AI For Business Isb

AI For Business Isb — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Double descent

    Double descent

    Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases again. This phenomenon has been considered surprising, as it contradicts assumptions about overfitting in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number of training data points (the model is just large enough to fit the training data). Or, more precisely, it is the maximum number of samples on which the model/training procedure achieves approximately on average 0 training error. == History == Early observations of what would later be called double descent in specific models date back to 1989. The term "double descent" was coined by Belkin et. al. in 2019, when the phenomenon gained popularity as a broader concept exhibited by many models. The latter development was prompted by a perceived contradiction between the conventional wisdom that too many parameters in the model result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern machine learning techniques tend to perform better with larger models. == Theoretical models == Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. A number of works have suggested that double descent can be explained using the concept of effective dimension: While a network may have a large number of parameters, in practice only a subset of those parameters are relevant for generalization performance, as measured by the local Hessian curvature. This explanation is formalized through PAC-Bayes compression-based generalization bounds, which show that less complex models are expected to generalize better under a Solomonoff prior.

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  • LIBSVM

    LIBSVM

    LIBSVM and LIBLINEAR are two popular open source machine learning libraries, both developed at the National Taiwan University and both written in C++ though with a C API. LIBSVM implements the sequential minimal optimization (SMO) algorithm for kernelized support vector machines (SVMs), supporting classification and regression. LIBLINEAR implements linear SVMs and logistic regression models trained using a coordinate descent algorithm. The SVM learning code from both libraries is often reused in other open source machine learning toolkits, including GATE, KNIME, Orange and scikit-learn. Bindings and ports exist for programming languages such as Java, MATLAB, R, Julia, and Python. It is available in e1071 library in R and scikit-learn in Python. Both libraries are free software released under the 3-clause BSD license.

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  • TabPFN

    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.

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  • Local tangent space alignment

    Local tangent space alignment

    Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a manifold is correctly unfolded, all of the tangent hyperplanes to the manifold will become aligned. It begins by computing the k-nearest neighbors of every point. It computes the tangent space at every point by computing the d-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by data samples, and thus can not be used for classification directly.

