Event cinema sometimes called alternative content cinema or livecasts refers to the use of movie theaters to display a varied range of live and recorded entertainment excluding traditional films, such as sport, opera, musicals, ballet, music, one-off TV specials, current affairs, comedy and religious services. == History and development == Event Cinema was set up at the start of the century with rock concerts by Bon Jovi (2001), David Bowie (2003), and Robbie Williams (2005) bringing non-film audiences into cinemas that had newly installed digital equipment. The Metropolitan Opera in New York through their partnership with Fathom Events is acknowledged as the trailblazer in this area, aggressively seeking out new markets and setting high standards for live broadcasts via satellite. Emulated by other opera houses worldwide such as the Royal Opera House following a close second, Glyndebourne, La Scala and the Sydney Opera House the genre of opera within the 'Event Cinema' industry has been a huge success, and has brought new, younger audiences into cash-strapped opera houses depended on state funding and wealthy benefactors for the first time - an unforeseen and happy consequence of digitisation. Ballet and theater have also been very successful, as have rock concerts, both live and recorded. The UK's National Theatre has been a huge success here with their season of live broadcasts under the banner 'NT Live', featuring big name casts such as Helen Mirren, whose recent turn as Queen Elizabeth II in The Audience was a sell out everywhere. (This was in partnership with another West End theatre and the NT are keen to help other theatres maximise their potential through live broadcasts). The Globe and the Royal Shakespeare Company are also producing work for live broadcast and recorded exhibition. As digitisation of cinemas matures, the Event Cinema industry is growing. The strongest territory is the US, followed by the UK and mainland European territories. Latin America is also a very strong market. Recent additions include Pompeii Live, a unique exhibition by the UK's British Museum, featuring celebrities and curators taking the audience on a live tour around the recreated set of Pompeii within the museum itself, and they are also exploring the schools market for the first time, following the live broadcast on June 18 with a daytime broadcast aimed at UK schools for the first time. If successful this will no doubt prove a model for future museums to emulate. An added incentive for exhibitors is the ability to show alternative content, i.e. alternative to mainstream, studio-driven content, such as live special events, sports, pre-show advertising and other digital or video content. In industry terms this has become known as 'Alternative Content', but has recently become known more widely as 'Event Cinema'. === Expanding markets === Some low-budget films that would normally not have a theatrical release because of distribution costs might be shown in smaller engagements than the typical large release studio pictures. The cost of duplicating a digital "print" is very low, so adding more theaters to a release has a small additional cost to the distributor. Movies that start with a small release could scale to a much larger release quickly if they were sufficiently successful, opening up the possibility that smaller movies could achieve box office success previously out of their reach. ==== Technical specifications ==== Event Cinema is also finding a market in 3rd world countries in which the higher costs and quality of DCI equipment are not yet affordable, as crucially there are no DCI specifications for Alternative Content as there is in mainstream [studio] content. This has led to an explosion in the variety of content on offer, but a lack of standardisation has led to questionable quality at times. As the industry matures, this lack of regulation is expected to change and there are moves afoot to introduce codes of practice and technical specifications. Recorded content complements mainstream studio content by maximising the 'downtime' that plagues the cinema industry, where screens worldwide spend a large proportion of their time in darkness and cinemas empty. Some cinema chains have targeted pensioners in particular, offering free tea and coffee for afternoon matinees of recorded opera, for example. Digital Cinema Packages (DCPs) have been useful to cinemas not yet equipped with satellite broadcasting capability and has enabled exhibitors to build their Event Cinema audience, which is not generally the 18-24 demographic that multiplexes are targeting. ==== New Audiences ==== Event Cinema has seen a return of an older, affluent audience, previously turned off by the multiplex experience, and cinemas are starting to capitalise on this by offering waiter-serviced, high class finger food and alcoholic beverages, complete with bars and restaurants, a world away from the traditional popcorn/soft drink model; art house cinemas are increasingly marketing themselves as 'destination' venues for an evening's entertainment, somewhere to spend an entire evening, rather than just a couple of hours. As exhibition admissions have plateau'd in recent years due to the explosion in VOD, tablet and mobile content technology, this new revenue stream has been a surprise and welcome addition to the cinema industry, though the US studios have been cautious in embracing the change as yet. The thrill of Live broadcasts means they are generally regarded as more popular than recorded events, but there are exceptions; artists with a loyal cult or teenage following tend to do particularly well in this area, as concert films featuring artists such as the Grateful Dead, Pearl Jam, JLS, Led Zeppelin and the Rolling Stones have shown. ==== The Future ==== As more and more distributors are emerging, offering an increasingly broad range of content to cinemas worldwide, the landscape itself is shifting: screen advertising companies, technical providers, and exhibitors themselves are reinventing themselves as Alternative Content or Event Cinema distributors, and the industry is witnessing a re-evaluation of business models and practices worldwide. Predictions are that this industry could be work in excess of US$1bn by 2015. An illustration of the growth of this industry is the news the establishment of a European trade association promoting the industry to the general public and supporting those involved in it and the Event Cinema Association.
