AI Generator Qr Code

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  StatMuse

  StatMuse Inc. is an American artificial intelligence company founded in 2014. It operates an eponymous website that hosts a database of sports statistics covering the four major North American sports leagues, the Women's National Basketball Association (WNBA), NCAA Division I men's basketball, NCAA Division I Football Bowl Subdivision, the Big Five association football leagues in Europe, and various professional golf tours. == History == The company was founded by friends Adam Elmore and Eli Dawson in 2014. In email correspondence to the Springfield News-Leader, Elmore detailed that he and Dawson, fans of the National Basketball Association (NBA), were compelled to create StatMuse after they realized there was no online platform where they could search "Lebron James most points" [sic] and quickly get a result "showing his highest scoring games." As a startup, the company's goal was to utilize a type of artificial intelligence called natural language processing (NLP) for sports. In 2015, the company was part of the second group of startups accepted into the Disney Accelerator program. The company secured support from several investors, including The Walt Disney Company, Techstars, Allen & Company, the NFL Players Association, Greycroft and NBA Commissioner David Stern. As part of their partnership with Disney, StatMuse signed a content deal with ESPN (owned by Disney) to provide stats content on social media and television during the 2015–16 NBA season. Initially, the company only had stats available for the NBA, but eventually expanded to provide stats for the other major North American sports leagues. The company's initial demographic was players of fantasy sports, but it eventually expanded to target general sports fans as well. StatMuse offers responses to user queries in the voices of sports-related public figures. Dawson shared with VentureBeat that StatMuse brings people in and records them saying different words and phrases. These celebrity voices were made accessible through Google's Google Assistant service, Microsoft's Cortana virtual assistant, and Amazon's Echo devices. The company launched its phone app in September 2017. The app allows users to access StatMuse's sports statistics database by submitting queries in their natural language. Upon the launch of the phone app, Fitz Tepper of TechCrunch wrote that: "The technology isn't perfect – some of the pauses between words are a bit awkward, making it clear that some phrases are being stitched together on the fly. But this is the exception, and on the whole, most responses sound pretty good." StatMuse plug-ins for Slack and Facebook Messenger were also made, providing text-based sports stats. In 2019, StatMuse received investment from the Google Assistant Investment program. The service launched a premium option dubbed StatMuse+ in May 2023, offering options that had previously been included for free, such as unlimited searches and full results in data tables. The premium version also included early access to new features and a personalized search history, as well as not having ads. The app received a variety of feedback. In January 2024, the service launched a Premier League version of the website dubbed StatMuse FC. It is planned to introduce more leagues on the website.

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  Proximal policy optimization

  Proximal policy optimization (PPO) is a reinforcement learning (RL) algorithm for training an intelligent agent. Specifically, it is a policy gradient method, often used for deep RL when the policy network is very large. == History == The predecessor to PPO, Trust Region Policy Optimization (TRPO), was published in 2015. It addressed the instability issue of another algorithm, the Deep Q-Network (DQN), by using the trust region method to limit the KL divergence between the old and new policies. However, TRPO uses the Hessian matrix (a matrix of second derivatives) to enforce the trust region, but the Hessian is inefficient for large-scale problems. PPO was published in 2017. It was essentially an approximation of TRPO that does not require computing the Hessian. The KL divergence constraint was approximated by simply clipping the policy gradient. Since 2018, PPO was the default RL algorithm at OpenAI. PPO has been applied to many areas, such as controlling a robotic arm, beating professional players at Dota 2 (OpenAI Five), and playing Atari games. == TRPO == TRPO, the predecessor of PPO, is an on-policy algorithm. It can be used for environments with either discrete or continuous action spaces. The pseudocode is as follows: Input: initial policy parameters θ 0 {\textstyle \theta _{0}} , initial value function parameters ϕ 0 {\textstyle \phi _{0}} Hyperparameters: KL-divergence limit δ {\textstyle \delta } , backtracking coefficient α {\textstyle \alpha } , maximum number of backtracking steps K {\textstyle K} for k = 0 , 1 , 2 , … {\textstyle k=0,1,2,\ldots } do Collect set of trajectories D k = { τ i } {\textstyle {\mathcal {D}}_{k}=\left\{\tau _{i}\right\}} by running policy π k = π ( θ k ) {\textstyle \pi _{k}=\pi \left(\theta _{k}\right)} in the environment. Compute rewards-to-go R ^ t {\textstyle {\hat {R}}_{t}} . Compute advantage estimates, A ^ t {\textstyle {\hat {A}}_{t}} (using any method of advantage estimation) based on the current value function V ϕ k {\textstyle V_{\phi _{k}}} . Estimate policy gradient as g ^ k = 1 | D k | ∑ τ ∈ D k ∑ t = 0 T ∇ θ log ⁡ π θ ( a t ∣ s t ) | θ k A ^ t {\displaystyle {\hat {g}}_{k}=\left.{\frac {1}{\left|{\mathcal {D}}_{k}\right|}}\sum _{\tau \in {\mathcal {D}}_{k}}\sum _{t=0}^{T}\nabla _{\theta }\log \pi _{\theta }\left(a_{t}\mid s_{t}\right)\right|_{\theta _{k}}{\hat {A}}_{t}} Use the conjugate gradient algorithm to compute x ^ k ≈ H ^ k − 1 g ^ k {\displaystyle {\hat {x}}_{k}\approx {\hat {H}}_{k}^{-1}{\hat {g}}_{k}} where H ^ k {\textstyle {\hat {H}}_{k}} is the Hessian of the sample average KL-divergence. Update the policy by backtracking line search with θ k + 1 = θ k + α j 2 δ x ^ k T H ^ k x ^ k x ^ k {\displaystyle \theta _{k+1}=\theta _{k}+\alpha ^{j}{\sqrt {\frac {2\delta }{{\hat {x}}_{k}^{T}{\hat {H}}_{k}{\hat {x}}_{k}}}}{\hat {x}}_{k}} where j ∈ { 0 , 1 , 2 , … K } {\textstyle j\in \{0,1,2,\ldots K\}} is the smallest value which improves the sample loss and satisfies the sample KL-divergence constraint. Fit value function by regression on mean-squared error: ϕ k + 1 = arg ⁡ min ϕ 1 | D k | T ∑ τ ∈ D k ∑ t = 0 T ( V ϕ ( s t ) − R ^ t ) 2 {\displaystyle \phi _{k+1}=\arg \min _{\phi }{\frac {1}{\left|{\mathcal {D}}_{k}\right|T}}\sum _{\tau \in {\mathcal {D}}_{k}}\sum _{t=0}^{T}\left(V_{\phi }\left(s_{t}\right)-{\hat {R}}_{t}\right)^{2}} typically via some gradient descent algorithm. == PPO == The pseudocode is as follows: Input: initial policy parameters θ 0 {\textstyle \theta _{0}} , initial value function parameters ϕ 0 {\textstyle \phi _{0}} for k = 0 , 1 , 2 , … {\textstyle k=0,1,2,\ldots } do Collect set of trajectories D k = { τ i } {\textstyle {\mathcal {D}}_{k}=\left\{\tau _{i}\right\}} by running policy π k = π ( θ k ) {\textstyle \pi _{k}=\pi \left(\theta _{k}\right)} in the environment. Compute rewards-to-go R ^ t {\textstyle {\hat {R}}_{t}} . Compute advantage estimates, A ^ t {\textstyle {\hat {A}}_{t}} (using any method of advantage estimation) based on the current value function V ϕ k {\textstyle V_{\phi _{k}}} . Update the policy by maximizing the PPO-Clip objective: θ k + 1 = arg ⁡ max θ 1 | D k | T ∑ τ ∈ D k ∑ t = 0 T min ( π θ ( a t ∣ s t ) π θ k ( a t ∣ s t ) A π θ k ( s t , a t ) , g ( ϵ , A π θ k ( s t , a t ) ) ) {\displaystyle \theta _{k+1}=\arg \max _{\theta }{\frac {1}{\left|{\mathcal {D}}_{k}\right|T}}\sum _{\tau \in {\mathcal {D}}_{k}}\sum _{t=0}^{T}\min \left({\frac {\pi _{\theta }\left(a_{t}\mid s_{t}\right)}{\pi _{\theta _{k}}\left(a_{t}\mid s_{t}\right)}}A^{\pi _{\theta _{k}}}\left(s_{t},a_{t}\right),\quad g\left(\epsilon ,A^{\pi _{\theta _{k}}}\left(s_{t},a_{t}\right)\right)\right)} typically via stochastic gradient ascent with Adam. Fit value function by regression on mean-squared error: ϕ k + 1 = arg ⁡ min ϕ 1 | D k | T ∑ τ ∈ D k ∑ t = 0 T ( V ϕ ( s t ) − R ^ t ) 2 {\displaystyle \phi _{k+1}=\arg \min _{\phi }{\frac {1}{\left|{\mathcal {D}}_{k}\right|T}}\sum _{\tau \in {\mathcal {D}}_{k}}\sum _{t=0}^{T}\left(V_{\phi }\left(s_{t}\right)-{\hat {R}}_{t}\right)^{2}} typically via some gradient descent algorithm. Like all policy gradient methods, PPO is used for training an RL agent whose actions are determined by a differentiable policy function by gradient ascent. Intuitively, a policy gradient method takes small policy update steps, so the agent can reach higher and higher rewards in expectation. Policy gradient methods may be unstable: A step size that is too big may direct the policy in a suboptimal direction, thus having little possibility of recovery; a step size that is too small lowers the overall efficiency. To solve the instability, PPO implements a clip function that constrains the policy update of an agent from being too large, so that larger step sizes may be used without negatively affecting the gradient ascent process. === Basic concepts === To begin the PPO training process, the agent is set in an environment to perform actions based on its current input. In the early phase of training, the agent can freely explore solutions and keep track of the result. Later, with a certain amount of transition samples and policy updates, the agent will select an action to take by randomly sampling from the probability distribution P ( A | S ) {\displaystyle P(A|S)} generated by the policy network. The actions that are most likely to be beneficial will have the highest probability of being selected from the random sample. After an agent arrives at a different scenario (a new state) by acting, it is rewarded with a positive reward or a negative reward. The objective of an agent is to maximize the cumulative reward signal across sequences of states, known as episodes. === Policy gradient laws: the advantage function === The advantage function (denoted as A {\displaystyle A} ) is central to PPO, as it tries to answer the question of whether a specific action of the agent is better or worse than some other possible action in a given state. By definition, the advantage function is an estimate of the relative value for a selected action. If the output of this function is positive, it means that the action in question is better than the average return, so the possibilities of selecting that specific action will increase. The opposite is true for a negative advantage output. The advantage function can be defined as A = Q − V {\displaystyle A=Q-V} , where Q {\displaystyle Q} is the discounted sum of rewards (the total weighted reward for the completion of an episode) and V {\displaystyle V} is the baseline estimate. Since the advantage function is calculated after the completion of an episode, the program records the outcome of the episode. Therefore, calculating advantage is essentially an unsupervised learning problem. The baseline estimate comes from the value function that outputs the expected discounted sum of an episode starting from the current state. In the PPO algorithm, the baseline estimate will be noisy (with some variance), as it also uses a neural network, like the policy function itself. With Q {\displaystyle Q} and V {\displaystyle V} computed, the advantage function is calculated by subtracting the baseline estimate from the actual discounted return. If A > 0 {\displaystyle A>0} , the actual return of the action is better than the expected return from experience; if A < 0 {\displaystyle A<0} , the actual return is worse. === Ratio function === In PPO, the ratio function ( r t {\displaystyle r_{t}} ) calculates the probability of selecting action a {\displaystyle a} in state s {\displaystyle s} given the current policy network, divided by the previous probability under the old policy. In other words: If r t ( θ ) > 1 {\displaystyle r_{t}(\theta )>1} , where θ {\displaystyle \theta } are the policy network parameters, then selecting action a {\displaystyle a} in state s {\displaystyle s} is more likely based on the current policy than the previous policy. If 0 ≤ r t ( θ ) < 1 {\displaystyle 0\leq r_{t}(\theta )<1} , then selecting actio