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  • Hierarchical RBF

    Hierarchical RBF

    In computer graphics, hierarchical RBF is an interpolation method based on radial basis functions (RBFs). Hierarchical RBF interpolation has applications in treatment of results from a 3D scanner, terrain reconstruction, and the construction of shape models in 3D computer graphics (such as the Stanford bunny, a popular 3D model). This problem is informally named as "large scattered data point set interpolation." == Method == The steps of the interpolation method (in three dimensions) are as follows: Let the scattered points be presented as set P = { c i = ( x i , y i , z i ) | i = 1 N ⊂ R 3 } {\displaystyle \mathbf {P} =\{\mathbf {c} _{i}=(\mathbf {x} _{i},\mathbf {y} _{i},\mathbf {z} _{i})\vert _{i=1}^{N}\subset \mathbb {R} ^{3}\}} Let there exist a set of values of some function in scattered points H = { h i | i = 1 N ⊂ R } {\displaystyle \mathbf {H} =\{\mathbf {h} _{i}\vert _{i=1}^{N}\subset \mathbb {R} \}} Find a function f ( x ) {\displaystyle \mathbf {f} (\mathbf {x} )} that will meet the condition f ( x ) = 1 {\displaystyle \mathbf {f} (\mathbf {x} )=1} for points lying on the shape and f ( x ) ≠ 1 {\displaystyle \mathbf {f} (\mathbf {x} )\neq 1} for points not lying on the shape As J. C. Carr et al. showed, this function takes the form f ( x ) = ∑ i = 1 N λ i φ ( x , c i ) {\displaystyle \mathbf {f} (\mathbf {x} )=\sum _{i=1}^{N}\lambda _{i}\varphi (\mathbf {x} ,\mathbf {c} _{i})} where φ {\displaystyle \varphi } is a radial basis function and λ {\displaystyle \lambda } are the coefficients that are the solution of the following linear system of equations: [ φ ( c 1 , c 1 ) φ ( c 1 , c 2 ) . . . φ ( c 1 , c N ) φ ( c 2 , c 1 ) φ ( c 2 , c 2 ) . . . φ ( c 2 , c N ) . . . . . . . . . . . . φ ( c N , c 1 ) φ ( c N , c 2 ) . . . φ ( c N , c N ) ] ∗ [ λ 1 λ 2 . . . λ N ] = [ h 1 h 2 . . . h N ] {\displaystyle {\begin{bmatrix}\varphi (c_{1},c_{1})&\varphi (c_{1},c_{2})&...&\varphi (c_{1},c_{N})\\\varphi (c_{2},c_{1})&\varphi (c_{2},c_{2})&...&\varphi (c_{2},c_{N})\\...&...&...&...\\\varphi (c_{N},c_{1})&\varphi (c_{N},c_{2})&...&\varphi (c_{N},c_{N})\end{bmatrix}}{\begin{bmatrix}\lambda _{1}\\\lambda _{2}\\...\\\lambda _{N}\end{bmatrix}}={\begin{bmatrix}h_{1}\\h_{2}\\...\\h_{N}\end{bmatrix}}} For determination of surface, it is necessary to estimate the value of function f ( x ) {\displaystyle \mathbf {f} (\mathbf {x} )} in specific points x. A lack of such method is a considerable complication on the order of O ( n 2 ) {\displaystyle \mathbf {O} (\mathbf {n} ^{2})} to calculate RBF, solve system, and determine surface. == Other methods == Reduce interpolation centers ( O ( n 2 ) {\displaystyle \mathbf {O} (\mathbf {n} ^{2})} to calculate RBF and solve system, O ( m n ) {\displaystyle \mathbf {O} (\mathbf {m} \mathbf {n} )} to determine surface) Compactly support RBF ( O ( n log ⁡ n ) {\displaystyle \mathbf {O} (\mathbf {n} \log {\mathbf {n} })} to calculate RBF, O ( n 1.2..1.5 ) {\displaystyle \mathbf {O} (\mathbf {n} ^{1.2..1.5})} to solve system, O ( m log ⁡ n ) {\displaystyle \mathbf {O} (\mathbf {m} \log {\mathbf {n} })} to determine surface) FMM ( O ( n 2 ) {\displaystyle \mathbf {O} (\mathbf {n} ^{2})} to calculate RBF, O ( n log ⁡ n ) {\displaystyle \mathbf {O} (\mathbf {n} \log {\mathbf {n} })} to solve system, O ( m + n log ⁡ n ) {\displaystyle \mathbf {O} (\mathbf {m} +\mathbf {n} \log {\mathbf {n} })} to determine surface) == Hierarchical algorithm == A hierarchical algorithm allows for an acceleration of calculations due to decomposition of intricate problems on the great number of simple (see picture). In this case, hierarchical division of space contains points on elementary parts, and the system of small dimension solves for each. The calculation of surface in this case is taken to the hierarchical (on the basis of tree-structure) calculation of interpolant. A method for a 2D case is offered by Pouderoux J. et al. For a 3D case, a method is used in the tasks of 3D graphics by W. Qiang et al. and modified by Babkov V.

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  • Taguchi loss function

    Taguchi loss function

    The Taguchi loss function is graphical depiction of loss developed by the Japanese business statistician Genichi Taguchi to describe a phenomenon affecting the value of products produced by a company. Praised by Dr. W. Edwards Deming (the business guru of the 1980s American quality movement), it made clear the concept that quality does not suddenly plummet when, for instance, a machinist exceeds a rigid blueprint tolerance. Instead 'loss' in value progressively increases as variation increases from the intended condition. This was considered a breakthrough in describing quality, and helped fuel the continuous improvement movement. The concept of Taguchi's quality loss function was in contrast with the American concept of quality, popularly known as goal post philosophy, the concept given by American quality guru Phil Crosby. Goal post philosophy emphasizes that if a product feature doesn't meet the designed specifications it is termed as a product of poor quality (rejected), irrespective of amount of deviation from the target value (mean value of tolerance zone). This concept has similarity with the concept of scoring a 'goal' in the game of football or hockey, because a goal is counted 'one' irrespective of the location of strike of the ball in the 'goal post', whether it is in the center or towards the corner. This means that if the product dimension goes out of the tolerance limit the quality of the product drops suddenly. Through his concept of the quality loss function, Taguchi explained that from the customer's point of view this drop of quality is not sudden. The customer experiences a loss of quality the moment product specification deviates from the 'target value'. This 'loss' is depicted by a quality loss function and it follows a parabolic curve mathematically given by L = k(y–m)2, where m is the theoretical 'target value' or 'mean value' and y is the actual size of the product, k is a constant and L is the loss. This means that if the difference between 'actual size' and 'target value' i.e. (y–m) is large, loss would be more, irrespective of tolerance specifications. In Taguchi's view tolerance specifications are given by engineers and not by customers; what the customer experiences is 'loss'. This equation is true for a single product; if 'loss' is to be calculated for multiple products the loss function is given by L = k[S2 + ( y ¯ {\displaystyle {\bar {y}}} – m)2], where S2 is the 'variance of product size' and y ¯ {\displaystyle {\bar {y}}} is the average product size. == Overview == The Taguchi loss function is important for a number of reasons—primarily, to help engineers better understand the importance of designing for variation.

