AI Headshot Business

AI Headshot Business — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Haskins Laboratories

  Haskins Laboratories, Inc. is an independent research laboratory, founded in 1935 and located in New Haven, Connecticut since 1970. Many current Haskins researchers are affiliated with Yale University's Child Study Center and/or the University of Connecticut. Haskins is a multidisciplinary and international community of researchers who conduct basic research on spoken and written language and global literacy. A guiding perspective of their research has been to view speech and language as emerging from biological processes, including those of adaptation, response to stimuli, and conspecific interaction. Haskins Laboratories has a long history of technological and theoretical innovation, from creating systems of rules for speech synthesis and development of an early working prototype of a reading machine for the blind to developing the landmark concept of phonemic awareness as the critical preparation for learning to read an alphabetic writing system. == Research tools and facilities == Haskins Laboratories is equipped, in-house, with a comprehensive suite of tools and capabilities to advance its mission of research into language and literacy. As of 2014, these included: Anechoic chamber Electroencephalography BioSemi 264 electrode, 24 bit Active Two System EGI 128 electrode, Geodesic EEG System 300 Electromagnetic articulography (EMMA) Carstens AG501 NDI WAVE Eye tracking: HL is equipped with 3 SR Research eye-trackers. 2 Model Eyelink 1000 systems. 1 Model Eyelink 1000plus system. Magnetic resonance imaging: Haskins has access to MRI scanners through agreements with the University of Connecticut and the Yale School of Medicine. On-site, HL has a Linux computer cluster dedicated to analysis of MRI data. Motion capture: HL is equipped with a Vicon motion capture system with one Basler high-speed digital camera, six Vicon MX T-20 cameras and a Vicon MX Giganet for synching camera data and connecting cameras to the data capture computer. Near infrared spectroscopy: HL has a TechEn CW6 8x8 system (four emitters; eight detectors). Ultrasound sonogram == History == Many researchers have contributed to scientific breakthroughs at Haskins Laboratories since its founding. All of them are indebted to the pioneering work and leadership of Caryl Parker Haskins, Franklin S. Cooper, Alvin Liberman, Seymour Hutner and Luigi Provasoli. The history presented here focuses on the research program of the division of Haskins Laboratories that, since the 1940s, has been most well known for its work in the areas of speech, language, and reading. === 1930s === Caryl Haskins and Franklin S. Cooper established Haskins Laboratories in 1935. It was originally affiliated with Harvard University, MIT, and Union College in Schenectady, NY. Caryl Haskins conducted research in microbiology, radiation physics, and other fields in Cambridge, MA and Schenectady. In 1939 Haskins Laboratories moved its center to New York City. Seymour Hutner joined the staff to set up a research program in microbiology, genetics, and nutrition. The descendant of the division led by Hutner program eventually became a department of Pace University in New York. The two identically named organizations are no longer formally affiliated. === 1940s === The U. S. Office of Scientific Research and Development, under Vannevar Bush asked Haskins Laboratories to evaluate and develop technologies for assisting blinded World War II veterans. Experimental psychologist Alvin Liberman joined Haskins Laboratories to assist in developing a "sound alphabet" to represent the letters in a text for use in a reading machine for the blind. Luigi Provasoli joined Haskins Laboratories to set up a research program in marine biology. The program in marine biology moved to Yale University in 1970 and disbanded with Provasoli's retirement in 1978. === 1950s === Franklin S. Cooper invented the pattern playback, a machine that converts pictures of the acoustic patterns of speech back into sound. With this device, Alvin Liberman, Cooper, and Pierre Delattre (and later joined by Katherine Safford Harris, Leigh Lisker, Arthur Abramson, and others), discovered the acoustic cues for the perception of phonetic segments (consonants and vowels). Liberman and colleagues proposed a motor theory of speech perception to resolve the acoustic complexity: they hypothesized that we perceive speech by tapping into a biological specialization, a speech module, that contains knowledge of the acoustic consequences of articulation. Liberman, aided by Frances Ingemann and others, organized the results of the work on speech cues into a groundbreaking set of rules for speech synthesis by the Pattern Playback. === 1960s === Franklin S. Cooper and Katherine Safford Harris, working with Peter MacNeilage, were the first researchers in the U.S. to use electromyographic techniques, pioneered at the University of Tokyo, to study the neuromuscular organization of speech. Leigh Lisker and Arthur Abramson looked for simplification at the level of articulatory action in the voicing of certain contrasting consonants. They showed that many acoustic properties of voicing contrasts arise from variations in voice onset time, the relative phasing of the onset of vocal cord vibration and the end of a consonant. Their work has been widely replicated and elaborated, here and abroad, over the following decades. Donald Shankweiler and Michael Studdert-Kennedy used a dichotic listening technique (presenting different nonsense syllables simultaneously to opposite ears) to demonstrate the dissociation of phonetic (speech) and auditory (nonspeech) perception by finding that phonetic structure devoid of meaning is an integral part of language, typically processed in the left cerebral hemisphere. Liberman, Cooper, Shankweiler, and Studdert-Kennedy summarized and interpreted fifteen years of research in "Perception of the Speech Code", still among the most cited papers in the speech literature. It set the agenda for many years of research at Haskins and elsewhere by describing speech as a code in which speakers overlap (or coarticulate) segments to form syllables. Researchers at Haskins connected their first computer to a speech synthesizer designed by Haskins Laboratories' engineers. Ignatius Mattingly, with British collaborators, John N. Holmes and J.N. Shearme, adapted the Pattern playback rules to write the first computer program for synthesizing continuous speech from a phonetically spelled input. A further step toward a reading machine for the blind combined Mattingly's program with an automatic look-up procedure for converting alphabetic text into strings of phonetic symbols. === 1970s === In 1970, Haskins Laboratories moved to New Haven, Connecticut, and entered into affiliation agreements with Yale University and the University of Connecticut; Haskins remains fully independent of both Yale and UConn, administratively and financially. The lab's original location in New Haven, at 270 Crown Street (from 1970 to 2005), was leased from Yale University. Isabelle Liberman, Donald Shankweiler, and Alvin Liberman teamed up with Ignatius Mattingly to study the relationship between speech perception and reading, a topic implicit in Haskins Laboratories' research program since its inception. They developed the concept of phonemic awareness, the knowledge that would-be readers must be aware of the phonemic structure of their language in order to be able to read. Leonard Katz related the work to contemporary cognitive theory and provided expertise in experimental design and data analysis. Under the broad rubric of the "alphabetic principle", this is the core of the lab's present program of reading pedagogy. Patrick Nye joined Haskins Laboratories to lead a team working on the reading machine for the blind. The project culminated when the addition of an optical character recognizer allowed investigators to assemble the first automatic text-to-speech reading machine. By the end of the decade this technology had advanced to the point where commercial concerns assumed the task of designing and manufacturing reading machines for the blind. In 1973, Franklin S. Cooper was selected to form a panel of six experts charged with investigating the famous 18-minute gap in the White House office tapes of President Richard Nixon related to the Watergate scandal. Building on earlier work, Philip Rubin developed the sinewave synthesis program, which was then used by Robert Remez, Rubin, and colleagues to show that listeners can perceive continuous speech without traditional speech cues from a pattern of sinewaves that track the changing resonances of the vocal tract. This paved the way for a view of speech as a dynamic pattern of trajectories through articulatory-acoustic space. Philip Rubin and colleagues developed Paul Mermelstein's anatomically simplified vocal tract model, originally worked on at Bell Laboratories, into the first articulatory synthesizer that can be controlled in a phy