Exposure Notification
The (Google/Apple) Exposure Notification System (GAEN) is a framework and protocol specification developed by Apple Inc. and Google to facilitate digital contact tracing during the COVID-19 pandemic. When used by health authorities, it augments more traditional contact tracing techniques by automatically logging close approaches among notification system users using Android or iOS smartphones. Exposure Notification is a decentralized reporting protocol built on a combination of Bluetooth Low Energy technology and privacy-preserving cryptography. It is an opt-in feature within COVID-19 apps developed and published by authorized health authorities. Unveiled on April 10, 2020, it was made available on iOS on May 20, 2020, as part of the iOS 13.5 update and on December 14, 2020, as part of the iOS 12.5 update for older iPhones. On Android, it was added to devices via a Google Play Services update, supporting all versions since Android Marshmallow. The Apple/Google protocol is similar to the Decentralized Privacy-Preserving Proximity Tracing (DP-3T) protocol created by the European DP-3T consortium and the Temporary Contact Number (TCN) protocol by Covid Watch, but is implemented at the operating system level, which allows for more efficient operation as a background process. Since May 2020, a variant of the DP-3T protocol is supported by the Exposure Notification Interface. Other protocols are constrained in operation because they are not privileged over normal apps. This leads to issues, particularly on iOS devices where digital contact tracing apps running in the background experience significantly degraded performance. The joint approach is also designed to maintain interoperability between Android and iOS devices, which constitute nearly all of the market. The ACLU stated the approach "appears to mitigate the worst privacy and centralization risks, but there is still room for improvement". In late April, Google and Apple shifted the emphasis of the naming of the system, describing it as an "exposure notification service", rather than "contact tracing" system. == Technical specification == Digital contact tracing protocols typically have two major responsibilities: encounter logging and infection reporting. Exposure Notification only involves encounter logging which is a decentralized architecture. The majority of infection reporting is centralized in individual app implementations. To handle encounter logging, the system uses Bluetooth Low Energy to send tracking messages to nearby devices running the protocol to discover encounters with other people. The tracking messages contain unique identifiers that are encrypted with a secret daily key held by the sending device. These identifiers change every 15–20 minutes as well as Bluetooth MAC address in order to prevent tracking of clients by malicious third parties through observing static identifiers over time. The sender's daily encryption keys are generated using a random number generator. Devices record received messages, retaining them locally for 14 days. If a user tests positive for infection, the last 14 days of their daily encryption keys can be uploaded to a central server, where it is then broadcast to all devices on the network. The method through which daily encryption keys are transmitted to the central server and broadcast is defined by individual app developers. The Google-developed reference implementation calls for a health official to request a one-time verification code (VC) from a verification server, which the user enters into the encounter logging app. This causes the app to obtain a cryptographically signed certificate, which is used to authorize the submission of keys to the central reporting server. The received keys are then provided to the protocol, where each client individually searches for matches in their local encounter history. If a match meeting certain risk parameters is found, the app notifies the user of potential exposure to the infection. Google and Apple intend to use the received signal strength (RSSI) of the beacon messages as a source to infer proximity. RSSI and other signal metadata will also be encrypted to resist deanonymization attacks. === Version 1.0 === To generate encounter identifiers, first a persistent 32-byte private Tracing Key ( t k {\displaystyle tk} ) is generated by a client. From this a 16 byte Daily Tracing Key is derived using the algorithm d t k i = H K D F ( t k , N U L L , 'CT-DTK' | | D i , 16 ) {\displaystyle dtk_{i}=HKDF(tk,NULL,{\text{'CT-DTK'}}||D_{i},16)} , where H K D F ( Key, Salt, Data, OutputLength ) {\displaystyle HKDF({\text{Key, Salt, Data, OutputLength}})} is a HKDF function using SHA-256, and D i {\displaystyle D_{i}} is the day number for the 24-hour window the broadcast is in starting from Unix Epoch Time. These generated keys are later sent to the central reporting server should a user become infected. From the daily tracing key a 16-byte temporary Rolling Proximity Identifier is generated every 10 minutes