In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theory, but the quantity in the role taken by the variance in the classic CLT has a more complicated definition. See also the general form of Bienaymé's identity. == Statement == Suppose that: the sequence X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } of random elements of some set is a Markov chain that has a stationary probability distribution; and the initial distribution of the process, i.e. the distribution of X 1 {\textstyle X_{1}} , is the stationary distribution, so that X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } are identically distributed. In the classic central limit theorem these random variables would be assumed to be independent, but here we have only the weaker assumption that the process has the Markov property; and g {\textstyle g} is some (measurable) real-valued function for which var ( g ( X 1 ) ) < + ∞ . {\textstyle \operatorname {var} (g(X_{1}))<+\infty .} Now let μ = E ( g ( X 1 ) ) , μ ^ n = 1 n ∑ k = 1 n g ( X k ) σ 2 := lim n → ∞ var ( n μ ^ n ) = lim n → ∞ n var ( μ ^ n ) = var ( g ( X 1 ) ) + 2 ∑ k = 1 ∞ cov ( g ( X 1 ) , g ( X 1 + k ) ) . {\displaystyle {\begin{aligned}\mu &=\operatorname {E} (g(X_{1})),\\{\widehat {\mu }}_{n}&={\frac {1}{n}}\sum _{k=1}^{n}g(X_{k})\\\sigma ^{2}&:=\lim _{n\to \infty }\operatorname {var} ({\sqrt {n}}{\widehat {\mu }}_{n})=\lim _{n\to \infty }n\operatorname {var} ({\widehat {\mu }}_{n})=\operatorname {var} (g(X_{1}))+2\sum _{k=1}^{\infty }\operatorname {cov} (g(X_{1}),g(X_{1+k})).\end{aligned}}} Then as n → ∞ , {\textstyle n\to \infty ,} we have n ( μ ^ n − μ ) → D Normal ( 0 , σ 2 ) , {\displaystyle {\sqrt {n}}({\hat {\mu }}_{n}-\mu )\ {\xrightarrow {\mathcal {D}}}\ {\text{Normal}}(0,\sigma ^{2}),} where the decorated arrow indicates convergence in distribution. == Monte Carlo Setting == The Markov chain central limit theorem can be guaranteed for functionals of general state space Markov chains under certain conditions. In particular, this can be done with a focus on Monte Carlo settings. An example of the application in a MCMC (Markov Chain Monte Carlo) setting is the following: Consider a simple hard spheres model on a grid. Suppose X = { 1 , … , n 1 } × { 1 , … , n 2 } ⊆ Z 2 {\displaystyle X=\{1,\ldots ,n_{1}\}\times \{1,\ldots ,n_{2}\}\subseteq Z^{2}} . A proper configuration on X {\displaystyle X} consists of coloring each point either black or white in such a way that no two adjacent points are white. Let χ {\displaystyle \chi } denote the set of all proper configurations on X {\displaystyle X} , N χ ( n 1 , n 2 ) {\displaystyle N_{\chi }(n_{1},n_{2})} be the total number of proper configurations and π be the uniform distribution on χ {\displaystyle \chi } so that each proper configuration is equally likely. Suppose our goal is to calculate the typical number of white points in a proper configuration; that is, if W ( x ) {\displaystyle W(x)} is the number of white points in x ∈ χ {\displaystyle x\in \chi } then we want the value of E π W = ∑ x ∈ χ W ( x ) N χ ( n 1 , n 2 ) {\displaystyle E_{\pi }W=\sum _{x\in \chi }{\frac {W(x)}{N_{\chi }{\bigl (}n_{1},n_{2}{\bigr )}}}} If n 1 {\displaystyle n_{1}} and n 2 {\displaystyle n_{2}} are even moderately large then we will have to resort to an approximation to E π W {\displaystyle E_{\pi }W} . Consider the following Markov chain on χ {\displaystyle \chi } . Fix p ∈ ( 0 , 1 ) {\displaystyle p\in (0,1)} and set X 1 = x 1 {\displaystyle X_{1}=x_{1}} where x 1 ∈ χ {\displaystyle x_{1}\in \chi } is an arbitrary proper configuration. Randomly choose a point ( x , y ) ∈ X {\displaystyle (x,y)\in X} and independently draw U ∼ U n i f o r m ( 0 , 1 ) {\displaystyle U\sim \mathrm {Uniform} (0,1)} . If u ≤ p {\displaystyle u\leq p} and all of the adjacent points are black then color ( x , y ) {\displaystyle (x,y)} white leaving all other points alone. Otherwise, color ( x , y ) {\displaystyle (x,y)} black and leave all other points alone. Call the resulting configuration X 1 {\displaystyle X_{1}} . Continuing in this fashion yields a Harris ergodic Markov chain { X 1 , X 2 , X 3 , … } {\displaystyle \{X_{1},X_{2},X_{3},\ldots \}} having π {\displaystyle \pi } as its invariant distribution. It is now a simple matter to estimate E π W {\displaystyle E_{\pi }W} with w n ¯ = ∑ i = 1 n W ( X i ) / n {\displaystyle {\overline {w_{n}}}=\sum _{i=1}^{n}W(X_{i})/n} . Also, since χ {\displaystyle \chi } is finite (albeit potentially large) it is well known that X {\displaystyle X} will converge exponentially fast to π {\displaystyle \pi } which implies that a CLT holds for w n ¯ {\displaystyle {\overline {w_{n}}}} . == Implications == Not taking into account the additional terms in the variance which stem from correlations (e.g. serial correlations in markov chain monte carlo simulations) can result in the problem of pseudoreplication when computing e.g. the confidence intervals for the sample mean.
