Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation includes resampling and sample splitting methods that use different portions of the data to test and train a model on different iterations. It is often used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. It can also be used to assess the quality of a fitted model and the stability of its parameters. In a prediction problem, a model is usually given a dataset of known data on which training is run (training dataset), and a dataset of unknown data (or first seen data) against which the model is tested (called the validation dataset or testing set). The goal of cross-validation is to test the model's ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias and to give an insight on how the model will generalize to an independent dataset (i.e., an unknown dataset, for instance from a real problem). One round of cross-validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, in most methods multiple rounds of cross-validation are performed using different partitions, and the validation results are combined (e.g. averaged) over the rounds to give an estimate of the model's predictive performance. In summary, cross-validation combines (averages) measures of fitness in prediction to derive a more accurate estimate of model prediction performance. == Motivation == Assume a model with one or more unknown parameters, and a data set to which the model can be fit (the training data set). The fitting process optimizes the model parameters to make the model fit the training data as well as possible. If an independent sample of validation data is taken from the same population as the training data, it will generally turn out that the model does not fit the validation data as well as it fits the training data. The size of this difference is likely to be large especially when the size of the training data set is small, or when the number of parameters in the model is large. Cross-validation is a way to estimate the size of this effect. === Example: linear regression === In linear regression, there exist real response values y 1 , … , y n {\textstyle y_{1},\ldots ,y_{n}} , and n p-dimensional vector covariates x1, ..., xn. The components of the vector xi are denoted xi1, ..., xip. If least squares is used to fit a function in the form of a hyperplane ŷ = a + βTx to the data (xi, yi) 1 ≤ i ≤ n, then the fit can be assessed using the mean squared error (MSE). The MSE for given estimated parameter values a and β on the training set (xi, yi) 1 ≤ i ≤ n is defined as: MSE = 1 n ∑ i = 1 n ( y i − y ^ i ) 2 = 1 n ∑ i = 1 n ( y i − a − β T x i ) 2 = 1 n ∑ i = 1 n ( y i − a − β 1 x i 1 − ⋯ − β p x i p ) 2 {\displaystyle {\begin{aligned}{\text{MSE}}&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-{\hat {y}}_{i})^{2}={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-{\boldsymbol {\beta }}^{T}\mathbf {x} _{i})^{2}\\&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-\beta _{1}x_{i1}-\dots -\beta _{p}x_{ip})^{2}\end{aligned}}} If the model is correctly specified, it can be shown under mild assumptions that the expected value of the MSE for the training set is (n − p − 1)/(n + p + 1) < 1 times the expected value of the MSE for the validation set (the expected value is taken over the distribution of training sets). Thus, a fitted model and computed MSE on the training set will result in an optimistically biased assessment of how well the model will fit an independent data set. This biased estimate is called the in-sample estimate of the fit, whereas the cross-validation estimate is an out-of-sample estimate. Since in linear regression it is possible to directly compute the factor (n − p − 1)/(n + p + 1) by which the training MSE underestimates the validation MSE under the assumption that the model specification is valid, cross-validation can be used for checking whether the model has been overfitted, in which case the MSE in the validation set will substantially exceed its anticipated value. (Cross-validation in the context of linear regression is also useful in that it can be used to select an optimally regularized cost function.) === General case === In most other regression procedures (e.g. logistic regression), there is no simple formula to compute the expected out-of-sample fit. Cross-validation is, thus, a generally applicable way to predict the performance of a model on unavailable data using numerical computation in place of theoretical analysis. == Types == Two types of cross-validation can be distinguished: exhaustive and non-exhaustive cross-validation. === Exhaustive cross-validation === Exhaustive cross-validation methods are cross-validation methods which learn and test on all possible ways to divide the original sample into a training and a validation set. ==== Leave-p-out cross-validation ==== Leave-p-out cross-validation (LpO CV) involves using p observations as the validation set and the remaining observations as the training set. This is repeated on all ways to cut the original sample on a validation set of p observations and a training set. LpO cross-validation require training and validating the model C p n {\displaystyle C_{p}^{n}} times, where n is the number of observations in the original sample, and where C p n {\displaystyle C_{p}^{n}} is the binomial coefficient. For p > 1 and for even moderately large n, LpO CV can become computationally infeasible. For example, with n = 100 and p = 30, C 30 100 ≈ 3 × 10 25 . {\displaystyle C_{30}^{100}\approx 3\times 10^{25}.