AI Coding Kya Hota Hai

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Amaq News Agency

Amaq News Agency (Arabic: وكالة أعماق الإخبارية, romanized: Wakālat Aʻmāq al-Ikhbārīyah) is a news outlet linked to the Islamic State (IS). Amaq is often the "first point of publication for claims of responsibility" for terrorist attacks in Western countries by the Islamic State. In March 2019, Amaq News Agency was designated as a foreign terrorist organization by the United States Department of State. == History == Among the founders of Amaq was Syrian journalist Baraa Kadek, who joined IS in late 2013, Abu Muhammad al-Furqan, and seven others who originally worked for Halab News Network. According to The New York Times, it has a direct connection with IS, from which it "gets tips". Its name was taken from Amik Valley in Hatay Province, which is mentioned in a hadith as the site of an "apocalyptic victory over non-believers". Amaq News Agency was first noticed by SITE during the Siege of Kobanî (Syria) in 2014, when its updates were shared among IS fighters. It became more widely known after it began reporting claims of responsibility for terrorist attacks in Western countries, such as the 2015 San Bernardino attack, for which IS officially claimed responsibility the next day. An Amaq cameraman shot the first footage of the capture of Palmyra in 2015. Amaq launched an official mobile app in 2015 and has warned against unofficial versions that reportedly have been used to spy on its users. It also uses a Telegram account. It had a WordPress-based blog, but it was removed without explanation in April 2016. On 12 June 2016, IS claimed responsibility for the Pulse nightclub shooting through Amaq, without prior knowledge of the attack. The shooter, Omar Mateen had later pledged allegiance to IS via a phone call with emergency services. On 31 May 2017, a Facebook post announced Amaq's founder, Baraa Kadek AKA Rayan Meshaal, had been killed with his daughter by an American airstrike on Mayadin. The post was reportedly made by his younger brother. Reuters could not immediately verify this account. On 27 July 2017, the US confirmed that Kadek had been killed by a coalition airstrike near Mayadin between 25 and 27 May 2017. In June 2017, German police arrested a 23-year-old Syrian man identified only as Mohammed G., accusing him of communicating with the alleged perpetrator of the 2016 Malmö Muslim community centre arson in order to report to Amaq. On 21 March 2019, the U.S. Department of State officially deemed Amaq an alias of IS, and thus a Foreign Terrorist Organization. On 22 March 2024, the Islamic State claimed responsibility for the Crocus City Hall attack through Amaq, U.S. officials confirmed the claim shortly after. A day after the attack, Amaq published a video of the attack, filmed by one of the attackers. It showed the attackers shooting victims and slitting the throat of another, while the filming attacker praises Allah and speaks against infidels. == Character == Amaq publishes a stream of short news reports, both text and video, on the mobile app Telegram. The reports take on the trappings of mainstream journalism, with "Breaking News" headings, and embedded reporters at the scenes of IS battles. The reports try to appear neutral, toning down the jihadist language and sectarian slurs IS uses in its official releases. Charlie Winter of the Transcultural Conflict and Violence Initiative at Georgia State University, and Rita Katz of SITE Intelligence Group in Washington say Amaq functions much like the state-owned news agency of IS, though the group does not acknowledge it as such. Katz said it behaves "like a state media". Amaq appears to have been allowed to develop by IS as a way to have a news outlet that is controlled by the group but is somewhat removed from it, giving IS more of the appearance of legitimacy. == Reliability == According to Rukmini Callimachi in The New York Times: "Despite a widespread view that the Islamic State opportunistically claims attacks with which it has little genuine connection, its track record—minus a handful of exceptions—suggests a more rigorous protocol. At times, the Islamic State has got details wrong, or inflated casualty figures, but the gist of its claims is typically correct." According to Callimachi, the group considers itself responsible for acts carried out by people who were inspired by its propaganda, as well as acts carried out by its own personnel and in some instances, had claimed attacks before the identities of the killers were known. Graeme Wood writing in The Atlantic in October 2017, wrote "The idea that the Islamic State simply scans the news in search of mass killings, then sends out press releases in hope of stealing glory, is false. Amaq may learn details of the attacks from mainstream media ... but its claim of credit typically flows from an Amaq-specific source." An October 2017 article in The Hill, points to two false claims made in the summer of 2017, the Resorts World Manila attack and a false claim that bombs had been planted at Charles de Gaulle Airport in Paris. Also, a claimed IS connection to the 2017 Las Vegas shooting proved to be false. According to Rita Katz on the SITE Intelligence Group website, calling a terrorist a "soldier of the caliphate (warrior from the caliphate)" in a statement issued by Amaq, was the usual way in which IS indicated that it inspired an attack. Centrally coordinated attacks were usually described as "executed by a detachment belonging to the Islamic State", and were often announced by both Amaq and by IS' central media command. == Online presence == In November 2019, Belgian police said they had carried out a successful cyberattack on Amaq, thus leaving IS without an operational communication channel. However, Amaq has since regained online presence, primarily on dark web platforms to make it harder for law enforcement to take them down without physical access to the server hosting the specific platform.
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Crossover (evolutionary algorithm)