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  CN2 algorithm

  The CN2 induction algorithm is a learning algorithm for rule induction. It is designed to work even when the training data is imperfect. It is based on ideas from the AQ algorithm and the ID3 algorithm. As a consequence it creates a rule set like that created by AQ but is able to handle noisy data like ID3. == Description of algorithm == The algorithm must be given a set of examples, TrainingSet, which have already been classified in order to generate a list of classification rules. A set of conditions, SimpleConditionSet, which can be applied, alone or in combination, to any set of examples is predefined to be used for the classification. routine CN2(TrainingSet) let the ClassificationRuleList be empty repeat let the BestConditionExpression be Find_BestConditionExpression(TrainingSet) if the BestConditionExpression is not nil then let the TrainingSubset be the examples covered by the BestConditionExpression remove from the TrainingSet the examples in the TrainingSubset let the MostCommonClass be the most common class of examples in the TrainingSubset append to the ClassificationRuleList the rule 'if ' the BestConditionExpression ' then the class is ' the MostCommonClass until the TrainingSet is empty or the BestConditionExpression is nil return the ClassificationRuleList routine Find_BestConditionExpression(TrainingSet) let the ConditionalExpressionSet be empty let the BestConditionExpression be nil repeat let the TrialConditionalExpressionSet be the set of conditional expressions, {x and y where x belongs to the ConditionalExpressionSet and y belongs to the SimpleConditionSet}. remove all formulae in the TrialConditionalExpressionSet that are either in the ConditionalExpressionSet (i.e., the unspecialized ones) or null (e.g., big = y and big = n) for every expression, F, in the TrialConditionalExpressionSet if F is statistically significant and F is better than the BestConditionExpression by user-defined criteria when tested on the TrainingSet then replace the current value of the BestConditionExpression by F while the number of expressions in the TrialConditionalExpressionSet > user-defined maximum remove the worst expression from the TrialConditionalExpressionSet let the ConditionalExpressionSet be the TrialConditionalExpressionSet until the ConditionalExpressionSet is empty return the BestConditionExpression

