AI Image Generation Tools

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  Neurorobotics

  Neurorobotics is the combined study of neuroscience, robotics, and artificial intelligence. It is the science and technology of embodied autonomous neural systems. Neural systems include brain-inspired algorithms (e.g. connectionist networks), computational models of biological neural networks (e.g. artificial spiking neural networks, large-scale simulations of neural microcircuits) and actual biological systems (e.g. in vivo and in vitro neural nets). Such neural systems can be embodied in machines with mechanic or any other forms of physical actuation. This includes robots, prosthetic or wearable systems but also, at smaller scale, micro-machines and, at the larger scales, furniture and infrastructures. Neurorobotics is that branch of neuroscience with robotics, which deals with the study and application of science and technology of embodied autonomous neural systems like brain-inspired algorithms. It is based on the idea that the brain is embodied and the body is embedded in the environment. Therefore, most neurorobots are required to function in the real world, as opposed to a simulated environment. Beyond brain-inspired algorithms for robots neurorobotics may also involve the design of brain-controlled robot systems. == Major classes of models == Neurorobots can be divided into various major classes based on the robot's purpose. Each class is designed to implement a specific mechanism of interest for study. Common types of neurorobots are those used to study motor control, memory, action selection, and perception. === Locomotion and motor control === Neurorobots are often used to study motor feedback and control systems, and have proved their merit in developing controllers for robots. Locomotion is modeled by a number of neurologically inspired theories on the action of motor systems. Locomotion control has been mimicked using models or central pattern generators, clumps of neurons capable of driving repetitive behavior, to make four-legged walking robots. Other groups have expanded the idea of combining rudimentary control systems into a hierarchical set of simple autonomous systems. These systems can formulate complex movements from a combination of these rudimentary subsets. This theory of motor action is based on the organization of cortical columns, which progressively integrate from simple sensory input into a complex afferent signals, or from complex motor programs to simple controls for each muscle fiber in efferent signals, forming a similar hierarchical structure. Another method for motor control uses learned error correction and predictive controls to form a sort of simulated muscle memory. In this model, awkward, random, and error-prone movements are corrected for using error feedback to produce smooth and accurate movements over time. The controller learns to create the correct control signal by predicting the error. Using these ideas, robots have been designed which can learn to produce adaptive arm movements or to avoid obstacles in a course. === Learning and memory systems === Robots designed to test theories of animal memory systems. Many studies examine the memory system of rats, particularly the rat hippocampus, dealing with place cells, which fire for a specific location that has been learned. Systems modeled after the rat hippocampus are generally able to learn mental maps of the environment, including recognizing landmarks and associating behaviors with them, allowing them to predict the upcoming obstacles and landmarks. Another study has produced a robot based on the proposed learning paradigm of barn owls for orientation and localization based on primarily auditory, but also visual stimuli. The hypothesized method involves synaptic plasticity and neuromodulation, a mostly chemical effect in which reward neurotransmitters such as dopamine or serotonin affect the firing sensitivity of a neuron to be sharper. The robot used in the study adequately matched the behavior of barn owls. Furthermore, the close interaction between motor output and auditory feedback proved to be vital in the learning process, supporting active sensing theories that are involved in many of the learning models. Neurorobots in these studies are presented with simple mazes or patterns to learn. Some of the problems presented to the neurorobot include recognition of symbols, colors, or other patterns and execute simple actions based on the pattern. In the case of the barn owl simulation, the robot had to determine its location and direction to navigate in its environment. === Action selection and value systems === Action selection studies deal with negative or positive weighting to an action and its outcome. Neurorobots can and have been used to study simple ethical interactions, such as the classical thought experiment where there are more people than a life raft can hold, and someone must leave the boat to save the rest. However, more neurorobots used in the study of action selection contend with much simpler persuasions such as self-preservation or perpetuation of the population of robots in the study. These neurorobots are modeled after the neuromodulation of synapses to encourage circuits with positive results. In biological systems, neurotransmitters such as dopamine or acetylcholine positively reinforce neural signals that are beneficial. One study of such interaction involved the robot Darwin VII, which used visual, auditory, and a simulated taste input to "eat" conductive metal blocks. The arbitrarily chosen good blocks had a striped pattern on them while the bad blocks had a circular shape on them. The taste sense was simulated by conductivity of the blocks. The robot had positive and negative feedbacks to the taste based on its level of conductivity. The researchers observed the robot to see how it learned its action selection behaviors based on the inputs it had. Other studies have used herds of small robots which feed on batteries strewn about the room, and communicate its findings to other robots. === Sensory perception === Neurorobots have also been used to study sensory perception, particularly vision. These are primarily systems that result from embedding neural models of sensory pathways in automatas. This approach gives exposure to the sensory signals that occur during behavior and also enables a more realistic assessment of the degree of robustness of the neural model. It is well known that changes in the sensory signals produced by motor activity provide useful perceptual cues that are used extensively by organisms. For example, researchers have used the depth information that emerges during replication of human head and eye movements to establish robust representations of the visual scene. == Biological robots == Biological robots are not officially neurorobots in that they are not neurologically inspired AI systems, but actual neuron tissue wired to a robot. This employs the use of cultured neural networks to study brain development or neural interactions. These typically consist of a neural culture raised on a multielectrode array (MEA), which is capable of both recording the neural activity and stimulating the tissue. In some cases, the MEA is connected to a computer which presents a simulated environment to the brain tissue and translates brain activity into actions in the simulation, as well as providing sensory feedback The ability to record neural activity gives researchers a window into a brain, which they can use to learn about a number of the same issues neurorobots are used for. An area of concern with the biological robots is ethics. Many questions are raised about how to treat such experiments. The central question concerns consciousness and whether or not the rat brain experiences it. There are many theories about how to define consciousness. == Implications for neuroscience == Neuroscientists benefit from neurorobotics because it provides a blank slate to test various possible methods of brain function in a controlled and testable environment. While robots are more simplified versions of the systems they emulate, they are more specific, allowing more direct testing of the issue at hand. They also have the benefit of being accessible at all times, while it is more difficult to monitor large portions of a brain while the human or animal is active, especially individual neurons. The development of neuroscience has produced neural treatments. These include pharmaceuticals and neural rehabilitation. Progress is dependent on an intricate understanding of the brain and how exactly it functions. It is difficult to study the brain, especially in humans, due to the danger associated with cranial surgeries. Neurorobots can improved the range of tests and experiments that can be performed in the study of neural processes.