Crossover in evolutionary algorithms and evolutionary computation, also called recombination, is a genetic operator used to combine the genetic information of two parents to generate new offspring. It is one way to stochastically generate new solutions from an existing population, and is analogous to the crossover that happens during sexual reproduction in biology. New solutions can also be generated by cloning an existing solution, which is analogous to asexual reproduction. Newly generated solutions may be mutated before being added to the population. The aim of recombination is to transfer good characteristics from two different parents to one child. Different algorithms in evolutionary computation may use different data structures to store genetic information, and each genetic representation can be recombined with different crossover operators. Typical data structures that can be recombined with crossover are bit arrays, vectors of real numbers, or trees. The list of operators presented below is by no means complete and serves mainly as an exemplary illustration of this dyadic genetic operator type. More operators and more details can be found in the literature. == Crossover for binary arrays == Traditional genetic algorithms store genetic information in a chromosome represented by a bit array. Crossover methods for bit arrays are popular and an illustrative example of genetic recombination. === One-point crossover === A point on both parents' chromosomes is picked randomly, and designated a 'crossover point'. Bits to the right of that point are swapped between the two parent chromosomes. This results in two offspring, each carrying some genetic information from both parents. === Two-point and k-point crossover === In two-point crossover, two crossover points are picked randomly from the parent chromosomes. The bits in between the two points are swapped between the parent organisms. Two-point crossover is equivalent to performing two single-point crossovers with different crossover points. This strategy can be generalized to k-point crossover for any positive integer k, picking k crossover points. === Uniform crossover === In uniform crossover, typically, each bit is chosen from either parent with equal probability. Other mixing ratios are sometimes used, resulting in offspring which inherit more genetic information from one parent than the other. In a uniform crossover, we don’t divide the chromosome into segments, rather we treat each gene separately. In this, we essentially flip a coin for each chromosome to decide whether or not it will be included in the off-spring. == Crossover for integer or real-valued genomes == For the crossover operators presented above and for most other crossover operators for bit strings, it holds that they can also be applied accordingly to integer or real-valued genomes whose genes each consist of an integer or real-valued number. Instead of individual bits, integer or real-valued numbers are then simply copied into the child genome. The offspring lie on the remaining corners of the hyperbody spanned by the two parents P 1 = ( 1.5 , 6 , 8 ) {\displaystyle P_{1}=(1.5,6,8)} and P 2 = ( 7 , 2 , 1 ) {\displaystyle P_{2}=(7,2,1)} , as exemplified in the accompanying image for the three-dimensional case. === Discrete recombination === If the rules of the uniform crossover for bit strings are applied during the generation of the offspring, this is also called discrete recombination. === Intermediate recombination === In this recombination operator, the allele values of the child genome a i {\displaystyle a_{i}} are generated by mixing the alleles of the two parent genomes a i , P 1 {\displaystyle a_{i,P_{1}}} and a i , P 2 {\displaystyle a_{i,P_{2}}} : α i = α i , P 1 ⋅ β i + α i , P 2 ⋅ ( 1 − β i ) w i t h β i ∈ [ − d , 1 + d ] {\displaystyle \alpha _{i}=\alpha _{i,P_{1}}\cdot \beta _{i}+\alpha _{i,P_{2}}\cdot \left(1-\beta _{i}\right)\quad {\mathsf {with}}\quad \beta _{i}\in \left[-d,1+d\right]} randomly equally distributed per gene i {\displaystyle i} The choice of the interval [ − d , 1 + d ] {\displaystyle [-d,1+d]} causes that besides the interior of the hyperbody spanned by the allele values of the parent genes additionally a certain environment for the range of values of the offspring is in question. A value of 0.25 {\displaystyle 0.25} is recommended for d {\displaystyle d} to counteract the tendency to reduce the allele values that otherwise exists at d = 0 {\displaystyle d=0} . The adjacent figure shows for the two-dimensional case the range of possible new alleles of the two exemplary parents P 1 = ( 3 , 6 ) {\displaystyle P_{1}=(3,6)} and P 2 = ( 9 , 2 ) {\displaystyle P_{2}=(9,2)} in intermediate recombination. The offspring of discrete recombination C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} are also plotted. Intermediate recombination satisfies the arithmetic calculation of the allele values of the child genome required by virtual alphabet theory. Discrete and intermediate recombination are used as a standard in the evolution strategy. == Crossover for permutations == For combinatorial tasks, permutations are usually used that are specifically designed for genomes that are themselves permutations of a set. The underlying set is usually a subset of N {\displaystyle \mathbb {N} } or N 0 {\displaystyle \mathbb {N} _{0}} . If 1- or n-point or uniform crossover for integer genomes is used for such genomes, a child genome may contain some values twice and others may be missing. This can be remedied by genetic repair, e.g. by replacing the redundant genes in positional fidelity for missing ones from the other child genome. In order to avoid the generation of invalid offspring, special crossover operators for permutations have been developed which fulfill the basic requirements of such operators for permutations, namely that all elements of the initial permutation are also present in the new one and only the order is changed. It can be distinguished between combinatorial tasks, where all sequences are admissible, and those where there are constraints in the form of inadmissible partial sequences. A well-known representative of the first task type is the traveling salesman problem (TSP), where the goal is to visit a set of cities exactly once on the shortest tour. An example of the constrained task type is the scheduling of multiple workflows. Workflows involve sequence constraints on some of the individual work steps. For example, a thread cannot be cut until the corresponding hole has been drilled in a workpiece. Such problems are also called order-based permutations. In the following, two crossover operators are presented as examples, the partially mapped crossover (PMX) motivated by the TSP and the order crossover (OX1) designed for order-based permutations. A second offspring can be produced in each case by exchanging the parent chromosomes. === Partially mapped crossover (PMX) === The PMX operator was designed as a recombination operator for TSP like Problems. The explanation of the procedure is illustrated by an example: === Order crossover (OX1) === The order crossover goes back to Davis in its original form and is presented here in a slightly generalized version with more than two crossover points. It transfers information about the relative order from the second parent to the offspring. First, the number and position of the crossover points are determined randomly. The resulting gene sequences are then processed as described below: Among other things, order crossover is well suited for scheduling multiple workflows, when used in conjunction with 1- and n-point crossover. === Further crossover operators for permutations === Over time, a large number of crossover operators for permutations have been proposed, so the following list is only a small selection. For more information, the reader is referred to the literature. cycle crossover (CX) order-based crossover (OX2) position-based crossover (POS) edge recombination voting recombination (VR) alternating-positions crossover (AP) maximal preservative crossover (MPX) merge crossover (MX) sequential constructive crossover operator (SCX) The usual approach to solving TSP-like problems by genetic or, more generally, evolutionary algorithms, presented earlier, is either to repair illegal descendants or to adjust the operators appropriately so that illegal offspring do not arise in the first place. Alternatively, Riazi suggests the use of a double chromosome representation, which avoids illegal offspring.
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Probably approximately correct learning

In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant. In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a certain class of possible functions. The goal is that, with high probability (the "probably" part), the selected function will have low generalization error (the "approximately correct" part). The learner must be able to learn the concept given any arbitrary approximation ratio, probability of success, or distribution of the samples. The model was later extended to treat noise (misclassified samples). An important innovation of the PAC framework is the introduction of computational complexity theory concepts to machine learning. In particular, the learner is expected to find efficient functions (time and space requirements bounded to a polynomial of the example size), and the learner itself must implement an efficient procedure (requiring an example count bounded to a polynomial of the concept size, modified by the approximation and likelihood bounds). == Definitions and terminology == In order to give the definition for something that is PAC-learnable, we first have to introduce some terminology. For the following definitions, two examples will be used. The first is the problem of character recognition given an array of n {\displaystyle n} bits encoding a binary-valued image. The other example is the problem of finding an interval that will correctly classify points within the interval as positive and the points outside of the range as negative. Let X {\displaystyle X} be a set called the instance space or the encoding of all the samples. In the character recognition problem, the instance space is X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} . In the interval problem the instance space, X {\displaystyle X} , is the set of all bounded intervals in R {\displaystyle \mathbb {R} } , where R {\displaystyle \mathbb {R} } denotes the set of all real numbers. A concept is a subset c ⊂ X {\displaystyle c\subset X} . One concept is the set of all patterns of bits in X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} that encode a picture of the letter "P". An example concept from the second example is the set of open intervals, { ( a , b ) ∣ 0 ≤ a ≤ π / 2 , π ≤ b ≤ 13 } {\displaystyle \{(a,b)\mid 0\leq a\leq \pi /2,\pi \leq b\leq {\sqrt {13}}\}} , each of which contains only the positive points. A concept class C {\displaystyle C} is a collection of concepts over X {\displaystyle X} . This could be the set of all subsets of the array of bits that are skeletonized 4-connected (width of the font is 1). Let EX ⁡ ( c , D ) {\displaystyle \operatorname {EX} (c,D)} be a procedure that draws an example, x {\displaystyle x} , using a probability distribution D {\displaystyle D} and gives the correct label c ( x ) {\displaystyle c(x)} , that is 1 if x ∈ c {\displaystyle x\in c} and 0 otherwise. Now, given 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} , assume there is an algorithm A {\displaystyle A} and a polynomial p {\displaystyle p} in 1 / ϵ , 1 / δ {\displaystyle 1/\epsilon ,1/\delta } (and other relevant parameters of the class C {\displaystyle C} ) such that, given a sample of size p {\displaystyle p} drawn according to EX ⁡ ( c , D ) {\displaystyle \operatorname {EX} (c,D)} , then, with probability of at least 1 − δ {\displaystyle 1-\delta } , A {\displaystyle A} outputs a hypothesis h ∈ C {\displaystyle h\in C} that has an average error less than or equal to ϵ {\displaystyle \epsilon } on X {\displaystyle X} with the same distribution D {\displaystyle D} . Further if the above statement for algorithm A {\displaystyle A} is true for every concept c ∈ C {\displaystyle c\in C} and for every distribution D {\displaystyle D} over X {\displaystyle X} , and for all 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} then C {\displaystyle C} is (efficiently) PAC learnable (or distribution-free PAC learnable). We can also say that A {\displaystyle A} is a PAC learning algorithm for C {\displaystyle C} . == Equivalence == Under some regularity conditions these conditions are equivalent: The concept class C is PAC learnable. The VC dimension of C is finite. C is a uniformly Glivenko-Cantelli class. C is compressible in the sense of Littlestone and Warmuth
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Bondy's theorem

