicians who contributed significantly to the foundations of Markov processes include William Feller, starting in 1930s, and then later Eugene Dynkin, starting in the 1950s. == Examples == Mark V. Shaney is a third-order Markov chain program, and a Markov text generator. It ingests the sample text (the Tao Te Ching, or the posts of a Usenet group) and creates a massive list of every sequence of three successive words (triplet) which occurs in the text. It then chooses two words at random, and looks for a word which follows those two in one of the triplets in its massive list. If there is more than one, it picks at random (identical triplets count separately, so a sequence which occurs twice is twice as likely to be picked as one which only occurs once). It then adds that word to the generated text. Then, in the same way, it picks a triplet that starts with the second and third words in the generated text, and that gives a fourth word. It adds the fourth word, then repeats with the third and fourth words, and so on. Random walks based on integers and the gambler's ruin problem are ex

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  • Thomas G. Dietterich

    Thomas G. Dietterich

    Thomas G. Dietterich is emeritus professor of computer science at Oregon State University. He is one of the pioneers of the field of machine learning. He served as executive editor of Machine Learning (journal) (1992–98) and helped co-found the Journal of Machine Learning Research. In response to the media's attention on the dangers of artificial intelligence, Dietterich has been quoted for an academic perspective to a broad range of media outlets including National Public Radio, Business Insider, Microsoft Research, CNET, and The Wall Street Journal. Among his research contributions were the invention of error-correcting output coding to multi-class classification, the formalization of the multiple-instance problem, the MAXQ framework for hierarchical reinforcement learning, and the development of methods for integrating non-parametric regression trees into probabilistic graphical models. == Biography and education == Thomas Dietterich was born in South Weymouth, Massachusetts, in 1954. His family later moved to New Jersey and then again to Illinois, where Tom graduated from Naperville Central High School. Dietterich then entered Oberlin College and began his undergraduate studies. In 1977, Dietterich graduated from Oberlin with a degree in mathematics, focusing on probability and statistics. Dietterich spent the following two years at the University of Illinois, Urbana-Champaign. After those two years, he began his doctoral studies in the Department of Computer Science at Stanford University. Dietterich received his Ph.D. in 1984 and moved to Corvallis, Oregon, where he was hired as an assistant professor in computer science. in 2013, he was named "Distinguished Professor". In 2016, Dietterich retired from his position at Oregon State University. Throughout his career, Dietterich has worked to promote scientific publication and conference presentations. For many years, he was the editor of the MIT Press series on Adaptive Computation and Machine Learning. He also held the position of co-editor of the Morgan Claypool Synthesis Series on Artificial Intelligence and Machine Learning. He has organized several conferences and workshops including serving as Technical Program Co-Chair of the National Conference on Artificial Intelligence (AAAI-90), Technical Program Chair of the Neural Information Processing Systems (NIPS-2000) and General Chair of NIPS-2001. He served as founding President of the International Machine Learning Society and he has been a member of the IMLS Board since its founding. He is currently also a member of the Steering Committee of the Asian Conference on Machine Learning. == Research interests == Professor Dietterich is interested in all aspects of machine learning. There are three major strands of his research. First, he is interested in the fundamental questions of artificial intelligence and how machine learning can provide the basis for building integrated intelligent systems. Second, he is interested in ways that people and computers can collaborate to solve challenging problems. And third, he is interested in applying machine learning to problems in the ecological sciences and ecosystem management as part of the emerging field of computational sustainability. Over his career, he has worked on a wide variety of problems ranging from drug design to user interfaces to computer security. His current focus is on ways that computer science methods can help advance ecological science and improve our management of the Earth's ecosystems. This passion has led to several projects including research in wildfire management, invasive vegetation and understanding the distribution and migration of birds. For example, Dietterich's research is helping scientists at the Cornell Lab of Ornithology answer questions like: How do birds decide to migrate north? How do they know when to land and stopover for a few days? How