Spreading activation

Spreading activation is a method for searching associative networks, biological and artificial neural networks, or semantic networks. The search process is initiated by labeling a set of source nodes (e.g. concepts in a semantic network) with weights or "activation" and then iteratively propagating or "spreading" that activation out to other nodes linked to the source nodes. Most often these "weights" are real values that decay as activation propagates through the network. When the weights are discrete this process is often referred to as marker passing. Activation may originate from alternate paths, identified by distinct markers, and terminate when two alternate paths reach the same node. However brain studies show that several different brain areas play an important role in semantic processing. Spreading activation in semantic networks as a model were invented in cognitive psychology to model the fan out effect. Spreading activation can also be applied in information retrieval, by means of a network of nodes representing documents and terms contained in those documents. == Cognitive psychology == As it relates to cognitive psychology, spreading activation is the theory of how the brain iterates through a network of associated ideas to retrieve specific information. The spreading activation theory presents the array of concepts within our memory as cognitive units, each consisting of a node and its associated elements or characteristics, all connected together by edges. A spreading activation network can be represented schematically, in a sort of web diagram with shorter lines between two nodes meaning the ideas are more closely related and will typically be associated more quickly to the original concept. In memory psychology, the spreading activation model holds that people organize their knowledge of the world based on their personal experiences, which in turn form the network of ideas that is the person's knowledge of the world. When a word (the target) is preceded by an associated word (the prime) in word recognition tasks, participants seem to perform better in the amount of time that it takes them to respond. For instance, subjects respond faster to the word "doctor" when it is preceded by "nurse" than when it is preceded by an unrelated word like "carrot". This semantic priming effect with words that are close in meaning within the cognitive network has been seen in a wide range of tasks given by experimenters, ranging from sentence verification to lexical decision and naming. As another example, if the original concept is "red" and the concept "vehicles" is primed, they are much more likely to say "fire engine" instead of something unrelated to vehicles, such as "cherries". If instead "fruits" was primed, they would likely name "cherries" and continue on from there. The activation of pathways in the network has everything to do with how closely linked two concepts are by meaning, as well as how a subject is primed. == Algorithm == A directed graph is populated by Nodes[ 1...N ] each having an associated activation value A [ i ] which is a real number in the range [0.0 ... 1.0]. A Link[ i, j ] connects source node[ i ] with target node[ j ]. Each edge has an associated weight W [ i, j ] usually a real number in the range [0.0 ... 1.0]. Parameters: Firing threshold F, a real number in the range [0.0 ... 1.0] Decay factor D, a real number in the range [0.0 ... 1.0] Steps: Initialize the graph setting all activation values A [ i ] to zero. Set one or more origin nodes to an initial activation value greater than the firing threshold F. A typical initial value is 1.0. For each unfired node [ i ] in the graph having an activation value A [ i ] greater than the node firing threshold F: For each Link [ i, j ] connecting the source node [ i ] with target node [ j ], adjust A [ j ] = A [ j ] + (A [ i ] W [ i, j ] D) where D is the decay factor. If a target node receives an adjustment to its activation value so that it would exceed 1.0, then set its new activation value to 1.0. Likewise maintain 0.0 as a lower bound on the target node's activation value should it receive an adjustment to below 0.0. Once a node has fired it may not fire again, although variations of the basic algorithm permit repeated firings and loops through the graph. Nodes receiving a new activation value that exceeds the firing threshold F are marked for firing on the next spreading activation cycle. If activation originates from more than one node, a variation of the algorithm permits marker passing to distinguish the paths by which activation is spread over the graph The procedure terminates when either there are no more nodes to fire or in the case of marker passing from multiple origins, when a node is reached from more than one path. Variations of the algorithm that permit repeated node firings and activation loops in the graph, terminate after a steady activation state, with respect to some delta, is reached, or when a maximum number of iterations is exceeded. == Examples ==