In mathematics, Bondy's theorem is a bound on the number of elements needed to distinguish the sets in a family of sets from each other. It belongs to the field of combinatorics, and is named after John Adrian Bondy, who published it in 1972. == Statement == The theorem is as follows: Let X be a set with n elements and let A1, A2, ..., An be distinct subsets of X. Then there exists a subset S of X with n − 1 elements such that the sets Ai ∩ S are all distinct. In other words, if we have a 0-1 matrix with n rows and n columns such that each row is distinct, we can remove one column such that the rows of the resulting n × (n − 1) matrix are distinct. == Example == Consider the 4 × 4 matrix [ 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 ] {\displaystyle {\begin{bmatrix}1&1&0&1\\0&1&0&1\\0&0&1&1\\0&1&1&0\end{bmatrix}}} where all rows are pairwise distinct. If we delete, for example, the first column, the resulting matrix [ 1 0 1 1 0 1 0 1 1 1 1 0 ] {\displaystyle {\begin{bmatrix}1&0&1\\1&0&1\\0&1&1\\1&1&0\end{bmatrix}}} no longer has this property: the first row is identical to the second row. Nevertheless, by Bondy's theorem we know that we can always find a column that can be deleted without introducing any identical rows. In this case, we can delete the third column: all rows of the 3 × 4 matrix [ 1 1 1 0 1 1 0 0 1 0 1 0 ] {\displaystyle {\begin{bmatrix}1&1&1\\0&1&1\\0&0&1\\0&1&0\end{bmatrix}}} are distinct. Another possibility would have been deleting the fourth column. == Learning theory application == From the perspective of computational learning theory, Bondy's theorem can be rephrased as follows: Let C be a concept class over a finite domain X. Then there exists a subset S of X with the size at most |C| − 1 such that S is a witness set for every concept in C. This implies that every finite concept class C has its teaching dimension bounded by |C| − 1.
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Reciprocal human machine learning

Reciprocal Human Machine Learning (RHML) is an interdisciplinary approach to designing human-AI interaction systems. RHML aims to enable continual learning between humans and machine learning models by having them learn from each other. This approach keeps the human expert "in the loop" to oversee and enhance machine learning performance and simultaneously support the human expert continue learning. == Background == RHML emerged in the context of the rise of big data analytics and artificial intelligence for intelligent tasks like sense-making and decision-making. As machine learning advanced to take on more roles, researchers realized fully autonomous systems had limitations and needed human guidance. RHML extends the concept of human-in-the-loop systems by promoting reciprocal learning. Humans learn from their interactions with machine learning models, staying up-to-date on evolving technology. The models also learn from human feedback and oversight. This amplification of learning on both sides is a key focus of RHML. The approach draws on theories of learning in dyads from education and psychology. It also builds on human-computer interaction and human-centered design principles. Implementing RHML requires developing specialized tools and interfaces tailored to the application == Applications == RHML has been explored across diverse domains including: Cybersecurity - Software to enable reciprocal learning between experts and AI models for social media threat detection. Organizational decision-making - RHML to structure collaboration between humans and AI systems. Workplace training - Using RHML for workers to learn from AI technologies on the job. Open science - Using human and AI collaboration to promote open science. Production and logistics - turning workers and intelligent machines into teammates. RHML maintains human oversight and control over AI systems, while enabling cutting-edge machine learning performance. This collaborative approach highlights the importance of keeping the human expert involved in the loop. An example of RHML in application is Free Spirit (AFSFCV), an open-source architecture first published in early 2025 as a whitepaper, proposing a visually structured approach to intent-based human–AI interaction.
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Linear classifier

In machine learning, a linear classifier makes a classification decision for each object based on a linear combination of its features. A simpler definition is to say that a linear classifier is one whose decision boundaries are linear. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use. == Definition == If the input feature vector to the classifier is a real vector x → {\displaystyle {\vec {x}}} , then the output score is y = f ( w → ⋅ x → ) = f ( ∑ j w j x j ) , {\displaystyle y=f({\vec {w}}\cdot {\vec {x}})=f\left(\sum _{j}w_{j}x_{j}\right),} where w → {\displaystyle {\vec {w}}} is a real vector of weights and f is a function that converts the dot product of the two vectors into the desired output. (In other words, w → {\displaystyle {\vec {w}}} is a one-form or linear functional mapping x → {\displaystyle {\vec {x}}} onto R.) The weight vector w → {\displaystyle {\vec {w}}} is learned from a set of labeled training samples. Often f is a threshold function, which maps all values of w → ⋅ x → {\displaystyle {\vec {w}}\cdot {\vec {x}}} above a certain threshold to the first class and all other values to the second class; e.g., f ( x ) = { 1 if w T ⋅ x > θ , 0 otherwise {\displaystyle f(\mathbf {x} )={\begin{cases}1&{\text{if }}\ \mathbf {w} ^{T}\cdot \mathbf {x} >\theta ,\\0&{\text{otherwise}}\end{cases}}} The superscript T indicates the transpose and θ {\displaystyle \theta } is a scalar threshold. A more complex f might give the probability that an item belongs to a certain class. For a two-class classification problem, one can visualize the operation of a linear classifier as splitting a high-dimensional input space with a hyperplane: all points on one side of the hyperplane are classified as "yes", while the others are classified as "no". A linear classifier is often used in situations where the speed of classification is an issue, since it is often the fastest classifier, especially when x → {\displaystyle {\vec {x}}} is sparse. Also, linear classifiers often work very well when the number of dimensions in x → {\displaystyle {\vec {x}}} is large, as in document classification, where each element in x → {\displaystyle {\vec {x}}} is typically the number of occurrences of a word in a document (see document-term matrix). In such cases, the classifier should be well-regularized. == Generative models vs. discriminative models == There are two broad classes of methods for determining the parameters of a linear classifier w → {\displaystyle {\vec {w}}} . They can be generative and discriminative models. Methods of the former model joint probability distribution, whereas methods of the latter model conditional density functions P ( c l a s s | x → ) {\displaystyle P({\rm {class}}|{\vec {x}})} . Examples of such algorithms include: Linear Discriminant Analysis (LDA)—assumes Gaussian conditional density models Naive Bayes classifier with multinomial or multivariate Bernoulli event models. The second set of methods includes discriminative models, which attempt to maximize the quality of the output on a training set. Additional terms in the training cost function can easily perform regularization of the final model. Examples of discriminative training of linear classifiers include: Logistic regression—maximum likelihood estimation of w → {\displaystyle {\vec {w}}} assuming that the observed training set was generated by a binomial model that depends on the output of the classifier. Perceptron—an algorithm that attempts to fix all errors encountered in the training set Fisher's Linear Discriminant Analysis—an algorithm (different than "LDA") that maximizes the ratio of between-class scatter to within-class scatter, without any other assumptions. It is in essence a method of dimensionality reduction for binary classification. Support vector machine—an algorithm that maximizes the margin between the decision hyperplane and the examples in the training set. Note: Despite its name, LDA does not belong to the class of discriminative models in this taxonomy. However, its name makes sense when we compare LDA to the other main linear dimensionality reduction algorithm: principal components analysis (PCA). LDA is a supervised learning algorithm that utilizes the labels of the data, while PCA is an unsupervised learning algorithm that ignores the labels. To summarize, the name is a historical artifact. Discriminative training often yields higher accuracy than modeling the conditional density functions. However, handling missing data is often easier with conditional density models. All of the linear classifier algorithms listed above can be converted into non-linear algorithms operating on a different input space φ ( x → ) {\displaystyle \varphi ({\vec {x}})} , using the kernel trick. === Discriminative training === Discriminative training of linear classifiers usually proceeds in a supervised way, by means of an optimization algorithm that is given a training set with desired outputs and a loss function that measures the discrepancy between the classifier's outputs and the desired outputs. Thus, the learning algorithm solves an optimization problem of the form arg ⁡ min w R ( w ) + C ∑ i = 1 N L ( y i , w T x i ) {\displaystyle {\underset {\mathbf {w} }{\arg \min }}\;R(\mathbf {w} )+C\sum _{i=1}^{N}L(y_{i},\mathbf {w} ^{\mathsf {T}}\mathbf {x} _{i})} where w is a vector of classifier parameters, L(yi, wTxi) is a loss function that measures the discrepancy between the classifier's prediction and the true output yi for the i'th training example, R(w) is a regularization function that prevents the parameters from getting too large (causing overfitting), and C is a scalar constant (set by the user of the learning algorithm) that controls the balance between the regularization and the loss function. Popular loss functions include the hinge loss (for linear SVMs) and the log loss (for linear logistic regression). If the regularization function R is convex, then the above is a convex problem. Many algorithms exist for solving such problems; popular ones for linear classification include (stochastic) gradient descent, L-BFGS, coordinate descent and Newton methods.
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Characteristic samples