do they choose where to make a nest? Tens of thousands of volunteer birdwatchers (citizen scientists) all over the world contribute data to the study by submitting their bird sightings to the eBird website. The amount of data is overwhelming – in March 2012 they had over 3.1 million bird observations. Machine learning can uncover patterns in data to model the migration of species. But there are many other applications for the same techniques which will allow organizations to better manage our forests, oceans, and endangered species, as well as improve traffic flow, water systems, the electrical power grid, and more. I realized I wanted to have an impact on something that really mattered – and certainly the whole Earth's ecosystem, of which we are a part, is under threat in so many ways. And so if there's some way that I can use my technical skills to improve both the science base and the tools needed for policy and management decisions, then I would like to do that. I am passionate about that. == Dangers of AI: an academic perspective == Dietterich has argued that the most realistic risks about the dangers of artificial intelligence are basic mistakes, breakdowns and cyberattacks, and the fact that it simply may not always work, rather than machines that become super powerful or destroy the human race. Dietterich considers machines becoming self-aware and trying to exterminate humans to be more science fiction than scientific fact. But to the extent that computer systems are given increasingly dangerous tasks, and asked to learn from and interpret their experiences, he said they may simply make mistakes. Instead, much of the work done in the AI safety community does indeed focus around accidents and design flaws. == Positions held == 2014–2016: President, Association for the Advancement of Artificial Intelligence (AAAI). 2013–present: Distinguished Professor of computer science, Oregon State University. 2011–present: Chief Scientist, BigML, Corvallis, OR. 2005–present: Director of Intelligent Systems Research, School of Electrical Engineering and Computer Science, Oregon State University. 2006–2008: Chief Scientist, Smart Desktop, Inc., Seattle, WA. 2004–2005: Chief Scientist, MyStrands, Inc., Corvallis, OR. 1995-2013: Professor of computer science, Oregon State University. 1998–1999: Visiting Senior Scientist, Institute for the Investigation of Artificial Intelligence, Barcelona, Spain. (Sabbatical leave position) 1988–1995: Associate Professor of computer science, Oregon State University. 1991–1993: Senior Scientist, Arris Pharmaceutical Corporation, S. San Francisco, CA. 1985–1988: Assistant Professor of computer science, Oregon State University. 1979–1984: Research Assistant, Heuristic Programming Project, Department of Computer Science, Stanford University. 1979 (Summer): Member of Technical Staff, Bell Telephone Laboratories, Naperville, Illinois. Computer-to-computer file transfer and micro-code distribution to remote switching systems. 1977 (Summer): Assistant to the Director of Planning and Research, Oberlin College, Oberlin, Ohio. Developed institutional planning database. == Awards and honors == Thomas Dietterich was honored by Oregon State University in the spring of 2013 as a "Distinguished Professor" for his work as a pioneer in the field of machine learning and being one of the mostly highly cited scientists in his field. He has also earned exclusive "Fellow" status in the Association for the Advancement of Artificial Intelligence, the American Association for the Advancement of Science and the Association for Computing Machinery. Over his career, he obtained more than $30 million in research grants, helped build a world-class research group at Oregon State, and created three software companies. He also co-founded two of the field's leading journals and was elected first president of the International Machine Learning Society. His other awards and honors include: ACM Distinguished Lecturer, 2012-2013 Fellow, American Association for the Advancement of Science, 2007 Oregon State University, College of Engineering Collaboration Award, 2004 Winner, JAIR Award for Best Paper in Previous Five Years, 2003 Fellow, Association for Computing Machinery, elected 2003 Oregon State University, College of Engineering Research Award, 1998 Fellow, Association for the Advancement of Artificial Intelligence, elected 1994 NSF Presidential Young Investigator, 1987-92 Nominated for Carter Award for Graduate Teaching, 1987, 1988 IBM Graduate Fellow, 1982, 1983 Upsilon Pi Epsilon, 1996 Sigma Xi, 1979–present State Farm Companies Foundation Fellowship, 1978 Member, Board of Trustees, Oberlin College, 1977-1980 Graduation with Honors in Mathematics, Oberlin College, 1977 Phi Beta Kappa, 1977 National Merit Scholar, 1973 == Selected publications == Liping Liu, Thomas G. Dietterich, Nan Li, Zhi-Hua Zhou (2016). Transductive Optimization of Top k Precision. International Joint Conference on Artificial Intelligence (IJCAI-2016). pp. 1781–1787. New York, NY Md. Amran Siddiqui, Alan Fern, Thomas G. Dietterich, Shubhomoy Da