Managed private cloud
Managed private cloud (also known as "hosted private cloud" or "single-tenant SaaS") refers to a principle in software architecture where a single instance of the software runs on a server, serves a single client organization (tenant), and is managed by a third party. The third-party provider is responsible for providing the hardware for the server and also for preliminary maintenance. This is in contrast to multitenancy, where multiple client organizations share a single server, or an on-premises deployment, where the client organization hosts its software instance. Managed private clouds also fall under the larger umbrella of cloud computing. == Adoption == The need for private clouds arose due to enterprises requiring a dedicated service and infrastructure for their cloud computing needs, such as for business-critical operations, improved security, and better control over their resources. Managed private cloud adoption is a popular choice among organizations. It has been on the rise due to enterprises requiring a dedicated cloud environment and preferring to avoid having to deal with management, maintenance, or future upgrade costs for the associated infrastructure and services. Such operational costs are unavoidable in on-premises private cloud data centers. == Advantages and challenges of managed private cloud == A managed private cloud cuts down on upkeep costs by outsourcing infrastructure management and maintenance to the managed cloud provider. It is easier to integrate an organization's existing software, services, and applications into a dedicated cloud hosting infrastructure which can be customized to the client's needs instead of a public cloud platform, whose hardware or infrastructure/software platform cannot be individualized to each client. Customers who choose a managed private cloud deployment usually choose them because of their desire for efficient cloud deployment, but also have the need for service customization or integration only available in a single-tenant environment. This chart shows the key benefits of the different types of deployments, and shows the overlap between these cloud solutions. This chart shows key drawbacks. Since deployments are done in a single-tenant environment, it is usually cost-prohibitive for small and medium-sized businesses. While server upkeep and maintenance are handled by the service provider, including network management and security, the client is charged for all such services. It is up to the potential client to determine if a managed private cloud solution aligns with their business objectives and budget. While the service provider maintains the upkeep of servers, network, and platform infrastructure, sensitive data is typically not stored on managed private clouds as it may leave business-critical information prone to breaches via third-party attacks on the cloud service provider. Common customizations and integrations include: Active Directory Single Sign-on Learning Management Systems Video Teleconferencing == Deployment strategies and service providers == Software companies have taken a variety of strategies in the Managed Private Cloud realm. Some software organizations have provided managed private cloud options internally, such as Microsoft. Companies that offer an on-premises deployment option, by definition, enable third-party companies to market Managed Private Cloud solutions. A few managed private cloud service providers are: Adobe Connect: Adobe Connect may be purchased for on-premises deployment, multi-tenant hosted deployment, managed private cloud as ACMS, or managed by third-party managed private cloud provider ConnectSolutions. Rackspace CenturyLink Microsoft licenses for Lync, SharePoint and Exchange may be purchased for on-premises deployment, a multi-tenant hosted deployment via Office 365, or managed by third-party cloud hosting from Azaleos, ConnectSolutions and others.
