AI Analytics Certification

AI Analytics Certification — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Comparison gallery of image scaling algorithms

This gallery shows the results of numerous image scaling algorithms. == Scaling methods == An image size can be changed in several ways. Consider resizing a 160x160 pixel photo to the following 40x40 pixel thumbnail and then scaling the thumbnail to a 160x160 pixel image. Also consider doubling the size of the following image containing text. == Examples of enlarged images == Below are examples of various images enlarged 4x using each scaling algorithm.
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Common Voice

Common Voice is a crowdsourcing project started by Mozilla to create a free and open speech corpus. The project is supported by volunteers who record sample sentences with a microphone and review recordings of other users. The transcribed sentences are collected in a voice database available under the public domain license CC0. This license ensures that developers can use the database for voice-to-text and text-to-voice applications without restrictions or costs. == Aims == Common Voice aims to provide diverse voice samples. According to Mozilla's Katharina Borchert, many existing projects took datasets from public radio or otherwise had datasets that underrepresented both women and people with pronounced accents. == Voice database == The first dataset was released in November 2017. More than 20,000 users worldwide had recorded 500 hours of English sentences. In February 2019, the first batch of languages was released for use. This included 18 languages such as English, French, German and Mandarin Chinese, but also less prevalent languages like Welsh and Kabyle. In total, this included almost 1,400 hours of recorded voice data from more than 42,000 contributors. By July 2020 the database had amassed 7,226 hours of voice recordings in 54 languages, 5,591 hours of which had been verified by volunteers. In May 2021, following the work to add Kinyarwanda, the project received a grant to add Kiswahili. At the beginning of 2022, Bengali.AI partnered with Common Voice to launch the "Bangla Speech Recognition" project that aims to make machines understand the Bangla language. 2000 hours of voice was collected. In September 2022, it was announced that the Twi language of Ghana was the 100th language to be added to the database. As of December 2025, Mozilla Common Voice collects voice data for over 250 languages, with the most hours having been collected in English, Catalan, Kinyarwanda, Belarusian and Esperanto.
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Apache Giraph

Apache Giraph is an Apache project to perform graph processing on big data. Giraph utilizes Apache Hadoop's MapReduce implementation to process graphs. Facebook used Giraph with some performance improvements to analyze one trillion edges using 200 machines in 4 minutes. Giraph is based on a paper published by Google about its own graph processing system called Pregel. It can be compared to other Big Graph processing libraries such as Cassovary. As of September 2023, it is no longer actively developed.
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Oscillatory neural network

An oscillatory neural network (ONN) is an artificial neural network that uses coupled oscillators as neurons. Oscillatory neural networks are closely linked to the Kuramoto model, and are inspired by the phenomenon of neural oscillations in the brain. Oscillatory neural networks have been trained to recognize images. Complex-Valued Oscillatory network has also been shown to store and retrieve multidimensional aperiodic signals. An oscillatory autoencoder has also been demonstrated, which uses a combination of oscillators and rate-coded neurons. A neuron made of two coupled oscillators, one having a fixed and the other having a tunable natural frequency, has been shown able to run logic gates such as XOR that conventional sigmoid neurons cannot.
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AI data center

An AI data center is a specialized data center facility designed for the computationally intensive tasks of training and running inference for artificial intelligence (AI) and machine learning models. Unlike general-purpose data centers, they are optimized for the parallel processing demands of AI workloads, typically using hardware such as AI accelerators (e.g., GPUs, TPUs) and high-speed interconnects. The global push to construct these specialized facilities accelerated dramatically during the AI boom of the 2020s. Memory manufacturers prioritized production of High Bandwidth Memory (HBM) essential for AI servers, which led to a global memory supply shortage amid a broader competition for advanced chips, power, and infrastructure. Major tech companies are estimated to spend $650 billion on AI data centers in 2026. == Architecture == Data centers for building and running large machine learning models contain specialized computer chips, GPUs, that use 2 to 4 times as much energy as their regular CPU counterparts (250-500 watts). AI data centers use 60 or more kilowatts per server rack, whereas more standard data centers typically use 5 to 10 kilowatts per rack. == Operators == As of August 2025, The Information tracked 18 planned or existing AI data centers in the United States, operated by Amazon Web Services, CoreWeave, Crusoe, Meta, Microsoft/OpenAI, Oracle, Tesla, and xAI. Other AI data center operators include Digital Realty and Alibaba. Data centers are also being built in China, India, Europe, Saudi Arabia, and Canada. The New Yorker described CoreWeave as the most prominent AI data center operator in the United States. Two types of data center providers for machine learning have been noted: hyperscalers and neoclouds. The Verge listed large technology companies such as Google, Meta, Microsoft, Oracle and Amazon as hyperscalers. The New York Times described neoclouds as "a new generation of data center providers". CoreWeave, Nebius, Nscale, and Lambda have been described as examples of neoclouds. In January 2025, OpenAI, in partnership with Oracle and Softbank, announced the Stargate project, which as of September 2025 is composed of six built or proposed AI data centers in the United States. In response to the Stargate project, Amazon launched in October 2025 an AI data center on 1,200 acres of farmland in Indiana. This data center, known as Project Rainier, is one of the largest AI data centers in the world, with Amazon spending $11 billion on the project. Rainier is specifically intended for training and running machine learning models from Anthropic. As of that time, this facility contains seven data centers (out of an estimated 30 planned) and will use 2.2 gigawatts of electricity (equivalent to 1 million households) and millions of gallons of water per year. Computer chips from Annapurna Labs and Anthropic, Trainium 2, were designed for use in such facilities. Amazon pumped millions of gallons of water out of the ground to construct the data center, and as of June 2025, Indiana state officials are investigating whether this dewatering process led to dry wells for local residents. In November 2025, Anthropic announced a plan in partnership with Fluidstack to develop artificial intelligence infrastructure in the United States, including data centers in New York and Texas, worth $50 billion. Other AI data center projects include the Colossus supercomputer from xAI, a Louisiana-based project from Meta, Hyperion, expected to use 5 GW of power, and a second Ohio-based Meta project, Prometheus, with a capacity of 1 GW. A 3,200-acre AI data center, capable of 4.4-4.5 GW of power and located on the decommissioned Homer City Generating Station, is under construction as of 2025, and will use seven 30-acre gas generating stations supplied by EQT. As of December 2025, CRH is working on over 100 data centers in the United States. In 2025, ExxonMobil and NextEra announced plans to build a data center powered by natural gas and using carbon capture technology, with 1.2 GW of power capacity. They previously purchased 2,500 acres of land in the Southeastern United States and plan to market the data center to an artificial intelligence company. The increased interest in AI data centers has led to several executives from companies in that space becoming billionaires, including CoreWeave, QTS, Nebius, Astera Labs, Groq, Fermi (which is connected to former United States Secretary of Energy Rick Perry), Snowflake and Cipher Mining. Several companies involved in cryptocurrency mining, such as Bitdeer, CoreWeave, Cipher Mining, TeraWulf, IREN, Core Scientific, and CleanSpark have also been involved with AI data centers. == Finances == Between January and August 2024, Microsoft, Meta, Google and Amazon collectively spent $125 billion on AI data centers. Citigroup forecasted that $2.8 trillion would be spent on AI data centers by 2030, while McKinsey and Company estimated that almost $7 trillion would be spent globally by that time. According to S&P Global, $61 billion has been spent on the data center market as a whole in 2025, while debt issuance for data centers was $182 billion during the same year. Large technology companies have offloaded the financial risks of building AI data centers by setting up special purpose vehicles or by contracting with neoclouds. For example, Meta's Hyperion was mostly funded by Blue Owl Capital, which did so using a bond offering from PIMCO. Those bonds were sold to a number of clients, including BlackRock. Meta did not borrow money itself and instead established a special purpose vehicle from which it would rent the data center. This deal was structured by Morgan Stanley for $30 billion, the largest known private capital transaction as of 2025. Neoclouds such as CoreWeave have gone into debt to buy computer chips from Nvidia for their data centers, and the chips themselves have been used for loan collateral. As of December 2025, CoreWeave took out three GPU-backed loans, collectively worth $12.4 billion, from private credit firms (Blackstone, Coatue, BlackRock, PIMCO) and from banks (Goldman Sachs, JPMorgan Chase, Wells Fargo). Thus, these companies provide an indirect connection between private credit and established banks. Data centers have also established asset-backed securities, and debt for data centers has its own derivative financial products. The real estate industry, including asset managers, public companies and private investors, has also invested in data centers. == Energy sourcing == == Environmental footprint == Average AI data centers have an electricity footprint equivalent to 100,000 households, and use billions of gallons of water for cooling their hardware. In 2025, the International Energy Agency estimated that the larger AI data centers currently under construction could consume as much electricity as 2 million households. A 2024 report from the United States Department of Energy stated that data centers overall used 17 billion gallons of water per year in the United States, primarily due to "rapid proliferation of AI servers", and that this usage was forecasted to grow to nearly 80 billion gallons by 2028. Researchers estimated that AI data centers in the United States would emit 24-44 million metric tons of carbon dioxide and use 731–1,125 million cubic meters of water per year between 2024 and 2030. Peaking power plants, which have been proposed as a power source for AI data centers, emit sulfur dioxide and have historically been located disproportionately near communities of color in the United States. Reciprocating internal combustion engines, proposed as another power source for a data center, emit PM 2.5, nitrogen oxides, and volatile organic compounds. == AI data centers in the United States == In the United States, both the Biden administration and second Trump administration supported the construction of AI data centers. In January 2025, then-president Joe Biden signed an executive order for federal government agencies to support AI data centers on federal sites built by private companies, study their effect on energy prices, and encourage their use of renewable energy. In April 2025, the United States Department of Energy suggested 16 possible sites, including Los Alamos National Laboratory, Sandia National Laboratories and Oak Ridge National Laboratory. In its July 2025 AI Action Plan, the second Trump administration supported increased production of AI data centers. Several US states have incentivized local data center construction. For example, in 2024, lawmakers in Michigan approved tax breaks for data center equipment and construction material. Some data center companies have also invested or promised to invest in the infrastructure of local communities. In December 2025, Democratic senators Elizabeth Warren, Chris Van Hollen, and Richard Blumenthal wrote to seven technology companies (Google, Microsoft, Amazon, Meta, CoreWeave, Digital Realty, and Equinix) that they w
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Effective fitness