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  UIMA

  UIMA ( yoo-EE-mə), short for Unstructured Information Management Architecture, is an OASIS standard for content analytics, originally developed at IBM. It provides a component software architecture for the development, discovery, composition, and deployment of multi-modal analytics for the analysis of unstructured information and integration with search technologies. == Structure == The UIMA architecture can be thought of in four dimensions: It specifies component interfaces in an analytics pipeline. It describes a set of design patterns. It suggests two data representations: an in-memory representation of annotations for high-performance analytics and an XML representation of annotations for integration with remote web services. It suggests development roles allowing tools to be used by users with diverse skills. == Implementations and uses == Apache UIMA, a reference implementation of UIMA, is maintained by the Apache Software Foundation. UIMA is used in a number of software projects: IBM Research's Watson uses UIMA for analyzing unstructured data. The Clinical Text Analysis and Knowledge Extraction System (Apache cTAKES) is a UIMA-based system for information extraction from medical records. DKPro Core is a collection of reusable UIMA components for general-purpose natural language processing.

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  VIGRA

  VIGRA is the abbreviation for "Vision with Generic Algorithms". It is a free open-source computer vision library which focuses on customizable algorithms and data structures. VIGRA component can be easily adapted to specific needs of target application without compromising execution speed, by using template techniques similar to those in the C++ Standard Template Library. == Features == VIGRA is cross-platform, with working builds on Microsoft Windows, Mac OS X, Linux, and OpenBSD. Since version 1.7.1, VIGRA provides Python bindings based on numpy framework. == History == VIGRA was originally designed and implemented by scientists at University of Hamburg faculty of computer science; its core maintainers are now working at Heidelberg Collaboratory for Image Processing (HCI) University of Heidelberg. In the meantime, many developers have contributed to the project. == Application == CellCognition and ilastik uses VIGRA computer vision library. OpenOffice.org uses VIGRA as part of its headless software rendering backend; LibreOffice does so until version 5.2.

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  VIGRA

  VIGRA is the abbreviation for "Vision with Generic Algorithms". It is a free open-source computer vision library which focuses on customizable algorithms and data structures. VIGRA component can be easily adapted to specific needs of target application without compromising execution speed, by using template techniques similar to those in the C++ Standard Template Library. == Features == VIGRA is cross-platform, with working builds on Microsoft Windows, Mac OS X, Linux, and OpenBSD. Since version 1.7.1, VIGRA provides Python bindings based on numpy framework. == History == VIGRA was originally designed and implemented by scientists at University of Hamburg faculty of computer science; its core maintainers are now working at Heidelberg Collaboratory for Image Processing (HCI) University of Heidelberg. In the meantime, many developers have contributed to the project. == Application == CellCognition and ilastik uses VIGRA computer vision library. OpenOffice.org uses VIGRA as part of its headless software rendering backend; LibreOffice does so until version 5.2.

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  Semantic folding

  Semantic folding theory describes a procedure for encoding the semantics of natural language text in a semantically grounded binary representation. This approach provides a framework for modelling how language data is processed by the neocortex. == Theory == Semantic folding theory draws inspiration from Douglas R. Hofstadter's Analogy as the Core of Cognition which suggests that the brain makes sense of the world by identifying and applying analogies. The theory hypothesises that semantic data must therefore be introduced to the neocortex in such a form as to allow the application of a similarity measure and offers, as a solution, the sparse binary vector employing a two-dimensional topographic semantic space as a distributional reference frame. The theory builds on the computational theory of the human cortex known as hierarchical temporal memory (HTM), and positions itself as a complementary theory for the representation of language semantics. A particular strength claimed by this approach is that the resulting binary representation enables complex semantic operations to be performed simply and efficiently at the most basic computational level. == Two-dimensional semantic space == Analogous to the structure of the neocortex, Semantic Folding theory posits the implementation of a semantic space as a two-dimensional grid. This grid is populated by context-vectors in such a way as to place similar context-vectors closer to each other, for instance, by using competitive learning principles. This vector space model is presented in the theory as an equivalence to the well known word space model described in the information retrieval literature. Given a semantic space (implemented as described above) a word-vector can be obtained for any given word Y by employing the following algorithm: For each position X in the semantic map (where X represents cartesian coordinates) if the word Y is contained in the context-vector at position X then add 1 to the corresponding position in the word-vector for Y else add 0 to the corresponding position in the word-vector for Y The result of this process will be a word-vector containing all the contexts in which the word Y appears and will therefore be representative of the semantics of that word in the semantic space. It can be seen that the resulting word-vector is also in a sparse distributed representation (SDR) format [Schütze, 1993] & [Sahlgreen, 2006]. Some properties of word-SDRs that are of particular interest with respect to computational semantics are: high noise resistance: As a result of similar contexts being placed closer together in the underlying map, word-SDRs are highly tolerant of false or shifted "bits". boolean logic: It is possible to manipulate word-SDRs in a meaningful way using boolean (OR, AND, exclusive-OR) and/or arithmetical (SUBtract) functions . sub-sampling: Word-SDRs can be sub-sampled to a high degree without any appreciable loss of semantic information. topological two-dimensional representation: The SDR representation maintains the topological distribution of the underlying map therefore words with similar meanings will have similar word-vectors. This suggests that a variety of measures can be applied to the calculation of semantic similarity, from a simple overlap of vector elements, to a range of distance measures such as: Euclidean distance, Hamming distance, Jaccard distance, cosine similarity, Levenshtein distance, Sørensen-Dice index, etc. == Semantic spaces == Semantic spaces in the natural language domain aim to create representations of natural language that are capable of capturing meaning. The original motivation for semantic spaces stems from two core challenges of natural language: Vocabulary mismatch (the fact that the same meaning can be expressed in many ways) and ambiguity of natural language (the fact that the same term can have several meanings). The application of semantic spaces in natural language processing (NLP) aims at overcoming limitations of rule-based or model-based approaches operating on the keyword level. The main drawback with these approaches is their brittleness, and the large manual effort required to create either rule-based NLP systems or training corpora for model learning. Rule-based and machine learning-based models are fixed on the keyword level and break down if the vocabulary differs from that defined in the rules or from the training material used for the statistical models. Research in semantic spaces dates back more than 20 years. In 1996, two papers were published that raised a lot of attention around the general idea of creating semantic spaces: latent semantic analysis from Microsoft and Hyperspace Analogue to Language from the University of California. However, their adoption was limited by the large computational effort required to construct and use those semantic spaces. A breakthrough with regard to the accuracy of modelling associative relations between words (e.g. "spider-web", "lighter-cigarette", as opposed to synonymous relations such as "whale-dolphin", "astronaut-driver") was achieved by explicit semantic analysis (ESA) in 2007. ESA was a novel (non-machine learning) based approach that represented words in the form of vectors with 100,000 dimensions (where each dimension represents an Article in Wikipedia). However practical applications of the approach are limited due to the large number of required dimensions in the vectors. More recently, advances in neural networking techniques in combination with other new approaches (tensors) led to a host of new recent developments: Word2vec from Google and GloVe from Stanford University. Semantic folding represents a novel, biologically inspired approach to semantic spaces where each word is represented as a sparse binary vector with 16,000 dimensions (a semantic fingerprint) in a 2D semantic map (the semantic universe). Sparse binary representation are advantageous in terms of computational efficiency, and allow for the storage of very large numbers of possible patterns. == Visualization == The topological distribution over a two-dimensional grid (outlined above) lends itself to a bitmap type visualization of the semantics of any word or text, where each active semantic feature can be displayed as e.g. a pixel. As can be seen in the images shown here, this representation allows for a direct visual comparison of the semantics of two (or more) linguistic items. Image 1 clearly demonstrates that the two disparate terms "dog" and "car" have, as expected, very obviously different semantics. Image 2 shows that only one of the meaning contexts of "jaguar", that of "Jaguar" the car, overlaps with the meaning of Porsche (indicating partial similarity). Other meaning contexts of "jaguar" e.g. "jaguar" the animal clearly have different non-overlapping contexts. The visualization of semantic similarity using Semantic Folding bears a strong resemblance to the fMRI images produced in a research study conducted by A.G. Huth et al., where it is claimed that words are grouped in the brain by meaning. voxels, little volume segments of the brain, were found to follow a pattern were semantic information is represented along the boundary of the visual cortex with visual and linguistic categories represented on posterior and anterior side respectively.