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  • Swish function

    Swish function

    The swish function is a family of mathematical function defined as follows: swish β ⁡ ( x ) = x sigmoid ⁡ ( β x ) = x 1 + e − β x . {\displaystyle \operatorname {swish} _{\beta }(x)=x\operatorname {sigmoid} (\beta x)={\frac {x}{1+e^{-\beta x}}}.} where β {\displaystyle \beta } can be constant (usually set to 1) or trainable and "sigmoid" refers to the logistic function. The swish family was designed to smoothly interpolate between a linear function and the Rectified linear unit (ReLU) function. When considering positive values, Swish is a particular case of doubly parameterized sigmoid shrinkage function defined in . Variants of the swish function include Mish. == Special values == For β = 0, the function is linear: f(x) = x/2. For β = 1, the function is the Sigmoid Linear Unit (SiLU). For β = 1.702, the function approximates GeLU. With β → ∞, the function converges to ReLU. Thus, the swish family smoothly interpolates between a linear function and the ReLU function. Since swish β ⁡ ( x ) = swish 1 ⁡ ( β x ) / β {\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta } , all instances of swish have the same shape as the default swish 1 {\displaystyle \operatorname {swish} _{1}} , zoomed by β {\displaystyle \beta } . One usually sets β > 0 {\displaystyle \beta >0} . When β {\displaystyle \beta } is trainable, this constraint can be enforced by β = e b {\displaystyle \beta =e^{b}} , where b {\displaystyle b} is trainable. swish 1 ⁡ ( x ) = x 2 + x 2 4 − x 4 48 + x 6 480 + O ( x 8 ) {\displaystyle \operatorname {swish} _{1}(x)={\frac {x}{2}}+{\frac {x^{2}}{4}}-{\frac {x^{4}}{48}}+{\frac {x^{6}}{480}}+O\left(x^{8}\right)} swish 1 ⁡ ( x ) = x 2 tanh ⁡ ( x 2 ) + x 2 swish 1 ⁡ ( x ) + swish − 1 ⁡ ( x ) = x tanh ⁡ ( x 2 ) swish 1 ⁡ ( x ) − swish − 1 ⁡ ( x ) = x {\displaystyle {\begin{aligned}\operatorname {swish} _{1}(x)&={\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)+{\frac {x}{2}}\\\operatorname {swish} _{1}(x)+\operatorname {swish} _{-1}(x)&=x\tanh \left({\frac {x}{2}}\right)\\\operatorname {swish} _{1}(x)-\operatorname {swish} _{-1}(x)&=x\end{aligned}}} == Derivatives == Because swish β ⁡ ( x ) = swish 1 ⁡ ( β x ) / β {\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta } , it suffices to calculate its derivatives for the default case. swish 1 ′ ⁡ ( x ) = x + sinh ⁡ ( x ) 4 cosh 2 ⁡ ( x 2 ) + 1 2 {\displaystyle \operatorname {swish} _{1}'(x)={\frac {x+\sinh(x)}{4\cosh ^{2}\left({\frac {x}{2}}\right)}}+{\frac {1}{2}}} so swish 1 ′ ⁡ ( x ) − 1 2 {\displaystyle \operatorname {swish} _{1}'(x)-{\frac {1}{2}}} is odd. swish 1 ″ ⁡ ( x ) = 1 − x 2 tanh ⁡ ( x 2 ) 2 cosh 2 ⁡ ( x 2 ) {\displaystyle \operatorname {swish} _{1}''(x)={\frac {1-{\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)}{2\cosh ^{2}\left({\frac {x}{2}}\right)}}} so swish 1 ″ ⁡ ( x ) {\displaystyle \operatorname {swish} _{1}''(x)} is even. == History == SiLU was first proposed alongside the GELU in 2016, then again proposed in 2017 as the Sigmoid-weighted Linear Unit (SiL) in reinforcement learning. The SiLU/SiL was then again proposed as the SWISH over a year after its initial discovery, originally proposed without the learnable parameter β, so that β implicitly equaled 1. The swish paper was then updated to propose the activation with the learnable parameter β. In 2017, after performing analysis on ImageNet data, researchers from Google indicated that using this function as an activation function in artificial neural networks improves the performance, compared to ReLU and sigmoid functions. It is believed that one reason for the improvement is that the swish function helps alleviate the vanishing gradient problem during backpropagation.