with the algorithm R P I i , j = Truncate ( H M A C ( d t k i , 'CT-RPI' | | T I N j ) , 16 ) {\displaystyle RPI_{i,j}={\text{Truncate}}(HMAC(dtk_{i},{\text{'CT-RPI'}}||TIN_{j}),16)} , where H M A C ( Key, Data ) {\displaystyle HMAC({\text{Key, Data}})} is a HMAC function using SHA-256, and T I N j {\displaystyle TIN_{j}} is the time interval number, representing a unique index for every 10 minute period in a 24-hour day. The Truncate function returns the first 16 bytes of the HMAC value. When two clients come within proximity of each other they exchange and locally store the current R P I i , j {\displaystyle RPI_{i,j}} as the encounter identifier. Once a registered health authority has confirmed the infection of a user, the user's Daily Tracing Key for the past 14 days is uploaded to the central reporting server. Clients then download this report and individually recalculate every Rolling Proximity Identifier used in the report period, matching it against the user's local encounter log. If a matching entry is found, then contact has been established and the app presents a notification to the user warning them of potential infection. === Version 1.1 === Unlike version 1.0 of the protocol, version 1.1 does not use a persistent tracing key, rather every day a new random 16-byte Temporary Exposure Key ( t e k i {\displaystyle tek_{i}} ) is generated. This is analogous to the daily tracing key from version 1.0. Here i {\displaystyle i} denotes the time is discretized in 10 minute intervals starting from Unix Epoch Time. From this two 128-bit keys are calculated, the Rolling Proximity Identifier Key ( R P I K i {\displaystyle RPIK_{i}} ) and the Associated Encrypted Metadata Key ( A E M K i {\displaystyle AEMK_{i}} ). R P I K i {\displaystyle RPIK_{i}} is calculated with the algorithm R P I K i = H K D F ( t e k i , N U L L , 'EN-RPIK' , 16 ) {\displaystyle RPIK_{i}=HKDF(tek_{i},NULL,{\text{'EN-RPIK'}},16)} , and A E M K i {\displaystyle AEMK_{i}} using the algorithm A E M K i = H K D F ( t e k i , N U L L , 'EN-AEMK' , 16 ) {\displaystyle AEMK_{i}=HKDF(tek_{i},NULL,{\text{'EN-AEMK'}},16)} . From these values a temporary Rolling Proximity Identifier ( R P I i , j {\displaystyle RPI_{i,j}} ) is generated every time the BLE MAC address changes, roughly every 15–20 minutes. The following algorithm is used: R P I i , j = A E S 128 ( R P I K i , 'EN-RPI' | | 0 x 000000000000 | | E N I N j ) {\displaystyle RPI_{i,j}=AES128(RPIK_{i},{\text{'EN-RPI'}}||{\mathtt {0x000000000000}}||ENIN_{j})} , where A E S 128 ( Key, Data ) {\displaystyle AES128({\text{Key, Data}})} is an AES cryptography function with a 128-bit key, the data is one 16-byte block, j {\displaystyle j} denotes the Unix Epoch Time at the moment the roll occurs, and E N I N j {\displaystyle ENIN_{j}} is the corresponding 10-minute interval number. Next, additional Associated Encrypted Metadata is encrypted. What the metadata represents is not specified, likely to allow the later expansion of the protocol. The following algorithm is used: Associated Encrypted Metadata i , j = A E S 128 _ C T R ( A E M K i , R P I i , j , Metadata ) {\displaystyle {\text{Associated Encrypted Metadata}}_{i,j}=AES128\_CTR(AEMK_{i},RPI_{i,j},{\text{Metadata}})} , where A E S 128 _ C T R ( Key, IV, Data ) {\displaystyle AES128\_CTR({\text{Key, IV, Data}})} denotes AES encryption with a 128-bit key in CTR mode. The Rolling Proximity Identifier and the Associated Encrypted Metadata are then combined and broadcast using BLE. Clients exchange and log these payloads. Once a registered health authority has confirmed the infection of a user, the user's Temporary Exposure Keys t e k i {\displaystyle tek_{i}} and their respective interval numbers i {\displaystyle i} for the past 14 days are uploaded to the central reporting server. Clients then download this report and individually recalculate every Rolling Proximity Identifier starting from interval number i {\displaystyle i} ,
VIGRA
VIGRA is the abbreviation for "Vision with Generic Algorithms". It is a free open-source computer vision library which focuses on customizable algorithms and data structures. VIGRA component can be easily adapted to specific needs of target application without compromising execution speed, by using template techniques similar to those in the C++ Standard Template Library. == Features == VIGRA is cross-platform, with working builds on Microsoft Windows, Mac OS X, Linux, and OpenBSD. Since version 1.7.1, VIGRA provides Python bindings based on numpy framework. == History == VIGRA was originally designed and implemented by scientists at University of Hamburg faculty of computer science; its core maintainers are now working at Heidelberg Collaboratory for Image Processing (HCI) University of Heidelberg. In the meantime, many developers have contributed to the project. == Application == CellCognition and ilastik uses VIGRA computer vision library. OpenOffice.org uses VIGRA as part of its headless software rendering backend; LibreOffice does so until version 5.2.