In natural evolution and artificial evolution (e.g. artificial life and evolutionary computation) the fitness (or performance or objective measure) of a schema is rescaled to give its effective fitness which takes into account crossover and mutation. Effective fitness is used in Evolutionary Computation to understand population dynamics. While a biological fitness function only looks at reproductive success, an effective fitness function tries to encompass things that are needed to be fulfilled for survival on population level. In homogeneous populations, reproductive fitness and effective fitness are equal. When a population moves away from homogeneity a higher effective fitness is reached for the recessive genotype. This advantage will decrease while the population moves toward an equilibrium. The deviation from this equilibrium displays how close the population is to achieving a steady state. When this equilibrium is reached, the maximum effective fitness of the population is achieved. Problem solving with evolutionary computation is realized with a cost function. If cost functions are applied to swarm optimization they are called a fitness function. Strategies like reinforcement learning and NEAT neuroevolution are creating a fitness landscape which describes the reproductive success of cellular automata. The effective fitness function models the number of fit offspring and is used in calculations that include evolutionary processes, such as mutation and crossover, important on the population level. The effective fitness model is superior to its predecessor, the standard reproductive fitness model. It advances in the qualitatively and quantitatively understanding of evolutionary concepts like bloat, self-adaptation, and evolutionary robustness. While reproductive fitness only looks at pure selection, effective fitness describes the flow of a population and natural selection by taking genetic operators into account. A normal fitness function fits to a problem, while an effective fitness function is an assumption if the objective was reached. The difference is important for designing fitness functions with algorithms like novelty search in which the objective of the agents is unknown. In the case of bacteria effective fitness could include production of toxins and rate of mutation of different plasmids, which are mostly stochastically determined == Applications == When evolutionary equations of the studied population dynamics are available, one can algorithmically compute the effective fitness of a given population. Though the perfect effective fitness model is yet to be found, it is already known to be a good framework to the better understanding of the moving of the genotype-phenotype map, population dynamics, and the flow on fitness landscapes. Models using a combination of Darwinian fitness functions and effective functions are better at predicting population trends. Effective models could be used to determine therapeutic outcomes of disease treatment. Other models could determine effective protein engineering and works towards finding novel or heightened biochemistry.
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Error tolerance (PAC learning)