Characteristic samples is a concept in the field of grammatical inference, related to passive learning. In passive learning, an inference algorithm I {\displaystyle I} is given a set of pairs of strings and labels S {\displaystyle S} , and returns a representation R {\displaystyle R} that is consistent with S {\displaystyle S} . Characteristic samples consider the scenario when the goal is not only finding a representation consistent with S {\displaystyle S} , but finding a representation that recognizes a specific target language. A characteristic sample of language L {\displaystyle L} is a set of pairs of the form ( s , l ( s ) ) {\displaystyle (s,l(s))} where: l ( s ) = 1 {\displaystyle l(s)=1} if and only if s ∈ L {\displaystyle s\in L} l ( s ) = − 1 {\displaystyle l(s)=-1} if and only if s ∉ L {\displaystyle s\notin L} Given the characteristic sample S {\displaystyle S} , I {\displaystyle I} 's output on it is a representation R {\displaystyle R} , e.g. an automaton, that recognizes L {\displaystyle L} . == Formal Definition == === The Learning Paradigm associated with Characteristic Samples === There are three entities in the learning paradigm connected to characteristic samples, the adversary, the teacher and the inference algorithm. Given a class of languages C {\displaystyle \mathbb {C} } and a class of representations for the languages R {\displaystyle \mathbb {R} } , the paradigm goes as follows: The adversary A {\displaystyle A} selects a language L ∈ C {\displaystyle L\in \mathbb {C} } and reports it to the teacher The teacher T {\displaystyle T} then computes a set of strings and label them correctly according to L {\displaystyle L} , trying to make sure that the inference algorithm will compute L {\displaystyle L} The adversary can add correctly labeled words to the set in order to confuse the inference algorithm The inference algorithm I {\displaystyle I} gets the sample and computes a representation R ∈ R {\displaystyle R\in \mathbb {R} } consistent with the sample. The goal is that when the inference algorithm receives a characteristic sample for a language L {\displaystyle L} , or a sample that subsumes a characteristic sample for L {\displaystyle L} , it will return a representation that recognizes exactly the language L {\displaystyle L} . === Sample === Sample S {\displaystyle S} is a set of pairs of the form ( s , l ( s ) ) {\displaystyle (s,l(s))} such that l ( s ) ∈ { − 1 , 1 } {\displaystyle l(s)\in \{-1,1\}} ==== Sample consistent with a language ==== We say that a sample S {\displaystyle S} is consistent with language L {\displaystyle L} if for every pair ( s , l ( s ) ) {\displaystyle (s,l(s))} in S {\displaystyle S} : l ( s ) = 1 if and only if s ∈ L {\displaystyle l(s)=1{\text{ if and only if }}s\in L} l ( s ) = − 1 if and only if s ∉ L {\displaystyle l(s)=-1{\text{ if and only if }}s\notin L} === Characteristic sample === Given an inference algorithm I {\displaystyle I} and a language L {\displaystyle L} , a sample S {\displaystyle S} that is consistent with L {\displaystyle L} is called a characteristic sample of L {\displaystyle L} for I {\displaystyle I} if: I {\displaystyle I} 's output on S {\displaystyle S} is a representation R {\displaystyle R} that recognizes L {\displaystyle L} . For every sample D {\displaystyle D} that is consistent with L {\displaystyle L} and also fulfils S ⊆ D {\displaystyle S\subseteq D} , I {\displaystyle I} 's output on D {\displaystyle D} is a representation R {\displaystyle R} that recognizes L {\displaystyle L} . A Class of languages C {\displaystyle \mathbb {C} } is said to have charistaristic samples if every L ∈ C {\displaystyle L\in \mathbb {C} } has a characteristic sample. == Related Theorems == === Theorem === If equivalence is undecidable for a class C {\textstyle \mathbb {C} } over Σ {\textstyle \Sigma } of cardinality bigger than 1, then C {\textstyle \mathbb {C} } doesn't have characteristic samples. ==== Proof ==== Given a class of representations C {\textstyle \mathbb {C} } such that equivalence is undecidable, for every polynomial p ( x ) {\displaystyle p(x)} and every n ∈ N {\displaystyle n\in \mathbb {N} } , there exist two representations r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} of sizes bounded by n {\displaystyle n} , that recognize different languages but are inseparable by any string of size bounded by p ( n ) {\displaystyle p(n)} . Assuming this is not the case, we can decide if r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} are equivalent by simulating their run on all strings of size smaller than p ( n ) {\displaystyle p(n)} , contradicting the assumption that equivalence is undecidable. === Theorem === If S 1 {\displaystyle S_{1}} is a characteristic sample for L 1 {\displaystyle L_{1}} and is also consistent with L 2 {\displaystyle L_{2}} , then every characteristic sample of L 2 {\displaystyle L_{2}} , is inconsistent with L 1 {\displaystyle L_{1}} . ==== Proof ==== Given a class C {\textstyle \mathbb {C} } that has characteristic samples, let R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} be representations that recognize L 1 {\displaystyle L_{1}} and L 2 {\displaystyle L_{2}} respectively. Under the assumption that there is a characteristic sample for L 1 {\displaystyle L_{1}} , S 1 {\displaystyle S_{1}} that is also consistent with L 2 {\displaystyle L_{2}} , we'll assume falsely that there exist a characteristic sample for L 2 {\displaystyle L_{2}} , S 2 {\displaystyle S_{2}} that is consistent with L 1 {\displaystyle L_{1}} . By the definition of characteristic sample, the inference algorithm I {\displaystyle I} must return a representation which recognizes the language if given a sample that subsumes the characteristic sample itself. But for the sample S 1 ∪ S 2 {\displaystyle S_{1}\cup S_{2}} , the answer of the inferring algorithm needs to recognize both L 1 {\displaystyle L_{1}} and L 2 {\displaystyle L_{2}} , in contradiction. === Theorem === If a class is polynomially learnable by example based queries, it is learnable with characteristic samples. == Polynomialy characterizable classes == === Regular languages === The proof that DFA's are learnable using characteristic samples, relies on the fact that every regular language has a finite number of equivalence classes with respect to the right congruence relation, ∼ L {\displaystyle \sim _{L}} (where x ∼ L y {\displaystyle x\sim _{L}y} for x , y ∈ Σ ∗ {\displaystyle x,y\in \Sigma ^{}} if and only if ∀ z ∈ Σ ∗ : x z ∈ L ↔ y z ∈ L {\displaystyle \forall z\in \Sigma ^{}:xz\in L\leftrightarrow yz\in L} ). Note that if x {\displaystyle x} , y {\displaystyle y} are not congruent with respect to ∼ L {\displaystyle \sim _{L}} , there exists a string z {\displaystyle z} such that x z ∈ L {\displaystyle xz\in L} but y z ∉ L {\displaystyle yz\notin L} or vice versa, this string is called a separating suffix. ==== Constructing a characteristic sample ==== The construction of a characteristic sample for a language L {\displaystyle L} by the teacher goes as follows. Firstly, by running a depth first search on a deterministic automaton A {\displaystyle A} recognizing L {\displaystyle L} , starting from its initial state, we get a suffix closed set of words, W {\displaystyle W} , ordered in shortlex order. From the fact above, we know that for every two states in the automaton, there exists a separating suffix that separates between every two strings that the run of A {\displaystyle A} on them ends in the respective states. We refer to the set of separating suffixes as S {\displaystyle S} . The labeled set (sample) of words the teacher gives the adversary is { ( w , l ( w ) ) | w ∈ W ⋅ S ∪ W ⋅ Σ ⋅ S } {\displaystyle \{(w,l(w))|w\in W\cdot S\cup W\cdot \Sigma \cdot S\}} where l ( w ) {\displaystyle l(w)} is the correct label of w {\displaystyle w} (whether it is in L {\displaystyle L} or not). We may assume that ϵ ∈ S {\displaystyle \epsilon \in S} . ==== Constructing a deterministic automata ==== Given the sample from the adversary W {\displaystyle W} , the construction of the automaton by the inference algorithm I {\displaystyle I} starts with defining P = prefix ( W ) {\displaystyle P={\text{prefix}}(W)} and S = suffix ( W ) {\displaystyle S={\text{suffix}}(W)} , which are the set of prefixes and suffixes of W {\displaystyle W} respectively. Now the algorithm constructs a matrix M {\displaystyle M} where the elements of P {\displaystyle P} function as the rows, ordered by the shortlex order, and the elements of S {\displaystyle S} function as the columns, ordered by the shortlex order. Next, the cells in the matrix are filled in the following manner for prefix p i {\displaystyle p_{i}} and suffix s j {\displaystyle s_{j}} : If p i s j ∈ W → M i j = l ( p i s j ) {\displaystyle p_{i}s_{j}\in W\rightarrow M_{ij}=l(p_{i}s_{j})} else, M i j = 0 {\displaystyle M_{ij}=0} Now, we say row i {\displaystyle i} and t {\displaystyle t} are distinguishable if there exi
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Vowpal Wabbit