Dimensionality reduction
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable. Dimensionality reduction is common in fields that deal with large numbers of observations and/or large numbers of variables, such as signal processing, speech recognition, neuroinformatics, and bioinformatics. Methods are commonly divided into linear and nonlinear approaches. Linear approaches can be further divided into feature selection and feature extraction. Dimensionality reduction can be used for noise reduction, data visualization, cluster analysis, or as an intermediate step to facilitate other analyses. == Feature selection == The process of feature selection aims to find a suitable subset of the input variables (features, or attributes) for the task at hand. The three strategies are: the filter strategy (e.g., information gain), the wrapper strategy (e.g., accuracy-guided search), and the embedded strategy (features are added or removed while building the model based on prediction errors). Data analysis such as regression or classification can be done in the reduced space more accurately than in the original space. == Feature projection == Feature projection (also called feature extraction) transforms the data from the high-dimensional space to a space of fewer dimensions. The data transformation may be linear, as in principal component analysis (PCA), but many nonlinear dimensionality reduction techniques also exist. For multidimensional data, tensor representation can be used in dimensionality reduction through multilinear subspace learning. === Principal component analysis (PCA) === The main linear technique for dimensionality reduction, principal component analysis, performs a linear mapping of the data to a lower-dimensional space in such a way that the variance of the data in the low-dimensional representation is maximized. In practice, the covariance (and sometimes the correlation) matrix of the data is constructed and the eigenvectors on this matrix are computed. The eigenvectors that correspond to the largest eigenvalues (the principal components) can now be used to reconstruct a large fraction of the variance of the original data. Moreover, the first few eigenvectors can often be interpreted in terms of the large-scale physical behavior of the system, because they often contribute the vast majority of the system's energy, especially in low-dimensional systems. Still, this must be proved on a case-by-case basis as not all systems exhibit this behavior. The original space (with dimension of the number of points) has been reduced (with data loss, but hopefully retaining the most important variance) to the space spanned by a few eigenvectors. === Non-negative matrix factorization (NMF) === NMF decomposes a non-negative matrix to the product of two non-negative ones, which has been a promising tool in fields where only non-negative signals exist, such as astronomy. NMF is well known since the multiplicative update rule by Lee & Seung, which has been continuously developed: the inclusion of uncertainties, the consideration of missing data and parallel computation, sequential construction which leads to the stability and linearity of NMF, as well as other updates including handling missing data in digital image processing. With a stable component basis during construction, and a linear modeling process, sequential NMF is able to preserve the flux in direct imaging of circumstellar structures in astronomy, as one of the methods of detecting exoplanets, especially for the direct imaging of circumstellar discs. In comparison with PCA, NMF does not remove the mean of the matrices, which leads to physical non-negative fluxes; therefore NMF is able to preserve more information than PCA as demonstrated by Ren et al. === Kernel PCA === Principal component analysis can be employed in a nonlinear way by means of the kernel trick. The resulting technique is capable of constructing nonlinear mappings that maximize the variance in the data. The resulting technique is called kernel PCA. === Graph-based kernel PCA === Other prominent nonlinear techniques include manifold learning techniques such as Isomap, locally linear embedding (LLE), Hessian LLE, Laplacian eigenmaps, and methods based on tangent space analysis. These techniques assume that the high-dimensional input data lies near a low-dimensional manifold embedded in the ambient space, and construct a low-dimensional representation using a cost function that retains local properties of the data; they can be viewed as defining a graph-based kernel for Kernel PCA. More recently, techniques have been proposed that, instead of defining a fixed kernel, try to learn the kernel using semidefinite programming. The most prominent example of such a technique is maximum variance unfolding (MVU). The central idea of MVU is to exactly preserve all pairwise distances between nearest neighbors (in the inner product space) while maximizing the distances between points that are not nearest neighbors. An alternative approach to neighborhood preservation is through the minimization of a cost function that measures differences between distances in the input and output spaces. Important examples of such techniques include: classical multidimensional scaling, which is identical to PCA; Isomap, which uses geodesic distances in the data space; diffusion maps, which use diffusion distances in the data space; t-distributed stochastic neighbor embedding (t-SNE), which minimizes the divergence between distributions over pairs of points; and curvilinear component analysis. A different approach to nonlinear dimensionality reduction is through the use of autoencoders, a special kind of feedforward neural networks with a bottleneck hidden layer. The training of deep encoders is typically performed using a greedy layer-wise pre-training (e.g., using a stack of restricted Boltzmann machines) that is followed by a finetuning stage based on backpropagation. === Linear discriminant analysis (LDA) === Linear discriminant analysis (LDA) is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition, and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. === Generalized discriminant analysis (GDA) === GDA deals with nonlinear discriminant analysis using kernel function operator. The underlying theory is close