Medical data breach

Medical data, including patients' identity information, health status, disease diagnosis and treatment, and biogenetic information, not only involve patients' privacy but also have a special sensitivity and important value, which may bring physical and mental distress and property loss to patients and even negatively affect social stability and national security once leaked. However, the development and application of medical AI must rely on a large amount of medical data for algorithm training, and the larger and more diverse the amount of data, the more accurate the results of its analysis and prediction will be. However, the application of big data technologies such as data collection, analysis and processing, cloud storage, and information sharing has increased the risk of data leakage. In the United States, the rate of such breaches has increased over time, with 176 million records breached by the end of 2017. By 2024, the U.S. Department of Health and Human Services reported 725 large healthcare data breaches affecting approximately 275 million individual records in a single year, marking a significant escalation in both the frequency and scale of incidents. == Black market for health data == In February 2015 an NPR report claimed that organized crime networks had ways of selling health data in the black market. In 2015 a Beazley employee estimated that medical records could sell on the black market for US$40-50. == How data is lost == Theft, data loss, hacking, and unauthorized account access are ways in which medical data breaches happen. Among reported breaches of medical information in the United States networked information systems accounted for the largest number of records breached. There are many data breaches happening in the US health care system, among business associates of the health care providers that continuously gain access to patients' data. == List of data breaches == In February 2024, a ransomware attack on Change Healthcare, a subsidiary of UnitedHealth Group, compromised the protected health information of approximately 100 million individuals, making it the largest healthcare data breach in United States history. The attack disrupted claims processing for healthcare providers nationwide for several weeks. In May 2024, MediSecure suffered a cyberattack involving ransomware in Australia. In May 2021, the Health Service Executive in the Republic of Ireland was the victim of a cyberattack involving ransomware, in the Health Service Executive cyberattack, with admission records and test results present in a sample of the data reviewed by the Financial Times. In October 2018, the Centers for Medicare and Medicaid Services in the US reported that around 75,000 individual records had been affected by a data breach that took place through the ACA Agent and Broker Portal. In 2018, Social Indicators Research published the scientific evidence of 173,398,820 (over 173 million) individuals affected in USA from October 2008 (when the data were collected) to September 2017 (when the statistical analysis took place). In 2015, Anthem Inc. lost data for 37 million people in the Anthem medical data breach In 2014 4.5 million people using Complete Health Systems had their data stolen In 2013-14 1 million people using Montana Department of Public Health and Human Services had their data stolen In 2013 4 million people using Advocate Health and Hospitals Corporation had their data stolen In 2011 4.9 million users of Tricare services had their data stolen due to an employee error by Science Applications International Corporation In 2011 1.9 million people using Health Net had their data stolen In 2011 1 million people using Nemours Foundation had their data stolen In 2010 6800 people using New York-Presbyterian Hospital and Columbia University Medical Center had their data breached. In response, those organizations agreed to pay the United States Department of Health and Human Services a US$4.8 million dollar fine. In 2009 1 million people using BlueCross BlueShield of Tennessee had their data stolen == Regulation == In the United States, the Health Insurance Portability and Accountability Act and Health Information Technology for Economic and Clinical Health Act require companies to report data breaches to affected individuals and the federal government. Under the HIPAA Breach Notification