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  KNIME

  KNIME ( ), the Konstanz Information Miner, is a data analytics, reporting and integrating platform. KNIME integrates various components for machine learning and data mining through its modular data pipelining "Building Blocks of Analytics" concept. A graphical user interface and use of Java Database Connectivity (JDBC) allows assembly of nodes blending different data sources, including preprocessing (extract, transform, load, or ETL), for modeling, data analysis and visualization with minimal, or no, programming. It is free and open-source software released under a GNU General Public License. Since 2006, KNIME has been used in pharmaceutical research, and in other areas including customer relationship management (CRM) and data analysis, business intelligence, text mining and financial data analysis. Recently, attempts were made to use KNIME as robotic process automation (RPA) tool. KNIME's headquarters are based in Zurich, with other offices in Konstanz, Berlin, and Austin (USA). == History == Development of KNIME began in January 2004, with a team of software engineers at the University of Konstanz, as an open-source platform. The original team, headed by Michael Berthold, came from a Silicon Valley pharmaceutical industry software company. The initial goal was to create a modular, highly scalable and open data processing platform that allows easy integration of different data loading, processing, transforming, analyzing, and visual exploring modules, without focus on any one application area. The platform was intended for collaborating, research, and for integrating various other data analysis projects. In 2006, the first version of KNIME was released. Several pharmaceutical companies began using KNIME, and several life science software vendors began integrating their tools into the platform. Later that year, after an article in the German magazine c't, users from a number of other areas joined ship. As of 2012, KNIME is in use by over 15,000 actual users (i.e. not counting downloads, but users regularly retrieving updates) in the life sciences and at banks, publishers, car manufacturer, telcos, consulting firms, and various other industries, and a large number of research groups, worldwide. Latest updates to KNIME Server and KNIME Big Data Extensions, provide support for Apache Spark 2.3, Parquet and HDFS-type storage. For the sixth year in a row, KNIME has been placed as a leader for data science and machine learning platforms in Gartner's Magic Quadrant. == Design philosophy, features == These are the design principles and features that KNIME software follows: Visual, Interactive Framework: KNIME Software prioritizes a user-friendly and intuitive approach to data analysis. This is achieved through a visual and interactive framework where data flows can be combined using a drag-and-drop interface. Users can develop customized and interactive applications by creating simple to advanced and highly-automated data pipelines. These may include, for example, access to databases, machine learning libraries, logic for workflow control (e.g., loops, switches, etc.), abstraction (e.g., interactive widgets), invocation, dynamic data apps, integrated deployment, or error handling. Modularity: processing units and data containers should remain independent of each other. This design choice enables easy distribution of computation and allows for the independent development of different algorithms. Data types within KNIME are encapsulated, meaning no types are predefined. This design choice facilitates adding new data types, and integrating them with extant types, while including type-specific renderers and comparators. This principle also enables inspecting results at the end of each single data operation. Extensibility: KNIME Software is designed to be extensible. Adding new processing nodes or views is made simple through a plug-in mechanism. This mechanism ensures that users can distribute their custom functionalities without the need for complicated install or uninstall procedures. Interleaving No-Code with Code: the platform supports integrating both visual programming (no-code) and script-based programming (e.g., Python, R, JavaScript) approaches to data analysis. This design principle is termed low-code. Automation and Scalability: for example, the use of parameterization via flow variables, or the encapsulation of workflow segments in components contribute to reduce manual work and errors in analyses. Further, the scheduling of workflow execution (available in KNIME Business Hub and KNIME Community Hub for Teams) reduces dependency on human resources. In terms of scalability, a few examples include the ability to handle large datasets (millions of rows), execute multiple processes simultaneously out of the box and reuse workflow segments. Full Usability: due to the open source nature, KNIME Analytics Platform provides free full usability with no limited trial periods. == Internals == KNIME allows users to visually create data flows (or pipelines), selectively execute some or all analysis steps, and later inspect the results, models, using interactive widgets and views. KNIME is written in Java and based on Eclipse. It makes use of an extension mechanism to add plug-ins providing added functions. The core version includes hundreds of modules for data integration (file input/output (I/O), database nodes supporting all common database management systems through JDBC or native connectors: SQLite, MS-Access, SQL Server, MySQL, Oracle, PostgreSQL, Vertica and H2), data transformation (filter, converter, splitter, combiner, joiner), and the commonly used methods of statistics, data mining, analysis and text analytics. Visualization is supported with the Report Designer extension. KNIME workflows can be used as data sets to create report templates that can be exported to document formats such as doc, ppt, xls, pdf and others. Other KNIME abilities are: KNIMEs core-architecture allows processing of large data volumes that are only limited by the available hard disk space (not limited to the available RAM). E.g., KNIME allows analyzing 300 million customer addresses, 20 million cell images, and 10 million molecular structures. Added plug-ins allow integrating methods for text mining, image mining, time series analysis, and networking. KNIME integrates various other open-source projects, e.g., machine learning algorithms from Weka, H2O, Keras, Spark, the R project and LIBSVM; plotly, JFreeChart, ImageJ, and the Chemistry Development Kit. KNIME is implemented in Java, allows for wrappers calling other code, in addition to providing nodes that allow it to run Java, Python, R, Ruby and other code fragments. Since 2021, KNIME's Python Integration utilizes Anaconda for Python distribution and environment management. == License == In 2024, KNIME version 5.3 is released under the same GPLv3 license as previous versions. As of version 2.1, KNIME is released under the GPLv3 license, with an exception that allow commercial software vendors to use the well-defined node application programming interface (API) to add proprietary extensions, or wrappers calling their tools from KNIME. == Courses == KNIME allows the performance of data analysis without programming skills. Several free, online courses are provided.

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  Tridium

  Tridium Inc. is an American engineering hardware and software company based in Richmond, Virginia, whose products facilitate and integrate the automation of building and other engineering control systems. Since November 2005, the company has operated as an independent business entity of Honeywell International Inc. == History == Tridium Inc. was founded in 1995. In 1999, Tridium launched the Niagara Framework, a software infrastructure that connects all systems and devices to a central console. In 2002, John Petze became president and CEO, replacing Jerry Frank. The company was acquired by Honeywell International Inc in 2005. == Products == Tridium's products facilitate by integrating building automation using open and proprietary communications protocols such as Modbus, Lonworks and BACnet. Tridium is the developer of Niagara Framework. The Niagara Framework is a universal software infrastructure that allows building controls integrators, HVAC and mechanical contractors to build custom, web-enabled applications for accessing, automating and controlling smart devices real-time via local network or over the Internet.

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  Sample exclusion dimension

  In computational learning theory, sample exclusion dimensions arise in the study of exact concept learning with queries. In algorithmic learning theory, a concept over a domain X is a Boolean function over X. Here we only consider finite domains. A partial approximation S of a concept c is a Boolean function over Y ⊆ X {\displaystyle Y\subseteq X} such that c is an extension to S. Let C be a class of concepts and c be a concept (not necessarily in C). Then a specifying set for c w.r.t. C, denoted by S is a partial approximation S of c such that C contains at most one extension to S. If we have observed a specifying set for some concept w.r.t. C, then we have enough information to verify a concept in C with at most one more mind change. The exclusion dimension, denoted by XD(C), of a concept class is the maximum of the size of the minimum specifying set of c' with respect to C, where c' is a concept not in C.

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  Rule-based machine learning

  Rule-based machine learning (RBML) is a term in computer science intended to encompass any machine learning method that identifies, learns, or evolves 'rules' to store, manipulate or apply. The defining characteristic of a rule-based machine learner is the identification and utilization of a set of relational rules that collectively represent the knowledge captured by the system. Rule-based machine learning approaches include learning classifier systems, association rule learning, artificial immune systems, and any other method that relies on a set of rules, each covering contextual knowledge. While rule-based machine learning is conceptually a type of rule-based system, it is distinct from traditional rule-based systems, which are often hand-crafted, and other rule-based decision makers. This is because rule-based machine learning applies some form of learning algorithm such as Rough sets theory to identify and minimise the set of features and to automatically identify useful rules, rather than a human needing to apply prior domain knowledge to manually construct rules and curate a rule set. == Rules == Rules typically take the form of an '{IF:THEN} expression', (e.g. {IF 'condition' THEN 'result'}, or as a more specific example, {IF 'red' AND 'octagon' THEN 'stop-sign}). An individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Therefore rule-based machine learning methods typically comprise a set of rules, or knowledge base, that collectively make up the prediction model usually known as decision algorithm. Rules can also be interpreted in various ways depending on the domain knowledge, data types(discrete or continuous) and in combinations. == RIPPER == Repeated incremental pruning to produce error reduction (RIPPER) is a propositional rule learner proposed by William W. Cohen as an optimized version of IREP.