Vowpal Wabbit (VW) is an open-source fast online interactive machine learning system library and program developed originally at Yahoo! Research, and currently at Microsoft Research. It was started and is led by John Langford. Vowpal Wabbit's interactive learning support is particularly notable including Contextual Bandits, Active Learning, and forms of guided Reinforcement Learning. Vowpal Wabbit provides an efficient scalable out-of-core implementation with support for a number of machine learning reductions, importance weighting, and a selection of different loss functions and optimization algorithms. == Notable features == The VW program supports: Multiple supervised (and semi-supervised) learning problems: Classification (both binary and multi-class) Regression Active learning (partially labeled data) for both regression and classification Multiple learning algorithms (model-types / representations) OLS regression Matrix factorization (sparse matrix SVD) Single layer neural net (with user specified hidden layer node count) Searn (Search and Learn) Latent Dirichlet Allocation (LDA) Stagewise polynomial approximation Recommend top-K out of N One-against-all (OAA) and cost-sensitive OAA reduction for multi-class Weighted all pairs Contextual-bandit (with multiple exploration/exploitation strategies) Multiple loss functions: squared error quantile hinge logistic poisson Multiple optimization algorithms Stochastic gradient descent (SGD) BFGS Conjugate gradient Regularization (L1 norm, L2 norm, & elastic net regularization) Flexible input - input features may be: Binary Numerical Categorical (via flexible feature-naming and the hash trick) Can deal with missing values/sparse-features Other features On the fly generation of feature interactions (quadratic and cubic) On the fly generation of N-grams with optional skips (useful for word/language data-sets) Automatic test-set holdout and early termination on multiple passes bootstrapping User settable online learning progress report + auditing of the model Hyperparameter optimization == Scalability == Vowpal wabbit has been used to learn a tera-feature (1012) data-set on 1000 nodes in one hour. Its scalability is aided by several factors: Out-of-core online learning: no need to load all data into memory The hashing trick: feature identities are converted to a weight index via a hash (uses 32-bit MurmurHash3) Exploiting multi-core CPUs: parsing of input and learning are done in separate threads. Compiled C++ code
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StyleGAN