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  Induction of regular languages

  In computational learning theory, induction of regular languages refers to the task of learning a formal description (e.g. grammar) of a regular language from a given set of example strings. Although E. Mark Gold has shown that not every regular language can be learned this way (see language identification in the limit), approaches have been investigated for a variety of subclasses. They are sketched in this article. For learning of more general grammars, see Grammar induction. == Definitions == A regular language is defined as a (finite or infinite) set of strings that can be described by one of the mathematical formalisms called "finite automaton", "regular grammar", or "regular expression", all of which have the same expressive power. Since the latter formalism leads to shortest notations, it shall be introduced and used here. Given a set Σ of symbols (a.k.a. alphabet), a regular expression can be any of ∅ (denoting the empty set of strings), ε (denoting the singleton set containing just the empty string), a (where a is any character in Σ; denoting the singleton set just containing the single-character string a), r + s (where r and s are, in turn, simpler regular expressions; denoting their set's union) r ⋅ s (denoting the set of all possible concatenations of strings from r's and s's set), r + (denoting the set of n-fold repetitions of strings from r's set, for any n ≥ 1), or r (similarly denoting the set of n-fold repetitions, but also including the empty string, seen as 0-fold repetition). For example, using Σ = {0,1}, the regular expression (0+1+ε)⋅(0+1) denotes the set of all binary numbers with one or two digits (leading zero allowed), while 1⋅(0+1)⋅0 denotes the (infinite) set of all even binary numbers (no leading zeroes). Given a set of strings (also called "positive examples"), the task of regular language induction is to come up with a regular expression that denotes a set containing all of them. As an example, given {1, 10, 100}, a "natural" description could be the regular expression 1⋅0, corresponding to the informal characterization "a 1 followed by arbitrarily many (maybe even none) 0's". However, (0+1) and 1+(1⋅0)+(1⋅0⋅0) is another regular expression, denoting the largest (assuming Σ = {0,1}) and the smallest set containing the given strings, and called the trivial overgeneralization and undergeneralization, respectively. Some approaches work in an extended setting where also a set of "negative example" strings is given; then, a regular expression is to be found that generates all of the positive, but none of the negative examples. == Lattice of automata == Dupont et al. have shown that the set of all structurally complete finite automata generating a given input set of example strings forms a lattice, with the trivial undergeneralized and the trivial overgeneralized automaton as bottom and top element, respectively. Each member of this lattice can be obtained by factoring the undergeneralized automaton by an appropriate equivalence relation. For the above example string set {1, 10, 100}, the picture shows at its bottom the undergeneralized automaton Aa,b,c,d in grey, consisting of states a, b, c, and d. On the state set {a,b,c,d}, a total of 15 equivalence relations exist, forming a lattice. Mapping each equivalence E to the corresponding quotient automaton language L(Aa,b,c,d / E) obtains the partially ordered set shown in the picture. Each node's language is denoted by a regular expression. The language may be recognized by quotient automata w.r.t. different equivalence relations, all of which are shown below the node. An arrow between two nodes indicates that the lower node's language is a proper subset of the higher node's. If both positive and negative example strings are given, Dupont et al. build the lattice from the positive examples, and then investigate the separation border between automata that generate some negative example and such that do not. Most interesting are those automata immediately below the border. In the picture, separation borders are shown for the negative example strings 11 (green), 1001 (blue), 101 (cyan), and 0 (red). Coste and Nicolas present an own search method within the lattice, which they relate to Mitchell's version space paradigm. To find the separation border, they use a graph coloring algorithm on the state inequality relation induced by the negative examples. Later, they investigate several ordering relations on the set of all possible state fusions. Kudo and Shimbo use the representation by automaton factorizations to give a unique framework for the following approaches (sketched below): k-reversible languages and the "tail clustering" follow-up approach, Successor automata and the predecessor-successor method, and pumping-based approaches (framework-integration challenged by Luzeaux, however). Each of these approaches is shown to correspond to a particular kind of equivalence relations used for factorization. == Approaches == === k-reversible languages === Angluin considers so-called "k-reversible" regular automata, that is, deterministic automata in which each state can be reached from at most one state by following a transition chain of length k. Formally, if Σ, Q, and δ denote the input alphabet, the state set, and the transition function of an automaton A, respectively, then A is called k-reversible if: ∀a0, ..., ak ∈ Σ ∀s1, s2 ∈ Q: δ(s1, a0...ak) = δ(s2, a0...ak) ⇒ s1 = s2, where δ means the homomorphic extension of δ to arbitrary words. Angluin gives a cubic algorithm for learning of the smallest k-reversible language from a given set of input words; for k = 0, the algorithm has even almost linear complexity. The required state uniqueness after k + 1 given symbols forces unifying automaton states, thus leading to a proper generalization different from the trivial undergeneralized automaton. This algorithm has been used to learn simple parts of English syntax; later, an incremental version has been provided. Another approach based on k-reversible automata is the tail clustering method. === Successor automata === From a given set of input strings, Vernadat and Richetin build a so-called successor automaton, consisting of one state for each distinct character and a transition between each two adjacent characters' states. For example, the singleton input set {aabbaabb} leads to an automaton corresponding to the regular expression (a+⋅b+). An extension of this approach is the predecessor-successor method which generalizes each character repetition immediately to a Kleene + and then includes for each character the set of its possible predecessors in its state. Successor automata can learn exactly the class of local languages. Since each regular language is the homomorphic image of a local language, grammars from the former class can be learned by lifting, if an appropriate (depending on the intended application) homomorphism is provided. In particular, there is such a homomorphism for the class of languages learnable by the predecessor-successor method. The learnability of local languages can be reduced to that of k-reversible languages. === Early approaches === Chomsky and Miller (1957) used the pumping lemma: they guess a part v of an input string uvw and try to build a corresponding cycle into the automaton to be learned; using membership queries they ask, for appropriate k, which of the strings uw, uvvw, uvvvw, ..., uvkw also belongs to the language to be learned, thereby refining the structure of their automaton. In 1959, Solomonoff generalized this approach to context-free languages, which also obey a pumping lemma. === Cover automata === Câmpeanu et al. learn a finite automaton as a compact representation of a large finite language. Given such a language F, they search a so-called cover automaton A such that its language L(A) covers F in the following sense: L(A) ∩ Σ≤ l = F, where l is the length of the longest string in F, and Σ≤ l denotes the set of all strings not longer than l. If such a cover automaton exists, F is uniquely determined by A and l. For example, F = {ad, read, reread } has l = 6 and a cover automaton corresponding to the regular expression (r⋅e)⋅a⋅d. For two strings x and y, Câmpeanu et al. define x ~ y if xz ∈ F ⇔ yz ∈ F for all strings z of a length such that both xz and yz are not longer than l. Based on this relation, whose lack of transitivity causes considerable technical problems, they give an O(n4) algorithm to construct from F a cover automaton A of minimal state count. Moreover, for union, intersection, and difference of two finite languages they provide corresponding operations on their cover automata. Păun et al. improve the time complexity to O(n2). === Residual automata === For a set S of strings and a string u, the Brzozowski derivative u−1S is defined as the set of all rest-strings obtainable from a string in S by cutting off its prefix u (if possible), formally: u−1S = {v ∈ Σ: uv ∈ S}, cf. picture. Denis et al. define a