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  AdaBoost

  AdaBoost (short for Adaptive Boosting) is a statistical classification meta-algorithm formulated by Yoav Freund and Robert Schapire in 1995, who won the 2003 Gödel Prize for their work. It can be used in conjunction with many types of learning algorithm to improve performance. The output of multiple weak learners is combined into a weighted sum that represents the final output of the boosted classifier. Usually, AdaBoost is presented for binary classification, although it can be generalized to multiple classes or bounded intervals of real values. AdaBoost is adaptive in the sense that subsequent weak learners (models) are adjusted in favor of instances misclassified by previous models. In some problems, it can be less susceptible to overfitting than other learning algorithms. The individual learners can be weak, but as long as the performance of each one is slightly better than random guessing, the final model can be proven to converge to a strong learner. Although AdaBoost is typically used to combine weak base learners (such as decision stumps), it has been shown to also effectively combine strong base learners (such as deeper decision trees), producing an even more accurate model. Every learning algorithm tends to suit some problem types better than others, and typically has many different parameters and configurations to adjust before it achieves optimal performance on a dataset. AdaBoost (with decision trees as the weak learners) is often referred to as the best out-of-the-box classifier. When used with decision tree learning, information gathered at each stage of the AdaBoost algorithm about the relative 'hardness' of each training sample is fed into the tree-growing algorithm such that later trees tend to focus on harder-to-classify examples. == Training == AdaBoost refers to a particular method of training a boosted classifier. A boosted classifier is a classifier of the form F T ( x ) = ∑ t = 1 T f t ( x ) {\displaystyle F_{T}(x)=\sum _{t=1}^{T}f_{t}(x)} where each f t {\displaystyle f_{t}} is a weak learner that takes an object x {\displaystyle x} as input and returns a value indicating the class of the object. For example, in the two-class problem, the sign of the weak learner's output identifies the predicted object class and the absolute value gives the confidence in that classification. Each weak learner produces an output hypothesis h {\displaystyle h} which fixes a prediction h ( x i ) {\displaystyle h(x_{i})} for each sample in the training set. At each iteration t {\displaystyle t} , a weak learner is selected and assigned a coefficient α t {\displaystyle \alpha _{t}} such that the total training error E t {\displaystyle E_{t}} of the resulting t {\displaystyle t} -stage boosted classifier is minimized. E t = ∑ i E [ F t − 1 ( x i ) + α t h ( x i ) ] {\displaystyle E_{t}=\sum _{i}E[F_{t-1}(x_{i})+\alpha _{t}h(x_{i})]} Here F t − 1 ( x ) {\displaystyle F_{t-1}(x)} is the boosted classifier that has been built up to the previous stage of training and f t ( x ) = α t h ( x ) {\displaystyle f_{t}(x)=\alpha _{t}h(x)} is the weak learner that is being considered for addition to the final classifier. === Weighting === At each iteration of the training process, a weight w i , t {\displaystyle w_{i,t}} is assigned to each sample in the training set equal to the current error E ( F t − 1 ( x i ) ) {\displaystyle E(F_{t-1}(x_{i}))} on that sample. These weights can be used in the training of the weak learner. For instance, decision trees can be grown which favor the splitting of sets of samples with large weights. == Derivation == This derivation follows Rojas (2009): Suppose we have a data set { ( x 1 , y 1 ) , … , ( x N , y N ) } {\displaystyle \{(x_{1},y_{1}),\ldots ,(x_{N},y_{N})\}} where each item x i {\displaystyle x_{i}} has an associated class y i ∈ { − 1 , 1 } {\displaystyle y_{i}\in \{-1,1\}} , and a set of weak classifiers { k 1 , … , k L } {\displaystyle \{k_{1},\ldots ,k_{L}\}} each of which outputs a classification k j ( x i ) ∈ { − 1 , 1 } {\displaystyle k_{j}(x_{i})\in \{-1,1\}} for each item. After the ( m − 1 ) {\displaystyle (m-1)} -th iteration our boosted classifier is a linear combination of the weak classifiers of the form: C ( m − 1 ) ( x i ) = α 1 k 1 ( x i ) + ⋯ + α m − 1 k m − 1 ( x i ) , {\displaystyle C_{(m-1)}(x_{i})=\alpha _{1}k_{1}(x_{i})+\cdots +\alpha _{m-1}k_{m-1}(x_{i}),} where the class will be the sign of C ( m − 1 ) ( x i ) {\displaystyle C_{(m-1)}(x_{i})} . At the m {\displaystyle m} -th iteration we want to extend this to a better boosted classifier by adding another weak classifier k m {\displaystyle k_{m}} , with another weight α m {\displaystyle \alpha _{m}} : C m ( x i ) = C ( m − 1 ) ( x i ) + α m k m ( x i ) {\displaystyle C_{m}(x_{i})=C_{(m-1)}(x_{i})+\alpha _{m}k_{m}(x_{i})} So it remains to determine which weak classifier is the best choice for k m {\displaystyle k_{m}} , and what its weight α m {\displaystyle \alpha _{m}} should be. We define the total error E {\displaystyle E} of C m {\displaystyle C_{m}} as the sum of its exponential loss on each data point, given as follows: E = ∑ i = 1 N e − y i C m ( x i ) = ∑ i = 1 N e − y i C ( m − 1 ) ( x i ) e − y i α m k m ( x i ) {\displaystyle E=\sum _{i=1}^{N}e^{-y_{i}C_{m}(x_{i})}=\sum _{i=1}^{N}e^{-y_{i}C_{(m-1)}(x_{i})}e^{-y_{i}\alpha _{m}k_{m}(x_{i})}} Letting w i ( 1 ) = 1 {\displaystyle w_{i}^{(1)}=1} and w i ( m ) = e − y i C m − 1 ( x i ) {\displaystyle w_{i}^{(m)}=e^{-y_{i}C_{m-1}(x_{i})}} for m > 1 {\displaystyle m>1} , we have: E = ∑ i = 1 N w i ( m ) e − y i α m k m ( x i ) {\displaystyle E=\sum _{i=1}^{N}w_{i}^{(m)}e^{-y_{i}\alpha _{m}k_{m}(x_{i})}} We can split this summation between those data points that are correctly classified by k m {\displaystyle k_{m}} (so y i k m ( x i ) = 1 {\displaystyle y_{i}k_{m}(x_{i})=1} ) and those that are misclassified (so y i k m ( x i ) = − 1 {\displaystyle y_{i}k_{m}(x_{i})=-1} ): E = ∑ y i = k m ( x i ) w i ( m ) e − α m + ∑ y i ≠ k m ( x i ) w i ( m ) e α m = ∑ i = 1 N w i ( m ) e − α m + ∑ y i ≠ k m ( x i ) w i ( m ) ( e α m − e − α m ) {\displaystyle {\begin{aligned}E&=\sum _{y_{i}=k_{m}(x_{i})}w_{i}^{(m)}e^{-\alpha _{m}}+\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}e^{\alpha _{m}}\\&=\sum _{i=1}^{N}w_{i}^{(m)}e^{-\alpha _{m}}+\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}\left(e^{\alpha _{m}}-e^{-\alpha _{m}}\right)\end{aligned}}} Since the only part of the right-hand side of this equation that depends on k m {\displaystyle k_{m}} is ∑ y i ≠ k m ( x i ) w i ( m ) {\textstyle \sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}} , we see that the k m {\displaystyle k_{m}} that minimizes E {\displaystyle E} is the one in the set { k 1 , … , k L } {\displaystyle \{k_{1},\ldots ,k_{L}\}} that minimizes ∑ y i ≠ k m ( x i ) w i ( m ) {\textstyle \sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}} [assuming that α m > 0 {\displaystyle \alpha _{m}>0} ], i.e. the weak classifier with the lowest weighted error (with weights w i ( m ) = e − y i C m − 1 ( x i ) {\displaystyle w_{i}^{(m)}=e^{-y_{i}C_{m-1}(x_{i})}} ). To determine the desired weight α m {\displaystyle \alpha _{m}} that minimizes E {\displaystyle E} with the k m {\displaystyle k_{m}} that we just determined, we differentiate: d E d α m = d ( ∑ y i = k m ( x i ) w i ( m ) e − α m + ∑ y i ≠ k m ( x i ) w i ( m ) e α m ) d α m {\displaystyle {\frac {dE}{d\alpha _{m}}}={\frac {d(\sum _{y_{i}=k_{m}(x_{i})}w_{i}^{(m)}e^{-\alpha _{m}}+\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}e^{\alpha _{m}})}{d\alpha _{m}}}} The value of α m {\displaystyle \alpha _{m}} that minimizes the above expression is: α m = 1 2 ln ⁡ ( ∑ y i = k m ( x i ) w i ( m ) ∑ y i ≠ k m ( x i ) w i ( m ) ) {\displaystyle \alpha _{m}={\frac {1}{2}}\ln \left({\frac {\sum _{y_{i}=k_{m}(x_{i})}w_{i}^{(m)}}{\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}}}\right)} We calculate the weighted error rate of the weak classifier to be ϵ m = ∑ y i ≠ k m ( x i ) w i ( m ) ∑ i = 1 N w i ( m ) {\displaystyle \epsilon _{m}={\frac {\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}}{\sum _{i=1}^{N}w_{i}^{(m)}}}} , so it follows that: α m = 1 2 ln ⁡ ( 1 − ϵ m ϵ m ) {\displaystyle \alpha _{m}={\frac {1}{2}}\ln \left({\frac {1-\epsilon _{m}}{\epsilon _{m}}}\right)} which is the negative logit function multiplied by 0.5. Due to the convexity of E {\displaystyle E} as a function of α m {\displaystyle \alpha _{m}} , this new expression for α m {\displaystyle \alpha _{m}} gives the global minimum of the loss function. Note: This derivation only applies when k m ( x i ) ∈ { − 1 , 1 } {\displaystyle k_{m}(x_{i})\in \{-1,1\}} , though it can be a good starting guess in other cases, such as when the weak learner is biased ( k m ( x ) ∈ { a , b } , a ≠ − b {\displaystyle k_{m}(x)\in \{a,b\},a\neq -b} ), has multiple leaves ( k m ( x ) ∈ { a , b , … , n } {\displaystyle k_{m}(x)\in \{a,b,\dots ,n\}} ) or is some other function k m ( x ) ∈ R {\displaystyle k_{m}(x)\in \mathbb {R} } . Thus we have derived the AdaBoost algorithm: At each