Rule, covered entities must notify affected individuals without unreasonable delay and no later than 60 days after discovering a breach of unsecured protected health information. Breaches affecting 500 or more individuals must also be reported to the HHS Secretary and to prominent media outlets serving the affected state or jurisdiction within the same timeframe; HHS publicly lists these larger breaches on its breach portal, commonly known as the "wall of shame." Breaches affecting fewer than 500 individuals are reported to HHS annually, no later than 60 days after the end of the calendar year in which they were discovered. Health Information Privacy Health Insurance Portability and Accountability Act of 1996 (HIPAA). - 45 CFR Parts 160 and 164, Standards for Privacy of Individually Identifiable Health Information and Security Standards for the Protection of Electronic Protected Health Information. HIPAA includes provisions designed to save health care businesses money by encouraging electronic transactions, as well as regulations to protect the security and confidentiality of patient information. The Privacy Rule became effective April 14, 2001, and most covered entities (health plans, health care clearinghouses, and health care providers that conduct certain financial and administrative transactions electronically) had until April 2003 to comply. This security provision became effective April 21, 2003. The Health Insurance Portability and Accountability Act (HIPAA) is the baseline set of federal regulations governing medical information. It does three things: i. i. i.Establish a structure for how personal health information is disclosed and establish the rights of individuals with respect to health information; ii.Specify security standards for the retention and transmission of electronic patient information; iii.Need a common format and data structure for the electronic exchange of health information. California-Specific Laws California’s medical privacy laws, primarily the Confidentiality of Medical Information Act (CMIA), the data breach sections of the Civil Code, and sections of the Health and Safety Code, provide HIPAA-like protections, although the terminology is different. HIPAA establishes a federal "minimum standard" that applies where there are gaps in California law, and HIPAA also specifies that stricter state laws will override or supersede HIPAA. California's health care privacy laws apply to providers who provide personal health records (PHR), while HIPAA only applies when the provider providing the PHR is a business associate of a covered entity. Federal law does not grant individuals the right to file a lawsuit in the event of a data breach (only the Attorney General can file a lawsuit), but California law does. This means that California law sets a higher standard for medical privacy, and that individuals in California enjoy stronger legal protections and more ways to hold entities that violate their medical privacy accountable. In the UK, the legal framework for how patient data is cared for and processed is the Data Protection Act 2018 (DPA), which incorporates the EU General Data Protection Regulation (GDPR) into law, and the common law duty of confidentiality (CLDC). The data protection legislation requires that the collection and processing of personal data be fair, lawful and transparent. This means that the collection and processing of data as defined by data protection legislation must always have a valid lawful basis and must also meet the requirements of the CLDC. In the China, Article 18 of the "National Health Care Big Data Standards, Security and Services Management Measures (for Trial Implementation)" (National Health Planning and Development (2018) No. 23) promulgated by the National Health Care Commission in 2018 states, "The responsible unit shall adopt measures such as data classification, important data backup, and encryption authentication to guarantee the security of health care big data." However, the scope and definition of important data are not covered. Although the "Information Security Technology-Healthcare Data Security Guide" (the "Guide") issued by the National Standardization Committee also proposes that important data should be evaluated and approved in accordance with the regulations, there is likewise no definition of the connotation and definition of important data.