In PAC learning, error tolerance refers to the ability of an algorithm to learn when the examples received have been corrupted in some way. In fact, this is a very common and important issue since in many applications it is not possible to access noise-free data. Noise can interfere with the learning process at different levels: the algorithm may receive data that have been occasionally mislabeled, or the inputs may have some false information, or the classification of the examples may have been maliciously adulterated. == Notation and the Valiant learning model == In the following, let X {\displaystyle X} be our n {\displaystyle n} -dimensional input space. Let H {\displaystyle {\mathcal {H}}} be a class of functions that we wish to use in order to learn a { 0 , 1 } {\displaystyle \{0,1\}} -valued target function f {\displaystyle f} defined over X {\displaystyle X} . Let D {\displaystyle {\mathcal {D}}} be the distribution of the inputs over X {\displaystyle X} . The goal of a learning algorithm A {\displaystyle {\mathcal {A}}} is to choose the best function h ∈ H {\displaystyle h\in {\mathcal {H}}} such that it minimizes e r r o r ( h ) = P x ∼ D ( h ( x ) ≠ f ( x ) ) {\displaystyle error(h)=P_{x\sim {\mathcal {D}}}(h(x)\neq f(x))} . Let us suppose we have a function s i z e ( f ) {\displaystyle size(f)} that can measure the complexity of f {\displaystyle f} . Let Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} be an oracle that, whenever called, returns an example x {\displaystyle x} and its correct label f ( x ) {\displaystyle f(x)} . When no noise corrupts the data, we can define learning in the Valiant setting: Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the Valiant setting if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} and a polynomial p ( ⋅ , ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot ,\cdot )} such that for any 0 < ε ≤ 1 {\displaystyle 0<\varepsilon \leq 1} and 0 < δ ≤ 1 {\displaystyle 0<\delta \leq 1} it outputs, in a number of calls to the oracle bounded by p ( 1 ε , 1 δ , n , size ( f ) ) {\displaystyle p\left({\frac {1}{\varepsilon }},{\frac {1}{\delta }},n,{\text{size}}(f)\right)} , a function h ∈ H {\displaystyle h\in {\mathcal {H}}} that satisfies with probability at least 1 − δ {\displaystyle 1-\delta } the condition error ( h ) ≤ ε {\displaystyle {\text{error}}(h)\leq \varepsilon } . In the following we will define learnability of f {\displaystyle f} when data have suffered some modification. == Classification noise == In the classification noise model a noise rate 0 ≤ η < 1 2 {\displaystyle 0\leq \eta <{\frac {1}{2}}} is introduced. Then, instead of Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} that returns always the correct label of example x {\displaystyle x} , algorithm A {\displaystyle {\mathcal {A}}} can only call a faulty oracle Oracle ( x , η ) {\displaystyle {\text{Oracle}}(x,\eta )} that will flip the label of x {\displaystyle x} with probability η {\displaystyle \eta } . As in the Valiant case, the goal of a learning algorithm A {\displaystyle {\mathcal {A}}} is to choose the best function h ∈ H {\displaystyle h\in {\mathcal {H}}} such that it minimizes e r r o r ( h ) = P x ∼ D ( h ( x ) ≠ f ( x ) ) {\displaystyle error(h)=P_{x\sim {\mathcal {D}}}(h(x)\neq f(x))} . In applications it is difficult to have access to the real value of η {\displaystyle \eta } , but we assume we have access to its upperbound η B {\displaystyle \eta _{B}} . Note that if we allow the noise rate to be 1 / 2 {\displaystyle 1/2} , then learning becomes impossible in any amount of computation time, because every label conveys no information about the target function. Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the classification noise model if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , η ) {\displaystyle {\text{Oracle}}(x,\eta )} and a polynomial p ( ⋅ , ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot ,\cdot )} such that for any 0 ≤ η ≤ 1 2 {\displaystyle 0\leq \eta \leq {\frac {1}{2}}} , 0 ≤ ε ≤ 1 {\displaystyle 0\leq \varepsilon \leq 1} and 0 ≤ δ ≤ 1 {\displaystyle 0\leq \delta \leq 1} it outputs, in a number of calls to the oracle bounded by p ( 1 1 − 2 η B , 1 ε , 1 δ , n , s i z e ( f ) ) {\displaystyle p\left({\frac {1}{1-2\eta _{B}}},{\frac {1}{\varepsilon }},{\frac {1}{\delta }},n,size(f)\right)} , a function h ∈ H {\displaystyle h\in {\mathcal {H}}} that satisfies with probability at least 1 − δ {\displaystyle 1-\delta } the condition e r r o r ( h ) ≤ ε {\displaystyle error(h)\leq \varepsilon } . == Statistical query learning == Statistical Query Learning is a kind of active learning problem in which the learning algorithm A {\displaystyle {\mathcal {A}}} can decide if to request information about the likelihood P f ( x ) {\displaystyle P_{f(x)}} that a function f {\displaystyle f} correctly labels example x {\displaystyle x} , and receives an answer accurate within a tolerance α {\displaystyle \alpha } . Formally, whenever the learning algorithm A {\displaystyle {\mathcal {A}}} calls the oracle Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} , it receives as feedback probability Q f ( x ) {\displaystyle Q_{f(x)}} , such that Q f ( x ) − α ≤ P f ( x ) ≤ Q f ( x ) + α {\displaystyle Q_{f(x)}-\alpha \leq P_{f(x)}\leq Q_{f(x)}+\alpha } . Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the statistical query learning model if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} and polynomials p ( ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot )} , q ( ⋅ , ⋅ , ⋅ ) {\displaystyle q(\cdot ,\cdot ,\cdot )} , and r ( ⋅ , ⋅ , ⋅ ) {\displaystyle r(\cdot ,\cdot ,\cdot )} such that for any 0 < ε ≤ 1 {\displaystyle 0<\varepsilon \leq 1} the following hold: Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} can evaluate P f ( x ) {\displaystyle P_{f(x)}} in time q ( 1 ε , n , s i z e ( f ) ) {\displaystyle q\left({\frac {1}{\varepsilon }},n,size(f)\right)} ; 1 α {\displaystyle {\frac {1}{\alpha }}} is bounded by r ( 1 ε , n , s i z e ( f ) ) {\displaystyle r\left({\frac {1}{\varepsilon }},n,size(f)\right)} A {\displaystyle {\mathcal {A}}} outputs a model h {\displaystyle h} such that e r r ( h ) < ε {\displaystyle err(h)<\varepsilon } , in a number of calls to the oracle bounded by p ( 1 ε , n , s i z e ( f ) ) {\displaystyle p\left({\frac {1}{\varepsilon }},n,size(f)\right)} . Note that the confidence parameter δ {\displaystyle \delta } does not appear in the definition of learning. This is because the main purpose of δ {\displaystyle \delta } is to allow the learning algorithm a small probability of failure due to an unrepresentative sample. Since now Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} always guarantees to meet the approximation criterion Q f ( x ) − α ≤ P f ( x ) ≤ Q f ( x ) + α {\displaystyle Q_{f(x)}-\alpha \leq P_{f(x)}\leq Q_{f(x)}+\alpha } , the failure probability is no longer needed. The statistical query model is strictly weaker than the PAC model: any efficiently SQ-learnable class is efficiently PAC learnable in the presence of classification noise, but there exist efficient PAC-learnable problems such as parity that are not efficiently SQ-learnable. == Malicious classification == In the malicious classification model an adversary generates errors to foil the learning algorithm. This setting describes situations of error burst, which may occur when for a limited time transmission equipment malfunctions repeatedly. Formally, algorithm A {\displaystyle {\mathcal {A}}} calls an oracle Oracle ( x , β ) {\displaystyle {\text{Oracle}}(x,\beta )} that returns a correctly labeled example x {\displaystyle x} drawn, as usual, from distribution D {\displaystyle {\mathcal {D}}} over the input space with probability 1 − β {\displaystyle 1-\beta } , but it returns with probability β {\displaystyle \beta } an example drawn from a distribution that is not related to D {\displaystyle {\mathcal {D}}} . Moreover, this maliciously chosen example may strategically selected by an adversary who has knowledge of f {\displaystyle f} , β {\displaystyle \beta } , D {\displaystyle {\mathcal {D}}} , or the current progress of the learning algorithm. Definition: Given a bound β B < 1 2 {\displaystyle \beta _{B}<{\frac {1}{2}}} for 0 ≤ β < 1 2 {\displaystyle 0\leq \beta <{\frac {1}{2}}} , we say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the malicious classification model, if there exist a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , β ) {\displaystyle {\text{Oracle}}(x,\beta )}
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Vapnik–Chervonenkis dimension