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  Micro stuttering

  Micro stuttering is a visual artifact in real-time computer graphics in which the time intervals between consecutively displayed frames are uneven, even though the average frame rate reported by benchmarking software appears adequate. Tools such as 3DMark typically compute frame rates over intervals of one second or more, which can conceal momentary drops in the instantaneous frame rate that the viewer perceives as hitching or jerking of on-screen motion. At low frame rates the effect is visible as a stutter in moving images, degrading the experience in interactive applications such as video games. In severe cases a lower but more consistent frame rate can appear smoother than a higher but more erratic one. The term gained prominence in the late 2000s in discussions of multi-GPU rendering (see History), but micro stuttering also affects single-GPU systems. Common causes on modern hardware include real-time shader compilation, asset streaming from storage, VRAM exhaustion, and driver bugs. == Causes == === Shader compilation === A common cause of micro stuttering on modern PCs is real-time shader compilation. Shaders are small programs that instruct the GPU on how to render visual effects such as lighting, shadows, and reflections. On consoles, developers can pre-compile all shaders for the known, fixed hardware. On PCs, the variety of GPU architectures means shaders must often be compiled at run time, either when the game launches or during gameplay itself. When the rendering engine encounters a shader that has not yet been compiled, the CPU must finish the compilation before the GPU can draw the affected object. This causes a spike in frame time that the player perceives as a hitch. The problem has been particularly associated with games built on Unreal Engine 4 running under DirectX 12, because DX12 shifts more shader management responsibility to the application. Several techniques exist to reduce shader compilation stutter. Pipeline State Object (PSO) pre-caching records the shader permutations used at runtime so that they can be compiled in advance on subsequent launches. Asynchronous shader compilation moves the work to background CPU threads to avoid blocking the main rendering thread. Platform-level services such as Steam's shader pre-caching distribute previously compiled shaders to users with matching GPU hardware. The Steam Deck, which contains a single fixed GPU, benefits from pre-compiled shader caches because all units share the same hardware configuration. === Other causes === Micro stuttering on single-GPU systems can have several additional causes. CPU bottlenecks or scheduling interruptions from background tasks can prevent the processor from preparing frames at regular intervals. Asset streaming during gameplay (loading textures, geometry, or audio from storage) can produce hitches sometimes called traversal stutter; the use of solid-state drives and technologies such as DirectStorage has reduced but not eliminated this. VRAM exhaustion forces data to be swapped between video memory and system memory over the PCI Express bus, which is slower. Graphics driver bugs can also introduce stutter; Nvidia released hotfix driver 551.46 in February 2024 to correct intermittent micro stuttering when V-Sync was enabled. == Measurement == Micro stuttering drew attention to the limitations of average frame rate as a performance metric. In 2013, Scott Wasson at The Tech Report published a series of articles advocating frame time analysis, in which the delivery time of every individual frame is recorded and plotted rather than collapsed into a single frames-per-second figure. This approach was adopted by other hardware review publications in the following years. GPU reviews now routinely report 1% low and 0.1% low frame rates alongside the average. The 1% low is the average frame rate of the slowest 1% of frames in a sample; it serves as an indicator of worst-case smoothness. A large gap between the average and the 1% low suggests poor frame pacing. Tools for capturing per-frame timing data include FRAPS, PresentMon, OCAT, CapFrameX, and MSI Afterburner with RivaTuner Statistics Server. == Mitigation == === Frame pacing === Frame pacing is a software technique that regulates the timing of frame delivery to produce even intervals between displayed frames. Game engines, GPU drivers, and platform libraries all implement frame pacing strategies to varying degrees. On mobile platforms, Google provides the Android Frame Pacing library (Swappy) as part of the Android Game Development Kit. In December 2025, the Khronos Group published the VK_EXT_present_timing Vulkan extension, giving developers explicit control over presentation timing in a cross-platform graphics API for the first time. === Variable refresh rate === Variable refresh rate (VRR) display technologies allow a monitor's refresh rate to change to match the GPU's frame output. Implementations include Nvidia G-Sync (2013), AMD FreeSync (2015), and the VESA Adaptive-Sync standard built into DisplayPort 1.2a and later. VRR eliminates the screen tearing that results from a mismatch between frame rate and refresh rate, and avoids the frame-holding behaviour of V-Sync that can itself cause stutter. It is effective at smoothing moderate frame rate fluctuations but cannot compensate for large sudden spikes in frame time such as those caused by shader compilation or heavy asset streaming. VRR support has become standard in gaming monitors, televisions (via HDMI 2.1), and the Xbox Series X/S and PlayStation 5 consoles. === Frame generation === Beginning with DLSS 3 on the GeForce RTX 40 series in 2022, Nvidia introduced AI-based frame generation, which uses dedicated optical flow hardware and a neural network to create new frames between traditionally rendered ones. AMD followed with FSR 3 in 2023, using an algorithmic approach, and the AI-based FSR 4 for the Radeon RX 9000 series in 2025. DLSS 4, released in January 2025 for the GeForce RTX 50 series, can generate up to three frames per rendered frame using a technique called Multi Frame Generation. Frame generation increases the displayed frame rate but introduces its own frame pacing concerns. If the underlying rendered frames are unevenly timed, the interpolated frames can make the unevenness more apparent rather than less. DLSS 4 addresses this with hardware-level flip metering on the GPU's display engine, which controls the timing of frame presentation more precisely than the CPU-based pacing used in DLSS 3. Both vendors pair frame generation with latency-reduction features (Nvidia Reflex and AMD Anti-Lag+) to offset the additional input latency that results from inserting synthetic frames into the pipeline. === Frame rate limiters === Capping the frame rate below the display's maximum refresh rate, using tools such as RivaTuner Statistics Server, in-game limiters, or driver-level settings, is a common way to improve frame pacing. Preventing the GPU from running ahead of the display reduces variability in frame delivery times and can produce a smoother result than an uncapped but more irregular frame rate. == History == === Multi-GPU configurations === Micro stuttering was first widely documented in the late 2000s as a side effect of multi-GPU configurations using Alternate Frame Rendering (AFR), in which consecutive frames are assigned to alternating GPUs. Because each GPU may take a different amount of time to complete its assigned frame — due to varying scene complexity, driver scheduling, or inter-GPU communication overhead — the resulting frame delivery is irregular even when the average frame rate is high. Both Nvidia SLI and AMD CrossFireX were affected, with dual-GPU setups exhibiting the worst frame pacing irregularities. In 2012 benchmarks using Battlefield 3, dual Radeon HD 7970 cards in CrossFire showed 85% variation in frame delivery times compared with 7% for a single card, while dual GeForce GTX 680 cards in SLI showed only 7% variation compared with 5% for a single card. Multi-GPU micro stuttering became a significant factor in the eventual decline and discontinuation of consumer multi-GPU gaming. Nvidia restricted SLI to a handful of enthusiast-class cards from the GeForce 10 series onward, then replaced it with NVLink on the GeForce RTX 20 series, which saw limited gaming adoption. AMD ceased active CrossFire development around 2017. By the mid-2020s, neither vendor's current consumer GPUs support multi-GPU rendering for games. Other factors that contributed to the decline include DirectX 12 placing multi-GPU support in the hands of game developers rather than driver authors, the incompatibility of temporal anti-aliasing and other temporal rendering techniques with AFR, and the increasing size, power draw, and cost of individual GPUs. The third-party utility RadeonPro could reduce CrossFire micro stuttering through dynamic V-Sync and frame pacing adjustments, and AMD later introduced a driver-level frame paci