The Style Generative Adversarial Network, or StyleGAN for short, is an extension to the GAN architecture introduced by Nvidia researchers in December 2018, and made source available in February 2019. StyleGAN depends on Nvidia's CUDA software, GPUs, and Google's TensorFlow, or Meta AI's PyTorch, which supersedes TensorFlow as the official implementation library in later StyleGAN versions. The second version of StyleGAN, called StyleGAN2, was published on February 5, 2020. It removes some of the characteristic artifacts and improves the image quality. Nvidia introduced StyleGAN3, described as an "alias-free" version, on June 23, 2021, and made source available on October 12, 2021. == History == A direct predecessor of the StyleGAN series is the Progressive GAN, published in 2017. In December 2018, Nvidia researchers distributed a preprint with accompanying software introducing StyleGAN, a GAN for producing an unlimited number of (often convincing) portraits of fake human faces. StyleGAN was able to run on Nvidia's commodity GPU processors. In February 2019, Uber engineer Phillip Wang used the software to create the website This Person Does Not Exist, which displayed a new face on each web page reload. Wang himself has expressed amazement, given that humans are evolved to specifically understand human faces, that nevertheless StyleGAN can competitively "pick apart all the relevant features (of human faces) and recompose them in a way that's coherent." In September 2019, a website called Generated Photos published 100,000 images as a collection of stock photos. The collection was made using a private dataset shot in a controlled environment with similar light and angles. Similarly, two faculty at the University of Washington's Information School used StyleGAN to create Which Face is Real?, which challenged visitors to differentiate between a fake and a real face side by side. The faculty stated the intention was to "educate the public" about the existence of this technology so they could be wary of it, "just like eventually most people were made aware that you can Photoshop an image". The second version of StyleGAN, called StyleGAN2, was published on February 5, 2020. It removes some of the characteristic artifacts and improves the image quality. In 2021, a third version was released, improving consistency between fine and coarse details in the generator. Dubbed "alias-free", this version was implemented with PyTorch. === Illicit use === In December 2019, Facebook took down a network of accounts with false identities, and mentioned that some of them had used profile pictures created with machine learning techniques. == Architecture == === Progressive GAN === Progressive GAN is a method for training GAN for large-scale image generation stably, by growing a GAN generator from small to large scale in a pyramidal fashion. Like SinGAN, it decomposes the generator as G = G 1 ∘ G 2 ∘ ⋯ ∘ G N {\displaystyle G=G_{1}\circ G_{2}\circ \cdots \circ G_{N}} , and the discriminator as D = D N ∘ D N − 1 ∘ ⋯ ∘ D 1 {\displaystyle D=D_{N}\circ D_{N-1}\circ \cdots \circ D_{1}} . During training, at first only G N , D N {\displaystyle G_{N},D_{N}} are used in a GAN game to generate 4x4 images. Then G N − 1 , D N − 1 {\displaystyle G_{N-1},D_{N-1}} are added to reach the second stage of GAN game, to generate 8x8 images, and so on, until we reach a GAN game to generate 1024x1024 images. To avoid discontinuity between stages of the GAN game, each new layer is "blended in" (Figure 2 of the paper). For example, this is how the second stage GAN game starts: Just before, the GAN game consists of the pair G N , D N {\displaystyle G_{N},D_{N}} generating and discriminating 4x4 images. Just after, the GAN game consists of the pair ( ( 1 − α ) + α ⋅ G N − 1 ) ∘ u ∘ G N , D N ∘ d ∘ ( ( 1 − α ) + α ⋅ D N − 1 ) {\displaystyle ((1-\alpha )+\alpha \cdot G_{N-1})\circ u\circ G_{N},D_{N}\circ d\circ ((1-\alpha )+\alpha \cdot D_{N-1})} generating and discriminating 8x8 images. Here, the functions u , d {\displaystyle u,d} are image up- and down-sampling functions, and α {\displaystyle \alpha } is a blend-in factor (much like an alpha in image composing) that smoothly glides from 0 to 1. === StyleGAN === StyleGAN is designed as a combination of Progressive GAN with neural style transfer. The key architectural choice of StyleGAN-1 is a progressive growth mechanism, similar to Progressive GAN. Each generated image starts as a constant 4 × 4 × 512 {\displaystyle 4\times 4\times 512} array, and repeatedly passed through style blocks. Each style block applies a "style latent vector" via affine transform ("adaptive instance normalization"), similar to how neural style transfer uses Gramian matrix. It then adds noise, and normalize (subtract the mean, then divide by the variance). At training time, usually only one style latent vector is used per image generated, but sometimes two ("mixing regularization") in order to encourage each style block to independently perform its stylization without expecting help from other style blocks (since they might receive an entirely different style latent vector). After training, multiple style latent vectors can be fed into each style block. Those fed to the lower layers control the large-scale styles, and those fed to the higher layers control the fine-detail styles. Style-mixing between two images x , x ′ {\displaystyle x,x'} can be performed as well. First, run a gradient descent to find z , z ′ {\displaystyle z,z'} such that G ( z ) ≈ x , G ( z ′ ) ≈ x ′ {\displaystyle G(z)\approx x,G(z')\approx x'} . This is called "projecting an image back to style latent space". Then, z {\displaystyle z} can be fed to the lower style blocks, and z ′ {\displaystyle z'} to the higher style blocks, to generate a composite image that has the large-scale style of x {\displaystyle x} , and the fine-detail style of x ′ {\displaystyle x'} . Multiple images can also be composed this way. === StyleGAN2 === StyleGAN2 improves upon StyleGAN in two ways. One, it applies the style latent vector to transform the convolution layer's weights instead, thus solving the "blob" problem. The "blob" problem roughly speaking is because using the style latent vector to normalize the generated image destroys useful information. Consequently, the generator learned to create a "distraction" by a large blob, which absorbs most of the effect of normalization (somewhat similar to using flares to distract a heat-seeking missile). Two, it uses residual connections, which helps it avoid the phenomenon where certain features are stuck at intervals of pixels. For example, the seam between two teeth may be stuck at pixels divisible by 32, because the generator learned to generate teeth during stage N-5, and consequently could only generate primitive teeth at that stage, before scaling up 5 times (thus intervals of 32). This was updated by the StyleGAN2-ADA ("ADA" stands for "adaptive"), which uses invertible data augmentation. It also tunes the amount of data augmentation applied by starting at zero, and gradually increasing it until an "overfitting heuristic" reaches a target level, thus the name "adaptive". === StyleGAN3 === StyleGAN3 improves upon StyleGAN2 by solving the "texture sticking" problem, which can be seen in the official videos. They analyzed the problem by the Nyquist–Shannon sampling theorem, and argued that the layers in the generator learned to exploit the high-frequency signal in the pixels they operate upon. To solve this, they proposed imposing strict lowpass filters between each generator's layers, so that the generator is forced to operate on the pixels in a way faithful to the continuous signals they represent, rather than operate on them as merely discrete signals. They further imposed rotational and translational invariance by using more signal filters. The resulting StyleGAN-3 is able to generate images that rotate and translate smoothly, and without texture sticking.
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Iris flower data set

The Iris flower data set or Fisher's Iris data set is a multivariate data set used and made famous by the British statistician and biologist Ronald Fisher in his 1936 paper The use of multiple measurements in taxonomic problems as an example of linear discriminant analysis. It is sometimes called Anderson's Iris data set because Edgar Anderson collected the data to quantify the morphologic variation of Iris flowers of three related species. Two of the three species were collected in the Gaspé Peninsula "all from the same pasture, and picked on the same day and measured at the same time by the same person with the same apparatus". The data set consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor). Four features were measured from each sample: the length and the width of the sepals and petals, in centimeters. Based on the combination of these four features, Fisher developed a linear discriminant model to distinguish each species. Fisher's paper was published in the Annals of Eugenics (today the Annals of Human Genetics). == Use of the data set == Originally used as an example data set on which Fisher's linear discriminant analysis was applied, it became a typical test case for many statistical classification techniques in machine learning such as support vector machines. The use of this data set in cluster analysis however is not common, since the data set only contains two clusters with rather obvious separation. One of the clusters contains Iris setosa, while the other cluster contains both Iris virginica and Iris versicolor and is not separable without the species information Fisher used. This makes the data set a good example to explain the difference between supervised and unsupervised techniques in data mining: Fisher's linear discriminant model can only be obtained when the object species are known: class labels and clusters are not necessarily the same. Nevertheless, all three species of Iris are separable in the projection on the nonlinear and branching principal component. The data set is approximated by the closest tree with some penalty for the excessive number of nodes, bending and stretching. Then the so-called "metro map" is constructed. The data points are projected into the closest node. For each node the pie diagram of the projected points is prepared. The area of the pie is proportional to the number of the projected points. It is clear from the diagram (left) that the absolute majority of the samples of the different Iris species belong to the different nodes. Only a small fraction of Iris-virginica is mixed with Iris-versicolor (the mixed blue-green nodes in the diagram). Therefore, the three species of Iris (Iris setosa, Iris virginica and Iris versicolor) are separable by the unsupervising procedures of nonlinear principal component analysis. To discriminate them, it is sufficient just to select the corresponding nodes on the principal tree. == Data set == The data set contains a set of 150 records under five attributes: sepal length, sepal width, petal length, petal width and species. The iris data set is widely used as a beginner's data set for machine learning purposes. The data set is included in R base and Python in the machine learning library scikit-learn, so that users can access it without having to find a source for it. Several versions of the data set have been published. === R code illustrating usage === The example R code shown below reproduce the scatterplot displayed at the top of this article: === Python code illustrating usage === This code gives:
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Sum of absolute transformed differences

The sum of absolute transformed differences (SATD) is a block matching criterion widely used in fractional motion estimation for video compression. It works by taking a frequency transform, usually a Hadamard transform, of the differences between the pixels in the original block and the corresponding pixels in the block being used for comparison. The transform itself is often of a small block rather than the entire macroblock. For example, in x264, a series of 4×4 blocks are transformed rather than doing the more processor-intensive 16×16 transform. == Comparison to other metrics == SATD is slower than the sum of absolute differences (SAD), both due to its increased complexity and the fact that SAD-specific MMX and SSE2 instructions exist, while there are no such instructions for SATD. However, SATD can still be optimized considerably with SIMD instructions on most modern CPUs. The benefit of SATD is that it more accurately models the number of bits required to transmit the residual error signal. As such, it is often used in video compressors, either as a way to drive and estimate rate explicitly, such as in the Theora encoder (since 1.1 alpha2), as an optional metric used in wide motion searches, such as in the Microsoft VC-1 encoder, or as a metric used in sub-pixel refinement, such as in x264.
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Learning classifier system