  Read more →
• 

  Croissant (metadata format)

  Croissant is a metadata format design to support sharing of datasets for machine learning applications. It is a platform-agnostic schema used to standardize metadata in data repositories like Hugging Face, kaggle, Dataverse and OpenML. == Structure == Croissant builds upon schema.org, uses primarily JSON-LD, and divides metadata in four "layers": Dataset Metadata, Resource, Structure and Semantic: The Dataset Metadata layer constrains which schema.org properties should be used, including additional properties, linking together the resources (files) of the dataset with general metadata, like licensing and citation information. The Resource layer describes the individual files and sets of those using two new classes, FileObject and FileSet. A FileSet may be a collection of related images. The Structure layer specifies how the files are organized in the dataset. A RecordSet class describes how resources are present, configurations that may very a lot between modality. This specification facilitates interoperability of the datasets. Finally, the Semantic layer adds information for practical reuse of the dataset, such as splits for train, test and validation subsets. It also provides a default extension for metadata related to responsible AI. The use of a standard machine-readable structure increases, for example, the discoverability of datasets in search engines such as Google Dataset Search. == History == Croissant was shared in arXiv in March 2024 and published in the proceedings of NeurIPS 2024. It started as community driven as a MLCommons Croissant Working Group, including stakeholders organizations from academia and industry, including Google, the open data institute, Sage Bionetworks and King's College London. Variations of Croissant are developed to support datasets in different areas of research, such as Geo-Croissant for geospatial datasets. Other technical extensions, such as support for RDF, soon followed.

  Read more →
• 

  Croissant (metadata format)

  Croissant is a metadata format design to support sharing of datasets for machine learning applications. It is a platform-agnostic schema used to standardize metadata in data repositories like Hugging Face, kaggle, Dataverse and OpenML. == Structure == Croissant builds upon schema.org, uses primarily JSON-LD, and divides metadata in four "layers": Dataset Metadata, Resource, Structure and Semantic: The Dataset Metadata layer constrains which schema.org properties should be used, including additional properties, linking together the resources (files) of the dataset with general metadata, like licensing and citation information. The Resource layer describes the individual files and sets of those using two new classes, FileObject and FileSet. A FileSet may be a collection of related images. The Structure layer specifies how the files are organized in the dataset. A RecordSet class describes how resources are present, configurations that may very a lot between modality. This specification facilitates interoperability of the datasets. Finally, the Semantic layer adds information for practical reuse of the dataset, such as splits for train, test and validation subsets. It also provides a default extension for metadata related to responsible AI. The use of a standard machine-readable structure increases, for example, the discoverability of datasets in search engines such as Google Dataset Search. == History == Croissant was shared in arXiv in March 2024 and published in the proceedings of NeurIPS 2024. It started as community driven as a MLCommons Croissant Working Group, including stakeholders organizations from academia and industry, including Google, the open data institute, Sage Bionetworks and King's College London. Variations of Croissant are developed to support datasets in different areas of research, such as Geo-Croissant for geospatial datasets. Other technical extensions, such as support for RDF, soon followed.

  Read more →
• 

  Competition in artificial intelligence

  Competition in artificial intelligence refers to the rivalry among companies, research institutions, and governments to develop and deploy the most capable artificial intelligence (AI) systems. The competition spans multiple domains, including large language models (LLMs), autonomous vehicles, robotics, computer vision systems, natural language processing (NLP), and AI-optimized hardware. == Background == Competition in AI is driven by potential economic, strategic, and scientific advantages. Breakthroughs in AI can enhance productivity, enable new products and services, and provide geopolitical leverage. The field has experienced rapid progress since the mid-2010s, particularly in machine learning and artificial neural networks, leading to intense rivalry among leading actors. == Corporate competition == Major technology companies are among the most visible competitors in AI. In the United States, firms such as OpenAI, Google DeepMind, Meta Platforms, Microsoft, Anthropic, and Nvidia compete in building advanced LLMs, generative AI platforms, and AI-optimized graphics processing units (GPUs). In China, companies such as Baidu, Alibaba Group, Tencent, and startups such DeepSeek have become leaders in AI deployment, often with state backing. The "[war for talent]" in AI research has become a defining feature of corporate competition. Leading firms often recruit top AI researchers from rivals, sometimes offering multi-million-dollar compensation packages. == National competition == Governments see leadership in AI as a strategic priority. The United States has funded AI research for military, economic, and societal applications, while China has set a target to lead the world in AI by 2030 through its "New Generation Artificial Intelligence Development Plan". Other nations, including the UK, India, Israel, Russia, South Korea, and members of the European Union, have launched national AI strategies. In February 2026 Anthropic said Chinese companies - DeepSeek, Moonshot AI, and MiniMax - were conducting "distillation attacks" in an attempt to copy their model's capabilities, and warned that business wars were closely tied to geopolitical ones: "foreign labs that illicitly distill American models can remove safeguards, feeding model capabilities into their own military, intelligence, and surveillance systems." == Sectors of competition == === Large language models and chatbots competition === Competition to produce the most capable generative text models, with benchmarks such as MMLU and ARC used to evaluate performance has been on scale since the emergence of AI. These systems leverage deep learning, especially transformer architectures, to understand and generate human-like language. Companies and research groups globally compete to develop chatbots that are more capable, reliable, and context-aware. Among the most well-known chatbots is ChatGPT, developed by OpenAI. Since its public release in 2022, ChatGPT has rapidly gained widespread attention for its ability to engage in coherent and versatile conversations, assist with creative writing, and solve complex problems. In response, technology firms introduced competing chatbots aiming to challenge or surpass ChatGPT's capabilities. Notably, DeepSeek, a Chinese AI company, launched an advanced chatbot integrated with their R1 language model, emphasizing strong natural language understanding and multilingual support. Similarly, Grok, developed by xAI (company), integrates conversational AI into vehicles and digital assistants, combining natural language processing with real-time data for personalized user interaction. These chatbots not only compete in language tasks but also demonstrate strategic reasoning capabilities by playing complex games such as chess and Go. This form of competition is reminiscent of historic AI milestones set by programs such as Deep Blue and AlphaGo. The OpenAI’s ChatGPT has been tested in playing chess at various levels, while DeepSeek’s chatbot showcased its prowess in online chess tournaments in early 2024, winning several matches against human and AI opponents. Grok, leveraging Tesla's vast data infrastructure, has demonstrated real-time strategic decision-making in simulation environments that include chess-like games. The competition pushes rapid innovation, with firms racing to improve chatbot conversational depth, reduce biases, increase factual accuracy, and integrate multimodal inputs like images and videos. At the same time, the competition raises questions about AI safety, ethical use, and the societal impacts of increasingly human-like chatbots. === Autonomous vehicles === Companies such as Waymo, Tesla, and Baidu are racing to deploy safe and reliable self-driving car technology. === AI chips === Rivalry between Nvidia, AMD, Intel, and Huawei in designing processors optimized for AI workloads. === Military applications === Development of AI-enabled drones, surveillance systems, and decision-support tools, with associated ethical debates. == Events == In 2023, OpenAI released GPT-4, prompting competitors such as Google DeepMind to accelerate the release of their own models, including Gemini. In 2024, Chinese AI company DeepSeek launched the R1 model, leading OpenAI to release an open-source system, GPT-OSS, as a strategic countermeasure. In 2022, Tesla and Waymo both expanded autonomous taxi services in U.S. cities, competing for regulatory approval and public trust. The U.S. Department of Defense's Project Maven and China's AI-enabled surveillance programs have been cited as examples of military AI rivalry. In 2025, Microsoft hired several senior engineers from Google DeepMind, highlighting the ongoing "talent poaching" competition in the AI sector. == Risks and concerns == Critics warn that unrestrained competition in AI can undermine safety, ethics, and governance. Concerns include the proliferation of biased or unsafe models, escalation in autonomous weapons, and reduced cooperation on safety standards.