to the support-vector machines (SVM) insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space. Similar to LDA, the objective of GDA is to find a projection for the features into a lower dimensional space by maximizing the ratio of between-class scatter to within-class scatter. === Autoencoder === Autoencoders can be used to learn nonlinear dimension reduction functions and codings together with an inverse function from the coding to the original representation. === t-SNE === T-distributed Stochastic Neighbor Embedding (t-SNE) is a nonlinear dimensionality reduction technique useful for the visualization of high-dimensional datasets. It is not recommended for use in analysis such as clustering or outlier detection since it does not necessarily preserve densities or distances well. === UMAP === Uniform manifold approximation and projection (UMAP) is a nonlinear dimensionality reduction technique. Visually, it is similar to t-SNE, but it assumes that the data is uniformly distributed on a locally connected Riemannian manifold and that the Riemannian metric is locally constant or approximately locally constant. == Dimension reduction == For high-dimensional datasets, dimension reduction is usually performed prior to applying a k-nearest neighbors (k-NN) algorithm in order to mitigate the curse of dimensionality. Feature extraction and dimension reduction can be combined in one step, using principal component analysis (PCA), linear discriminant analysis (LDA), canonical correlation analysis (CCA), or non-negative matrix factorization (NMF) techniques to pre-process the data, followed by clustering via k-NN on feature vectors in a reduced-dimension space. In machine learning, this process is also called low-dimensional embedding. For high-dimensional datasets (e.g., when performing similarity search on live video streams, DNA data, or high-dimensional time series), running a fast approximate k-NN search using locality-sensitive hashing, random projection, "sketches", or other high-dimensional similarity search techniques from the VLDB conference toolbox may be the only fe
Multinomial logistic regression
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.). Multinomial logistic regression is known by a variety of other names, including polytomous LR, multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model. == Background == Multinomial logistic regression is used when the dependent variable in question is nominal (equivalently categorical, meaning that it falls into any one of a set of categories that cannot be ordered in any meaningful way) and for which there are more than two categories. Some examples would be: Which major will a college student choose, given their grades, stated likes and dislikes, etc.? Which blood type does a person have, given the results of various diagnostic tests? In a hands-free mobile phone dialing application, which person's name was spoken, given various properties of the speech signal? Which candidate will a person vote for, given particular demographic characteristics? Which country will a firm locate an office in, given the characteristics of the firm and of the various candidate countries? These are all statistical classification problems. They all have in common a dependent variable to be predicted that comes from one of a limited set of items that cannot be meaningfully ordered, as well as a set of independent variables (also known as features, explanators, etc.), which are used to predict the dependent variable. Multinomial logistic regression is a particular solution to classification problems that use a linear combination of the observed features and some problem-specific parameters to estimate the probability of each particular value of the dependent variable. The best values of the parameters for a given problem are usually determined from some training data (e.g. some people for whom both the diagnostic test results and blood types are known, or some examples of known words being spoken). == Assumptions == The multinomial logistic model assumes that data are case-specific; that is, each independent variable has a single value for each case. As with other types of regression, there is no need for the independent variables to be statistically independent from each other (unlike, for example, in a naive Bayes classifier); however, collinearity is assumed to be relatively low, as it becomes difficult to differentiate between the impact of several variables if this is not the case. If the multinomial logit is used to model choices, it relies on the assumption of independence of irrelevant alternatives (IIA), which is not always desirable. This assumption states that the odds of preferring one class over another do not depend on the presence or absence of other "irrelevant" alternatives. For example, the relative probabilities of taking a car or bus to work do not change if a bicycle is added as an additional possibility. This allows the choice of K alternatives to be modeled as a set of K − 1 independent binary choices, in which one alternative is chosen as a "pivot" and the other K − 1 compared against it, one at a time. The IIA hypothesis is a core hypothesis in rational choice theory; however numerous studies in psychology show that individuals often violate this assumption when making choices. An example of a problem case arises if choices include a car and a blue bus. Suppose the odds ratio between the two is 1 : 1. Now if the option of a red bus is introduced, a person may be indifferent between a red and a blue bus, and hence may exhibit a car : blue bus : red bus odds ratio of 1 : 0.5 : 0.5, thus maintaining a 1 : 1 ratio of car : any bus while adopting a changed car : blue bus ratio of 1 : 0.5. Here the red bus option was not in fact irrelevant, because a red bus was a perfect substitute for a blue bus. If the multinomial logit is used to model choices, it may in some situations impose too much constraint on the relative preferences between the different alternatives. It is especially important to take into account if the analysis aims to predict how choices would change if one alternative were to disappear (for instance if one political candidate withdraws from a three candidate race). Other models like the nested logit or the multinomial probit may