} A variant of LpO cross-validation with p=2 known as leave-pair-out cross-validation has been recommended as a nearly unbiased method for estimating the area under ROC curve of binary classifiers. ==== Leave-one-out cross-validation ==== Leave-one-out cross-validation (LOOCV) is a particular case of leave-p-out cross-validation with p = 1. The process looks similar to jackknife; however, with cross-validation one computes a statistic on the left-out sample(s), while with jackknifing one computes a statistic from the kept samples only. LOO cross-validation requires less computation time than LpO cross-validation because there are only C 1 n = n {\displaystyle C_{1}^{n}=n} passes rather than C p n {\displaystyle C_{p}^{n}} . However, n {\displaystyle n} passes may still require quite a large computation time, in which case other approaches such as k-fold cross validation may be more appropriate. Pseudo-code algorithm: Input: x, {vector of length N with x-values of incoming points} y, {vector of length N with y-values of the expected result} interpolate( x_in, y_in, x_out ), { returns the estimation for point x_out after the model is trained with x_in-y_in pairs} Output: err, {estimate for the prediction error} Steps: err ← 0 for i ← 1, ..., N do // define the cross-validation subsets x_in ← (x[1], ..., x[i − 1], x[i + 1], ..., x[N]) y_in ← (y[1], ..., y[i − 1], y[i + 1], ..., y[N]) x_out ← x[i] y_out ← interpolate(x_in, y_in, x_out) err ← err + (y[i] − y_out)^2 end for err ← err/N === Non-exhaustive cross-validation === Non-exhaustive cross validation methods do not compute all ways of splitting the original sample. These methods are approximations of leave-p-out cross-validation. ==== k-fold cross-validation ==== In k-fold cross-validation, the original sample is randomly partitioned into k equal sized subsamples, often referred to as "folds". Of the k subsamples, a single subsample is retained as the validation data for testing the model, and the remaining k − 1 subsamples are used as training data. The cross-validation process is then repeated k times, with each of the k subsamples used exactly once as the validation data. The k results can then be averaged to produce a single estimation. The advantage of this method over repeated random sub-sampling (see below) is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold cross-validation is commonly used, but in general k remains an unfixed parameter. For example, setting k = 2 results in 2-fold cross-validation. In 2-fold cross-validation, the dataset is randomly shuffled into two sets d0 and d1, so that both sets are equal size (this is usually implemented by shuffling the data array and then splitting it in two). We then train on d0 and validate on d1, followed by training on d1 and validating on d0. When k = n (the number of observations), k-fold cross-validation is equivalent to leave-one-out cr
Screen generator
A screen generator, also known as a screen painter, screen mapper, or forms generator is a software package (or component thereof) which enables data entry screens to be generated declaratively, by "painting" them on the screen WYSIWYG-style, or through filling-in forms, rather than requiring writing of code to display them manually. 4GLs commonly incorporate a screen generator feature. They are also commonly found bundled with database systems, especially entry-level databases. A screen generator is one aspect of an application generator, which can also include other functions such as report generation and a data dictionary. The earliest screen generators were character-based; by the 1990s, GUI support became common, and then support for generating HTML forms as well. Some screen generators work by generating code to display the screen in a high-level language (for example, COBOL); others store the screen definition in a data file or in database tables, and then have a runtime component responsible for actually displaying the form and receiving and validating user input. == Examples == Examples of screen generators include: IBM Screen Definition Facility II: generates screens for CICS BMS, IMS MFS, ISPF, GDDM and CSP/AD. Performix for Informix. Microsoft Visual Basic the forms component of Microsoft Access Oracle Developer, in particular its Oracle Forms component the QDesign component of PowerHouse SystemBuilder/SB+ the Screen Painter component of SAP's ABAP Workbench the FoxView component of FoxPro. FoxView was originally developed by Luis Castro as a dBASE screen generator named ViewGen; Fox purchased it and bundled it with FoxPro 1.0. Later, Fox replaced Castro's code with their own screen painter code. dBASE included a built-in screen generator in dBASE IV onwards; in dBASE III and earlier, third party screen generators were available, including the already mentioned ViewGen DPS 1100 for UNIVAC 1100 series mainframes.
Grid network
A grid network is a computer network consisting of a number of computer systems connected in a grid topology. In a regular grid topology, each node in the network is connected with two neighbors along one or more dimensions. If the network is one-dimensional, and the chain of nodes is connected to form a circular loop, the resulting topology is known as a ring. Network systems such as FDDI use two counter-rotating token-passing rings to achieve high reliability and performance. In general, when an n-dimensional grid network is connected circularly in more than one dimension, the resulting network topology is a torus, and the network is called "toroidal". When the number of nodes along each dimension of a toroidal network is 2, the resulting network is called a hypercube. A parallel computing cluster or multi-core processor is often connected in regular interconnection network such as a de Bruijn graph, a hypercube graph, a hypertree network, a fat tree network, a torus, or cube-connected cycles. A grid network is not the same as a grid computer or a computational grid, although the nodes in a grid network are usually computers, and grid computing requires some kind of computer network or "universal coding" to interconnect the computers.