In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the size (capacity, complexity, expressive power, richness, or flexibility) of a class of sets. The notion can be extended to classes of binary functions. It is defined as the cardinality of the largest set of points that the function class can shatter—that is, for which all possible binary labelings can be realized by some function in the class. It was originally defined by Vladimir Vapnik and Alexey Chervonenkis. Informally, the capacity of a classification model is related to how complicated it can be. For example, consider the thresholding of a high-degree polynomial: if the polynomial evaluates above zero, that point is classified as positive, otherwise as negative. A high-degree polynomial can be wiggly, so that it can fit a given set of training points well. Such a polynomial has a high capacity. A much simpler alternative is to threshold a linear function. This function may not fit the training set well, because it has a low capacity. This notion of capacity is made rigorous below. == Definitions == === VC dimension of a set-family === Let C = { C } C ∈ C {\displaystyle {\mathcal {C}}=\{C\}_{C\in {\mathcal {C}}}} be a family of sets (also called set family, collection of sets or set of sets) and X {\displaystyle X} a set. Their intersection is defined as the following set family: C ∩ X := { C ∩ X ∣ C ∈ C } . {\displaystyle {\mathcal {C}}\cap X:=\{C\cap X\mid C\in {\mathcal {C}}\}.} Here typically X {\displaystyle X} and each C ∈ C {\displaystyle C\in {\mathcal {C}}} are subsets of a big "universe" of possibilities U {\displaystyle U} where intersection takes place. We say that a set X {\displaystyle X} is shattered by C {\displaystyle {\mathcal {C}}} if P ( X ) = C ∩ X {\displaystyle {\mathcal {P}}(X)={\mathcal {C}}\cap X} i.e. the set of intersections contains (hence is equal to) all the subsets of X {\displaystyle X} . For finite sets X {\displaystyle X} this is equivalent to | C ∩ X | = 2 | X | . {\displaystyle |{\mathcal {C}}\cap X|=2^{|X|}.} The VC dimension D {\displaystyle D} of C {\displaystyle {\mathcal {C}}} is the cardinality of the largest set that is shattered by C {\displaystyle {\mathcal {C}}} . If arbitrarily large sets can be shattered, the VC dimension of C {\displaystyle {\mathcal {C}}} is ∞ {\displaystyle \infty } . === VC dimension of a classification model === A binary classification model f {\displaystyle f} with some parameter vector θ {\displaystyle \theta } is said to shatter a set of generally positioned data points ( x 1 , x 2 , … , x n ) {\displaystyle (x_{1},x_{2},\ldots ,x_{n})} if, for every assignment of labels to those points, there exists a θ {\displaystyle \theta } such that the model f {\displaystyle f} makes no errors when evaluating that set of data points. The VC dimension of a model f {\displaystyle f} is the maximum number of points that can be arranged so that f {\displaystyle f} shatters them. More formally, it is the maximum cardinal D {\displaystyle D} such that there exists a generally positioned data point set of cardinality D {\displaystyle D} that can be shattered by f {\displaystyle f} . == Examples == f {\displaystyle f} is a constant classifier (with no parameters); Its VC dimension is 0 since it cannot shatter even a single point. In general, the VC dimension of a finite classification model, which can return at most 2 d {\displaystyle 2^{d}} different classifiers, is at most d {\displaystyle d} (this is an upper bound on the VC dimension; the Sauer–Shelah lemma gives a lower bound on the dimension). f {\displaystyle f} is a single-parametric threshold classifier on real numbers; i.e., for a certain threshold θ {\displaystyle \theta } , the classifier f θ {\displaystyle f_{\theta }} returns 1 if the input number is larger than θ {\displaystyle \theta } and 0 otherwise. The VC dimension of f {\displaystyle f} is 1 because: (a) It can shatter a single point. For every point x {\displaystyle x} , a classifier f θ {\displaystyle f_{\theta }} labels it as 0 if θ > x {\displaystyle \theta >x} and labels it as 1 if θ < x {\displaystyle \theta x + 2 {\displaystyle \theta >x+2} , as (1,0) if θ ∈ [ x − 4 , x − 2 ) {\displaystyle \theta \in [x-4,x-2)} , as (1,1) if θ ∈ [ x − 2 , x ] {\displaystyle \theta \in [x-2,x]} , and as (0,1) if θ ∈ ( x , x + 2 ] {\displaystyle \theta \in (x,x+2]} . (b) It cannot shatter any set of three points. For every set of three numbers, if the smallest and the largest are labeled 1, then the middle one must also be labeled 1, so not all labelings are possible. f {\displaystyle f} is a straight line as a classification model on points in a two-dimensional plane (this is the model used by a perceptron). The line should separate positive data points from negative data points. There exist sets of 3 points that can indeed be shattered using this model (any 3 points that are not collinear can be shattered). However, no set of 4 points can be shattered: by Radon's theorem, any four points can be partitioned into two subsets with intersecting convex hulls, so it is not possible to separate one of these two subsets from the other. Thus, the VC dimension of this particular classifier is 3. It is important to remember that while one can choose any arrangement of points, the arrangement of those points cannot change when attempting to shatter for some label assignment. Note, only 3 of the 23 = 8 possible label assignments are shown for the three points. f {\displaystyle f} is a single-parametric sine classifier, i.e., for a certain parameter θ {\displaystyle \theta } , the classifier f θ {\displaystyle f_{\theta }} returns 1 if the input number x {\displaystyle x} has sin ⁡ ( θ x ) > 0 {\displaystyle \sin(\theta x)>0} and 0 otherwise. The VC dimension of f {\displaystyle f} is infinite, since it can shatter any finite subset of the set { 2 − m ∣ m ∈ N } {\displaystyle \{2^{-m}\mid m\in \mathbb {N} \}} . == Uses == === In statistical learning theory === The VC dimension can predict a probabilistic upper bound on the test error of a classification model. Vapnik proved that the probability of the test error (i.e., risk with 0–1 loss function) distancing from an upper bound (on data that is drawn i.i.d. from the same distribution as the training set) is given by: Pr ( test error ⩽ training error + 1 N [ D ( log ⁡ ( 2 N D ) + 1 ) − log ⁡ ( η 4 ) ] ) = 1 − η , {\displaystyle \Pr \left({\text{test error}}\leqslant {\text{training error}}+{\sqrt {{\frac {1}{N}}\left[D\left(\log \left({\tfrac {2N}{D}}\right)+1\right)-\log \left({\tfrac {\eta }{4}}\right)\right]}}\,\right)=1-\eta ,} where D {\displaystyle D} is the VC dimension of the classification model, 0 < η ⩽ 1 {\displaystyle 0<\eta \leqslant 1} , and N {\displaystyle N} is the size of the training set (restriction: this formula is valid when D ≪ N {\displaystyle D\ll N} . When D {\displaystyle D} is larger, the test-error may be much higher than the training-error. This is due to overfitting). The VC dimension also appears in sample-complexity bounds. A space of binary functions with VC dimension D {\displaystyle D} can be learned with: N = Θ ( D + ln ⁡ 1 δ ε 2 ) {\displaystyle N=\Theta \left({\frac {D+\ln {1 \over \delta }}{\varepsilon ^{2}}}\right)} samples, where ε {\displaystyle \varepsilon } is the learning error and δ {\displaystyle \delta } is the failure probability. Thus, the sample-complexity is a linear function of the VC dimension of the hypothesis space. === In computational geometry === The VC dimension is one of the critical parameters in the size of ε-nets, which determines the complexity of approximation algorithms based on them; range sets without finite VC dimension may not have finite ε-nets at all. == Bounds == The VC dimension of the dual set-family of C {\displaystyle {\mathcal {C}}} is strictly less than 2 vc ⁡ ( C ) + 1 {\displaystyle 2^{\operatorname {vc} ({\mathcal {C}})+1}} , and this is best possible. The VC dimension of a finite set-family C {\displaystyle {\mathcal {C}}} is at most log 2 ⁡ | C | {\displaystyle \log _{2}|{\mathcal {C}}|} . This is because | C ∩ X | ≤ | X | {\displaystyle |{\mathcal {C}}\cap X|\leq |X|} by definition. Given a set-fa
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Open-source robotics