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  List of text mining software

  Text mining computer programs are available from many commercial and open source companies and sources. == Commercial == Angoss – Angoss Text Analytics provides entity and theme extraction, topic categorization, sentiment analysis and document summarization capabilities via the embedded AUTINDEX – is a commercial text mining software package based on sophisticated linguistics by IAI (Institute for Applied Information Sciences), Saarbrücken. DigitalMR – social media listening & text+image analytics tool for market research. FICO Score – leading provider of analytics. General Sentiment – Social Intelligence platform that uses natural language processing to discover affinities between the fans of brands with the fans of traditional television shows in social media. Stand alone text analytics to capture social knowledge base on billions of topics stored to 2004. IBM LanguageWare – the IBM suite for text analytics (tools and Runtime). IBM SPSS – provider of Modeler Premium (previously called IBM SPSS Modeler and IBM SPSS Text Analytics), which contains advanced NLP-based text analysis capabilities (multi-lingual sentiment, event and fact extraction), that can be used in conjunction with Predictive Modeling. Text Analytics for Surveys provides the ability to categorize survey responses using NLP-based capabilities for further analysis or reporting. Inxight – provider of text analytics, search, and unstructured visualization technologies. (Inxight was bought by Business Objects that was bought by SAP AG in 2008). Language Computer Corporation – text extraction and analysis tools, available in multiple languages. Lexalytics – provider of a text analytics engine used in Social Media Monitoring, Voice of Customer, Survey Analysis, and other applications. Salience Engine. The software provides the unique capability of merging the output of unstructured, text-based analysis with structured data to provide additional predictive variables for improved predictive models and association analysis. Linguamatics – provider of natural language processing (NLP) based enterprise text mining and text analytics software, I2E, for high-value knowledge discovery and decision support. Mathematica – provides built in tools for text alignment, pattern matching, clustering and semantic analysis. See Wolfram Language, the programming language of Mathematica. MATLAB offers Text Analytics Toolbox for importing text data, converting it to numeric form for use in machine and deep learning, sentiment analysis and classification tasks. Medallia – offers one system of record for survey, social, text, written and online feedback. NetMiner – software for network analysis and text mining. Supports social media and bibliographic data collection, NLP for english and chinese, sentiment analysis, work co-occurrence network(text network analysis) and visualization. NetOwl – suite of multilingual text and entity analytics products, including entity extraction, link and event extraction, sentiment analysis, geotagging, name translation, name matching, and identity resolution, among others. PolyAnalyst - text analytics environment. PoolParty Semantic Suite - graph-based text mining platform. RapidMiner with its Text Processing Extension – data and text mining software. SAS – SAS Text Miner and Teragram; commercial text analytics, natural language processing, and taxonomy software used for Information Management. Sketch Engine – a corpus manager and analysis software which providing creating text corpora from uploaded texts or the Web including part-of-speech tagging and lemmatization or detecting a particular website. Sysomos – provider social media analytics software platform, including text analytics and sentiment analysis on online consumer conversations. WordStat – Content analysis and text mining add-on module of QDA Miner for analyzing large amounts of text data. == Open source == Carrot2 – text and search results clustering framework. GATE – general Architecture for Text Engineering, an open-source toolbox for natural language processing and language engineering. Gensim – large-scale topic modelling and extraction of semantic information from unstructured text (Python). KH Coder – for Quantitative Content Analysis or Text Mining The KNIME Text Processing extension. Natural Language Toolkit (NLTK) – a suite of libraries and programs for symbolic and statistical natural language processing (NLP) for the Python programming language. OpenNLP – natural language processing. Orange with its text mining add-on. The PLOS Text Mining Collection. The programming language R provides a framework for text mining applications in the package tm. The Natural Language Processing task view contains tm and other text mining library packages. spaCy – open-source Natural Language Processing library for Python Stanbol – an open source text mining engine targeted at semantic content management. Voyant Tools – a web-based text analysis environment, created as a scholarly project.

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  K-nearest neighbors algorithm