Evolutionary multimodal optimization
In applied mathematics, multimodal optimization deals with optimization tasks that involve finding all or most of the multiple (at least locally optimal) solutions of a problem, as opposed to a single best solution. Evolutionary multimodal optimization is a branch of evolutionary computation, which is closely related to machine learning. Wong provides a short survey, wherein the chapter of Shir and the book of Preuss cover the topic in more detail. == Motivation == Knowledge of multiple solutions to an optimization task is especially helpful in engineering, when due to physical (and/or cost) constraints, the best results may not always be realizable. In such a scenario, if multiple solutions (locally and/or globally optimal) are known, the implementation can be quickly switched to another solution and still obtain the best possible system performance. Multiple solutions could also be analyzed to discover hidden properties (or relationships) of the underlying optimization problem, which makes them important for obtaining domain knowledge. In addition, the algorithms for multimodal optimization usually not only locate multiple optima in a single run, but also preserve their population diversity, resulting in their global optimization ability on multimodal functions. Moreover, the techniques for multimodal optimization are usually borrowed as diversity maintenance techniques to other problems. == Background == Classical techniques of optimization would need multiple restart points and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. Evolutionary algorithms (EAs) due to their population based approach, provide a natural advantage over classical optimization techniques. They maintain a population of possible solutions, which are processed every generation, and if the multiple solutions can be preserved over all these generations, then at termination of the algorithm we will have multiple good solutions, rather than only the best solution. Note that this is against the natural tendency of classical optimization techniques, which will always converge to the best solution, or a sub-optimal solution (in a rugged, “badly behaving” function). Finding and maintenance of multiple solutions is wherein lies the challenge of using EAs for multi-modal optimization. Niching is a generic term referred to as the technique of finding and preserving multiple stable niches, or favorable parts of the solution space possibly around multiple solutions, so as to prevent convergence to a single solution. The field of Evolutionary algorithms encompasses genetic algorithms (GAs), evolution strategy (ES), differential evolution (DE), particle swarm optimization (PSO), and other methods. Attempts have been made to solve multi-modal optimization in all these realms and most, if not all the various methods implement niching in some form or the other. == Multimodal optimization using genetic algorithms/evolution strategies == De Jong's crowding method, Goldberg's sharing function approach, Petrowski's clearing method, restricted mating, maintaining multiple subpopulations are some of the popular approaches that have been proposed by the community. The first two methods are especially well studied, however, they do not perform explicit separation into solutions belonging to different basins of attraction. The application of multimodal optimization within ES was not explicit for many years, and has been explored only recently. A niching framework utilizing derandomized ES was introduced by Shir, proposing the CMA-ES as a niching optimizer for the first time. The underpinning of that framework was the selection of a peak individual per subpopulation in each generation, followed by its sampling to produce the consecutive dispersion of search-points. The biological analogy of this machinery is an alpha-male winning all the imposed competitions and dominating thereafter its ecological niche, which then obtains all the sexual resources therein to generate its offspring. Recently, an evolutionary multiobjective optimization (EMO) approach was proposed, in which a suitable second objective is added to the originally single objective multimodal optimization problem, so that the multiple solutions form a weak pareto-optimal front. Hence, the multimodal optimization problem can be solved for its multiple solutions using an EMO algorithm. Improving upon their work, the same authors have made their algorithm self-adaptive, thus eliminating the need for pre-specifying the parameters. An approach that does not use any radius for separating the population into subpopulations (or species) but employs the space topology instead is proposed in.