Webby Awards

The Webby Awards (colloquially referred to as the Webbys) are awards for excellence on the Internet presented annually by the International Academy of Digital Arts and Sciences, a judging body composed of over three thousand industry experts and technology innovators. Categories include websites, advertising and media, online film and video, mobile sites and apps, and social. Two winners are selected in each category, one by members of The International Academy of Digital Arts and Sciences, and one by the public who cast their votes during Webby People's Voice voting. Each winner presents a five-word acceptance speech, a trademark of the annual awards show. In its early years, the award was hailed as the "Internet's highest honor" and was associated with the phrase "The Oscars of the Internet." == History == In its early years, the organization was one of several vying to be the premiere internet awards show. Both shows would compare themselves to the Oscars, as did media outlets such as The New York Times to Canada's Globe & Mail. The winners of the First Annual Webby Awards in 1995 were presented by John Brancato and Michael Ferris, writers for Columbia Pictures. It was held at the Hollywood Roosevelt Hotel. The televised Webby Awards were sponsored by the Academy of Web Design and Cool Site of the Day. The first Webby Awards were produced by Kay Dangaard at the Hollywood Roosevelt Hotel as a nod to the first site of the Academy of Motion Picture Arts and Sciences (Oscars). That first year, they were called "Webbie" Awards. The first "Site of the Year" winner was the pioneer webisodic serial The Spot. The modern Webby Awards were co-founded by Tiffany Shlain, a filmmaker, when she was hired by The Web Magazine to re-establish them, and were first held in San Francisco in 1997. They quickly became known for its requirement that winners give their acceptance speeches in five words. After this, the awards became more successful than the magazine and IDG closed the publication. Shlain and co-founder Maya Draisin Farrah continued to run The Webby Awards until 2004. The International Academy of Digital Arts and Sciences, which selects the winners of The Webby Awards, was established in 1998 by co-founders Tiffany Shlain, Spencer Ante and Maya Draisin. Members of the Academy include Kevin Spacey, Grimes, Questlove, Internet inventor Vint Cerf, Instagram's Head of Fashion Partnerships Eva Chen, comedian Jimmy Kimmel, Twitter founder Biz Stone, Vice Media co-founder and CEO Shane Smith, Tumblr's David Karp, Director of Harvard's Berkman Klein Center for Internet & Society Susan P. Crawford, Refinery29's Executive Creative Director Piera Gelardi, and CEO and co-founder of Gimlet Media Alex Blumberg. The Webby Awards is owned and operated by the Webby Media Group, a division of Recognition Media, which also owns and produces the Lovie Awards in Europe and Netted by the Webbys, a daily email publication launched in 2009. David-Michel Davies, CEO of Webby Media Group, current Executive Director of the Webby Awards and co-founder of Internet Week New York, was named Executive Director of the Webby Awards in 2005. In 2009, the 13th Annual Webby Awards received nearly 10,000 entries from all 50 US states and over 60 countries. That same year, more than 500,000 votes were cast in The Webby People's Voice Awards. In 2012, the 16th Annual Webby awards received 1.5 million votes from more than 200 countries for the People's Voice awards. In 2015, the 19th Annual Webby Awards received nearly 13,000 entries from all 50 U.S. states and over 60 countries worldwide. == Nomination process == The 2000 awards began the transition to nominee submissions. Previously, nominees had been selected by an internal committee. As early as 2017, organizations wanting to nominate themselves were charged $395 for a single entry. An "ad campaign entry" would cost $595. By 2024, those fees had risen to $495 and $675, respectively. Executive Academy Members with category-specific expertise evaluate the shortlisted entries based on the appropriate Website, Advertising & Media, Online Film & Video, Mobile Sites & Apps, and Social category criteria, and cast ballots to determine Webby Honorees, Nominees and Webby Winners. Deloitte provides vote tabulation consulting for the Webby Awards. In addition to the award given in each category by the International Academy of Digital Arts and Sciences, another winner is selected in each category as determined by the general public during People's Voice voting. Winners of both the Academy-selected and People's Voice-selected awards are invited to the Webbys. == Awards granted == The Webby Awards are presented in over a hundred categories among all four types of entries. A website can be entered in multiple categories and receive multiple awards. In each category, two awards are handed out: a Webby Award selected by The International Academy of Digital Arts and Sciences, and a People's Voice Award selected by the general public. == Ceremony == Between 2005 and 2019, the Webby Awards were presented in New York City. Many of the ceremony hosts are comedians and comedic actors. Comedian Rob Corddry hosted the ceremony from 2005 to 2007. Seth Meyers of Saturday Night Live hosted in 2008 and 2009, B.J. Novak of the sitcom The Office in 2010, and Lisa Kudrow in 2011. Comedian, actor, and writer Patton Oswalt hosted from 2012 to 2014. Comedian Hannibal Buress hosted in 2015. The Webbys are famous for limiting recipients to five-word speeches, which are often humorous, although some exceed the limit. In 2005 when accepting his Lifetime Achievement Award, former Vice President Al Gore's speech was "Please don't recount this vote." He was introduced by Vint Cerf who used the same format to state, "We all invented the Internet." In 2013, the creator of the Graphics Interchange Format (GIF), Steve Wilhite, accepted his Webby and delivered his now famous five-word speech, "It's pronounced 'Jif' not 'Gif'." == Criticism == The Webbys have been criticized for their pay-to-enter and pay-to-attend policy (winners and nominees also have to pay to attend the award ceremony), and thus for not taking most websites into consideration before distributing their awards. Gawker, its Valleywag column, and others, have called the awards a scam, with Valleywag saying, "...somewhere along the way, the organizers figured out that this goofy charade could be milked for profit." In response, Webby Awards executive director David-Michel Davies told the Wall Street Journal that entry fees "provide the best and most sustainable model for ensuring that our judging process remains consistent and rigorous and is not dependent on things like sponsorships that can fluctuate from year to year." == Anthem Awards == In 2021, the Webby organization started a new line of awards, the Anthem Awards, to honor the purpose and mission-driven work of people, companies and organizations worldwide. The finalists and winners are selected by the International Academy of Digital Arts and Sciences.