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  Diffusion map

  Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of a data set into Euclidean space (often low-dimensional) whose coordinates can be computed from the eigenvectors and eigenvalues of a diffusion operator on the data. The Euclidean distance between points in the embedded space is equal to the "diffusion distance" between probability distributions centered at those points. Different from linear dimensionality reduction methods such as principal component analysis (PCA), diffusion maps are part of the family of nonlinear dimensionality reduction methods which focus on discovering the underlying manifold that the data has been sampled from. By integrating local similarities at different scales, diffusion maps give a global description of the data-set. Compared with other methods, the diffusion map algorithm is robust to noise perturbation and computationally inexpensive. == Definition of diffusion maps == Following and , diffusion maps can be defined in four steps. === Connectivity === Diffusion maps exploit the relationship between heat diffusion and random walk Markov chain. The basic observation is that if we take a random walk on the data, walking to a nearby data-point is more likely than walking to another that is far away. Let ( X , A , μ ) {\displaystyle (X,{\mathcal {A}},\mu )} be a measure space, where X {\displaystyle X} is the data set and μ {\displaystyle \mu } represents the distribution of the points on X {\displaystyle X} . Based on this, the connectivity k {\displaystyle k} between two data points, x {\displaystyle x} and y {\displaystyle y} , can be defined as the probability of walking from x {\displaystyle x} to y {\displaystyle y} in one step of the random walk. Usually, this probability is specified in terms of a kernel function of the two points: k : X × X → R {\displaystyle k:X\times X\rightarrow \mathbb {R} } . For example, the popular Gaussian kernel: k ( x , y ) = exp ⁡ ( − | | x − y | | 2 ϵ ) {\displaystyle k(x,y)=\exp \left(-{\frac {||x-y||^{2}}{\epsilon }}\right)} More generally, the kernel function has the following properties k ( x , y ) = k ( y , x ) {\displaystyle k(x,y)=k(y,x)} ( k {\displaystyle k} is symmetric) k ( x , y ) ≥ 0 ∀ x , y {\displaystyle k(x,y)\geq 0\,\,\forall x,y} ( k {\displaystyle k} is positivity preserving). The kernel constitutes the prior definition of the local geometry of the data-set. Since a given kernel will capture a specific feature of the data set, its choice should be guided by the application that one has in mind. This is a major difference with methods such as principal component analysis, where correlations between all data points are taken into account at once. Given ( X , k ) {\displaystyle (X,k)} , we can then construct a reversible discrete-time Markov chain on X {\displaystyle X} (a process known as the normalized graph Laplacian construction): d ( x ) = ∫ X k ( x , y ) d μ ( y ) {\displaystyle d(x)=\int _{X}k(x,y)d\mu (y)} and define: p ( x , y ) = k ( x , y ) d ( x ) {\displaystyle p(x,y)={\frac {k(x,y)}{d(x)}}} Although the new normalized kernel does not inherit the symmetric property, it does inherit the positivity-preserving property and gains a conservation property: ∫ X p ( x , y ) d μ ( y ) = 1 {\displaystyle \int _{X}p(x,y)d\mu (y)=1} === Diffusion process === From p ( x , y ) {\displaystyle p(x,y)} we can construct a transition matrix of a Markov chain ( M {\displaystyle M} ) on X {\displaystyle X} . In other words, p ( x , y ) {\displaystyle p(x,y)} represents the one-step transition probability from x {\displaystyle x} to y {\displaystyle y} , and M t {\displaystyle M^{t}} gives the t-step transition matrix. We define the diffusion matrix L {\displaystyle L} (it is also a version of graph Laplacian matrix) L i , j = k ( x i , x j ) {\displaystyle L_{i,j}=k(x_{i},x_{j})\,} We then define the new kernel L i , j ( α ) = k ( α ) ( x i , x j ) = L i , j ( d ( x i ) d ( x j ) ) α {\displaystyle L_{i,j}^{(\alpha )}=k^{(\alpha )}(x_{i},x_{j})={\frac {L_{i,j}}{(d(x_{i})d(x_{j}))^{\alpha }}}\,} or equivalently, L ( α ) = D − α L D − α {\displaystyle L^{(\alpha )}=D^{-\alpha }LD^{-\alpha }\,} where D is a diagonal matrix and D i , i = ∑ j L i , j . {\displaystyle D_{i,i}=\sum _{j}L_{i,j}.} We apply the graph Laplacian normalization to this new kernel: M = ( D ( α ) ) − 1 L ( α ) , {\displaystyle M=({D}^{(\alpha )})^{-1}L^{(\alpha )},\,} where D ( α ) {\displaystyle D^{(\alpha )}} is a diagonal matrix and D i , i ( α ) = ∑ j L i , j ( α ) . {\displaystyle {D}_{i,i}^{(\alpha )}=\sum _{j}L_{i,j}^{(\alpha )}.} p ( x j , t | x i ) = M i , j t {\displaystyle p(x_{j},t|x_{i})=M_{i,j}^{t}\,} One of the main ideas of the diffusion framework is that running the chain forward in time (taking larger and larger powers of M {\displaystyle M} ) reveals the geometric structure of X {\displaystyle X} at larger and larger scales (the diffusion process). Specifically, the notion of a cluster in the data set is quantified as a region in which the probability of escaping this region is low (within a certain time t). Therefore, t not only serves as a time parameter, but it also has the dual role of scale parameter. The eigendecomposition of the matrix M t {\displaystyle M^{t}} yields M i , j t = ∑ l λ l t ψ l ( x i ) ϕ l ( x j ) {\displaystyle M_{i,j}^{t}=\sum _{l}\lambda _{l}^{t}\psi _{l}(x_{i})\phi _{l}(x_{j})\,} where { λ l } {\displaystyle \{\lambda _{l}\}} is the sequence of eigenvalues of M {\displaystyle M} and { ψ l } {\displaystyle \{\psi _{l}\}} and { ϕ l } {\displaystyle \{\phi _{l}\}} are the biorthogonal left and right eigenvectors respectively. Due to the spectrum decay of the eigenvalues, only a few terms are necessary to achieve a given relative accuracy in this sum. ==== Parameter α and the diffusion operator ==== The reason to introduce the normalization step involving α {\displaystyle \alpha } is to tune the influence of the data point density on the infinitesimal transition of the diffusion. In some applications, the sampling of the data is generally not related to the geometry of the manifold we are interested in describing. In this case, we can set α = 1 {\displaystyle \alpha =1} and the diffusion operator approximates the Laplace–Beltrami operator. We then recover the Riemannian geometry of the data set regardless of the distribution of the points. To describe the long-term behavior of the point distribution of a system of stochastic differential equations, we can use α = 0.5 {\displaystyle \alpha =0.5} and the resulting Markov chain approximates the Fokker–Planck diffusion. With α = 0 {\displaystyle \alpha =0} , it reduces to the classical graph Laplacian normalization. === Diffusion distance === The diffusion distance at time t {\displaystyle t} between two points can be measured as the similarity of two points in the observation space with the connectivity between them. It is given by D t ( x i , x j ) 2 = ∑ y ( p ( y , t | x i ) − p ( y , t | x j ) ) 2 ϕ 0 ( y ) {\displaystyle D_{t}(x_{i},x_{j})^{2}=\sum _{y}{\frac {(p(y,t|x_{i})-p(y,t|x_{j}))^{2}}{\phi _{0}(y)}}} where ϕ 0 ( y ) {\displaystyle \phi _{0}(y)} is the stationary distribution of the Markov chain, given by the first left eigenvector of M {\displaystyle M} . Explicitly: ϕ 0 ( y ) = d ( y ) ∑ z ∈ X d ( z ) {\displaystyle \phi _{0}(y)={\frac {d(y)}{\sum _{z\in X}d(z)}}} Intuitively, D t ( x i , x j ) {\displaystyle D_{t}(x_{i},x_{j})} is small if there is a large number of short paths connecting x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} . There are several interesting features associated with the diffusion distance, based on our previous discussion that t {\displaystyle t} also serves as a scale parameter: Points are closer at a given scale (as specified by D t ( x i , x j ) {\displaystyle D_{t}(x_{i},x_{j})} ) if they are highly connected in the graph, therefore emphasizing the concept of a cluster. This distance is robust to noise, since the distance between two points depends on all possible paths of length t {\displaystyle t} between the points. From a machine learning point of view, the distance takes into account all evidences linking x i {\displaystyle x_{i}} to x j {\displaystyle x_{j}} , allowing us to conclude that this distance is appropriate for the design of inference algorithms based on the majority of preponderance. === Diffusion process and low-dimensional embedding === The diffusion distance can be calculated using the eigenvectors by D t ( x i , x j ) 2 = ∑ l λ l 2 t ( ψ l ( x i ) − ψ l ( x j ) ) 2 {\displaystyle D_{t}(x_{i},x_{j})^{2}=\sum _{l}\lambda _{l}^{2t}(\psi _{l}(x_{i})-\psi _{l}(x_{j}))^{2}\,} So the eigenvectors can be used as a new set of coordinates for the data. The diffusion map is defined as: Ψ t ( x ) = ( λ 1 t ψ 1 ( x ) , λ 2 t ψ 2 ( x ) , … , λ k t ψ k ( x ) ) {\displaystyle \Psi _{t}(x)=(\lambda _{1}^{t}\psi _{1}(x),\lambda _{2}^{t}\psi _{2}(x),\ld