Learning classifier systems, or LCS, are a paradigm of rule-based machine learning methods that combine a discovery component (e.g. typically a genetic algorithm in evolutionary computation) with a learning component (performing either supervised learning, reinforcement learning, or unsupervised learning). Learning classifier systems seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions (e.g. behavior modeling, classification, data mining, regression, function approximation, or game strategy). This approach allows complex solution spaces to be broken up into smaller, simpler parts for the reinforcement learning that is inside artificial intelligence research. The founding concepts behind learning classifier systems came from attempts to model complex adaptive systems, using rule-based agents to form an artificial cognitive system (i.e. artificial intelligence). == Methodology == The architecture and components of a given learning classifier system can be quite variable. It is useful to think of an LCS as a machine consisting of several interacting components. Components may be added or removed, or existing components modified/exchanged to suit the demands of a given problem domain (like algorithmic building blocks) or to make the algorithm flexible enough to function in many different problem domains. As a result, the LCS paradigm can be flexibly applied to many problem domains that call for machine learning. The major divisions among LCS implementations are as follows: (1) Michigan-style architecture vs. Pittsburgh-style architecture, (2) reinforcement learning vs. supervised learning, (3) incremental learning vs. batch learning, (4) online learning vs. offline learning, (5) strength-based fitness vs. accuracy-based fitness, and (6) complete action mapping vs best action mapping. These divisions are not necessarily mutually exclusive. For example, XCS, the best known and best studied LCS algorithm, is Michigan-style, was designed for reinforcement learning but can also perform supervised learning, applies incremental learning that can be either online or offline, applies accuracy-based fitness, and seeks to generate a complete action mapping. === Elements of a generic LCS algorithm === Keeping in mind that LCS is a paradigm for genetic-based machine learning rather than a specific method, the following outlines key elements of a generic, modern (i.e. post-XCS) LCS algorithm. For simplicity let us focus on Michigan-style architecture with supervised learning. See the illustrations on the right laying out the sequential steps involved in this type of generic LCS. ==== Environment ==== The environment is the source of data upon which an LCS learns. It can be an offline, finite training dataset (characteristic of a data mining, classification, or regression problem), or an online sequential stream of live training instances. Each training instance is assumed to include some number of features (also referred to as attributes, or independent variables), and a single endpoint of interest (also referred to as the class, action, phenotype, prediction, or dependent variable). Part of LCS learning can involve feature selection, therefore not all of the features in the training data need to be informative. The set of feature values of an instance is commonly referred to as the state. For simplicity let's assume an example problem domain with Boolean/binary features and a Boolean/binary class. For Michigan-style systems, one instance from the environment is trained on each learning cycle (i.e. incremental learning). Pittsburgh-style systems perform batch learning, where rule sets are evaluated in each iteration over much or all of the training data. ==== Rule/classifier/population ==== A rule is a context dependent relationship between state values and some prediction. Rules typically take the form of an {IF:THEN} expression, (e.g. {IF 'condition' THEN 'action'}, or as a more specific example, {IF 'red' AND 'octagon' THEN 'stop-sign'}). A critical concept in LCS and rule-based machine learning alike, is that an individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Think of a rule as a "local-model" of the solution space. Rules can be represented in many different ways to handle different data types (e.g. binary, discrete-valued, ordinal, continuous-valued). Given binary data LCS traditionally applies a ternary rule representation (i.e. rules can include either a 0, 1, or '#' for each feature in the data). The 'don't care' symbol (i.e. '#') serves as a wild card within a rule's condition allowing rules, and the system as a whole to generalize relationships between features and the target endpoint to be predicted. Consider the following rule (#1###0 ~ 1) (i.e. condition ~ action). This rule can be interpreted as: IF the second feature = 1 AND the sixth feature = 0 THEN the class prediction = 1. We would say that the second and sixth features were specified in this rule, while the others were generalized. This rule, and the corresponding prediction are only applicable to an instance when the condition of the rule is satisfied by the instance. This is more commonly referred to as matching. In Michigan-style LCS, each rule has its own fitness, as well as a number of other rule-parameters associated with it that can describe the number of copies of that rule that exist (i.e. the numerosity), the age of the rule, its accuracy, or the accuracy of its reward predictions, and other descriptive or experiential statistics. A rule along with its parameters is often referred to as a classifier. In Michigan-style systems, classifiers are contained within a population [P] that has a user defined maximum number of classifiers. Unlike most stochastic search algorithms (e.g. evolutionary algorithms), LCS populations start out empty (i.e. there is no need to randomly initialize a rule population). Classifiers will instead be initially introduced to the population with a covering mechanism. In any LCS, the trained model is a set of rules/classifiers, rather than any single rule/classifier. In Michigan-style LCS, the entire trained (and optionally, compacted) classifier population forms the prediction model. ==== Matching ==== One of the most critical and often time-consuming elements of an LCS is the matching process. The first step in an LCS learning cycle takes a single training instance from the environment and passes it to [P] where matching takes place. In step two, every rule in [P] is now compared to the training instance to see which rules match (i.e. are contextually relevant to the current instance). In step three, any matching rules are moved to a match set [M]. A rule matches a training instance if all feature values specified in the rule condition are equivalent to the corresponding feature value in the training instance. For example, assuming the training instance is (001001 ~ 0), these rules would match: (###0## ~ 0), (00###1 ~ 0), (#01001 ~ 1), but these rules would not (1##### ~ 0), (000##1 ~ 0), (#0#1#0 ~ 1). Notice that in matching, the endpoint/action specified by the rule is not taken into consideration. As a result, the match set may contain classifiers that propose conflicting actions. In the fourth step, since we are performing supervised learning, [M] is divided into a correct set [C] and an incorrect set [I]. A matching rule goes into the correct set if it proposes the correct action (based on the known action of the training instance), otherwise it goes into [I]. In reinforcement learning LCS, an action set [A] would be formed here instead, since the correct action is not known. ==== Covering ==== At this point in the learning cycle, if no classifiers made it into either [M] or [C] (as would be the case when the population starts off empty), the covering mechanism is applied (fifth step). Covering is a form of online smart population initialization. Covering randomly generates a rule that matches the current training instance (and in the case of supervised learning, that rule is also generated with the correct action. Assuming the training instance is (001001 ~ 0), covering might generate any of the following rules: (#0#0## ~ 0), (001001 ~ 0), (#010## ~ 0). Covering not only ensures that each learning cycle there is at least one correct, matching rule in [C], but that any rule initialized into the population will match at least one training instance. This prevents LCS from exploring the search space of rules that do not match any training instances. ==== Parameter updates/credit assignment/learning ==== In the sixth step, the rule parameters of any rule in [M] are updated to reflect the new experience gained from the current training instance. Depending on the LCS algorithm, a number of updates can take place at this step. For supervised learning, we can simply update the accuracy/error of a
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TowIt