  Read more →
• 

  Biohybrid microswimmer

  A biohybrid microswimmer also known as biohybrid nanorobot, can be defined as a microswimmer that consist of both biological and artificial constituents, for instance, one or several living microorganisms attached to one or various synthetic parts. In recent years nanoscopic and mesoscopic objects have been designed to collectively move through direct inspiration from nature or by harnessing its existing tools. Small mesoscopic to nanoscopic systems typically operate at low Reynolds numbers (Re ≪ 1), and understanding their motion becomes challenging. For locomotion to occur, the symmetry of the system must be broken. In addition, collective motion requires a coupling mechanism between the entities that make up the collective. To develop mesoscopic to nanoscopic entities capable of swarming behaviour, it has been hypothesised that the entities are characterised by broken symmetry with a well-defined morphology, and are powered with some material capable of harvesting energy. If the harvested energy results in a field surrounding the object, then this field can couple with the field of a neighbouring object and bring some coordination to the collective behaviour. Such robotic swarms have been categorised by an online expert panel as among the 10 great unresolved group challenges in the area of robotics. Although investigation of their underlying mechanism of action is still in its infancy, various systems have been developed that are capable of undergoing controlled and uncontrolled swarming motion by harvesting energy (e.g., light, thermal, etc.). Over the past decade, biohybrid microrobots, in which living mobile microorganisms are physically integrated with untethered artificial structures, have gained growing interest to enable the active locomotion and cargo delivery to a target destination. In addition to the motility, the intrinsic capabilities of sensing and eliciting an appropriate response to artificial and environmental changes make cell-based biohybrid microrobots appealing for transportation of cargo to the inaccessible cavities of the human body for local active delivery of diagnostic and therapeutic agents. == Background == Biohybrid microswimmers can be defined as microswimmers that consist of both biological and artificial constituents, for instance, one or several living microorganisms attached to one or various synthetic parts. The pioneers of this field, ahead of their time, were Montemagno and Bachand with a 1999 work regarding specific attachment strategies of biological molecules to nanofabricated substrates enabling the preparation of hybrid inorganic/organic nanoelectromechanical systems, so called NEMS. They described the production of large amounts of F1-ATPase from the thermophilic bacteria Bacillus PS3 for the preparation of F1-ATPase biomolecular motors immobilized on a nanoarray pattern of gold, copper or nickel produced by electron beam lithography. These proteins were attached to one micron microspheres tagged with a synthetic peptide. Consequently, they accomplished the preparation of a platform with chemically active sites and the development of biohybrid devices capable of converting energy of biomolecular motors into useful work. One of the most fundamental questions in science is what defines life. Collective motion is one of the hallmarks of life. This is commonly observed in nature at various dimensional levels as energized entities gather, in a concerted effort, into motile aggregated patterns. These motile aggregated events can be noticed, among many others, as dynamic swarms; e.g., unicellular organisms such as bacteria, locust swarms, or the flocking behaviour of birds. Ever since Newton established his equations of motion, the mystery of motion on the microscale has emerged frequently in scientific history, as famously demonstrated by a couple of articles that should be discussed briefly. First, an essential concept, popularized by Osborne Reynolds, is that the relative importance of inertia and viscosity for the motion of a fluid depends on certain details of the system under consideration. The Reynolds number Re, named in his honor, quantifies this comparison as a dimensionless ratio of characteristic inertial and viscous forces: R e = ρ u l μ {\displaystyle \mathrm {Re} ={\frac {\rho ul}{\mu }}} Here, ρ represents the density of the fluid; u is a characteristic velocity of the system (for instance, the velocity of a swimming particle); l is a characteristic length scale (e.g., the swimmer size); and μ is the viscosity of the fluid. Taking the suspending fluid to be water, and using experimentally observed values for u, one can determine that inertia is important for macroscopic swimmers like fish (Re = 100), while viscosity dominates the motion of microscale swimmers like bacteria (Re = 10−4). The overwhelming importance of viscosity for swimming at the micrometer scale has profound implications for swimming strategy. This has been discussed memorably by E. M. Purcell, who invited the reader into the world of microorganisms and theoretically studied the conditions of their motion. In the first place, propulsion strategies of large scale swimmers often involve imparting momentum to the surrounding fluid in periodic discrete events, such as vortex shedding, and coasting between these events through inertia. This cannot be effective for microscale swimmers like bacteria: due to the large viscous damping, the inertial coasting time of a micron-sized object is on the order of 1 μs. The coasting distance of a microorganism moving at a typical speed is about 0.1 angstroms (Å). Purcell concluded that only forces that are exerted in the present moment on a microscale body contribute to its propulsion, so a constant energy conversion method is essential. Microorganisms have optimized their metabolism for continuous energy production, while purely artificial microswimmers (microrobots) must obtain energy from the environment, since their on-board-storage-capacity is very limited. As a further consequence of the continuous dissipation of energy, biological and artificial microswimmers do not obey the laws of equilibrium statistical physics, and need to be described by non-equilibrium dynamics. Mathematically, Purcell explored the implications of low Reynolds number by taking the Navier-Stokes equation and eliminating the inertial terms: μ ∇ 2 u − ∇ p = 0 {\displaystyle {\begin{aligned}\mu \nabla ^{2}\mathbf {u} -{\boldsymbol {\nabla }}p&={\boldsymbol {0}}\\\end{aligned}}} where u {\displaystyle \mathbf {u} } is the velocity of the fluid and ∇ p {\displaystyle {\boldsymbol {\nabla }}p} is the gradient of the pressure. As Purcell noted, the resulting equation — the Stokes equation — contains no explicit time dependence. This has some important consequences for how a suspended body (e.g., a bacterium) can swim through periodic mechanical motions or deformations (e.g., of a flagellum). First, the rate of motion is practically irrelevant for the motion of the microswimmer and of the surrounding fluid: changing the rate of motion will change the scale of the velocities of the fluid and of the microswimmer, but it will not change the pattern of fluid flow. Secondly, reversing the direction of mechanical motion will simply reverse all velocities in the system. These properties of the Stokes equation severely restrict the range of feasible swimming strategies. Recent publications of biohybrid microswimmers include the use of sperm cells, contractive muscle cells, and bacteria as biological components, as they can efficiently convert chemical energy into movement, and additionally are capable of performing complicated motion depending on environmental conditions. In this sense, biohybrid microswimmer systems can be described as the combination of different functional components: cargo and carrier. The cargo is an element of interest to be moved (and possibly released) in a customized way. The carrier is the component responsible for the movement of the biohybrid, transporting the desired cargo, which is linked to its surface. The great majority of these systems rely on biological motile propulsion for the transportation of synthetic cargo for targeted drug delivery/ There are also examples of the opposite case: artificial microswimmers with biological cargo systems. Over the past decade, biohybrid microrobots, in which living mobile microorganisms are physically integrated with untethered artificial structures, have gained growing interest to enable the active locomotion and cargo delivery to a target destination. In addition to the motility, the intrinsic capabilities of sensing and eliciting an appropriate response to artificial and environmental changes make cell-based biohybrid microrobots appealing for transportation of cargo to the inaccessible cavities of the human body for local active delivery of diagnostic and therapeutic agents. Active locomotion, targeting and steering of concentrated therape