  In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method. It was first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. In classification, a new example is assigned a label based on the labels of its k nearest training examples; in regression, the prediction is computed from the values of those neighbors. Most often, it is used for classification, as a k-NN classifier, the output of which is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small). If k = 1, then the object is simply assigned to the class of that single nearest neighbor. The k-NN algorithm can also be generalized for regression. In k-NN regression, also known as nearest neighbor smoothing, the output is the property value for the object. This value is the average of the values of k nearest neighbors. If k = 1, then the output is simply assigned to the value of that single nearest neighbor, also known as nearest neighbor interpolation. For both classification and regression, a useful technique can be to assign weights to the contributions of the neighbors, so that nearer neighbors contribute more to the average than distant ones. For example, a common weighting scheme consists of giving each neighbor a weight of 1/d, where d is the distance to the neighbor. The input consists of the k closest training examples in a data set. The neighbors are taken from a set of objects for which the class (for k-NN classification) or the object property value (for k-NN regression) is known. This can be thought of as the training set for the algorithm, though no explicit training step is required. A peculiarity (sometimes even a disadvantage) of the k-NN algorithm is its sensitivity to the local structure of the data. In k-NN classification the function is only approximated locally and all computation is deferred until function evaluation. Since this algorithm relies on distance, if the features represent different physical units or come in vastly different scales, then feature-wise normalizing of the training data can greatly improve its accuracy. == Statistical setting == Suppose we have pairs ( X 1 , Y 1 ) , ( X 2 , Y 2 ) , … , ( X n , Y n ) {\displaystyle (X_{1},Y_{1}),(X_{2},Y_{2}),\dots ,(X_{n},Y_{n})} taking values in R d × { 1 , 2 } {\displaystyle \mathbb {R} ^{d}\times \{1,2\}} , where Y is the class label of X, so that X | Y = r ∼ P r {\displaystyle X|Y=r\sim P_{r}} for r = 1 , 2 {\displaystyle r=1,2} (and probability distributions P r {\displaystyle P_{r}} ). Given some norm ‖ ⋅ ‖ {\displaystyle \|\cdot \|} on R d {\displaystyle \mathbb {R} ^{d}} and a point x ∈ R d {\displaystyle x\in \mathbb {R} ^{d}} , let ( X ( 1 ) , Y ( 1 ) ) , … , ( X ( n ) , Y ( n ) ) {\displaystyle (X_{(1)},Y_{(1)}),\dots ,(X_{(n)},Y_{(n)})} be a reordering of the training data such that ‖ X ( 1 ) − x ‖ ≤ ⋯ ≤ ‖ X ( n ) − x ‖ {\displaystyle \|X_{(1)}-x\|\leq \dots \leq \|X_{(n)}-x\|} . == Algorithm == The training examples are vectors in a multidimensional feature space, each with a class label. The training phase of the algorithm consists only of storing the feature vectors and class labels of the training samples. In the classification phase, k is a user-defined constant, and an unlabeled vector (a query or test point) is classified by assigning the label which is most frequent among the k training samples nearest to that query point. A commonly used distance metric for continuous variables is Euclidean distance. For discrete variables, such as for text classification, another metric can be used, such as the overlap metric (or Hamming distance). In the context of gene expression microarray data, for example, k-NN has been employed with correlation coefficients, such as Pearson and Spearman, as a metric. Often, the classification accuracy of k-NN can be improved significantly if the distance metric is learned with specialized algorithms such as large margin nearest neighbor or neighborhood components analysis. A drawback of the basic "majority voting" classification occurs when the class distribution is skewed. That is, examples of a more frequent class tend to dominate the prediction of the new example, because they tend to be common among the k nearest neighbors due to their large number. One way to overcome this problem is to weight the classification, taking into account the distance from the test point to each of its k nearest neighbors. The class (or value, in regression problems) of each of the k nearest points is multiplied by a weight proportional to the inverse of the distance from that point to the test point. Another way to overcome skew is by abstraction in data representation. For example, in a self-organizing map (SOM), each node is a representative (a center) of a cluster of similar points, regardless of their density in the original training data. k-NN can then be applied to the SOM. == Parameter selection == The best choice of k depends upon the data; generally, larger values of k reduces effect of the noise on the classification, but make boundaries between classes less distinct. A good k can be selected by various heuristic techniques (see hyperparameter optimization). The special case where the class is predicted to be the class of the closest training sample (i.e. when k = 1) is called the nearest neighbor algorithm. The accuracy of the k-NN algorithm can be severely degraded by the presence of noisy or irrelevant features, or if the feature scales are not consistent with their importance. Much research effort has been put into selecting or scaling features to improve classification. A particularly popular approach is the use of evolutionary algorithms to optimize feature scaling. Another popular approach is to scale features by the mutual information of the training data with the training classes. In binary (two class) classification problems, it is helpful to choose k to be an odd number as this avoids tied votes. One popular way of choosing the empirically optimal k in this setting is via bootstrap method. == The 1-nearest neighbor classifier == The most intuitive nearest neighbour type classifier is the one nearest neighbour classifier that assigns a point x to the class of its closest neighbour in the feature space, that is C n 1 n n ( x ) = Y ( 1 ) {\displaystyle C_{n}^{1nn}(x)=Y_{(1)}} . As the size of training data set approaches infinity, the one nearest neighbour classifier guarantees an error rate of no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the data). == The weighted nearest neighbour classifier == The k-nearest neighbour classifier can be viewed as assigning the k nearest neighbours a weight 1 / k {\displaystyle 1/k} and all others 0 weight. This can be generalised to weighted nearest neighbour classifiers. That is, where the ith nearest neighbour is assigned a weight w n i {\displaystyle w_{ni}} , with ∑ i = 1 n w n i = 1 {\textstyle \sum _{i=1}^{n}w_{ni}=1} . An analogous result on the strong consistency of weighted nearest neighbour classifiers also holds. Let C n w n n {\displaystyle C_{n}^{wnn}} denote the weighted nearest classifier with weights { w n i } i = 1 n {\displaystyle \{w_{ni}\}_{i=1}^{n}} . Subject to regularity conditions, which in asymptotic theory are conditional variables which require assumptions to differentiate among parameters with some criteria. On the class distributions the excess risk has the following asymptotic expansion R R ( C n w n n ) − R R ( C Bayes ) = ( B 1 s n 2 + B 2 t n 2 ) { 1 + o ( 1 ) } , {\displaystyle {\mathcal {R}}_{\mathcal {R}}(C_{n}^{wnn})-{\mathcal {R}}_{\mathcal {R}}(C^{\text{Bayes}})=\left(B_{1}s_{n}^{2}+B_{2}t_{n}^{2}\right)\{1+o(1)\},} for constants B 1 {\displaystyle B_{1}} and B 2 {\displaystyle B_{2}} where s n 2 = ∑ i = 1 n w n i 2 {\displaystyle s_{n}^{2}=\sum _{i=1}^{n}w_{ni}^{2}} and t n = n − 2 / d ∑ i = 1 n w n i { i 1 + 2 / d − ( i − 1 ) 1 + 2 / d } {\displaystyle t_{n}=n^{-2/d}\sum _{i=1}^{n}w_{ni}\left\{i^{1+2/d}-(i-1)^{1+2/d}\right\}} . The optimal weighting scheme { w n i ∗ } i = 1 n {\displaystyle \{w_{ni}^{}\}_{i=1}^{n}} , that balances the two terms in the display above, is given as follows: set k ∗ = ⌊ B n 4 d + 4 ⌋ {\displaystyle k^{}=\lfloor Bn^{\frac {4}{d+4}}\rfloor } , w n i ∗ = 1 k ∗ [ 1 + d 2 − d 2 k ∗ 2 / d { i 1 + 2 / d − ( i − 1 ) 1 + 2 / d } ] {\displaystyle w_{ni}^{}={\frac {1}{k^{}}}\left[1+{\frac {d}{2}}-{\frac {d}{2{k^{}}^{2/d}}}\{i^{1+2/d}-(i-1)^{1+2/d}\}\right]} for i = 1 , 2 , … , k ∗ {\displaystyle i=1,2,\dots ,k^{}} and w n i ∗ = 0 {\displaystyle w_{ni}^{}=0} for i = k ∗ + 1 , … , n {\displaystyle i=k^{}+1,\dots ,n} . With optimal weights the dominant term in the asymptotic expansion of the excess risk is O ( n − 4 d + 4 ) {\displaystyle {\mathcal {O}}(n^{-{\frac {4}{d+4}}})}

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  Margin classifier

  In machine learning (ML), a margin classifier is a type of classification model which is able to give an associated distance from the decision boundary for each data sample. For instance, if a linear classifier is used, the distance (typically Euclidean, though others may be used) of a sample from the separating hyperplane is the margin of that sample. The notion of margins is important in several ML classification algorithms, as it can be used to bound the generalization error of these classifiers. These bounds are frequently shown using the VC dimension. The generalization error bound in boosting algorithms and support vector machines is particularly prominent. == Margin for boosting algorithms == The margin for an iterative boosting algorithm given a dataset with two classes can be defined as follows: the classifier is given a sample pair ( x , y ) {\displaystyle (x,y)} , where x ∈ X {\displaystyle x\in X} is a domain space and y ∈ Y = { − 1 , + 1 } {\displaystyle y\in Y=\{-1,+1\}} is the sample's label. The algorithm then selects a classifier h j ∈ C {\displaystyle h_{j}\in C} at each iteration j {\displaystyle j} where C {\displaystyle C} is a space of possible classifiers that predict real values. This hypothesis is then weighted by α j ∈ R {\displaystyle \alpha _{j}\in R} as selected by the boosting algorithm. At iteration t {\displaystyle t} , the margin of a sample x {\displaystyle x} can thus be defined as y ∑ j t α j h j ( x ) ∑ | α j | . {\displaystyle {\frac {y\sum _{j}^{t}\alpha _{j}h_{j}(x)}{\sum |\alpha _{j}|}}.} By this definition, the margin is positive if the sample is labeled correctly, or negative if the sample is labeled incorrectly. This definition may be modified and is not the only way to define the margin for boosting algorithms. However, there are reasons why this definition may be appealing. == Examples of margin-based algorithms == Many classifiers can give an associated margin for each sample. However, only some classifiers utilize information of the margin while learning from a dataset. Many boosting algorithms rely on the notion of a margin to assign weight to samples. If a convex loss is utilized (as in AdaBoost or LogitBoost, for instance) then a sample with a higher margin will receive less (or equal) weight than a sample with a lower margin. This leads the boosting algorithm to focus weight on low-margin samples. In non-convex algorithms (e.g., BrownBoost), the margin still dictates the weighting of a sample, though the weighting is non-monotone with respect to the margin. == Generalization error bounds == One theoretical motivation behind margin classifiers is that their generalization error may be bound by the algorithm parameters and a margin term. An example of such a bound is for the AdaBoost algorithm. Let S {\displaystyle S} be a set of m {\displaystyle m} data points, sampled independently at random from a distribution D {\displaystyle D} . Assume the VC-dimension of the underlying base classifier is d {\displaystyle d} and m ≥ d ≥ 1 {\displaystyle m\geq d\geq 1} . Then, with probability 1 − δ {\displaystyle 1-\delta } , we have the bound: P D ( y ∑ j t α j h j ( x ) ∑ | α j | ≤ 0 ) ≤ P S ( y ∑ j t α j h j ( x ) ∑ | α j | ≤ θ ) + O ( 1 m d log 2 ⁡ ( m / d ) / θ 2 + log ⁡ ( 1 / δ ) ) {\displaystyle P_{D}\left({\frac {y\sum _{j}^{t}\alpha _{j}h_{j}(x)}{\sum |\alpha _{j}|}}\leq 0\right)\leq P_{S}\left({\frac {y\sum _{j}^{t}\alpha _{j}h_{j}(x)}{\sum |\alpha _{j}|}}\leq \theta \right)+O\left({\frac {1}{\sqrt {m}}}{\sqrt {d\log ^{2}(m/d)/\theta ^{2}+\log(1/\delta )}}\right)} for all θ > 0 {\displaystyle \theta >0} .