Open-source robotics is a branch of robotics where robots are developed with open-source hardware and free and open-source software, publicly sharing blueprints, schematics, and source code. It is thus closely related to the open design movement, the maker movement and open science. == Requirements == Open source robotics means that information about the hardware is easily discerned, so that others can easily rebuild it. In turn, this requires design to use only easily available standard subcomponents and tools, and for the build process to be documented in detail including a bill of materials and detailed ('Ikea style') step-by-step building and testing instructions. (A CAD file alone is not sufficient, as it does not show the steps for performing or testing the build). These requirements are standard to open source hardware in general, and are formalised by various licences, certifications, especially those defined by the peer-reviewed journals Journal of Open Hardware and HardwareX. Licensing requirements for software are the same as for any open source software. But in addition, for software components to be of practical use in real robot systems, they need to be compatible with other software, usually as defined by some robotics middleware community standard. == Hardware systems == Applications to date include: Robot arms, e.g. PARA or Thor Wheeled mobile robots. e.g. OpenScout Four-legged robots such as the Open Dynamic Robot Initiative UAV quadcopters (drones) such as Agilicious Humanoid robots, e.g. iCub, Berkeley Humanoid Lite Self-driving cars, e.g. OpenPodcar (→ Personal rapid transit) Submersible robots, eg. OpenFish Laboratory robotics such as chemical liquid handling Vertical farming Swarm robots, e.g. HeRoSwarm Domestic tasks: vacuum cleaning, floor washing and grass mowing Robot sports including robot combat and autonomous racing Education == Hardware subcomponents == Most open source hardware definitions allow non-open subcomponents to be used in modular design, as long as they are easily available. However many designs try to push openness down into as many subcomponents as possible, with the aim of ultimately reaching fully open designs. Open hardware manual-drive vehicles and their subcomponents, such as from Open Source Ecology, are often used as starting points and extended with automation systems. Open subcomponents can include open-source computing hardware as subcomponents, such as Arduino and RISC-V, as well as open source motors and drivers such as the Open Source Motor Controller and ODrive. Open hardware robotics interface boards can simplify interfacing between middleware software and physical hardware. == Software subcomponents == === Middleware === Robotics middleware is software which links multiple other software components together. In robotics, this specifically means real-time communication systems with standardized message passing protocols. The predominant open source middleware is ROS2, the robot operating system, now as version 2. Other alternatives include ROS1, YARP — used in the iCub, URBI, and Orca. Open source middleware is usually run on an open source operating system, especially the Ubuntu distribution of Linux. === Driver software === Most robot sensors and actuators require software drivers. There is little standardization of open source software at this level, because each hardware device is different. Creating open drivers for closed hardware is difficult as it requires both low level programming and reverse engineering. === Simulation software === Open source robotics simulators include Gazebo, MuJoCo and Webots. Open source 3D game engines such as Godot are also sometimes used as simulators, when equipped with suitable middleware interfaces. === Automation software === At the level of AI, many standard algorithms have open source software implementations, mostly in ROS2. Major components include: Machine vision systems such as the YOLO object detector. 3D photogrammetry Navigation including SLAM and planning such as nav2 Arm inverse kinematics such as moveIt2 == Community == The first signs of the increasing popularity of building and sharing robot designs were found with the maker culture community. What began with small competitions for remote operated vehicles (e.g. Robot combat), soon developed to the building of autonomous telepresence robots such as Sparky and then true robots (being able to take decisions themselves) as the Open Automaton Project. Several commercial companies now also produce kits for making simple robots. The community has adopted open source hardware licenses, certifications, and peer-reviewed publications, which check that source has been made correctly and permanently available under community definitions, and which validate that this has been done. These processes have become critically important due to many historical projects claiming to be open source but them reverting on the promise due to commercialisation or other pressures. As with other forms of open source hardware, the community continues to debate precise criteria for 'ease of build'. A common standard is that designs should be buildable by a technical university student, in a few days, using typical fablab tools, but definitions of all of these subterms can also be debated. Compared to other forms of open source hardware, open source robotics typically includes a large software element, so involves software as well as hardware engineers. Open source concepts are more established in open source software than hardware, so robotics is a field in which those concepts can be shared and transferred from software to hardware. While the community in open source robotics is multi-faceted with a wide range of backgrounds, a sizable sub-community uses the ROS middleware and meets at the ROSCon conferences to discuss development of ROS itself and automation components built on it.
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European Conference on Computer Vision

The European Conference on Computer Vision (ECCV) is a biennial research conference with the proceedings published by Springer Science+Business Media. Similar to ICCV in scope and quality, it is held those years which ICCV is not. It is considered to be one of the top conferences in computer vision, alongside CVPR and ICCV, with an 'A' rating from the Australian Ranking of ICT Conferences and an 'A1' rating from the Brazilian ministry of education. The acceptance rate for ECCV 2010 was 24.4% for posters and 3.3% for oral presentations. Like other top computer vision conferences, ECCV has tutorial talks, technical sessions, and poster sessions. The conference is usually spread over five to six days with the main technical program occupying three days in the middle, and tutorial and workshops, focused on specific topics, being held in the beginning and at the end. The ECCV presents the Koenderink Prize annually to recognize fundamental contributions in computer vision. == Location == The conference is usually held in autumn in Europe.
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Logic learning machine