  Read more →
• 

  Intelligent control

  Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcement learning, evolutionary computation and genetic algorithms. == Overview == Intelligent control can be divided into the following major sub-domains: Neural network control Machine learning control Reinforcement learning Bayesian control Fuzzy control Neuro-fuzzy control Expert Systems Genetic control New control techniques are created continuously as new models of intelligent behavior are created and computational methods developed to support them. === Neural network controller === Neural networks have been used to solve problems in almost all spheres of science and technology. Neural network control basically involves two steps: System identification Control It has been shown that a feedforward network with nonlinear, continuous and differentiable activation functions have universal approximation capability. Recurrent networks have also been used for system identification. Given, a set of input-output data pairs, system identification aims to form a mapping among these data pairs. Such a network is supposed to capture the dynamics of a system. For the control part, deep reinforcement learning has shown its ability to control complex systems. === Bayesian controllers === Bayesian probability has produced a number of algorithms that are in common use in many advanced control systems, serving as state space estimators of some variables that are used in the controller. The Kalman filter and the Particle filter are two examples of popular Bayesian control components. The Bayesian approach to controller design often requires an important effort in deriving the so-called system model and measurement model, which are the mathematical relationships linking the state variables to the sensor measurements available in the controlled system. In this respect, it is very closely linked to the system-theoretic approach to control design.

  Read more →
• 

  Learning rate

  In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. Too high a learning rate will make the learning jump over minima, but too low a learning rate will either take too long to converge or get stuck in an undesirable local minimum. In order to achieve faster convergence, prevent oscillations and getting stuck in undesirable local minima the learning rate is often varied during training either in accordance to a learning rate schedule or by using an adaptive learning rate. The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization algorithms. == Learning rate schedule == Initial rate can be left as system default or can be selected using a range of techniques. A learning rate schedule changes the learning rate during learning and is most often changed between epochs/iterations. This is mainly done with two parameters: decay and momentum. There are many different learning rate schedules but the most common are time-based, step-based and exponential. Decay serves to settle the learning in a nice place and avoid oscillations, a situation that may arise when too high a constant learning rate makes the learning jump back and forth over a minimum, and is controlled by a hyperparameter. Momentum is analogous to a ball rolling down a hill; we want the ball to settle at the lowest point of the hill (corresponding to the lowest error). Momentum both speeds up the learning (increasing the learning rate) when the error cost gradient is heading in the same direction for a long time and also avoids local minima by 'rolling over' small bumps. Momentum is controlled by a hyperparameter analogous to a ball's mass which must be chosen manually—too high and the ball will roll over minima which we wish to find, too low and it will not fulfil its purpose. The formula for factoring in the momentum is more complex than for decay but is most often built in with deep learning libraries such as Keras. Time-based learning schedules alter the learning rate depending on the learning rate of the previous time iteration. Factoring in the decay the mathematical formula for the learning rate is: η n + 1 = η 0 1 + d n {\displaystyle \eta _{n+1}={\frac {\eta _{0}}{1+dn}}} where η {\displaystyle \eta } is the learning rate, η 0 {\displaystyle \eta _{0}} is the original learning rate, d {\displaystyle d} is a decay parameter and n {\displaystyle n} is the iteration step. Step-based learning schedules changes the learning rate according to some predefined steps. The decay application formula is here defined as: η n = η 0 d ⌊ 1 + n r ⌋ {\displaystyle \eta _{n}=\eta _{0}d^{\left\lfloor {\frac {1+n}{r}}\right\rfloor }} where η n {\displaystyle \eta _{n}} is the learning rate at iteration n {\displaystyle n} , η 0 {\displaystyle \eta _{0}} is the initial learning rate, d {\displaystyle d} is how much the learning rate should change at each drop (0.5 corresponds to a halving) and r {\displaystyle r} corresponds to the drop rate, or how often the rate should be dropped (10 corresponds to a drop every 10 iterations). The floor function ( ⌊ … ⌋ {\displaystyle \lfloor \dots \rfloor } ) here drops the value of its input to 0 for all values smaller than 1. Exponential learning schedules are similar to step-based, but instead of steps, a decreasing exponential function is used. The mathematical formula for factoring in the decay is: η n = η 0 e − d n {\displaystyle \eta _{n}=\eta _{0}e^{-dn}} where d {\displaystyle d} is a decay parameter. == Adaptive learning rate == The issue with learning rate schedules is that they all depend on hyperparameters that must be manually chosen for each given learning session and may vary greatly depending on the problem at hand or the model used. To combat this, there are many different types of adaptive gradient descent algorithms such as Adagrad, Adadelta, RMSprop, and Adam which are generally built into deep learning libraries such as Keras.