Digital asset
A digital asset is anything that exists only in digital form and comes with a distinct usage right or distinct permission for use. Data that do not possess those rights are not considered assets. Digital assets include, but are not limited to: digital documents, audio content, motion pictures, and other relevant digital data currently in circulation or stored on digital appliances, such as personal computers, laptops, portable media players, tablets, data storage devices, and telecommunication devices. This encompasses any apparatus that currently exists or will exist as technology progresses to accommodate the conception of new modalities capable of carrying digital assets. This holds true regardless of the ownership of the physical device on which the digital asset is located. == Types == Types of digital assets include, but are not limited to: software, photography, logos, illustrations, animations, audiovisual media, presentations, spreadsheets, digital paintings, word documents, electronic mails, websites, and various other digital formats with their respective metadata. The number of different types of digital assets is exponentially increasing due to the rising number of devices that leverage these assets, such as smartphones, serving as conduits for digital media. In Intel's presentation at the 'Intel Developer Forum 2013,' they introduced several new types of digital assets related to medicine, education, voting, friendships, conversations, and reputation, among others. == Digital asset management system == A digital asset management (DAM) is an integrated structure that combines software, hardware, and/or other services to manage, store, ingest, organize, and retrieve digital assets. These systems enable users to find and use content when needed. == Digital asset metadata == Metadata is data about other data. Any structured information that defines a specification of any form of data is referred to as metadata. Metadata is also a claimed relationship between two entities, often used to establish connections or associations. Librarian Lorcan Dempsey says "Think of metadata as data which removes from a user (human or machine) the need to have full advance knowledge of the existence or characteristics of things of potential interest in the environment". At first, the term metadata was used for digital data exclusively, but nowadays metadata can apply to both physical and digital data. Catalogs, inventories, registers, and other similar standardized forms of organizing, managing, and retrieving resources contain metadata. Metadata can be stored and contained directly within the file it refers to or independently from it with the help of other forms of data management such as a DAM system. The more metadata is assigned to an asset the easier it gets to categorize it, especially as the amount of information grows. The asset's value rises the more metadata it has for it becomes more accessible, easier to manage, and more complex. Structured metadata can be shared with open protocols like OAI-PMH to allow further aggregation and processing. Open data sources like institutional repositories have thus been aggregated to form large datasets and academic search engines comprising tens of millions of open access works, like BASE, CORE, and Unpaywall. == Issues == Due to a lack of either legislation or legal precedent, there is limited existing governmental control and regulation surrounding digital assets in the United States and other large economies globally. Many of the control issues relating to access and transferability are maintained by individual companies. Some consequences of this include 'What is to become of the assets once their owner is deceased?' as well as can, and, if so, how, may they be inherited. This subject was broached in a bogus story about Bruce Willis allegedly looking to sue Apple as the end user agreement prevented him from bequeathing his iTunes collection to his children. Another case of this was when a soldier died on duty and the family requested access to the Yahoo! account. When Yahoo! refused to grant access, the probate judge ordered them to give the emails to the family but Yahoo! still was not required to give access. The Music Modernization Act was passed in September 2018 by the U.S. Congress to create a new music licensing system, with the aim to help songwriters get paid more.
Gaumina
Gaumina is the largest interactive agency in the Baltics, providing services of web design, web development, online advertising, video, multimedia, mobile and viral. The company works on projects for Procter & Gamble, Nokia, Nissan, Unilever, YX Energi, 7 Up, Vodafone, MTV, Dunnes Stores, Philip Morris, FIBA Europe as well as Irish public sector. == History == Founded in 1998, Gaumina accounts for 39 percent of the Lithuanian interactive market and has completed more than 2,000 online projects. Since 2004 the company has been operating in the UK and Ireland as Gaumina.co.uk. In 2007 Gaumina gained wide media coverage for winning three awards in three days. A website developed by Gaumina won the Best Social Networking website award at the same the Irish Golden Spiders awards. A website developed by Gaumina was named among the 21 best European multimedia projects of 2007 in the final of Europrix Top Talent Award in Austria. The company was also named one of the winners of the national Innovation Prize 2007, awarding the Lithuania's most innovative companies, in the category of Innovative Enterprise. The agency was named "Digital Agency of the Year" by International advertising festival Golden Hammer in September 2008. The agency also won the main prize at the best at Best Use of Film, Digital Animation or Motion Graphics category by the Irish Golden Spider awards in November 2008. Gaumina is currently managed by CEO Darius Bagdžiūnas.
Language engineering
Language engineering involves the creation of natural language processing systems, whose cost and outputs are measurable and predictable. It is a distinct field contrasted to natural language processing and computational linguistics. A recent trend of language engineering is the use of Semantic Web technologies for the creation, archiving, processing, and retrieval of machine processable language data. Meta-Language Engineering is a proposed extension of Language Engineering first recorded in 2025, associated with the work of Delyone de Paula Canedo Filho. The term is used to designate an approach that, in addition to natural language processing, encompasses the symbolic, cognitive, and epistemological structuring of language systems.
The Dodo (website)
The Dodo is an American online publisher focused on animals. The website was launched in January 2014 by Izzie Lerer, the daughter of media executive Kenneth Lerer, and journalist Kerry Lauerman. The Dodo has become one of the most popular Facebook publishers, garnering 1 billion video views from the social network in November 2015. The Dodo is headquartered in New York, New York. == History == The company—named after the first recorded species that humans drove to extinction—was founded by Lerer out of "a personal passion for the subject manner". Lerer has a PhD in animal studies with a focus on animal ethics and human relationships from Columbia University, launching the website after noticing the viral success of animal videos online but seeing no one "really owned the space." The Dodo's editorial and video production staff unionized with the Writers Guild of America, East in April 2018.