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  Radial basis function

  In mathematics a radial basis function (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input and some fixed point, either the origin, so that φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} \right\|)} , or some other fixed point c {\textstyle \mathbf {c} } , called a center, so that φ ( x ) = φ ^ ( ‖ x − c ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} -\mathbf {c} \right\|)} . Any function φ {\textstyle \varphi } that satisfies the property φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} \right\|)} is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection { φ k } k {\displaystyle \{\varphi _{k}\}_{k}} which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Lowe in 1988, which stemmed from Michael J. D. Powell's seminal research from 1977. RBFs are also used as a kernel in support vector classification. The technique has proven effective and flexible enough that radial basis functions are now applied in a variety of engineering applications. == Definition == A radial function is a function φ : [ 0 , ∞ ) → R {\textstyle \varphi :[0,\infty )\to \mathbb {R} } . When paired with a norm ‖ ⋅ ‖ : V → [ 0 , ∞ ) {\textstyle \|\cdot \|:V\to [0,\infty )} on a vector space, a function of the form φ c = φ ( ‖ x − c ‖ ) {\textstyle \varphi _{\mathbf {c} }=\varphi (\|\mathbf {x} -\mathbf {c} \|)} is said to be a radial kernel centered at c ∈ V {\textstyle \mathbf {c} \in V} . A radial function and the associated radial kernels are said to be radial basis functions if, for any finite set of nodes { x k } k = 1 n ⊆ V {\displaystyle \{\mathbf {x} _{k}\}_{k=1}^{n}\subseteq V} , all of the following conditions are true: === Examples === Commonly used types of radial basis functions include (writing r = ‖ x − x i ‖ {\textstyle r=\left\|\mathbf {x} -\mathbf {x} _{i}\right\|} and using ε {\textstyle \varepsilon } to indicate a shape parameter that can be used to scale the input of the radial kernel): == Approximation == Radial basis functions are typically used to build up function approximations of the form where the approximating function y ( x ) {\textstyle y(\mathbf {x} )} is represented as a sum of N {\displaystyle N} radial basis functions, each associated with a different center x i {\textstyle \mathbf {x} _{i}} , and weighted by an appropriate coefficient w i . {\textstyle w_{i}.} The weights w i {\textstyle w_{i}} can be estimated using the matrix methods of linear least squares, because the approximating function is linear in the weights w i {\textstyle w_{i}} . Approximation schemes of this kind have been particularly used in time series prediction and control of nonlinear systems exhibiting sufficiently simple chaotic behaviour and 3D reconstruction in computer graphics (for example, hierarchical RBF and Pose Space Deformation). == RBF Network == The sum can also be interpreted as a rather simple single-layer type of artificial neural network called a radial basis function network, with the radial basis functions taking on the role of the activation functions of the network. It can be shown that any continuous function on a compact interval can in principle be interpolated with arbitrary accuracy by a sum of this form, if a sufficiently large number N {\textstyle N} of radial basis functions is used. The approximant y ( x ) {\textstyle y(\mathbf {x} )} is differentiable with respect to the weights w i {\textstyle w_{i}} . The weights could thus be learned using any of the standard iterative methods for neural networks. Using radial basis functions in this manner yields a reasonable interpolation approach provided that the fitting set has been chosen such that it covers the entire range systematically (equidistant data points are ideal). However, without a polynomial term that is orthogonal to the radial basis functions, estimates outside the fitting set tend to perform poorly. == RBFs for PDEs == Radial basis functions are used to approximate functions and so can be used to discretize and numerically solve Partial Differential Equations (PDEs). This was first done in 1990 by E. J. Kansa who developed the first RBF based numerical method. It is called the Kansa method and was used to solve the elliptic Poisson equation and the linear advection-diffusion equation. The function values at points x {\displaystyle \mathbf {x} } in the domain are approximated by the linear combination of RBFs: The derivatives are approximated as such: where N {\displaystyle N} are the number of points in the discretized domain, d {\displaystyle d} the dimension of the domain and λ {\displaystyle \lambda } the scalar coefficients that are unchanged by the differential operator. Different numerical methods based on Radial Basis Functions were developed thereafter. Some methods are the RBF-FD method, the RBF-QR method and the RBF-PUM method.