  Read more →
• 

  Aporia (company)

  Aporia is a machine learning observability platform based in Tel Aviv, Israel. The company has a US office located in San Jose, California. Aporia has developed software for monitoring and controlling undetected defects and failures used by other companies to detect and report anomalies, and warn in the early stages of faults. == History == Aporia was founded in 2019 by Liran Hason and Alon Gubkin. In April 2021, the company raised a $5 million seed round for its monitoring platform for ML models. In February 2022, the company closed a Series A round of $25 million for its ML observability platform. Aporia was named by Forbes as the Next Billion-Dollar Company in June 2022. In November, the company partnered with ClearML, an MLOPs platform, to improve ML pipeline optimization. In January 2023, Aporia launched Direct Data Connectors, a novel technology allowing organizations to monitor their ML models in minutes (previously the process of integrating ML monitoring into a customer’s cloud environment took weeks or more.) DDC (Direct Data Connectors) enables users to connect Aporia to their preferred data source and monitor all of their data at once, without data sampling or data duplication (which is a huge security risk for major organizations. In April 2023, Aporia announced the company partnered with Amazon Web Services (AWS) to provide more reliable ML observability to AWS consumers by deploying Aporia's architecture to their AWS environment, this will allow customers to monitor their models in production regardless of platform.

  Read more →
• 

  Conference app

  A conference app, also known as an event app or meeting app, is a mobile app developed to help attendees and meeting planners manage their conference experience. It typically includes conference proceedings and venue information, allowing users to create personalized schedules and engage with other users. A conference app can be a native app or web-based. In recent years, conference apps have gained in popularity as a sustainable solution for event management by reducing paper produced by printed materials. Advanced features often include real-time notifications for updates or changes, integration with virtual meeting platforms for hybrid or fully online events, and analytics tools for organizers to measure attendance and engagement. Additionally, some apps support sponsorship and exhibitor features, enabling businesses to showcase their products or services directly within the app.

  Read more →
• 

  Action model learning

  Action model learning (sometimes abbreviated action learning) is an area of machine learning concerned with the creation and modification of a software agent's knowledge about the effects and preconditions of the actions that can be executed within its environment. This knowledge is usually represented in a logic-based action description language and used as input for automated planners. Learning action models is important when goals change. When an agent acted for a while, it can use its accumulated knowledge about actions in the domain to make better decisions. Thus, learning action models differs from reinforcement learning. It enables reasoning about actions instead of expensive trials in the world. Action model learning is a form of inductive reasoning, where new knowledge is generated based on the agent's observations. The usual motivation for action model learning is the fact that manual specification of action models for planners is often a difficult, time-consuming, and error-prone task (especially in complex environments). == Action models == Given a training set E {\displaystyle E} consisting of examples e = ( s , a , s ′ ) {\displaystyle e=(s,a,s')} , where s , s ′ {\displaystyle s,s'} are observations of a world state from two consecutive time steps t , t ′ {\displaystyle t,t'} and a {\displaystyle a} is an action instance observed in time step t {\displaystyle t} , the goal of action model learning in general is to construct an action model ⟨ D , P ⟩ {\displaystyle \langle D,P\rangle } , where D {\displaystyle D} is a description of domain dynamics in action description formalism like STRIPS, ADL or PDDL and P {\displaystyle P} is a probability function defined over the elements of D {\displaystyle D} . However, many state of the art action learning methods assume determinism and do not induce P {\displaystyle P} . In addition to determinism, individual methods differ in how they deal with other attributes of domain (e.g. partial observability or sensoric noise). == Action learning methods == === State of the art === Recent action learning methods take various approaches and employ a wide variety of tools from different areas of artificial intelligence and computational logic. As an example of a method based on propositional logic, we can mention SLAF (Simultaneous Learning and Filtering) algorithm, which uses agent's observations to construct a long propositional formula over time and subsequently interprets it using a satisfiability (SAT) solver. Another technique, in which learning is converted into a satisfiability problem (weighted MAX-SAT in this case) and SAT solvers are used, is implemented in ARMS (Action-Relation Modeling System). Two mutually similar, fully declarative approaches to action learning were based on logic programming paradigm Answer Set Programming (ASP) and its extension, Reactive ASP. In another example, bottom-up inductive logic programming approach was employed. Several different solutions are not directly logic-based. For example, the action model learning using a perceptron algorithm or the multi level greedy search over the space of possible action models. In the older paper from 1992, the action model learning was studied as an extension of reinforcement learning. Nonetheless, further algorithms can be found that operate under different assumptions: FAMA can work even when some observations are missing, and it produces a general (lifted) planning model. It treats learning an action model like a planning problem, making sure the learned model matches the observations given. NOLAM can learn general action models even from noisy or imperfect data. LOCM focuses only on the order of actions in the data, ignoring any details about the states between those actions. The family of safe action model (SAM) learning methods create models that guarantee any plans made with them will actually work in the real world. There's also an extension called N-SAM that can learn action models with numeric conditions and effects. Additionally, numeric action models like N-SAM can be used to improve reinforcement learning (RL) performance through the RAMP algorithm. === Literature === Most action learning research papers are published in journals and conferences focused on artificial intelligence in general (e.g. Journal of Artificial Intelligence Research (JAIR), Artificial Intelligence, Applied Artificial Intelligence (AAI) or AAAI conferences). Despite mutual relevance of the topics, action model learning is usually not addressed in planning conferences like the International Conference on Automated Planning and Scheduling (ICAPS).