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  • Spectral shape analysis

    Spectral shape analysis

    Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc. == Laplace == The Laplace–Beltrami operator is involved in many important differential equations, such as the heat equation and the wave equation. It can be defined on a Riemannian manifold as the divergence of the gradient of a real-valued function f: Δ f := div ⁡ grad ⁡ f . {\displaystyle \Delta f:=\operatorname {div} \operatorname {grad} f.} Its spectral components can be computed by solving the Helmholtz equation (or Laplacian eigenvalue problem): Δ φ i + λ i φ i = 0. {\displaystyle \Delta \varphi _{i}+\lambda _{i}\varphi _{i}=0.} The solutions are the eigenfunctions φ i {\displaystyle \varphi _{i}} (modes) and corresponding eigenvalues λ i {\displaystyle \lambda _{i}} , representing a diverging sequence of positive real numbers. The first eigenvalue is zero for closed domains or when using the Neumann boundary condition. For some shapes, the spectrum can be computed analytically (e.g. rectangle, flat torus, cylinder, disk or sphere). For the sphere, for example, the eigenfunctions are the spherical harmonics. The most important properties of the eigenvalues and eigenfunctions are that they are isometry invariants. In other words, if the shape is not stretched (e.g. a sheet of paper bent into the third dimension), the spectral values will not change. Bendable objects, like animals, plants and humans, can move into different body postures with only minimal stretching at the joints. The resulting shapes are called near-isometric and can be compared using spectral shape analysis. == Discretizations == Geometric shapes are often represented as 2D curved surfaces, 2D surface meshes (usually triangle meshes) or 3D solid objects (e.g. using voxels or tetrahedra meshes). The Helmholtz equation can be solved for all these cases. If a boundary exists, e.g. a square, or the volume of any 3D geometric shape, boundary conditions need to be specified. Several discretizations of the Laplace operator exist (see Discrete Laplace operator) for the different types of geometry representations. Many of these operators do not approximate well the underlying continuous operator. == Spectral shape descriptors == === ShapeDNA and its variants === The ShapeDNA is one of the first spectral shape descriptors. It is the normalized beginning sequence of the eigenvalues of the Laplace–Beltrami operator. Its main advantages are the simple representation (a vector of numbers) and comparison, scale invariance, and in spite of its simplicity a very good performance for shape retrieval of non-rigid shapes. Competitors of shapeDNA include singular values of Geodesic Distance Matrix (SD-GDM) and Reduced BiHarmonic Distance Matrix (R-BiHDM). However, the eigenvalues are global descriptors, therefore the shapeDNA and other global spectral descriptors cannot be used for local or partial shape analysis. === Global point signature (GPS) === The global point signature at a point x {\displaystyle x} is a vector of scaled eigenfunctions of the Laplace–Beltrami operator computed at x {\displaystyle x} (i.e. the spectral embedding of the shape). The GPS is a global feature in the sense that it cannot be used for partial shape matching. === Heat kernel signature (HKS) === The heat kernel signature makes use of the eigen-decomposition of the heat kernel: h t ( x , y ) = ∑ i = 0 ∞ exp ⁡ ( − λ i t ) φ i ( x ) φ i ( y ) . {\displaystyle h_{t}(x,y)=\sum _{i=0}^{\infty }\exp(-\lambda _{i}t)\varphi _{i}(x)\varphi _{i}(y).} For each point on the surface the diagonal of the heat kernel h t ( x , x ) {\displaystyle h_{t}(x,x)} is sampled at specific time values t j {\displaystyle t_{j}} and yields a local signature that can also be used for partial matching or symmetry detection. === Wave kernel signature (WKS) === The WKS follows a similar idea to the HKS, replacing the heat equation with the Schrödinger wave equation. === Improved wave kernel signature (IWKS) === The IWKS improves the WKS for non-rigid shape retrieval by introducing a new scaling function to the eigenvalues and aggregating a new curvature term. === Spectral graph wavelet signature (SGWS) === SGWS is a local descriptor that is not only isometric invariant, but also compact, easy to compute and combines the advantages of both band-pass and low-pass filters. An important facet of SGWS is the ability to combine the advantages of WKS and HKS into a single signature, while allowing a multiresolution representation of shapes. == Spectral Matching == The spectral decomposition of the graph Laplacian associated with complex shapes (see Discrete Laplace operator) provides eigenfunctions (modes) which are invariant to isometries. Each vertex on the shape could be uniquely represented with a combinations of the eigenmodal values at each point, sometimes called spectral coordinates: s ( x ) = ( φ 1 ( x ) , φ 2 ( x ) , … , φ N ( x ) ) for vertex x . {\displaystyle s(x)=(\varphi _{1}(x),\varphi _{2}(x),\ldots ,\varphi _{N}(x)){\text{ for vertex }}x.} Spectral matching consists of establishing the point correspondences by pairing vertices on different shapes that have the most similar spectral coordinates. Early work focused on sparse correspondences for stereoscopy. Computational efficiency now enables dense correspondences on full meshes, for instance between cortical surfaces. Spectral matching could also be used for complex non-rigid image registration, which is notably difficult when images have very large deformations. Such image registration methods based on spectral eigenmodal values indeed capture global shape characteristics, and contrast with conventional non-rigid image registration methods which are often based on local shape characteristics (e.g., image gradients).