Logic learning machine (LLM) is a machine learning method based on the generation of intelligible rules. LLM is an efficient implementation of the Switching Neural Network (SNN) paradigm, developed by Marco Muselli, Senior Researcher at the Italian National Research Council CNR-IEIIT in Genoa. LLM has been employed in many different sectors, including the field of medicine (orthopedic patient classification, DNA micro-array analysis and Clinical Decision Support Systems), financial services and supply chain management. == History == The Switching Neural Network approach was developed in the 1990s to overcome the drawbacks of the most commonly used machine learning methods. In particular, black box methods, such as multilayer perceptron and support vector machine, had good accuracy but could not provide deep insight into the studied phenomenon. On the other hand, decision trees were able to describe the phenomenon but often lacked accuracy. Switching Neural Networks made use of Boolean algebra to build sets of intelligible rules able to obtain very good performance. In 2014, an efficient version of Switching Neural Network was developed and implemented in the Rulex suite with the name Logic Learning Machine. Also, an LLM version devoted to regression problems was developed. == General == Like other machine learning methods, LLM uses data to build a model able to perform a good forecast about future behaviors. LLM starts from a table including a target variable (output) and some inputs and generates a set of rules that return the output value y {\displaystyle y} corresponding to a given configuration of inputs. A rule is written in the form: if premise then consequence where consequence contains the output value whereas premise includes one or more conditions on the inputs. According to the input type, conditions can have different forms: for categorical variables the input value must be in a given subset: x 1 ∈ { A , B , C , . . . } {\displaystyle x_{1}\in \{A,B,C,...\}} . for ordered variables the condition is written as an inequality or an interval: x 2 ≤ α {\displaystyle x_{2}\leq \alpha } or β ≤ x 3 ≤ γ {\displaystyle \beta \leq x_{3}\leq \gamma } A possible rule is therefore in the form if x 1 ∈ { A , B , C , . . . } {\displaystyle x_{1}\in \{A,B,C,...\}} AND x 2 ≤ α {\displaystyle x_{2}\leq \alpha } AND β ≤ x 3 ≤ γ {\displaystyle \beta \leq x_{3}\leq \gamma } then y = y ¯ {\displaystyle y={\bar {y}}} == Types == According to the output type, different versions of the Logic Learning Machine have been developed: Logic Learning Machine for classification, when the output is a categorical variable, which can assume values in a finite set Logic Learning Machine for regression, when the output is an integer or real number.
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Mixture model

In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population. However, while problems associated with "mixture distributions" relate to deriving the properties of the overall population from those of the sub-populations, "mixture models" are used to make statistical inferences about the properties of the sub-populations given only observations on the pooled population, without sub-population identity information. Mixture models are used for clustering, under the name model-based clustering, and also for density estimation. Mixture models should not be confused with models for compositional data, i.e., data whose components are constrained to sum to a constant value (1, 100%, etc.). However, compositional models can be thought of as mixture models, where members of the population are sampled at random. Conversely, mixture models can be thought of as compositional models, where the total size reading population has been normalized to 1. == Structure == === General mixture model === A typical finite-dimensional mixture model is a hierarchical model consisting of the following components: N random variables that are observed, each distributed according to a mixture of K components, with the components belonging to the same parametric family of distributions (e.g., all normal, all Zipfian, etc.) but with different parameters. However, it is also possible to have a finite mixture model where each component belongs to a different parametric family of distributions, for example, a mixture of a multivariate normal distribution and a generalized hyperbolic distribution. N random latent variables specifying the identity of the mixture component of each observation, each distributed according to a K-dimensional categorical distribution A set of K mixture weights, which are probabilities that sum to 1. A set of K parameters, each specifying the parameter of the corresponding mixture component. In many cases, each "parameter" is actually a set of parameters. For example, if the mixture components are Gaussian distributions, there will be a mean and variance for each component. If the mixture components are categorical distributions (e.g., when each observation is a token from a finite alphabet of size V), there will be a vector of V probabilities summing to 1. In addition, in a Bayesian setting, the mixture weights and parameters will themselves be random variables, and prior distributions will be placed over the variables. In such a case, the weights are typically viewed as a K-dimensional random vector drawn from a Dirichlet distribution (the conjugate prior of the categorical distribution), and the parameters will be distributed according to their respective conjugate priors. Mathematically, a basic parametric mixture model can be described as follows: K = number of mixture components N = number of observations θ i = 1 … K = parameter of distribution of observation associated with component i ϕ i = 1 … K = mixture weight, i.e., prior probability of a particular component i ϕ = K -dimensional vector composed of all the individual ϕ 1 … K ; must sum to 1 z i = 1 … N = component of observation i x i = 1 … N = observation i F ( x | θ ) = probability distribution of an observation, parametrized on θ z i = 1 … N ∼ Categorical ⁡ ( ϕ ) x i = 1 … N | z i = 1 … N ∼ F ( θ z i ) {\displaystyle {\begin{array}{lcl}K&=&{\text{number of mixture components}}\\N&=&{\text{number of observations}}\\\theta _{i=1\dots K}&=&{\text{parameter of distribution of observation associated with component }}i\\\phi _{i=1\dots K}&=&{\text{mixture weight, i.e., prior probability of a particular component }}i\\{\boldsymbol {\phi }}&=&K{\text{-dimensional vector composed of all the individual }}\phi _{1\dots K}{\text{; must sum to 1}}\\z_{i=1\dots N}&=&{\text{component of observation }}i\\x_{i=1\dots N}&=&{\text{observation }}i\\F(x|\theta )&=&{\text{probability distribution of an observation, parametrized on }}\theta \\z_{i=1\dots N}&\sim &\operatorname {Categorical} ({\boldsymbol {\phi }})\\x_{i=1\dots N}|z_{i=1\dots N}&\sim &F(\theta _{z_{i}})\end{array}}} In a Bayesian setting, all parameters are associated with random variables, as follows: K , N = as above θ i = 1 … K , ϕ i = 1 … K , ϕ = as above z i = 1 … N , x i = 1 … N , F ( x | θ ) = as above α = shared hyperparameter for component parameters β = shared hyperparameter for mixture weights H ( θ | α ) = prior probability distribution of component parameters, parametrized on α θ i = 1 … K ∼ H ( θ | α ) ϕ ∼ S y m m e t r i c - D i r i c h l e t K ⁡ ( β ) z i = 1 … N | ϕ ∼ Categorical ⁡ ( ϕ ) x i = 1 … N | z i = 1 … N , θ i = 1 … K ∼ F ( θ z i ) {\displaystyle {\begin{array}{lcl}K,N&=&{\text{as above}}\\\theta _{i=1\dots K},\phi _{i=1\dots K},{\boldsymbol {\phi }}&=&{\text{as above}}\\z_{i=1\dots N},x_{i=1\dots N},F(x|\theta )&=&{\text{as above}}\\\alpha &=&{\text{shared hyperparameter for component parameters}}\\\beta &=&{\text{shared hyperparameter for mixture weights}}\\H(\theta |\alpha )&=&{\text{prior probability distribution of component parameters, parametrized on }}\alpha \\\theta _{i=1\dots K}&\sim &H(\theta |\alpha )\\{\boldsymbol {\phi }}&\sim &\operatorname {Symmetric-Dirichlet} _{K}(\beta )\\z_{i=1\dots N}|{\boldsymbol {\phi }}&\sim &\operatorname {Categorical} ({\boldsymbol {\phi }})\\x_{i=1\dots N}|z_{i=1\dots N},\theta _{i=1\dots K}&\sim &F(\theta _{z_{i}})\end{array}}} This characterization uses F and H to describe arbitrary distributions over observations and parameters, respectively. Typically H will be the conjugate prior of F. The two most common choices of F are Gaussian aka "normal" (for real-valued observations) and categorical (for discrete observations). Other common possibilities for the distribution of the mixture components are: Binomial distribution, for the number of "positive occurrences" (e.g., successes, yes votes, etc.) given a fixed number of total occurrences Multinomial distribution, similar to the binomial distribution, but for counts of multi-way occurrences (e.g., yes/no/maybe in a survey) Negative binomial distribution, for binomial-type observations but where the quantity of interest is the number of failures before a given number of successes occurs Poisson distribution, for the number of occurrences of an event in a given period of time, for an event that is characterized by a fixed rate of occurrence Exponential distribution, for the time before the next event occurs, for an event that is characterized by a fixed rate of occurrence Log-normal distribution, for positive real numbers that are assumed to grow exponentially, such as incomes or prices Multivariate normal distribution (aka multivariate Gaussian distribution), for vectors of correlated outcomes that are individually Gaussian-distributed Multivariate Student's t-distribution, for vectors of heavy-tailed correlated outcomes A vector of Bernoulli-distributed values, corresponding, e.g., to a black-and-white image, with each value representing a pixel; see the handwriting-recognition example below === Specific examples === ==== Gaussian mixture model ==== A typical non-Bayesian Gaussian mixture model looks like this: K , N = as above ϕ i = 1 … K , ϕ = as above z i = 1 … N , x i = 1 … N = as above θ i = 1 … K = { μ i = 1 … K , σ i = 1 … K 2 } μ i = 1 … K = mean of component i σ i = 1 … K 2 = variance of component i z i = 1 … N ∼ Categorical ⁡ ( ϕ ) x i = 1 … N ∼ N ( μ z i , σ z i 2 ) {\displaystyle {\begin{array}{lcl}K,N&=&{\text{as above}}\\\phi _{i=1\dots K},{\boldsymbol {\phi }}&=&{\text{as above}}\\z_{i=1\dots N},x_{i=1\dots N}&=&{\text{as above}}\\\theta _{i=1\dots K}&=&\{\mu _{i=1\dots K},\sigma _{i=1\dots K}^{2}\}\\\mu _{i=1\dots K}&=&{\text{mean of component }}i\\\sigma _{i=1\dots K}^{2}&=&{\text{variance of component }}i\\z_{i=1\dots N}&\sim &\operatorname {Categorical} ({\boldsymbol {\phi }})\\x_{i=1\dots N}&\sim &{\mathcal {N}}(\mu _{z_{i}},\sigma _{z_{i}}^{2})\end{array}}} A Bayesian version of a Gaussian mixture model is as follows: K , N = as above ϕ i = 1 … K , ϕ = as above z i = 1 … N , x i = 1 … N = as above θ i = 1 … K = { μ i = 1 … K , σ i = 1 … K 2 } μ i = 1 … K = mean of component i σ i = 1 … K 2 = variance of component i μ 0 , λ , ν , σ 0 2 = shared hyperparameters μ i = 1 … K ∼ N ( μ 0 , λ σ i 2 ) σ i = 1 … K 2 ∼ I n v e r s e - G a m m a ⁡ ( ν , σ 0 2 ) ϕ ∼ S y m m e t r i c - D i r i c h l e t K ⁡ ( β ) z i = 1 … N ∼ Categorical ⁡ ( ϕ ) x i = 1 … N ∼ N ( μ z i , σ z i 2 ) {\displaystyle {\begin{array}{lcl}K,N&=&{\text{as above}}\\\phi _{i=1\dots K},{\boldsymbol {\phi }}&=&{\text{as above}}\\z_{i=1\dots N},x_{i=1\dots N}&=&{\text{as above}}\\\theta _{i=1\
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Seccomp