  Read more →
• 

  Admissible heuristic

  In computer science, specifically in algorithms related to pathfinding, a heuristic function is said to be admissible if it never overestimates the cost of reaching the goal, i.e. the cost it estimates to reach the goal is not higher than the lowest possible cost from the current point in the path. In other words, it should act as a lower bound. It is related to the concept of consistent heuristics. While all consistent heuristics are admissible, not all admissible heuristics are consistent. == Search algorithms == An admissible heuristic is used to estimate the cost of reaching the goal state in an informed search algorithm. In order for a heuristic to be admissible to the search problem, the estimated cost must always be lower than or equal to the actual cost of reaching the goal state. The search algorithm uses the admissible heuristic to find an estimated optimal path to the goal state from the current node. For example, in A search the evaluation function (where n {\displaystyle n} is the current node) is: f ( n ) = g ( n ) + h ( n ) {\displaystyle f(n)=g(n)+h(n)} where f ( n ) {\displaystyle f(n)} = the evaluation function. g ( n ) {\displaystyle g(n)} = the cost from the start node to the current node h ( n ) {\displaystyle h(n)} = estimated cost from current node to goal. h ( n ) {\displaystyle h(n)} is calculated using the heuristic function. With a non-admissible heuristic, the A algorithm could overlook the optimal solution to a search problem due to an overestimation in f ( n ) {\displaystyle f(n)} . == Formulation == n {\displaystyle n} is a node h {\displaystyle h} is a heuristic h ( n ) {\displaystyle h(n)} is cost indicated by h {\displaystyle h} to reach a goal from n {\displaystyle n} h ∗ ( n ) {\displaystyle h^{}(n)} is the optimal cost to reach a goal from n {\displaystyle n} h ( n ) {\displaystyle h(n)} is admissible if, ∀ n {\displaystyle \forall n} h ( n ) ≤ h ∗ ( n ) {\displaystyle h(n)\leq h^{}(n)} == Construction == An admissible heuristic can be derived from a relaxed version of the problem, or by information from pattern databases that store exact solutions to subproblems of the problem, or by using inductive learning methods. == Examples == Two different examples of admissible heuristics apply to the fifteen puzzle problem: Hamming distance Manhattan distance The Hamming distance is the total number of misplaced tiles. It is clear that this heuristic is admissible since the total number of moves to order the tiles correctly is at least the number of misplaced tiles (each tile not in place must be moved at least once). The cost (number of moves) to the goal (an ordered puzzle) is at least the Hamming distance of the puzzle. The Manhattan distance of a puzzle is defined as: h ( n ) = ∑ all tiles d i s t a n c e ( tile, correct position ) {\displaystyle h(n)=\sum _{\text{all tiles}}{\mathit {distance}}({\text{tile, correct position}})} Consider the puzzle below in which the player wishes to move each tile such that the numbers are ordered. The Manhattan distance is an admissible heuristic in this case because every tile will have to be moved at least the number of spots in between itself and its correct position. The subscripts show the Manhattan distance for each tile. The total Manhattan distance for the shown puzzle is: h ( n ) = 3 + 1 + 0 + 1 + 2 + 3 + 3 + 4 + 3 + 2 + 4 + 4 + 4 + 1 + 1 = 36 {\displaystyle h(n)=3+1+0+1+2+3+3+4+3+2+4+4+4+1+1=36} == Optimality proof == If an admissible heuristic is used in an algorithm that, per iteration, progresses only the path of lowest evaluation (current cost + heuristic) of several candidate paths, terminates the moment its exploration reaches the goal and, crucially, closes all optimal paths before terminating (something that's possible with A search algorithm if special care isn't taken), then this algorithm can only terminate on an optimal path. To see why, consider the following proof by contradiction: Assume such an algorithm managed to terminate on a path T with a true cost Ttrue greater than the optimal path S with true cost Strue. This means that before terminating, the evaluated cost of T was less than or equal to the evaluated cost of S (or else S would have been picked). Denote these evaluated costs Teval and Seval respectively. The above can be summarized as follows, Strue < Ttrue Teval ≤ Seval If our heuristic is admissible it follows that at this penultimate step Teval = Ttrue because any increase on the true cost by the heuristic on T would be inadmissible and the heuristic cannot be negative. On the other hand, an admissible heuristic would require that Seval ≤ Strue which combined with the above inequalities gives us Teval < Ttrue and more specifically Teval ≠ Ttrue. As Teval and Ttrue cannot be both equal and unequal our assumption must have been false and so it must be impossible to terminate on a more costly than optimal path. As an example, let us say we have costs as follows:(the cost above/below a node is the heuristic, the cost at an edge is the actual cost) 0 10 0 100 0 START ---- O ----- GOAL | | 0| |100 | | O ------- O ------ O 100 1 100 1 100 So clearly we would start off visiting the top middle node, since the expected total cost, i.e. f ( n ) {\displaystyle f(n)} , is 10 + 0 = 10 {\displaystyle 10+0=10} . Then the goal would be a candidate, with f ( n ) {\displaystyle f(n)} equal to 10 + 100 + 0 = 110 {\displaystyle 10+100+0=110} . Then we would clearly pick the bottom nodes one after the other, followed by the updated goal, since they all have f ( n ) {\displaystyle f(n)} lower than the f ( n ) {\displaystyle f(n)} of the current goal, i.e. their f ( n ) {\displaystyle f(n)} is 100 , 101 , 102 , 102 {\displaystyle 100,101,102,102} . So even though the goal was a candidate, we could not pick it because there were still better paths out there. This way, an admissible heuristic can ensure optimality. However, note that although an admissible heuristic can guarantee final optimality, it is not necessarily efficient.

  Read more →
• 

  Label noise

  Label noise refers to errors or inaccuracies in the class labels of data instances. This is a widespread issue in machine learning datasets, arising from human annotator mistakes, unclear labeling instructions, automated labeling methods, or adversarial attacks in supervised learning. Label noise can be roughly divided into random noise, where labels are flipped independently of input features, and systematic noise, where mislabeling is dependent on certain patterns or biases in the data. Label noise can be damaging to model performance, especially for complex models that may overfit to noisy labels rather than generalizable patterns. Many approaches have been proposed to deal with the effects of label noise, including robust loss functions, noise-tolerant algorithms, data cleaning methods, and semi-supervised learning approaches. To reduce the impact of wrong labels during training, techniques like label smoothing, sample reweighting and using trusted validation sets are used. The role of noise-robust training paradigms and curriculum learning strategies to improve resilience against mislabeled data is also explored in recent research.

  Read more →
• 

  Zé Delivery

  Zé Delivery is a startup developed by Brazilian drinks company AmBev which offers an app for delivering drinks. The app is available for Android and iOS. Created in 2016 by AmBev's ZX Ventures hub, the service has an international presence in Argentina, Paraguay, Bolivia, Panama and the Dominican Republic. It is also present in more than 300 Brazilian cities. Because it has an extensive category of alcoholic beverages, the service is only used by people over 18. It also offers soft drinks, juices, energy drinks and other non-alcoholic beverages.

  Read more →
• 

  Tensor (machine learning)