Transkribus
Transkribus is a platform for the text recognition, image analysis and structure recognition of historical documents. The platform was created in the context of the two EU projects "tranScriptorium" (2013–2015) and "READ" (Recognition and Enrichment of Archival Documents – 2016–2019). It was developed by the University of Innsbruck. Since July 1, 2019 the platform has been directed and further developed by the READ-COOP, a non-profit cooperative. The platform integrates tools developed by research groups throughout Europe, including the Pattern Recognition and Human Language Technology (PRHLT) group of the Technical University of Valencia and the Computational Intelligence Technology Lab (CITlab) group of University of Rostock. Comparable programs that offer similar functions are eScriptorium and OCR4All.
Premature convergence
Premature convergence is an unwanted effect in evolutionary algorithms (EA), a metaheuristic that mimics the basic principles of biological evolution as a computer algorithm for solving an optimization problem. The effect means that the population of an EA has converged too early, resulting in being suboptimal. In this context, the parental solutions, through the aid of genetic operators, are not able to generate offspring that are superior to, or outperform, their parents. Premature convergence is a common problem found in evolutionary algorithms, as it leads to a loss, or convergence of, a large number of alleles, subsequently making it very difficult to search for a specific gene in which the alleles were present. An allele is considered lost if, in a population, a gene is present, where all individuals are sharing the same value for that particular gene. An allele is, as defined by De Jong, considered to be a converged allele, when 95% of a population share the same value for a certain gene. == Strategies for preventing premature convergence == Strategies to regain genetic variation can be: a mating strategy called incest prevention, uniform crossover, mimicking sexual selection, favored replacement of similar individuals (preselection or crowding), segmentation of individuals of similar fitness (fitness sharing), increasing population size niche and specie The genetic variation can also be regained by mutation though this process is highly random. A general strategy to reduce the risk of premature convergence is to use structured populations instead of the commonly used panmictic ones. == Identification of the occurrence of premature convergence == It is hard to determine when premature convergence has occurred, and it is equally hard to predict its presence in the future. One measure is to use the difference between the average and maximum fitness values, as used by Patnaik & Srinivas, to then vary the crossover and mutation probabilities. Population diversity is another measure which has been extensively used in studies to measure premature convergence. However, although it has been widely accepted that a decrease in the population diversity directly leads to premature convergence, there have been little studies done on the analysis of population diversity. In other words, by using the term population diversity, the argument for a study in preventing premature convergence lacks robustness, unless specified what their definition of population diversity is. There are models to counter the effect and risk of premature convergence that do not compromise core GA parameters like population size, mutation rate, and other core mechanisms. These models were inspired by biological ecology, where genetic interactions are limited by external mechanisms such as spatial topologies or speciation. These ecological models, such as the Eco-GA, adopt diffusion-based strategies to improve the robustness of GA runs and increase the likelihood of reaching near-global optima. == Causes for premature convergence == There are a number of presumed or hypothesized causes for the occurrence of premature convergence. === Self-adaptive mutations === Rechenberg introduced the idea of self-adaptation of mutation distributions in evolution strategies. According to Rechenberg, the control parameters for these mutation distributions evolved internally through self-adaptation, rather than predetermination. He called it the 1/5-success rule of evolution strategies (1 + 1)-ES: The step size control parameter would be increased by some factor if the relative frequency of positive mutations through a determined period of time is larger than 1/5, vice versa if it is smaller than 1/5. Self-adaptive mutations may very well be one of the causes for premature convergence. Accurately locating of optima can be enhanced by self-adaptive mutation, as well as accelerating the search for this optima. This has been widely recognized, though the mechanism's underpinnings of this have been poorly studied, as it is often unclear whether the optima is found locally or globally. Self-adaptive methods can cause global convergence to global optimum, provided that the selection methods used are using elitism, as well as that the rule of self-adaptation doesn't interfere with the mutation distribution, which has the property of ensuring a positive minimum probability when hitting a random subset. This is for non-convex objective functions with sets that include bounded lower levels of non-zero measurements. A study by Rudolph suggests that self-adaption mechanisms among elitist evolution strategies do resemble the 1/5-success rule, and could very well get caught by a local optimum that include a positive probability. === Panmictic populations === Most EAs use unstructured or panmictic populations where basically every individual in the population is eligible for mate selection based on fitness. Thus, The genetic information of an only slightly better individual can spread in a population within a few generations, provided that no better other offspring is produced during this time. Especially in comparatively small populations, this can quickly lead to a loss of genotypic diversity and thus to premature convergence. A well-known countermeasure is to switch to alternative population models which introduce substructures into the population that preserve genotypic diversity over a longer period of time and thus counteract the tendency towards premature convergence. This has been shown for various EAs such as genetic algorithms, the evolution strategy, other EAs or memetic algorithms.