"TowIt" is a free, global, cross-platform mobile app, website, and Web API that allows civilians to report parking violations and dangerous driving in real-time. The mission is to remove the barriers required to make cities effectively fight and deter bad parking and dangerous driving habits. The company ultimately aims to better existing social controls in order to drive necessary behavioral change through increased education, real-time reporting, optimized enforcement, as well as the resulting reactivity. == User base and adoption == The application has users reporting vehicular infractions in upwards of 30 countries. The top reporting countries are: Portugal, Canada, United States of America and Australia. Users have adopted TowIt for a variety of reasons, usually central to their geographical location and the prominent offences in those specific areas. For instance, the majority of Portuguese reports are cars parked on sidewalks, footpaths and pedestrian crossings, Australian reports are largely focused on the abuse of disabled parking spaces, and in Toronto or San Francisco users generally capture cars parked in bicycle lanes. == Functions == === Data collection === TowIt gathers data on individual parking offences, the prominence of various offence types, as well as recurring offenders. This allows the company to identify trends and hotspots in order to take action against problem vehicles, as well as to help improve urban planning, traffic congestion and gridlock management. Individuals modify or improve an aspect of their behavior in response to their awareness of being observed, theoretically more so when demonstrating selfishness, egocentrism, narcissism and anti-social behavior. The company states that by becoming a user, one can "help TowIt relieve congestion, reduce collisions, open up economies, improve the environment and enhance the lives of urban residents and suburban commuters alike". The company has acknowledged that there are numerous legislative changes that would be required to integrate with governments at any level in many countries. A simple three-step process allows users to take a photo of an offending vehicle and subsequently verifying the offending vehicle's license plate information before submitting by tapping the TowIt (submit) button. Photographical evidence can only be captured with the camera from within the TowIt application. An Internet connection is required. The company has stated that this was purposefully done for quality control and report validation purposes. Users may only submit and view their own report history on either the iOS or Android applications. Globally submitted reports are displayed uncensored and in aggregate only on the Android application and the TowIt website. The "Global Feed" feature was removed from iOS (see iTunes Connect Acceptance Issues). TowIt's back-end automatically geotags the report and compares it to local parking by-law data, including by-law types, locations, times, side(s) of street, etc.- where available. Valid reports are posted to the global feed, to the TowIt website, and passed on to municipalities and police for enforcement (where connected). === Technologies used under license === TowIt currently utilizes the following software or software libraries under license: AngularJS, Apache Cordova, Apple iTunes Store EULA, Chart.js, Google Play Distribution Agreement, Ionic Framework, MongoDB, Moment.js, Python 2.7, Python Flask, and jQuery. == Company history == The TowIt application was conceived by Michael Duncan McArthur on December 5, 2014, as a response to Toronto Mayor John Tory's election mandate to "get this city moving". The application was announced via TowIt's official Twitter page on January 6, 2015. After the initial public announcement, Michael & Gregory were contacted by members of John Tory's staff on January 8, 2015, and invited to demo a prototype at Toronto City Hall on January 12, 2015. The two were also invited to meet with Toronto Councillor Norm Kelly, in his City Hall office, for a subsequent demo of the live Android application on January 28, 2015. A similar meeting and demo took place with members of the Traffic Services department of Toronto Police Service on February 2, 2015. Michael & Gregory teamed up with friends and Toronto-based developers Dae-Seon Moon, Jesse Malone, and Marcus Veres to complete the prototype in time to meet the city's imposed demo deadline and to launch the initial Android version of the application. TowIt officially launched on the Android platform on January 16, 2015. A subsequent iOS launch took place on March 19, 2015. === iTunes connect acceptance issues === The iOS version of the application was delayed for approximately two months, only after significant deliberation with Apple's iTunes Connect review board around (as then stated) rule: "14.1 - Any App that is defamatory, offensive, mean-spirited, or likely to place the targeted individual or group in harm's way will be rejected." The result was having to remove the "Global Feed" feature from the iOS platform, in which civilian users could view all recent reports from within the application. This feature still exists on the Android platform. === Business and legal === TowIt engaged Wildeboer Dellelce, one of Canada's leading business law and transactional corporate finance law firms, on January 17, 2015. The company filed for incorporation as "TowIt Solutions Inc." by both Michael & Gregory in the Canadian province of Ontario on January 22, 2015. TowIt continues to operate under a Freemium business model. The company is 100% bootstrapped and has received no outside investment to date. TowIt was accepted into the MaRS Discovery District's Venture Services program on March 4, 2015. === Lobbyist registration === After receiving initial press coverage in January and February 2015, an unknown entity reported Michael & Gregory's initial communications with city staff to the City of Toronto's Lobbyist Registrar. This complaint resulted in legal threats of fines received on February 10, 2015, for apparently and unknowingly breaking municipal lobbying by-laws. These fines (of up to $100,000) were eventually withdrawn after Michael & Gregory immediately provided all records of communication with city officials and registered as lobbyists in the City of Toronto on the subjects of By-law / Regulation, Parking, and Technology. Their registration was accepted by the Lobbyist Registrar on March 6, 2015. However, communication with Toronto city staff was reduced greatly as a result, which the company believes may have been the desired intent of the original complaint. === Outreach and activism === TowIt encourages its global user base to reach out to their local government representatives to promote the app at the users' own will. This tactic is used not only to demonstrate grassroots support, but also to avoid future lobbying issues. On June 2, 2015, the company officially partnered with Australian campaign "No Permit No Park" who advocate for the creation of inclusive communities. == Reception == The Best Planning Apps for 2016 by Planetizen, 5 Toronto apps you should be using by Indie88, 12 Best Apps Made In Canada by TechVibes.
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Multi expression programming

Multi Expression Programming (MEP) is an evolutionary algorithm for generating mathematical functions describing a given set of data. MEP is a Genetic Programming variant encoding multiple solutions in the same chromosome. MEP representation is not specific (multiple representations have been tested). In the simplest variant, MEP chromosomes are linear strings of instructions. This representation was inspired by Three-address code. MEP strength consists in the ability to encode multiple solutions, of a problem, in the same chromosome. In this way, one can explore larger zones of the search space. For most of the problems this advantage comes with no running-time penalty compared with genetic programming variants encoding a single solution in a chromosome. == Representation == MEP chromosomes are arrays of instructions represented in Three-address code format. Each instruction contains a variable, a constant, or a function. If the instruction is a function, then the arguments (given as instruction's addresses) are also present. === Example of MEP program === Here is a simple MEP chromosome (labels on the left side are not a part of the chromosome): 1: a 2: b 3: + 1, 2 4: c 5: d 6: + 4, 5 7: 3, 5 == Fitness computation == When the chromosome is evaluated it is unclear which instruction will provide the output of the program. In many cases, a set of programs is obtained, some of them being completely unrelated (they do not have common instructions). For the above chromosome, here is the list of possible programs obtained during decoding: E1 = a, E2 = b, E4 = c, E5 = d, E3 = a + b. E6 = c + d. E7 = (a + b) d. Each instruction is evaluated as a possible output of the program. The fitness (or error) is computed in a standard manner. For instance, in the case of symbolic regression, the fitness is the sum of differences (in absolute value) between the expected output (called target) and the actual output. == Fitness assignment process == Which expression will represent the chromosome? Which one will give the fitness of the chromosome? In MEP, the best of them (which has the lowest error) will represent the chromosome. This is different from other GP techniques: In Linear genetic programming the last instruction will give the output. In Cartesian Genetic Programming the gene providing the output is evolved like all other genes. Note that, for many problems, this evaluation has the same complexity as in the case of encoding a single solution in each chromosome. Thus, there is no penalty in running time compared to other techniques. == Software == === MEPX === MEPX is a cross-platform (Windows, macOS, and Linux Ubuntu) free software for the automatic generation of computer programs. It can be used for data analysis, particularly for solving symbolic regression, statistical classification and time-series problems. === libmep === Libmep is a free and open source library implementing Multi Expression Programming technique. It is written in C++. === hmep === hmep is a new open source library implementing Multi Expression Programming technique in Haskell programming language.
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Confirmatory blockmodeling

Confirmatory blockmodeling is a deductive approach in blockmodeling, where a blockmodel (or part of it) is prespecify before the analysis, and then the analysis is fit to this model. When only a part of analysis is prespecify (like individual cluster(s) or location of the block types), it is called partially confirmatory blockmodeling. This is so-called indirect approach, where the blockmodeling is done on the blockmodel fitting (e.g., a priori hypothesized blockmodel). Opposite approach to the confirmatory blockmodeling is an inductive exploratory blockmodeling.
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