be used in such cases as they allow for violation of the IIA. == Model == === Introduction === There are multiple equivalent ways to describe the mathematical model underlying multinomial logistic regression. This can make it difficult to compare different treatments of the subject in different texts. The article on logistic regression presents a number of equivalent formulations of simple logistic regression, and many of these have analogues in the multinomial logit model. The idea behind all of them, as in many other statistical classification techniques, is to construct a linear predictor function that constructs a score from a set of weights that are linearly combined with the explanatory variables (features) of a given observation using a dot product: score ( X i , k ) = β k ⋅ X i , {\displaystyle \operatorname {score} (\mathbf {X} _{i},k)={\boldsymbol {\beta }}_{k}\cdot \mathbf {X} _{i},} where Xi is the vector of explanatory variables describing observation i, βk is a vector of weights (or regression coefficients) corresponding to outcome k, and score(Xi, k) is the score associated with assigning observation i to category k. In discrete choice theory, where observations represent people and outcomes represent choices, the score is considered the utility associated with person i choosing outcome k. The predicted outcome is the one with the highest score. The difference between the multinomial logit model and numerous other methods, models, algorithms, etc. with the same basic setup (the perceptron algorithm, support vector machines, linear discriminant analysis, etc.) is the procedure for determining (training) the optimal weights/coefficients and the way that the score is interpreted. In particular, in the multinomial logit model, the score can directly be converted to a probability value, indicating the probability of observation i choosing outcome k given the measured characteristics of the observation. This provides a principled way of incorporating the prediction of a particular multinomial logit model into a larger procedure that may involve multiple such predictions, each with a possibility of error. Without such means of combining predictions, errors tend to multiply. For example, imagine a large predictive model that is broken down into a series of submodels where the prediction of a given submodel is used as the input of another submodel, and that prediction is in turn used as the input into a third submodel, etc. If each submodel has 90% accuracy in its predictions, and there are five submodels in series, then the overall model has only 0.95 = 59% accuracy. If each submodel has 80% accuracy, then overall accuracy drops to 0.85 = 33% accuracy. This issue is known as error propagation and is a serious problem in real-world predictive models, which are usually composed of numerous parts. Predicting probabilities of each possible outcome, rather than simply making a single optimal prediction, is one means of alleviating this issue. === Setup === The basic setup is the same as in logistic regression, the only difference being that the dependent variables are categorical rather than binary, i.e. there are K possible outcomes rather than just two. The following description is somewhat shortened; for more details, consult the logistic regression article. ==== Data points ==== Specifically, it is assumed that we have a series of N observed data points. Each data point i (ranging from 1 to N) consists of a set of M explanatory variables x1,i ... xM,i (also known as independent variables, predictor variables, features, etc.), and an associated categorical outcome Yi (also known as dependent variable, response variable), which can take on one of K possible values. These possible values represent logically separate categories (e.g. different political parties, blood types, etc.), and are often described mathematically by arbitrarily assigning each a number from 1 to K. The explanatory variables and outcome represent observed properties of the data points, and are often thought of as originating in the observations of N "experiments" — although an "experiment" may consist of nothing more than gathering data. The goal of multinomial logistic regression is to construct a model that explains the relationship between the explanatory variables and the outcome, so tha
2024–present global memory supply shortage
A global computer memory supply shortage started in 2024 due to supply constraints and rapid price escalation in the semiconductor memory market, particularly affecting DRAM and NAND flash memory. This shortage is sometimes labelled by tech media outlets as "RAMmageddon" or the "RAMpocalypse". Unlike the 2020–2023 global chip shortage, which stemmed primarily from pandemic-related supply chain disruptions from COVID-19, this shortage is driven by a structural reallocation of manufacturing capacity toward high-margin products for artificial intelligence infrastructure, creating scarcity of computer memory in consumer and enterprise PC markets. According to a 2026 Kearney's PERLab analysis, the shortage is expected to last at least until 2030, with CEOs agreeing with the timelines. == Background == Following a severe market downturn in 2022–2023, major memory manufacturers—Samsung Electronics, SK Hynix, and Micron Technology—implemented strategic production cuts to stabilize pricing. By mid-2024, the rapid expansion of generative AI services triggered unprecedented demand for specialized memory products, particularly High Bandwidth Memory (HBM) used in AI accelerators and data center GPUs. Specialized components of semiconductor technology are also experiencing supply constraints due to high demand in AI application. For example, glass cloth, a high-performance glass fiber substrate used for power efficient high speed data transfer and a crucial component of semiconductor manufacturing, is experiencing a supply crisis. Nitto Boseki, a Japanese firm having overwhelming monopoly in its production, is not able to meet increased demands, making chip-makers such as Qualcomm, Apple, Nvidia and AMD compete for securing supply. There are also reports of smaller electronics companies struggling to find suppliers for components such as NAND flash. Memory suppliers are adapting to increased demands and market