Digital heritage

The Charter on the Preservation of Digital Heritage of UNESCO defines digital heritage as embracing "cultural, educational, scientific and administrative resources, as well as technical, legal, medical and other kinds of information created digitally, or converted into digital form from existing analogue resources". Digital heritage also includes the use of digital media in the service of understanding and preserving cultural or natural heritage. The digitization of both cultural heritage and Natural heritage serves to enable the permanent access of current and future generations to culturally important objects ranging from literature and paintings to flora, fauna, or habitats. It is also used in the preservation and access of objects with enduring or significant historical, scientific, or cultural value including buildings, archeological sites, and natural phenomena. The main idea is the transformation of a material object into a virtual copy. It should not be confused with digital humanities, which uses digitizing technology to specifically help with research. There have been several debates concerning the efficiency of the process of digitizing heritage. Some of the drawbacks refer to the deterioration and technological obsolescence due to the lack of funding for archival materials and underdeveloped policies that would regulate such a process. Another main social debate has taken place around the restricted accessibility due to the digital divide that exists around the world. Nevertheless, new technologies enable easy, instant and cross boarder access to the digitized work. Many of these technologies include spatial and surveying technology to gain aerial or 3D images. Digital heritage is also used to monitor cultural heritage sites over years to help with preservation, maintenance, and sustainable tourism. It aims to observe any changes, diseases, or deterioration that may occur on objects. == Cultural and natural heritage == Digital Heritage that is not born-digital can be divided into two separate groups—digital cultural heritage and digital natural heritage. Digital cultural heritage is the maintenance or preservation of cultural objects through digitization. These are objects, in some cases entire cities, that are considered of cultural importance. These objects are sometimes able to be digitized or physically represented in minute detail. Digital cultural heritage also includes intangible heritage. These are things such as "oral traditions, customs, value systems, skills, traditional dances, diets, performances" and other unique features of a culture. Intangible heritage is particularly vulnerable to destruction due to urbanization. There are several projects and programs which concentrate on digital cultural heritage. One such project is Mapping Gothic France, which aims to document and preserve cathedrals across France using images, VR tours, laser scans, and panoramas. This allows for scientific and historical study and preservation of the cathedrals and also provides detailed access to the sites for anyone in the world. The aim of projects like these is to help with the preservation and restoration of cultural objects. After the fire at Notre-Dame de Paris in 2019, digital scans are a major component in the ongoing restoration. Digital natural heritage pertains to objects of natural heritage that are considered of cultural, scientific, or aesthetic importance. Digital heritage in this instance is used not only to grant access to these objects, but to monitor any changes over time, such as with plant or animal habitats. Geographic information systems are a form of technology that is used primarily in the study of natural heritage. Western Australia has one such digital heritage project where they have created a digital repository of native plants important to both the region and the Aboriginal people. This is in order to protect and preserve the important biological heritage of Western Australia. == Educational impact == The digitization of these heritage objects has impacts around the world and across many disciplines. The increase of digital items means that people, especially the youth, are able to learn about new objects and cultures online through various media. They provide viewers with a more in-depth experience with an item or place, instead of just an image. The media is also able to be curated to age- or educational-level appropriateness, making learning easier. Some of the technology used in education, especially in museums, includes mobile apps, virtual reality, social media, and video games. Cultural heritage institutions are using this technology to try to expand access, increase appreciation for these items, and to gain new viewpoints on their collections. Digital heritage also helps scientists, archeologists, or other historians and specialists collect data on these objects, providing more information on the objects and the past. Digital Heritage is still currently being studied and improved by several sectors invested in cultural and intellectual preservation. It is particularly of interest to museums, governments, and academic institutions. Research by these groups are creating new concepts, methodologies, and techniques for the implementation of digital heritage to protect this type of cultural and natural heritage. As new technologies are created, museums and other heritage institutions are provided with more ways of disseminating their information and engaging with the public. A lack of resources within certain groups may still hinder everyone from accessing digital heritage. == Technologies used == The digitization of cultural heritage is attained through several means. Some of the main technology used is spatial and surveying technology. Space archaeological technology - Observations from space satellites are non-intrusive and can be integrated with other technologies on the ground. It is used to photograph vast areas of earth and help with research. Remnants of ancient civilizations or other human objects are also able to be spotted via satellite imaging. Unmanned aerial vehicles - UAV, such as drones, are commonly used in digitization of cultural heritage objects. The Great Wall of China is one such site that has been digitized and analyzed through unmanned aerial vehicle investigation. The resulting images, 3-D scans, maps, and other data are used to evaluate and maintain the Great Wall. Laser Scanning - Laser scanning is used to scan an area and recreate spatially accurate depictions, such as a 3D model. Virtual and Augmented Reality - VR is used primarily for education but does have uses for reconstruction and research. It is used to provide users with an immersive experience, as though they are actually at the site. Geographic Information systems - GIS are used primarily to study objects and sites over time. It is also important in studying the socioeconomic status of the past. 3D Modeling - 3D modeling has become more widely used due to an increase in technology that works specifically with heritage sites. It is often used in tandem with GIS to reconstruct objects for restoration, documentation, preservation, and educational purposes. Data is collected using satellite or other aerial imaging and ground-based imaging. There is some concern about the accuracy and authenticity of these types of digital reconstructions and their effects on the sites themselves. A major barrier to digital heritage is the amount of resources it takes to undertake such projects, such as money, time, and technology. Money and the lack of qualified personnel are two that are considered the most obstructive. This is especially an issue in less developed areas or within underfunded groups such as minorities. == Virtual heritage == A particular branch of digital heritage, known as "virtual heritage", is formed by the use of information technology with the aim of recreating the experience of existing cultural heritage, as in (approximations of) virtual reality. It is hard to differentiate this branch from the core contribution of digital heritage which is storing the heritage data digitally. Parsinejad et al. developed two techniques for Digital Twinning of the architectural assets and representation of the physical assets virtually in the museum context. Two techniques are hand recording and digital recording and both have challenges in adoption and implementation of Digital Twin as a revolutionary concept. == Digital heritage stewardship == Digital heritage stewardship is a form of digital curation which is modeled after collaborative curation. Digital heritage stewardship means stepping away from typical curatorial practices (e.g. discovering, arranging, and sharing information, material, and/or content) in favor of practices which allow its stakeholders the opportunity to contribute historical, political, and social context and culture. The collaborative practice encourages the creation, engagement, and maintena