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  Mix automation

  In music recording, mix automation allows the mixing console to remember the mixing engineer's dynamic adjustment of faders during a musical piece in the post-production editing process. A timecode is necessary for the synchronization of automation. Modern mixing consoles and digital audio workstations use comprehensive mix automation. The need for automated mixing originated from the late 1970s transition form 8-track to 16-track and then 24-track multitrack recording, as mixing could be laborious and require multiple people and hands, and the results could be almost impossible to reproduce. With 48-track recording - synchronized twin 24-track recorders (for a net 46 audio tracks, with one on each machine for SMPTE timecode) - came larger recording and mixing consoles with even more channel faders to manage during mixdown. Manufacturers, such as Neve Electronics (now AMS Neve) and Solid State Logic (SSL), both English companies, developed systems that enabled one engineer to oversee every detail of a complex mix, although the computers required to power these desks remained a rarity into the late 1970s. According to record producer Roy Thomas Baker, Queen's 1975 single "Bohemian Rhapsody" was one of the first mixes to be done with automation. == Types == Voltage Controlled Automation fader levels are regulated by voltage-controlled amplifiers (VCA). VCAs control the audio level and not the actual fader. Moving Fader Automation a motor is attached to the fader, which then can be controlled by the console, digital audio workstation (DAW), or user. Software Controlled Automation the software can be internal to the console, or external as part of a DAW. The virtual fader can be adjusted in the software by the user. MIDI Automation the communications protocol MIDI can be used to send messages to the console to control automation. == Modes == Auto Write used the first time automation is created or when writing over existing automation Auto Touch writes automation data only while a fader is touched/faders return to any previously automated position after release Auto Latch starts writing automation data when a fader is touched/stays in position after release Auto Read digital Audio Workstation performs the written automation Auto Off automation is temporarily disabled All of these include the mute button. If mute is pressed during writing of automation, the audio track will be muted during playback of that automation. Depending on software, other parameters such as panning, sends, and plug-in controls can be automated as well. In some cases, automation can be written using a digital potentiometer instead of a fader.

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  Ordination (statistics)

  Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near each other share attributes (i.e., are similar to some degree), and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes or latent variables, are then characterized numerically and/or graphically in a biplot. The first ordination method, principal components analysis, was suggested by Karl Pearson in 1901. == Methods == Ordination methods can broadly be categorized in eigenvector-, algorithm-, or model-based methods. Many classical ordination techniques, including principal components analysis, correspondence analysis (CA) and its derivatives (detrended correspondence analysis, canonical correspondence analysis, and redundancy analysis, belong to the first group). The second group includes some distance-based methods such as non-metric multidimensional scaling, and machine learning methods such as T-distributed stochastic neighbor embedding and nonlinear dimensionality reduction. The third group includes model-based ordination methods, which can be considered as multivariate extensions of Generalized Linear Models. Model-based ordination methods are more flexible in their application than classical ordination methods, so that it is for example possible to include random-effects. Unlike in the aforementioned two groups, there is no (implicit or explicit) distance measure in the ordination. Instead, a distribution needs to be specified for the responses as is typical for statistical models. These and other assumptions, such as the assumed mean-variance relationship, can be validated with the use of residual diagnostics, unlike in other ordination methods. == Applications == Ordination can be used on the analysis of any set of multivariate objects. It is frequently used in several environmental or ecological sciences, particularly plant community ecology. It is also used in genetics and systems biology for microarray data analysis and in psychometrics.

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  Averaged one-dependence estimators