  In machine learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor"), may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition factors data tensors into smaller tensors. Operations on data tensors can be expressed in terms of matrix multiplication and the Kronecker product. The computation of gradients, a crucial aspect of backpropagation, can be performed using software libraries such as PyTorch and TensorFlow. Computations are often performed on graphics processing units (GPUs) using CUDA, and on dedicated hardware such as Google's Tensor Processing Unit or Nvidia's Tensor core. These developments have greatly accelerated neural network architectures, and increased the size and complexity of models that can be trained. == History == A tensor is by definition a multilinear map. In mathematics, this may express a multilinear relationship between sets of algebraic objects. In physics, tensor fields, considered as tensors at each point in space, are useful in expressing mechanics such as stress or elasticity. In machine learning, the exact use of tensors depends on the statistical approach being used. In 2001, the field of signal processing and statistics were making use of tensor methods. Pierre Comon surveys the early adoption of tensor methods in the fields of telecommunications, radio surveillance, chemometrics and sensor processing. Linear tensor rank methods (such as, Parafac/CANDECOMP) analyzed M-way arrays ("data tensors") composed of higher order statistics that were employed in blind source separation problems to compute a linear model of the data. He noted several early limitations in determining the tensor rank and efficient tensor rank decomposition. In the early 2000s, multilinear tensor methods crossed over into computer vision, computer graphics and machine learning with papers by Vasilescu or in collaboration with Terzopoulos, such as Human Motion Signatures, TensorFaces TensorTextures and Multilinear Projection. Multilinear algebra, the algebra of higher-order tensors, is a suitable and transparent framework for analyzing the multifactor structure of an ensemble of observations and for addressing the difficult problem of disentangling the causal factors based on second order or higher order statistics associated with each causal factor. Tensor (multilinear) factor analysis disentangles and reduces the influence of different causal factors with multilinear subspace learning. When treating an image or a video as a 2- or 3-way array, i.e., "data matrix/tensor", tensor methods reduce spatial or time redundancies as demonstrated by Wang and Ahuja. Yoshua Bengio, Geoff Hinton and their collaborators briefly discuss the relationship between deep neural networks and tensor factor analysis beyond the use of M-way arrays ("data tensors") as inputs. One of the early uses of tensors for neural networks appeared in natural language processing. A single word can be expressed as a vector via Word2vec. Thus a relationship between two words can be encoded in a matrix. However, for more complex relationships such as subject-object-verb, it is necessary to build higher-dimensional networks. In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From 2014 to 2015, tensor methods become more common in convolutional neural networks (CNNs). Tensor methods organize neural network weights in a "data tensor", analyze and reduce the number of neural network weights. Lebedev et al. accelerated CNN networks for character classification (the recognition of letters and digits in images) by using 4D kernel tensors. == Definition == Let F {\displaystyle \mathbb {F} } be a field (such as the real numbers R {\displaystyle \mathbb {R} } or the complex numbers C {\displaystyle \mathbb {C} } ). A tensor T ∈ F I 1 × I 2 × … × I C {\displaystyle {\mathcal {T}}\in {\mathbb {F} }^{I_{1}\times I_{2}\times \ldots \times I_{C}}} is a multilinear transformation from a set of domain vector spaces to a range vector space: T : { F I 1 × F I 2 × … F I C } ↦ F I 0 {\displaystyle {\mathcal {T}}:\{{\mathbb {F} }^{I_{1}}\times {\mathbb {F} }^{I_{2}}\times \ldots {\mathbb {F} }^{I_{C}}\}\mapsto {\mathbb {F} }^{I_{0}}} Here, C {\displaystyle C} and I 0 , I 1 , … , I C {\displaystyle I_{0},I_{1},\ldots ,I_{C}} are positive integers, and ( C + 1 ) {\displaystyle (C+1)} is the number of modes of a tensor (also known as the number of ways of a multi-way array). The dimensionality of mode c {\displaystyle c} is I c {\displaystyle I_{c}} , for 0 ≤ c ≤ C {\displaystyle 0\leq c\leq C} . In statistics and machine learning, an image is vectorized when viewed as a single observation, and a collection of vectorized images is organized as a "data tensor". For example, a set of facial images { d i p , i e , i l , i v ∈ R I X } {\displaystyle \{{\mathbb {d} }_{i_{p},i_{e},i_{l},i_{v}}\in {\mathbb {R} }^{I_{X}}\}} with I X {\displaystyle I_{X}} pixels that are the consequences of multiple causal factors, such as a facial geometry i p ( 1 ≤ i p ≤ I P ) {\displaystyle i_{p}(1\leq i_{p}\leq I_{P})} , an expression i e ( 1 ≤ i e ≤ I E ) {\displaystyle i_{e}(1\leq i_{e}\leq I_{E})} , an illumination condition i l ( 1 ≤ i l ≤ I L ) {\displaystyle i_{l}(1\leq i_{l}\leq I_{L})} , and a viewing condition i v ( 1 ≤ i v ≤ I V ) {\displaystyle i_{v}(1\leq i_{v}\leq I_{V})} may be organized into a data tensor (ie. multiway array) D ∈ R I X × I P × I E × I L × V {\displaystyle {\mathcal {D}}\in {\mathbb {R} }^{I_{X}\times I_{P}\times I_{E}\times I_{L}\times V}} where I P {\displaystyle I_{P}} are the total number of facial geometries, I E {\displaystyle I_{E}} are the total number of expressions, I L {\displaystyle I_{L}} are the total number of illumination conditions, and I V {\displaystyle I_{V}} are the total number of viewing conditions. Tensor factorizations methods such as TensorFaces and multilinear (tensor) independent component analysis factorizes the data tensor into a set of vector spaces that span the causal factor representations, where an image is the result of tensor transformation T {\displaystyle {\mathcal {T}}} that maps a set of causal factor representations to the pixel space. Another approach to using tensors in machine learning is to embed various data types directly. For example, a grayscale image, commonly represented as a discrete 2-way array D ∈ R I R X × I C X {\displaystyle {\mathbf {D} }\in {\mathbb {R} }^{I_{RX}\times I_{CX}}} with dimensionality I R X × I C X {\displaystyle I_{RX}\times I_{CX}} where I R X {\displaystyle I_{RX}} are the number of rows and I C X {\displaystyle I_{CX}} are the number of columns. When an image is treated as 2-way array or 2nd order tensor (i.e. as a collection of column/row observations), tensor factorization methods compute the image column space, the image row space and the normalized PCA coefficients or the ICA coefficients. Similarly, a color image with RGB channels, D ∈ R N × M × 3 . {\displaystyle {\mathcal {D}}\in \mathbb {R} ^{N\times M\times 3}.} may be viewed as a 3rd order data tensor or 3-way array.-------- In natural language processing, a word might be expressed as a vector v {\displaystyle v} via the Word2vec algorithm. Thus v {\displaystyle v} becomes a mode-1 tensor v ↦ A ∈ R N . {\displaystyle v\mapsto {\mathcal {A}}\in \mathbb {R} ^{N}.} The embedding of subject-object-verb semantics requires embedding relationships among three words. Because a word is itself a vector, subject-object-verb semantics could be expressed using mode-3 tensors v a × v b × v c ↦ A ∈ R N × N × N . {\displaystyle v_{a}\times v_{b}\times v_{c}\mapsto {\mathcal {A}}\in \mathbb {R} ^{N\times N\times N}.} In practice the neural network designer is primarily concerned with the specification of embeddings, the connection of tensor layers, and the operations performed on them in a network. Modern machine learning frameworks manage the optimization, tensor factorization and backpropagation automatically. === As unit values === Tensors may be used as the unit values of neural networks which extend the concept of scalar, vector and matrix values to multiple dimensions. The output value of single layer unit y m {\displaystyle y_{m}} is the sum-product of its input units and the connection weights filtered through the activation function f {\displaystyle f} : y m = f ( ∑ n x n u m , n ) , {\displaystyle y_{m}=f\left(\sum _{n}x_{n}u_{m,n}\right),} where y m ∈ R .