Digital exhibition

Digital Exhibition includes both the projection technologies, such as High Definition, and delivery technologies of a film to a movie theater. Delivery technologies include disk drives, satellite relay, and fiber optics. This can save money in distribution but is usually more expensive overall due to maintenance and standardization of technology. However, there are benefits to digital exhibition, for example it requires less assembly by the exhibitor and can contain the trailers that the distributor wishes.

Cross-validation (statistics)

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

Acquisition of DirecTV by AT&T

AT&T Inc. announced an agreement with the DirecTV Group on May 18, 2014, to acquire the company for $48.5 billion in a joint cash-stock transaction and assumed debts of $18.6 billion for a total offer of $67.1 billion. Due to stalling growth in the wireless sector, AT&T began diversifying into mass media to expand its consumer offerings. After regulatory agencies approved the purchase on July 24, 2015, AT&T briefly became the largest Pay-TV provider. DirecTV was brought under AT&T's communication segment and DirecTV Now was launched on November 30, 2016, as an alternative to cord-cutting. In the years following the purchase, DirecTV lost millions of subscribers across its satellite and streaming services and by 2019, calls grew for AT&T to divest itself off the business. Initially, AT&T rejected these calls and defended the acquisition, but by February 2021, it reached a deal with TPG Inc. to transfer ownership of DirecTV. Under the terms of the agreement, AT&T would retain a 70% majority stake in DirecTV but would no longer oversee its daily operations. The deal was finalized by August 2, 2021, with AT&T receiving $7.1 billion. By July 3, 2025, AT&T sold its majority stake to TPG, ending any ties of involvement. == Background and Development == === AT&T's history === The company to bear the name "AT&T" was founded on March 3, 1885, as American Telephone and Telegraph Company (or AT&T Corporation) by Theodore Newton Vail as a long-distance subsidiary of the Bell Telephone Company. By December 1899, the Bell Telephone's assets were transferred to AT&T, with the latter gaining control of the Bell System, a regional network of local telecom companies. Theodore Vail became AT&T's President in 1907 and under his leadership, AT&T gained a monopoly over the telephone sector in the United States. This near century dominance earned AT&T the nickname of "Ma Bell." In 1974, the U.S. Department of Justice sued AT&T on accounts of antitrust violations. AT&T challenged the lawsuit, but in 1982, it reached a settlement with the DOJ to break apart its Bell System monopoly into seven regional companies. On January 1, 1984, the Bell System came to an end and led to a reshaped telecom industry. One of these regional companies, Southwestern Bell, emerged as the smallest, but after the passage of the 1996 Telecom Act, deregulated telecom rules allowed SBC to become a major telecom company. AT&T briefly became the largest cable and broadband company by the end of the 20th Century, but later deconsolidated to exit those industries. In 2005, SBC acquired its former parent, AT&T, and took on its branding as AT&T Inc, while retaining its previous business history. The newly reincorporated AT&T acquired BellSouth in 2006 and reconstituted much of its former Bell System. === DirecTV's history === == Acquisition Timeline == == Managing DirecTV == == Divestment and Spinoff ==