  Averaged one-dependence estimators (AODE) is a probabilistic classification learning technique. It was developed to address the attribute-independence problem of the popular naive Bayes classifier. It frequently develops substantially more accurate classifiers than naive Bayes at the cost of a modest increase in the amount of computation. == The AODE classifier == AODE seeks to estimate the probability of each class y given a specified set of features x1, ... xn, P(y | x1, ... xn). To do so it uses the formula P ^ ( y ∣ x 1 , … x n ) = ∑ i : 1 ≤ i ≤ n ∧ F ( x i ) ≥ m P ^ ( y , x i ) ∏ j = 1 n P ^ ( x j ∣ y , x i ) ∑ y ′ ∈ Y ∑ i : 1 ≤ i ≤ n ∧ F ( x i ) ≥ m P ^ ( y ′ , x i ) ∏ j = 1 n P ^ ( x j ∣ y ′ , x i ) {\displaystyle {\hat {P}}(y\mid x_{1},\ldots x_{n})={\frac {\sum _{i:1\leq i\leq n\wedge F(x_{i})\geq m}{\hat {P}}(y,x_{i})\prod _{j=1}^{n}{\hat {P}}(x_{j}\mid y,x_{i})}{\sum _{y^{\prime }\in Y}\sum _{i:1\leq i\leq n\wedge F(x_{i})\geq m}{\hat {P}}(y^{\prime },x_{i})\prod _{j=1}^{n}{\hat {P}}(x_{j}\mid y^{\prime },x_{i})}}} where P ^ ( ⋅ ) {\displaystyle {\hat {P}}(\cdot )} denotes an estimate of P ( ⋅ ) {\displaystyle P(\cdot )} , F ( ⋅ ) {\displaystyle F(\cdot )} is the frequency with which the argument appears in the sample data and m is a user specified minimum frequency with which a term must appear in order to be used in the outer summation. In recent practice m is usually set at 1. == Derivation of the AODE classifier == We seek to estimate P(y | x1, ... xn). By the definition of conditional probability P ( y ∣ x 1 , … x n ) = P ( y , x 1 , … x n ) P ( x 1 , … x n ) . {\displaystyle P(y\mid x_{1},\ldots x_{n})={\frac {P(y,x_{1},\ldots x_{n})}{P(x_{1},\ldots x_{n})}}.} For any 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n} , P ( y , x 1 , … x n ) = P ( y , x i ) P ( x 1 , … x n ∣ y , x i ) . {\displaystyle P(y,x_{1},\ldots x_{n})=P(y,x_{i})P(x_{1},\ldots x_{n}\mid y,x_{i}).} Under an assumption that x1, ... xn are independent given y and xi, it follows that P ( y , x 1 , … x n ) = P ( y , x i ) ∏ j = 1 n P ( x j ∣ y , x i ) . {\displaystyle P(y,x_{1},\ldots x_{n})=P(y,x_{i})\prod _{j=1}^{n}P(x_{j}\mid y,x_{i}).} This formula defines a special form of One Dependence Estimator (ODE), a variant of the naive Bayes classifier that makes the above independence assumption that is weaker (and hence potentially less harmful) than the naive Bayes' independence assumption. In consequence, each ODE should create a less biased estimator than naive Bayes. However, because the base probability estimates are each conditioned by two variables rather than one, they are formed from less data (the training examples that satisfy both variables) and hence are likely to have more variance. AODE reduces this variance by averaging the estimates of all such ODEs. == Features of the AODE classifier == Like naive Bayes, AODE does not perform model selection and does not use tuneable parameters. As a result, it has low variance. It supports incremental learning whereby the classifier can be updated efficiently with information from new examples as they become available. It predicts class probabilities rather than simply predicting a single class, allowing the user to determine the confidence with which each classification can be made. Its probabilistic model can directly handle situations where some data are missing. AODE has computational complexity O ( l n 2 ) {\displaystyle O(ln^{2})} at training time and O ( k n 2 ) {\displaystyle O(kn^{2})} at classification time, where n is the number of features, l is the number of training examples and k is the number of classes. This makes it infeasible for application to high-dimensional data. However, within that limitation, it is linear with respect to the number of training examples and hence can efficiently process large numbers of training examples. == Implementations == The free Weka machine learning suite includes an implementation of AODE.

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  Generalized canonical correlation

  In statistics, the generalized canonical correlation analysis (gCCA), is a way of making sense of cross-correlation matrices between the sets of random variables when there are more than two sets. While a conventional CCA generalizes principal component analysis (PCA) to two sets of random variables, a gCCA generalizes PCA to more than two sets of random variables. The canonical variables represent those common factors that can be found by a large PCA of all of the transformed random variables after each set underwent its own PCA. == Applications == The Helmert-Wolf blocking (HWB) method of estimating linear regression parameters can find an optimal solution only if all cross-correlations between the data blocks are zero. They can always be made to vanish by introducing a new regression parameter for each common factor. The gCCA method can be used for finding those harmful common factors that create cross-correlation between the blocks. However, no optimal HWB solution exists if the random variables do not contain enough information on all of the new regression parameters.

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  Histogram of oriented displacements

  Histogram of oriented displacements (HOD) is a 2D trajectory descriptor. The trajectory is described using a histogram of the directions between each two consecutive points. Given a trajectory T = {P1, P2, P3, ..., Pn}, where Pt is the 2D position at time t. For each pair of positions Pt and Pt+1, calculate the direction angle θ(t, t+1). Value of θ is between 0 and 360. A histogram of the quantized values of θ is created. If the histogram is of 8 bins, the first bin represents all θs between 0 and 45. The histogram accumulates the lengths of the consecutive moves. For each θ, a specific histogram bin is determined. The length of the line between Pt and Pt+1 is then added to the specific histogram bin. To show the intuition behind the descriptor, consider the action of waving hands. At the end of the action, the hand falls down. When describing this down movement, the descriptor does not care about the position from which the hand started to fall. This fall will affect the histogram with the appropriate angles and lengths, regardless of the position where the hand started to fall. HOD records for each moving point: how much it moves in each range of directions. HOD has a clear physical interpretation. It proposes that, a simple way to describe the motion of an object, is to indicate how much distance it moves in each direction. If the movement in all directions are saved accurately, the movement can be repeated from the initial position to the final destination regardless of the displacements order. However, the temporal information will be lost, as the order of movements is not stored-this is what we solve by applying the temporal pyramid, as shown in section \ref{sec:temp-pyramid}. If the angles quantization range is small, classifiers that use the descriptor will overfit. Generalization needs some slack in directions-which can be done by increasing the quantization range.