Error level analysis
Error level analysis (ELA) is the analysis of compression artifacts in digital data with lossy compression such as JPEG. == Principles == When used, lossy compression is normally applied uniformly to a set of data, such as an image, resulting in a uniform level of compression artifacts. Alternatively, the data may consist of parts with different levels of compression artifacts. This difference may arise from the different parts having been repeatedly subjected to the same lossy compression a different number of times, or the different parts having been subjected to different kinds of lossy compression. A difference in the level of compression artifacts in different parts of the data may therefore indicate that the data has been edited. In the case of JPEG, even a composite with parts subjected to matching compressions will have a difference in the compression artifacts. In order to make the typically faint compression artifacts more readily visible, the data to be analyzed is subjected to an additional round of lossy compression, this time at a known, uniform level, and the result is subtracted from the original data under investigation. The resulting difference image is then inspected manually for any variation in the level of compression artifacts. In 2007, N. Krawetz denoted this method "error level analysis". Additionally, digital data formats such as JPEG sometimes include metadata describing the specific lossy compression used. If in such data the observed compression artifacts differ from those expected from the given metadata description, then the metadata may not describe the actual compressed data, and thus indicate that the data have been edited. == Limitations == By its nature, data without lossy compression, such as a PNG image, cannot be subjected to error level analysis. Consequently, since editing could have been performed on data without lossy compression with lossy compression applied uniformly to the edited, composite data, the presence of a uniform level of compression artifacts does not rule out editing of the data. Additionally, any non-uniform compression artifacts in a composite may be removed by subjecting the composite to repeated, uniform lossy compression. Also, if the image color space is reduced to 256 colors or less, for example, by conversion to GIF, then error level analysis will generate useless results. More significant, the actual interpretation of the level of compression artifacts in a given segment of the data is subjective, and the determination of whether editing has occurred is therefore not robust. == Controversy == In May 2013, Dr Neal Krawetz used error level analysis on the 2012 World Press Photo of the Year and concluded on his Hacker Factor blog that it was "a composite" with modifications that "fail to adhere to the acceptable journalism standards used by Reuters, Associated Press, Getty Images, National Press Photographer's Association, and other media outlets". The World Press Photo organizers responded by letting two independent experts analyze the image files of the winning photographer and subsequently confirmed the integrity of the files. One of the experts, Hany Farid, said about error level analysis that "It incorrectly labels altered images as original and incorrectly labels original images as altered with the same likelihood". Krawetz responded by clarifying that "It is up to the user to interpret the results. Any errors in identification rest solely on the viewer". In May 2015, the citizen journalism team Bellingcat wrote that error level analysis revealed that the Russian Ministry of Defense had edited satellite images related to the Malaysia Airlines Flight 17 disaster. In a reaction to this, image forensics expert Jens Kriese said about error level analysis: "The method is subjective and not based entirely on science", and that it is "a method used by hobbyists". On his Hacker Factor Blog, the inventor of error level analysis Neal Krawetz criticized both Bellingcat's use of error level analysis as "misinterpreting the results" but also on several points Jens Kriese's "ignorance" regarding error level analysis.