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  Qapital

  Qapital is a personal finance mobile application (app) for the iOS and Android operating systems, developed by Qapital, LLC. The app is designed to motivate users to save money through a gamification of their spending behavior. It moves money from a user's checking account to a separate Qapital account, when certain rules are triggered. Its database is used by psychology professor Dan Ariely to study consumer behavior. Qapital was released in Sweden in 2013, then in the US in early 2015. The application was later withdrawn from the Swedish market in April 2015, in order to focus on the US market. == History == The idea for Qapital was conceived by ex-bankers in Sweden. The software was designed by twin brothers Daniel and Andreas Källbom of Studio Källbom and released in Sweden in December 2013. The original software was a personal finance dashboard, similar to Mint.com, to show its users how they spent their money. Qapital introduced the app into the US market with a different design in 2014 and started focusing exclusively on the US market. The app was re-designed to focus on building savings rather than managing personal finances. The Swedish version shut down in April 2015. The app was initially restricted to the iOS platform, but an Android version was released at the end of 2015. Shortly after its US launch, Qapital invited psychology professor Dan Ariely to join its team as its "chief behavioral economist". He uses the app's database to conduct research into behavioral economics and Qapital in turn uses Ariely's research in design and programming decisions. In 2017, Qapital added checking and debit card services to the app. == Concept and features == Qapital is a free personal finance app for iOS and Android devices, intended to encourage its users to save money. Qapital directs each of its users to set savings goals, then automatically transfers money from their checking account to an account for savings, when a rule established in the app is met. It uses the "if this then that" (IFTTT) rule-based web-service. For example, one rule could be that if a user purchases a cup of coffee, then the app will round up the charge to the nearest dollar and deposit the difference into savings. Users connect their bank accounts to Qapital, so it knows when purchases are made. When a rule is met, money for savings are transferred to a Qapital account operated in partnership with Lincoln Savings Bank. As of 2015, Qapital can connect to more than 180 other apps, such as Facebook, Twitter, Dropbox and Instagram. For example, connecting to Jawbone allows the user to set a rule that if they take a certain number of steps during the day, a set amount of money is transferred to savings. The app also allows users to monitor activity among their other financial accounts, such as deposits and withdrawals. == Reception == In an October 2015 review, PC Magazine gave Qapital four out of five marks and an editor rating of "excellent." The review praised the app for having a "lovely design" and criticized it for being a, "bit simplistic in some of its rules." Bankrate, in a May 2015 review, gave the app a score of 3/5 for "ease of use," 5/5 for "features," 4/5 for "effectiveness," 4/5 for "value," for a total score of 16/20. The reviewer criticized Qapital's savings account for providing a low-interest rate, but concluded that its numerous features make the app "intriguing" and "it would be difficult to find a standard bank app more fun to use than Qapital."

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  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.

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  Genetic operator

  A genetic operator is an operator used in evolutionary algorithms (EA) to guide the algorithm towards a solution to a given problem. There are three main types of operators (mutation, crossover and selection), which must work in conjunction with one another in order for the algorithm to be successful. Genetic operators are used to create and maintain genetic diversity (mutation operator), combine existing solutions (also known as chromosomes) into new solutions (crossover) and select between solutions (selection). The classic representatives of evolutionary algorithms include genetic algorithms, evolution strategies, genetic programming and evolutionary programming. In his book discussing the use of genetic programming for the optimization of complex problems, computer scientist John Koza has also identified an 'inversion' or 'permutation' operator; however, the effectiveness of this operator has never been conclusively demonstrated and this operator is rarely discussed in the field of genetic programming. For combinatorial problems, however, these and other operators tailored to permutations are frequently used by other EAs. Mutation (or mutation-like) operators are said to be unary operators, as they only operate on one chromosome at a time. In contrast, crossover operators are said to be binary operators, as they operate on two chromosomes at a time, combining two existing chromosomes into one new chromosome. == Operators == Genetic variation is a necessity for the process of evolution. Genetic operators used in evolutionary algorithms are analogous to those in the natural world: survival of the fittest, or selection; reproduction (crossover, also called recombination); and mutation. === Selection === Selection operators give preference to better candidate solutions (chromosomes), allowing them to pass on their 'genes' to the next generation (iteration) of the algorithm. The best solutions are determined using some form of objective function (also known as a 'fitness function' in evolutionary algorithms), before being passed to the crossover operator. Different methods for choosing the best solutions exist, for example, fitness proportionate selection and tournament selection. A further or the same selection operator is used to determine the individuals for being selected to form the next parental generation. The selection operator may also ensure that the best solution(s) from the current generation always become(s) a member of the next generation without being altered; this is known as elitism or elitist selection. === Crossover === Crossover is the process of taking more than one parent solutions (chromosomes) and producing a child solution from them. By recombining portions of good solutions, the evolutionary algorithm is more likely to create a better solution. As with selection, there are a number of different methods for combining the parent solutions, including the edge recombination operator (ERO) and the 'cut and splice crossover' and 'uniform crossover' methods. The crossover method is often chosen to closely match the chromosome's representation of the solution; this may become particularly important when variables are grouped together as building blocks, which might be disrupted by a non-respectful crossover operator. Similarly, crossover methods may be particularly suited to certain problems; the ERO is considered a good option for solving the travelling salesman problem. === Mutation === The mutation operator encourages genetic diversity amongst solutions and attempts to prevent the evolutionary algorithm converging to a local minimum by stopping the solutions becoming too close to one another. In mutating the current pool of solutions, a given solution may change between slightly and entirely from the previous solution. By mutating the solutions, an evolutionary algorithm can reach an improved solution solely through the mutation operator. Again, different methods of mutation may be used; these range from a simple bit mutation (flipping random bits in a binary string chromosome with some low probability) to more complex mutation methods in which genes in the solution are changed, for example by adding a random value from the Gaussian distribution to the current gene value. As with the crossover operator, the mutation method is usually chosen to match the representation of the solution within the chromosome. == Combining operators == While each operator acts to improve the solutions produced by the evolutionary algorithm working individually, the operators must work in conjunction with each other for the algorithm to be successful in finding a good solution. Using the selection operator on its own will tend to fill the solution population with copies of the best solution from the population. If the selection and crossover operators are used without the mutation operator, the algorithm will tend to converge to a local minimum, that is, a good but sub-optimal solution to the problem. Using the mutation operator on its own leads to a random walk through the search space. Only by using all three operators together can the evolutionary algorithm become a noise-tolerant global search algorithm, yielding good solutions to the problem at hand.

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