seccomp (short for secure computing) is a computer security facility in the Linux kernel. seccomp allows a process to make a one-way transition into a "secure" state where it cannot make any system calls except exit(), sigreturn(), read() and write() to already-open file descriptors. Should it attempt any other system calls, the kernel will either just log the event or terminate the process with SIGKILL or SIGSYS. In this sense, it does not virtualize the system's resources but isolates the process from them entirely. seccomp mode is enabled via the prctl(2) system call using the PR_SET_SECCOMP argument, or (since Linux kernel 3.17) via the seccomp(2) system call. seccomp mode used to be enabled by writing to a file, /proc/self/seccomp, but this method was removed in favor of prctl(). In some kernel versions, seccomp disables the RDTSC x86 instruction, which returns the number of elapsed processor cycles since power-on, used for high-precision timing. seccomp-bpf is an extension to seccomp that allows filtering of system calls using a configurable policy implemented using Berkeley Packet Filter rules. It is used by OpenSSH and vsftpd as well as the Google Chrome/Chromium web browsers on ChromeOS and Linux. (In this regard seccomp-bpf achieves similar functionality, but with more flexibility and higher performance, to the older systrace—which seems to be no longer supported for Linux.) Some consider seccomp comparable to OpenBSD pledge(2) and FreeBSD capsicum(4). == History == seccomp was first devised by Andrea Arcangeli in January 2005 for use in public grid computing and was originally intended as a means of safely running untrusted compute-bound programs. It was merged into the Linux kernel mainline in kernel version 2.6.12, which was released on March 8, 2005. == Software using seccomp or seccomp-bpf == Android uses a seccomp-bpf filter in the zygote since Android 8.0 Oreo. systemd's sandboxing options are based on seccomp. QEMU, the Quick Emulator, the core component to the modern virtualization together with KVM uses seccomp on the parameter --sandbox Docker – software that allows applications to run inside of isolated containers. Docker can associate a seccomp profile with the container using the --security-opt parameter. Arcangeli's CPUShare was the only known user of seccomp for a while. Writing in February 2009, Linus Torvalds expresses doubt whether seccomp is actually used by anyone. However, a Google engineer replied that Google is exploring using seccomp for sandboxing its Chrome web browser. Firejail is an open source Linux sandbox program that utilizes Linux namespaces, Seccomp, and other kernel-level security features to sandbox Linux and Wine applications. As of Chrome version 20, seccomp-bpf is used to sandbox Adobe Flash Player. As of Chrome version 23, seccomp-bpf is used to sandbox the renderers. Snap specify the shape of their application sandbox using "interfaces" which snapd translates to seccomp, AppArmor and other security constructs vsftpd uses seccomp-bpf sandboxing as of version 3.0.0. OpenSSH has supported seccomp-bpf since version 6.0. Mbox uses ptrace along with seccomp-bpf to create a secure sandbox with less overhead than ptrace alone. LXD, a Ubuntu "hypervisor" for containers Firefox and Firefox OS, which use seccomp-bpf Tor supports seccomp since 0.2.5.1-alpha Lepton, a JPEG compression tool developed by Dropbox uses seccomp Kafel is a configuration language, which converts readable policies into seccompb-bpf bytecode Subgraph OS uses seccomp-bpf Flatpak uses seccomp for process isolation Bubblewrap is a lightweight sandbox application developed from Flatpak minijail uses seccomp for process isolation SydBox uses seccomp-bpf to improve the runtime and security of the ptrace sandboxing used to sandbox package builds on Exherbo Linux distribution. File, a Unix program to determine filetypes, uses seccomp to restrict its runtime environment Zathura, a minimalistic document viewer, uses seccomp filter to implement different sandbox modes Tracker, a indexing and preview application for the GNOME desktop environment, uses seccomp to prevent automatic exploitation of parsing vulnerabilities in media files
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Random forest

Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that works by creating a multitude of decision trees during training. For classification tasks, the output of the random forest is the class selected by most trees. For regression tasks, the output is the average of the predictions of the trees. Random forests correct for decision trees' habit of overfitting to their training set. The first algorithm for random decision forests was created in 1995 by Tin Kam Ho using the random subspace method, which, in Ho's formulation, is a way to implement the "stochastic discrimination" approach to classification proposed by Eugene Kleinberg. An extension of the algorithm was developed by Leo Breiman and Adele Cutler, who registered "Random Forests" as a trademark in 2006 (as of 2019, owned by Minitab, Inc.). The extension combines Breiman's "bagging" idea and random selection of features, introduced first by Ho and later independently by Amit and Geman in order to construct a collection of decision trees with controlled variance. == History == The general method of random decision forests was first proposed by Salzberg and Heath in 1993, with a method that used a randomized decision tree algorithm to create multiple trees and then combine them using majority voting. This idea was developed further by Ho in 1995. Ho established that forests of trees splitting with oblique hyperplanes can gain accuracy as they grow without suffering from overtraining, as long as the forests are randomly restricted to be sensitive to only selected feature dimensions. A subsequent work along the same lines concluded that other splitting methods behave similarly, as long as they are randomly forced to be insensitive to some feature dimensions. This observation that a more complex classifier (a larger forest) gets more accurate nearly monotonically is in sharp contrast to the common belief that the complexity of a classifier can only grow to a certain level of accuracy before being hurt by overfitting. The explanation of the forest method's resistance to overtraining can be found in Kleinberg's theory of stochastic discrimination. The early development of Breiman's notion of random forests was influenced by the work of Amit and Geman who introduced the idea of searching over a random subset of the available decisions when splitting a node, in the context of growing a single tree. The idea of random subspace selection from Ho was also influential in the design of random forests. This method grows a forest of trees, and introduces variation among the trees by projecting the training data into a randomly chosen subspace before fitting each tree or each node. Finally, the idea of randomized node optimization, where the decision at each node is selected by a randomized procedure, rather than a deterministic optimization was first introduced by Thomas G. Dietterich. The proper introduction of random forests was made in a paper by Leo Breiman, that has become one of the world's most cited papers. This paper describes a method of building a forest of uncorrelated trees using a CART like procedure, combined with randomized node optimization and bagging. In addition, this paper combines several ingredients, some previously known and some novel, which form the basis of the modern practice of random forests, in particular: Using out-of-bag error as an estimate of the generalization error. Measuring variable importance through permutation. The report also offers the first theoretical result for random forests in the form of a bound on the generalization error which depends on the strength of the trees in the forest and their correlation. == Algorithm == === Preliminaries: decision tree learning === Decision trees are a popular method for various machine learning tasks. Tree learning is almost "an off-the-shelf procedure for data mining", say Hastie et al., "because it is invariant under scaling and various other transformations of feature values, is robust to inclusion of irrelevant features, and produces inspectable models. However, they are seldom accurate". In particular, trees that are grown very deep tend to learn highly irregular patterns: they overfit their training sets, i.e. have low bias, but very high variance. Random forests are a way of averaging multiple deep decision trees, trained on different parts of the same training set, with the goal of reducing the variance. This comes at the expense of a small increase in the bias and some loss of interpretability, but generally greatly boosts the performance in the final model. === Bagging === The training algorithm for random forests applies the general technique of bootstrap aggregating, or bagging, to tree learners. Given a training set X = x1, ..., xn with responses Y = y1, ..., yn, bagging repeatedly (B times) selects a random sample with replacement of the training set and fits trees to these samples: After training, predictions for unseen samples x' can be made by averaging the predictions from all the individual regression trees on x': f ^ = 1 B ∑ b = 1 B f b ( x ′ ) {\displaystyle {\hat {f}}={\frac {1}{B}}\sum _{b=1}^{B}f_{b}(x')} or by taking the plurality vote in the case of classification trees. This bootstrapping procedure leads to better model performance because it decreases the variance of the model, without increasing the bias. This means that while the predictions of a single tree are highly sensitive to noise in its training set, the average of many trees is not, as long as the trees are not correlated. Simply training many trees on a single training set would give strongly correlated trees (or even the same tree many times, if the training algorithm is deterministic); bootstrap sampling is a way of de-correlating the trees by showing them different training sets. Additionally, an estimate of the uncertainty of the prediction can be made as the standard deviation of the predictions from all the individual regression trees on x′: σ = ∑ b = 1 B ( f b ( x ′ ) − f ^ ) 2 B − 1 . {\displaystyle \sigma ={\sqrt {\frac {\sum _{b=1}^{B}(f_{b}(x')-{\hat {f}})^{2}}{B-1}}}.} The number B of samples (equivalently, of trees) is a free parameter. Typically, a few hundred to several thousand trees are used, depending on the size and nature of the training set. B can be optimized using cross-validation, or by observing the out-of-bag error: the mean prediction error on each training sample xi, using only the trees that did not have xi in their bootstrap sample. The training and test error tend to level off after some number of trees have been fit. === From bagging to random forests === The above procedure describes the original bagging algorithm for trees. Random forests also include another type of bagging scheme: they use a modified tree learning algorithm that selects, at each candidate split in the learning process, a random subset of the features. This process is sometimes called "feature bagging". The reason for doing this is the correlation of the trees in an ordinary bootstrap sample: if one or a few features are very strong predictors for the response variable (target output), these features will be selected in many of the B trees, causing them to become correlated. An analysis of how bagging and random subspace projection contribute to accuracy gains under different conditions is given by Ho. Typically, for a classification problem with p {\displaystyle p} features, p {\displaystyle {\sqrt {p}}} (rounded down) features are used in each split. For regression problems the inventors recommend p / 3 {\displaystyle p/3} (rounded down) with a minimum node size of 5 as the default. In practice, the best values for these parameters should be tuned on a case-to-case basis for every problem. === ExtraTrees === Adding one further step of randomization yields extremely randomized trees, or ExtraTrees. As with ordinary random forests, they are an ensemble of individual trees, but there are two main differences: (1) each tree is trained using the whole learning sample (rather than a bootstrap sample), and (2) the top-down splitting is randomized: for each feature under consideration, a number of random cut-points are selected, instead of computing the locally optimal cut-point (based on, e.g., information gain or the Gini impurity). The values are chosen from a uniform distribution within the feature's empirical range (in the tree's training set). Then, of all the randomly chosen splits, the split that yields the highest score is chosen to split the node. Similar to ordinary random forests, the number of randomly selected features to be considered at each node can be specified. Default values for this parameter are p {\displaystyle {\sqrt {p}}} for classification and p {\displaystyle p} for regression, where p {\displaystyle p} is the number of features in the model. === Random forests for high-dimensional data === The basic random forest procedure may
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Neural Networks (journal)

Neural Networks is a monthly peer-reviewed scientific journal and an official journal of the International Neural Network Society, European Neural Network Society, and Japanese Neural Network Society. == History == The journal was established in 1988 and is published by Elsevier. It covers all aspects of research on artificial neural networks. The founding editor-in-chief was Stephen Grossberg (Boston University). The current editors-in-chief are DeLiang Wang (Ohio State University) and Taro Toyoizumi (RIKEN Center for Brain Science). == Abstracting and indexing == The journal is abstracted and indexed in Scopus and the Science Citation Index Expanded. According to the Journal Citation Reports, the journal has a 2022 impact factor of 7.8.
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