unpredictability by requiring prepayment or shorter time-frame of payment, which makes it more difficult for smaller firms to acquire capital to survive. By 2026, due to steadily increased demand on resources, CPUs are also experiencing shortage issues due to low fabrication capacity, prioritisation of server CPUs, and increased demand, with CPU prices also being forecast to increase by as much as 15%. The demand on memory has also increased strain on other electronic components such as hard disk devices, with reports such as Western Digital's hard disk supply for 2026 being booked for enterprise applications before February 2026. A 2024 McKinsey analysis projected that global demand for AI-ready data center capacity would grow at approximately 33% annually through 2030, with AI workloads consuming roughly 70% of total data center capacity by the decade's end. In addition, according to Kearney's State of Semiconductor 2025 Report, executives were already expecting a shortage in the <8nm wafer size with memory chips being mentioned as an acute source of concern. Multiple companies mentioned being prepared for it through long-term agreements with RAM suppliers or amassing additional inventory. On 24 March 2026, Google announced TurboQuant, a memory compression technology focused on large language models (LLM) and vector search engines, which it claimed achieves 6x lower memory consumption in tested local LLMs and 8x performance enhancement in tests running on H100 accelerators. The technology is also a drop in enhancement for existing inference pipeline. Amid speculation about memory demand trends, memory manufacturers, SanDisk, Micron, Western Digital and Seagate, among other companies involved in memory manufacture experienced stock price declines. Prices of memory kits also reduced in the following months, although still at inflated prices. == Causes == === HBM production displacement === HBM manufacturing requires significantly more wafer capacity per bit than standard DRAM modules. Industry sources reported that as manufacturers allocated increasing wafer capacity to HBM production to meet contracts with AI infrastructure providers, the supply of conventional DDR4 and DDR5 modules for consumer PCs and smartphones contracted sharply. By September 2025, Samsung Electronics had reportedly expanded its 1c DRAM capacity to target 60,000 wafers per month specifically for HBM4 production, further diverting resources from consumer memory lines. === Geopolitical and trade barriers === The supply chain was further constrained by escalating trade tensions between the United States and China. Throughout 2025, fears of U.S. regulatory backlash and new tariff structures led major manufacturers like Samsung and SK Hynix to halt sales of older semiconductor manufacturing equipment to Chinese entities, effectively capping production capacity in the region. Additionally, proposed tariff policies by the U.S. administration in late 2025 prompted supply chain realignments, with Apple reportedly accelerating plans to source all U.S.-bound iPhones from India to avoid potential levies. === NAND flash capacity constraints === In the NAND flash segment, manufacturers prioritized higher-margin enterprise SSDs for data center applications while phasing out older process nodes more rapidly than anticipated. In November 2025, contract prices for NAND wafers increased by more than 60% month-over-month for certain product categories, with 512GB TLC experiencing the steepest rise as legacy manufacturing capacity was retired. == Impact on industry and consumers == === Manufacturer responses === Major PC manufacturers responded to component cost increases with significant price adjustments and supply chain strategies. Dell Technologies Chief Operating Officer Jeff Clarke stated during a November 2025 analyst call that the company had "never witnessed costs escalating at the current pace," describing tighter availability across DRAM, hard drives, and NAND flash memory. Analysts at Morgan Stanley downgraded Dell Technologies stock from "Overweight" to "Underweight" in late 2025, citing the company's heavy exposure to rising server memory costs. The firm warned that skyrocketing memory prices could significantly erode margins for server and PC OEMs. Conversely, Apple Inc. was reportedly less affected than its competitors, having secured long-term supply agreements for DRAM through the first quarter of 2026. Lenovo Chief Financial Officer Winston Cheng described the cost surge as "unprecedented" and disclosed that the company's memory inventories were approximately 50% above normal levels in anticipation of further price increases. === Consumer electronics sector === The shortage particularly affected smartphone manufacturers and other consumer electronics producers. DRAM prices reportedly rose by 172% throughout 2025, leading manufacturers like Samsung to halt new orders for DDR5 modules to reassess pricing structures and Micron to exit its 'Crucial' brand of consumer products. In Tokyo's Akihabara electronics district, retailers began limiting purchases of memory products to prevent hoarding, with prices for popular DDR5 memory modules more than doubling in some cases. Despite the broad trend of rising hardware costs, some companies engaged in aggressive pricing strategies to maintain market share; for example, Sony reduced the price of the PlayStation 5 by $100 for Black Friday 2025, potentially absorbing increased component costs to stimulate software ecosystem growth. Due to memory prices more than doubling in a single quarter, HP revealed in its Q1 2026 earnings call that memory costs account for 35% of PC build materials up from 15-18% previous quarter. Despite showing strong Q1 2026 earning driven by Windows 11 upgrade cycle and AI PC adoption, HP warned investors of low operating margins and up to double digit percentage decline for coming quarter. Trendforce, an IT analytics company, updated its forecast from 1.7% year-over-year growth in PC market to 2.6% year-over-year decline for 2026, amid backdrop of steadily increasing prices and supply crisis. Research and analytics firms, Gartner and IDC expect worldwide PC market to decline 10-11% and smartphone market to decline 8-9% in 2026. Gartner also projects that rising memory prices will make low-margin entry level laptops under 500 USD financially unviable in two years. The RAM shortage has delayed the release of Valve's second Steam Machine due to increased memory prices. The device was originally set to launch in early 2026. === AI infrastructure competition === Technology companies including Google, Amazon, Microsoft, and Meta Platforms placed open-ended orders with memory suppliers, indicating they would accept as much supply as available regardless of cost, according to Reuters sources. The limited supply of AI chips has been cited as a reason for the slow down in compute growth. In October 2025, OpenAI formally announced a strategic partnership using letters of intent with Samsung Electronics and SK Hynix