List of datasets for machine-learning research
These datasets are used in machine learning (ML) research and have been cited in peer-reviewed academic journals. Datasets are an integral part of the field of machine learning. Major advances in this field can result from advances in learning algorithms (such as deep learning), computer hardware, and, less intuitively, the availability of high-quality training datasets. High-quality labeled training datasets for supervised and semi-supervised machine-learning algorithms are usually difficult and expensive to produce because of the large amount of time needed to label the data. Although they do not need to be labeled, high-quality unlabeled datasets for unsupervised learning can also be difficult and costly to produce. Many organizations, including governments, publish and share their datasets, often using common metadata formats (such as Croissant). The datasets are classified, based on the licenses, into two groups: open data and non-open data. The datasets from various governmental-bodies are presented in List of open government data sites. The datasets are ported on open data portals. They are made available for searching, depositing and accessing through interfaces like Open API. The datasets are made available as various sorted types and subtypes. == List of sorting used for datasets == The data portal is classified based on its type of license. The open source license based data portals are known as open data portals which are used by many government organizations and academic institutions. == List of open data portals == == List of portals suitable for multiple types of applications == The data portal sometimes lists a wide variety of subtypes of datasets pertaining to many machine learning applications. == List of portals suitable for a specific subtype of applications == The data portals which are suitable for a specific subtype of machine learning application are listed in the subsequent sections. == Image data == == Text data == These datasets consist primarily of text for tasks such as natural language processing, sentiment analysis, translation, and cluster analysis. === Reviews === === News articles === === Messages === === Twitter and tweets === === Dialogues === === Legal === === Other text === == Sound data == These datasets consist of sounds and sound features used for tasks such as speech recognition and speech synthesis. === Speech === === Music === === Other sounds === == Signal data == Datasets containing electric signal information requiring some sort of signal processing for further analysis. === Electrical === === Motion-tracking === === Other signals === == Chemical data == Datasets from physical systems. === Chemical Reactions with transition states (TS) === === OpenReACT-CHON-EFH === OpenReACT-CHON-EFH (Open Reaction Dataset of Atomic ConfiguraTions comprising C, H, O and N with Energies, Forces and Hessians) is a 2025 open-access benchmark for machine-learning interatomic potentials. RTP set – 35,087 stationary-point geometries (reactant, transition state and product) drawn from 11,961 elementary reactions, each labeled with density-functional energies, atomic forces and full Hessian matrices at the ωB97X-D/6-31G(d) level. IRC set – 34,248 structures along 600 minimum-energy reaction paths, used to test extrapolation beyond trained stationary points. NMS set – 62,527 off-equilibrium geometries generated by normal-mode sampling to probe model robustness under thermal perturbations. The collection underpins the study Does Hessian Data Improve the Performance of Machine Learning Potentials? and was used to train and benchmark the machine-learning interatomic potentials reported therein. The dataset itself is distributed under a CC licence via Figshare. == Physical data == Datasets from physical systems. === High-energy physics === === Systems === === Astronomy === === Earth science === === Other physical === == Biological data == Datasets from biological systems. === Human === === Animal === === Fungi === === Plant === === Microbe === === Drug discovery === == Anomaly data == == Question answering data == This section includes datasets that deals with structured data. == Dialog or instruction prompted data == This section includes datasets that contains multi-turn text with at least two actors, a "user" and an "agent". The user makes requests for the agent, which performs the request. == Cybersecurity == == Climate and sustainability == == Code data == == Multivariate data == === Financial === === Weather === === Census === === Transit === === Internet === === Games === === Other multivariate === == Curated repositories of datasets == As datasets come in myriad formats and can sometimes be difficult to use, there has been considerable work put into curating and standardizing the format of datasets to make them easier to use for machine learning research. OpenML: Web platform with Python, R, Java, and other APIs for downloading hundreds of machine learning datasets, evaluating algorithms on datasets, and benchmarking algorithm performance against dozens of other algorithms. PMLB: A large, curated repository of benchmark datasets for evaluating supervised machine learning algorithms. Provides classification and regression datasets in a standardized format that are accessible through a Python API. Metatext NLP: https://metatext.io/datasets web repository maintained by community, containing nearly 1000 benchmark datasets, and counting. Provides many tasks from classification to QA, and various languages from English, Portuguese to Arabic. Appen: Off The Shelf and Open Source Datasets hosted and maintained by the company. These biological, image, physical, question answering, signal, sound, text, and video resources number over 250 and can be applied to over 25 different use cases.