  Read more →
• 

  Conditional random field

  Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. The kind of graph used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions. Other examples where CRFs are used are: labeling or parsing of sequential data for natural language processing or biological sequences, part-of-speech tagging, shallow parsing, named entity recognition, gene finding, peptide critical functional region finding, and object recognition and image segmentation in computer vision. == Description == CRFs are a type of discriminative undirected probabilistic graphical model. Lafferty, McCallum and Pereira define a CRF on observations X {\displaystyle {\boldsymbol {X}}} and random variables Y {\displaystyle {\boldsymbol {Y}}} as follows: Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph such that Y = ( Y v ) v ∈ V {\displaystyle {\boldsymbol {Y}}=({\boldsymbol {Y}}_{v})_{v\in V}} , so that Y {\displaystyle {\boldsymbol {Y}}} is indexed by the vertices of G {\displaystyle G} . Then ( X , Y ) {\displaystyle ({\boldsymbol {X}},{\boldsymbol {Y}})} is a conditional random field when each random variable Y v {\displaystyle {\boldsymbol {Y}}_{v}} , conditioned on X {\displaystyle {\boldsymbol {X}}} , obeys the Markov property with respect to the graph; that is, its probability is dependent only on its neighbours in G and not its past states: P ( Y v | X , { Y w : w ≠ v } ) = P ( Y v | X , { Y w : w ∼ v } ) {\displaystyle P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\neq v\})=P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\sim v\})} , where w ∼ v {\displaystyle {\mathit {w}}\sim v} means that w {\displaystyle w} and v {\displaystyle v} are neighbors in G {\displaystyle G} . What this means is that a CRF is an undirected graphical model whose nodes can be divided into exactly two disjoint sets X {\displaystyle {\boldsymbol {X}}} and Y {\displaystyle {\boldsymbol {Y}}} , the observed and output variables, respectively; the conditional distribution p ( Y | X ) {\displaystyle p({\boldsymbol {Y}}|{\boldsymbol {X}})} is then modeled. === Inference === For general graphs, the problem of exact inference in CRFs is intractable. The inference problem for a CRF is basically the same as for an MRF and the same arguments hold. However, there exist special cases for which exact inference is feasible: If the graph is a chain or a tree, message passing algorithms yield exact solutions. The algorithms used in these cases are analogous to the forward-backward and Viterbi algorithm for the case of HMMs. If the CRF only contains pair-wise potentials and the energy is submodular, combinatorial min cut/max flow algorithms yield exact solutions. If exact inference is impossible, several algorithms can be used to obtain approximate solutions. These include: Loopy belief propagation Alpha expansion Mean field inference Linear programming relaxations === Parameter learning === Learning the parameters θ {\displaystyle \theta } is usually done by maximum likelihood learning for p ( Y i | X i ; θ ) {\displaystyle p(Y_{i}|X_{i};\theta )} . If all nodes have exponential family distributions and all nodes are observed during training, this optimization is convex. It can be solved for example using gradient descent algorithms, or Quasi-Newton methods such as the L-BFGS algorithm. On the other hand, if some variables are unobserved, the inference problem has to be solved for these variables. Exact inference is intractable in general graphs, so approximations have to be used. === Examples === In sequence modeling, the graph of interest is usually a chain graph. An input sequence of observed variables X {\displaystyle X} represents a sequence of observations and Y {\displaystyle Y} represents a hidden (or unknown) state variable that needs to be inferred given the observations. The Y i {\displaystyle Y_{i}} are structured to form a chain, with an edge between each Y i − 1 {\displaystyle Y_{i-1}} and Y i {\displaystyle Y_{i}} . As well as having a simple interpretation of the Y i {\displaystyle Y_{i}} as "labels" for each element in the input sequence, this layout admits efficient algorithms for: model training, learning the conditional distributions between the Y i {\displaystyle Y_{i}} and feature functions from some corpus of training data. decoding, determining the probability of a given label sequence Y {\displaystyle Y} given X {\displaystyle X} . inference, determining the most likely label sequence Y {\displaystyle Y} given X {\displaystyle X} . The conditional dependency of each Y i {\displaystyle Y_{i}} on X {\displaystyle X} is defined through a fixed set of feature functions of the form f ( i , Y i − 1 , Y i , X ) {\displaystyle f(i,Y_{i-1},Y_{i},X)} , which can be thought of as measurements on the input sequence that partially determine the likelihood of each possible value for Y i {\displaystyle Y_{i}} . The model assigns each feature a numerical weight and combines them to determine the probability of a certain value for Y i {\displaystyle Y_{i}} . Linear-chain CRFs have many of the same applications as conceptually simpler hidden Markov models (HMMs), but relax certain assumptions about the input and output sequence distributions. An HMM can loosely be understood as a CRF with very specific feature functions that use constant probabilities to model state transitions and emissions. Conversely, a CRF can loosely be understood as a generalization of an HMM that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence. Notably, in contrast to HMMs, CRFs can contain any number of feature functions, the feature functions can inspect the entire input sequence X {\displaystyle X} at any point during inference, and the range of the feature functions need not have a probabilistic interpretation. == Variants == === Higher-order CRFs and semi-Markov CRFs === CRFs can be extended into higher order models by making each Y i {\displaystyle Y_{i}} dependent on a fixed number k {\displaystyle k} of previous variables Y i − k , . . . , Y i − 1 {\displaystyle Y_{i-k},...,Y_{i-1}} . In conventional formulations of higher order CRFs, training and inference are only practical for small values of k {\displaystyle k} (such as k ≤ 5), since their computational cost increases exponentially with k {\displaystyle k} . However, another recent advance has managed to ameliorate these issues by leveraging concepts and tools from the field of Bayesian nonparametrics. Specifically, the CRF-infinity approach constitutes a CRF-type model that is capable of learning infinitely-long temporal dynamics in a scalable fashion. This is effected by introducing a novel potential function for CRFs that is based on the Sequence Memoizer (SM), a nonparametric Bayesian model for learning infinitely-long dynamics in sequential observations. To render such a model computationally tractable, CRF-infinity employs a mean-field approximation of the postulated novel potential functions (which are driven by an SM). This allows for devising efficient approximate training and inference algorithms for the model, without undermining its capability to capture and model temporal dependencies of arbitrary length. There exists another generalization of CRFs, the semi-Markov conditional random field (semi-CRF), which models variable-length segmentations of the label sequence Y {\displaystyle Y} . This provides much of the power of higher-order CRFs to model long-range dependencies of the Y i {\displaystyle Y_{i}} , at a reasonable computational cost. Finally, large-margin models for structured prediction, such as the structured Support Vector Machine can be seen as an alternative training procedure to CRFs. === Latent-dynamic conditional random field === Latent-dynamic conditional random fields (LDCRF) or discriminative probabilistic latent variable models (DPLVM) are a type of CRFs for sequence tagging tasks. They are latent variable models that are trained discriminatively. In an LDCRF, like in any sequence tagging task, given a sequence of observations x = x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} , the main problem the model must solve is how to assign a sequence of labels y = y 1 , … , y n {\displaystyle y_{1},\dots ,y_{n}} from one finite set

  Read more →