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  Error-driven learning

  In reinforcement learning, error-driven learning is a method for adjusting a model's (intelligent agent's) parameters based on the difference between its output results and the ground truth. These models stand out as they depend on environmental feedback, rather than explicit labels or categories. They are based on the idea that language acquisition involves the minimization of the prediction error (MPSE). By leveraging these prediction errors, the models consistently refine expectations and decrease computational complexity. Typically, these algorithms are operated by the GeneRec algorithm. Error-driven learning has widespread applications in cognitive sciences and computer vision. These methods have also found successful application in natural language processing (NLP), including areas like part-of-speech tagging, parsing, named entity recognition (NER), machine translation (MT), speech recognition (SR), and dialogue systems. == Formal Definition == Error-driven learning models are ones that rely on the feedback of prediction errors to adjust the expectations or parameters of a model. The key components of error-driven learning include the following: A set S {\displaystyle S} of states representing the different situations that the learner can encounter. A set A {\displaystyle A} of actions that the learner can take in each state. A prediction function P ( s , a ) {\displaystyle P(s,a)} that gives the learner's current prediction of the outcome of taking action a {\displaystyle a} in state s {\displaystyle s} . An error function E ( o , p ) {\displaystyle E(o,p)} that compares the actual outcome o {\displaystyle o} with the prediction p {\displaystyle p} and produces an error value. An update rule U ( p , e ) {\displaystyle U(p,e)} that adjusts the prediction p {\displaystyle p} in light of the error e {\displaystyle e} . == Algorithms == Error-driven learning algorithms refer to a category of reinforcement learning algorithms that leverage the disparity between the real output and the expected output of a system to regulate the system's parameters. Typically applied in supervised learning, these algorithms are provided with a collection of input-output pairs to facilitate the process of generalization. The widely utilized error backpropagation learning algorithm is known as GeneRec, a generalized recirculation algorithm primarily employed for gene prediction in DNA sequences. Many other error-driven learning algorithms are derived from alternative versions of GeneRec. == Applications == === Cognitive science === Simpler error-driven learning models effectively capture complex human cognitive phenomena and anticipate elusive behaviors. They provide a flexible mechanism for modeling the brain's learning process, encompassing perception, attention, memory, and decision-making. By using errors as guiding signals, these algorithms adeptly adapt to changing environmental demands and objectives, capturing statistical regularities and structure. Furthermore, cognitive science has led to the creation of new error-driven learning algorithms that are both biologically acceptable and computationally efficient. These algorithms, including deep belief networks, spiking neural networks, and reservoir computing, follow the principles and constraints of the brain and nervous system. Their primary aim is to capture the emergent properties and dynamics of neural circuits and systems. === Computer vision === Computer vision is a complex task that involves understanding and interpreting visual data, such as images or videos. In the context of error-driven learning, the computer vision model learns from the mistakes it makes during the interpretation process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This repeated process of learning from errors helps improve the model's performance over time. For NLP to do well at computer vision, it employs deep learning techniques. This form of computer vision is sometimes called neural computer vision (NCV), since it makes use of neural networks. NCV therefore interprets visual data based on a statistical, trial and error approach and can deal with context and other subtleties of visual data. === Natural Language Processing === ==== Part-of-speech tagging ==== Part-of-speech (POS) tagging is a crucial component in Natural Language Processing (NLP). It helps resolve human language ambiguity at different analysis levels. In addition, its output (tagged data) can be used in various applications of NLP such as information extraction, information retrieval, question Answering, speech eecognition, text-to-speech conversion, partial parsing, and grammar correction. ==== Parsing ==== Parsing in NLP involves breaking down a text into smaller pieces (phrases) based on grammar rules. If a sentence cannot be parsed, it may contain grammatical errors. In the context of error-driven learning, the parser learns from the mistakes it makes during the parsing process. When an error is encountered, the parser updates its internal model to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the parser's performance over time. In conclusion, error-driven learning plays a crucial role in improving the accuracy and efficiency of NLP parsers by allowing them to learn from their mistakes and adapt their internal models accordingly. ==== Named entity recognition (NER) ==== NER is the task of identifying and classifying entities (such as persons, locations, organizations, etc.) in a text. Error-driven learning can help the model learn from its false positives and false negatives and improve its recall and precision on (NER). In the context of error-driven learning, the significance of NER is quite profound. Traditional sequence labeling methods identify nested entities layer by layer. If an error occurs in the recognition of an inner entity, it can lead to incorrect identification of the outer entity, leading to a problem known as error propagation of nested entities. This is where the role of NER becomes crucial in error-driven learning. By accurately recognizing and classifying entities, it can help minimize these errors and improve the overall accuracy of the learning process. Furthermore, deep learning-based NER methods have shown to be more accurate as they are capable of assembling words, enabling them to understand the semantic and syntactic relationship between various words better. ==== Machine translation ==== Machine translation is a complex task that involves converting text from one language to another. In the context of error-driven learning, the machine translation model learns from the mistakes it makes during the translation process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. ==== Speech recognition ==== Speech recognition is a complex task that involves converting spoken language into written text. In the context of error-driven learning, the speech recognition model learns from the mistakes it makes during the recognition process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. ==== Dialogue systems ==== Dialogue systems are a popular NLP task as they have promising real-life applications. They are also complicated tasks since many NLP tasks deserving study are involved. In the context of error-driven learning, the dialogue system learns from the mistakes it makes during the dialogue process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. == Advantages == Error-driven learning has several advantages over other types of machine learning algorithms: They can learn from feedback and correct their mistakes, which makes them adaptive and robust to noise and changes in the data. They can handle large and high-dimensional data sets, as they do not require explicit feature engineering or prior knowledge of the data distribution. They can achieve high accuracy and performance, as they can learn complex and nonlinear relationships between the input and the output. == Limitations == Although error driven learning has its advantages, their algorithms also have the following limitations: They can suffer from overfitting, which means that they memorize the training data and fail to generalize to new and unseen data. This can be mitigated by using regularization techniques, such as adding a penalty term to the loss function, or reducing the complexity of the model. They can be sensitive to the choice of

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  Curriculum learning

  Curriculum learning is a technique in machine learning in which a model is trained on examples of increasing difficulty, where the definition of "difficulty" may be provided externally or discovered as part of the training process. This is intended to attain good performance more quickly, or to converge to a better local optimum if the global optimum is not found. == Approach == Most generally, curriculum learning is the technique of successively increasing the difficulty of examples in the training set that is presented to a model over multiple training iterations. This can produce better results than exposing the model to the full training set immediately under some circumstances; most typically, when the model is able to learn general principles from easier examples, and then gradually incorporate more complex and nuanced information as harder examples are introduced, such as edge cases. This has been shown to work in many domains, most likely as a form of regularization. There are several major variations in how the technique is applied: A concept of "difficulty" must be defined. This may come from human annotation or an external heuristic; for example in language modeling, shorter sentences might be classified as easier than longer ones. Another approach is to use the performance of another model, with examples accurately predicted by that model being classified as easier (providing a connection to boosting). Difficulty can be increased steadily or in distinct epochs, and in a deterministic schedule or according to a probability distribution. This may also be moderated by a requirement for diversity at each stage, in cases where easier examples are likely to be disproportionately similar to each other. Applications must also decide the schedule for increasing the difficulty. Simple approaches may use a fixed schedule, such as training on easy examples for half of the available iterations and then all examples for the second half. Other approaches use self-paced learning to increase the difficulty in proportion to the performance of the model on the current set. Since curriculum learning only concerns the selection and ordering of training data, it can be combined with many other techniques in machine learning. The success of the method assumes that a model trained for an easier version of the problem can generalize to harder versions, so it can be seen as a form of transfer learning. Some authors also consider curriculum learning to include other forms of progressively increasing complexity, such as increasing the number of model parameters. It is frequently combined with reinforcement learning, such as learning a simplified version of a game first. Some domains have shown success with anti-curriculum learning: training on the most difficult examples first. One example is the ACCAN method for speech recognition, which trains on the examples with the lowest signal-to-noise ratio first. == History == The term "curriculum learning" was introduced by Yoshua Bengio et al in 2009, with reference to the psychological technique of shaping in animals and structured education for humans: beginning with the simplest concepts and then building on them. The authors also note that the application of this technique in machine learning has its roots in the early study of neural networks such as Jeffrey Elman's 1993 paper Learning and development in neural networks: the importance of starting small. Bengio et al showed good results for problems in image classification, such as identifying geometric shapes with progressively more complex forms, and language modeling, such as training with a gradually expanding vocabulary. They conclude that, for curriculum strategies, "their beneficial effect is most pronounced on the test set", suggesting good generalization. The technique has since been applied to many other domains: Natural language processing: Part-of-speech tagging Intent detection Sentiment analysis Machine translation Speech recognition Language model pre-training Image recognition: Facial recognition Object detection Reinforcement learning: Game-playing Graph learning Matrix factorization

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