TabPFN
TabPFN (Tabular Prior-data Fitted Network) is a machine learning model for tabular datasets proposed in 2022. It uses a transformer architecture. It is intended for supervised classification and regression analysis on tabular datasets, particularly focusing on small- to medium-sized datasets. The latest version, TabPFN-3, was released in May 2026 and supports datasets with up to one million rows and 200 features. == History == TabPFN was first introduced in a 2022 pre-print and presented at ICLR 2023. TabPFN v2 was published in 2025 in Nature by Hollmann and co-authors. The source code is published on GitHub under a modified Apache License and on PyPi. Writing for ICLR blogs, McCarter states that the model has attracted attention due to its performance on small dataset benchmarks. TabPFN v2.5 was released on November 6, 2025. TabPFN-3 was released on May 12, 2026. Prior Labs, founded in 2024, aims to commercialize TabPFN. As of April 2026, the open-source TabPFN repository had more than 6,000 stars on GitHub. == Overview and pre-training == TabPFN supports classification, regression and generative tasks. It leverages "Prior-Data Fitted Networks" models to model tabular data. By using a transformer pre-trained on synthetic tabular datasets, TabPFN avoids benchmark contamination and costs of curating real-world data. TabPFN v2 was pre-trained on approximately 130 million such datasets. Synthetic datasets are generated using causal models or Bayesian neural networks; this can include simulating missing values, imbalanced data, and noise. Random inputs are passed through these models to generate outputs, with a bias towards simpler causal structures. During pre-training, TabPFN predicts the masked target values of new data points given training data points and their known targets, effectively learning a generic learning algorithm that is executed by running a neural network forward pass. The new dataset is then processed in a single forward pass without retraining. The model's transformer encoder processes features and labels by alternating attention across rows and columns. TabPFN v2 handles numerical and categorical features, missing values, and supports tasks like regression and synthetic data generation, while TabPFN-2.5 scales this approach to datasets with up to 50,000 rows and 2,000 features. TabPFN-3 introduced a redesigned architecture with row-compression, an attention-based many-class decoder, native missing-value handling, and inference optimizations such as row chunking and a reduced key-value cache, with benchmark-validated regimes of up to 1 million rows with 200 features, 100,000 rows with 2,000 features, or 1,000 rows with 20,000 features. Since TabPFN is pre-trained, in contrast to other deep learning methods, it does not require costly hyperparameter optimization. == Research == TabPFN is the subject of on-going research. Applications for TabPFN have been investigated for domains such as chemoproteomics, insurance risk classification, and metagenomics. In clinical research, TabPFN was used in a study on the early detection of pancreatic cancer from blood samples, where it was combined with metabolomic data and reported high diagnostic performance. == Applications == TabPFN has been used in industrial and biomedical contexts. Hitachi Ltd. has been reported to use the model for predictive maintenance in rail networks, with its use described as helping to identify track issues earlier and reduce manual inspections. In the biomedical domain, Oxford Cancer Analytics has used TabPFN in the analysis of proteomic data in lung disease research. A 2025 ML Contests report noted that the winners of DrivenData's PREPARE challenge used TabPFN to generate features for gradient-boosted decision tree models. == Limitations == TabPFN has been criticized for its "one large neural network is all you need" approach to modeling problems. Further, its performance is limited in high-dimensional and large-scale datasets. == Scaling Mode == In late November 2025, Prior Labs introduced ‘‘Scaling Mode’’, an operating mode for TabPFN designed to remove the fixed upper bound on training set size. Earlier versions of TabPFN had been optimized and validated primarily for datasets of up to 100,000 rows, whereas Scaling Mode was reported to extend support to substantially larger datasets, with benchmarked experiments on datasets containing up to 10 million rows. According to Prior Labs, Scaling Mode preserves the existing TabPFN architecture, including its alternating row-attention and column-attention design, as well as the same feature-count limits as prior releases. Inference remains based on a single forward pass rather than dataset-specific gradient-descent training, while scalability is described as being constrained primarily by available compute and memory resources. Prior Labs reported benchmark results on an internal collection of datasets ranging from 1 million to 10 million rows across industry and scientific applications. In these benchmarks, Scaling Mode was compared with CatBoost, XGBoost, LightGBM, and TabPFN 2.5 using 50,000-row subsampling. The company stated that predictive performance improved monotonically with increasing training set size and that no diminishing returns from scaling were observed within the tested range. Prior Labs also announced the release through company and executive social media channels. TabPFN-3 later incorporated related scaling improvements, including row chunking and a reduced key-value cache, into the model architecture and inference pipeline.