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  • Pachinko allocation

    Pachinko allocation

    In machine learning and natural language processing, the pachinko allocation model (PAM) is a topic model. Topic models are a suite of algorithms to uncover the hidden thematic structure of a collection of documents. The algorithm improves upon earlier topic models such as latent Dirichlet allocation (LDA) by modeling correlations between topics in addition to the word correlations which constitute topics. PAM provides more flexibility and greater expressive power than latent Dirichlet allocation. While first described and implemented in the context of natural language processing, the algorithm may have applications in other fields such as bioinformatics. The model is named for pachinko machines—a game popular in Japan, in which metal balls bounce down around a complex collection of pins until they land in various bins at the bottom. == History == Pachinko allocation was first described by Wei Li and Andrew McCallum in 2006. The idea was extended with hierarchical Pachinko allocation by Li, McCallum, and David Mimno in 2007. In 2007, McCallum and his colleagues proposed a nonparametric Bayesian prior for PAM based on a variant of the hierarchical Dirichlet process (HDP). The algorithm has been implemented in the MALLET software package published by McCallum's group at the University of Massachusetts Amherst. == Model == PAM connects words in V and topics in T with an arbitrary directed acyclic graph (DAG), where topic nodes occupy the interior levels and the leaves are words. The probability of generating a whole corpus is the product of the probabilities for every document: P ( D | α ) = ∏ d P ( d | α ) {\displaystyle P(\mathbf {D} |\alpha )=\prod _{d}P(d|\alpha )}

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  • Language Weaver

    Language Weaver

    Language Weaver is the machine translation (MT) technology and brand of RWS. The brand name was revived in 2021 following the acquisition of SDL and Iconic Translation Machines Ltd. and the merging of the respective teams and technologies. Language Weaver was formerly a standalone company that was acquired by SDL in 2010. == History == Language Weaver was a Los Angeles, California–based company founded in 2002 as a spin-out company from the University of Southern California. The company was founded to commercialise a statistical approach to automatic language translation and natural language processing known as statistical machine translation (SMT). The company's name is a reference to one of the pioneers of machine translation — Warren Weaver — who first proposed the idea of using computers to ‘decode’ or ‘decrypt’ language in a memorandum back in 1947. Language Weaver’s statistical approach to machine translation was cutting-edge at the time, and a significant improvement over previous approaches such as Rule-Based MT. Language Weaver grew steadily over an 8 year period, with staff numbers totalling 96 across offices in US, Europe, and Japan. The company had significant business with Government organisations where its name continues to hold strong recognition to this day. In July 2010, Language Weaver was acquired by SDL plc for $42.5 million and the company was renamed SDL Language Weaver. == SDL Language Weaver == SDL Language Weaver was the primary machine translation technology at SDL where, over time, it evolved from SMT to syntax-based MT, to Neural Machine Translation. The Language Weaver brand was retired in 2015 in favour of SDL BeGlobal for the cloud-based solution, and SDL Enterprise Translation Server for the on-premise solution. Later, these products were rebranded again as SDL Machine Translation Cloud and SDL Machine Translation Edge respectively. == 2021 Relaunch == The Language Weaver brand was revived in 2021 following the acquisition of SDL by RWS, and the merger of the SDL MT and Iconic Translation Machines teams and technologies. The combined technologies of both companies, based on state-of-the-art Transformer-based Neural Machine Translation, are now sold as "Language Weaver" for cloud-based MT, and "Language Weaver Edge" for on-premise MT. == Supported languages == As of September 2021, Language Weaver supports the following languages and language varieties:

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