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  • Time-aware long short-term memory

    Time-aware long short-term memory

    Time-aware LSTM (T-LSTM) is a long short-term memory (LSTM) unit capable of handling irregular time intervals in longitudinal patient records. T-LSTM was developed by researchers from Michigan State University, IBM Research, and Cornell University and was first presented in the Knowledge Discovery and Data Mining (KDD) conference. Experiments using real and synthetic data proved that T-LSTM auto-encoder outperformed widely used frameworks including LSTM and MF1-LSTM auto-encoders.

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  • Piranesi (software)

    Piranesi (software)

    Piranesi is an interactive paint system that enables the user to create artistic images from 3D scenes created using conventional modeling applications. == Image format == Piranesi uses the proprietary EPix file format. For every pixel, additional information is stored, such as distance from the viewer and material settings. EPix files can be rendered from 3D scenes using a fixed viewpoint by Piranesi's companion software, Vedute.

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  • Local tangent space alignment

    Local tangent space alignment

    Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a manifold is correctly unfolded, all of the tangent hyperplanes to the manifold will become aligned. It begins by computing the k-nearest neighbors of every point. It computes the tangent space at every point by computing the d-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by data samples, and thus can not be used for classification directly.

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  • Fitness approximation

    Fitness approximation

    Fitness approximation aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based on data collected from numerical simulations or physical experiments. The machine learning models for fitness approximation are also known as meta-models or surrogates, and evolutionary optimization based on approximated fitness evaluations are also known as surrogate-assisted evolutionary approximation. Fitness approximation in evolutionary optimization can be seen as a sub-area of data-driven evolutionary optimization. == Approximate models in function optimization == === Motivation === In many real-world optimization problems including engineering problems, the number of fitness function evaluations needed to obtain a good solution dominates the optimization cost. In order to obtain efficient optimization algorithms, it is crucial to use prior information gained during the optimization process. Conceptually, a natural approach to utilizing the known prior information is building a model of the fitness function to assist in the selection of candidate solutions for evaluation. A variety of techniques for constructing such a model, often also referred to as surrogates, metamodels or approximation models – for computationally expensive optimization problems have been considered. === Approaches === Common approaches to constructing approximate models based on learning and interpolation from known fitness values of a small population include: Low-degree polynomials and regression models Fourier surrogate modeling Artificial neural networks including Multilayer perceptrons Radial basis function network Support vector machines Due to the limited number of training samples and high dimensionality encountered in engineering design optimization, constructing a globally valid approximate model remains difficult. As a result, evolutionary algorithms using such approximate fitness functions may converge to local optima. Therefore, it can be beneficial to selectively use the original fitness function together with the approximate model.

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  • Joseph Nechvatal

    Joseph Nechvatal

    Joseph Nechvatal (born January 15, 1951) is an American post-conceptual digital artist and art theoretician who creates computer-assisted paintings and computer animations, often using custom computer viruses. == Life and work == Joseph Nechvatal was born in Chicago. He studied fine art and philosophy at Southern Illinois University Carbondale, Cornell University, and Columbia University. He earned a Doctor of Philosophy in Philosophy of Art and Technology at the Planetary Collegium at University of Wales, Newport and has taught art theory and art history at the School of Visual Arts. He has had many solo exhibitions and is one of five artists that art historian Patrick Frank examines in his 2024 book Art of the 1980s: As If the Digital Mattered. His work in the late 1970s and early 1980s chiefly consisted of postminimal gray palimpsest-like drawings that were often photo-mechanically enlarged. Beginning in 1979 he became associated with the artist group Colab, organized the Public Arts International/Free Speech series, and helped established the non-profit group ABC No Rio. In 1983 he co-founded the avant-garde electronic art music audio project Tellus Audio Cassette Magazine. In 1984, Nechvatal began work on an opera called XS: The Opera Opus (1984-6) with the no wave musical composer Rhys Chatham. He began using computers and robotics to make post-conceptual paintings in 1986 and later, in his signature work, began to employ self-created computer viruses. From 1991 to 1993, he was artist-in-residence at the Louis Pasteur Atelier in Arbois, France and at the Saline Royale/Ledoux Foundation's computer lab. There he worked on The Computer Virus Project, his first artistic experiment with computer viruses and computer virus animation. He exhibited computer-robotic paintings at Documenta 8 in 1987. In 2002 he extended his experimentation into viral artificial life through a collaboration with the programmer Stephane Sikora of music2eye in a work called the Computer Virus Project II. Nechvatal has also created a noise music work called viral symphOny, a collaborative sound symphony created by using his computer virus software at the Institute for Electronic Arts at Alfred University. In 2021 Pentiments released Nechvatal's retrospective audio cassette called Selected Sound Works (1981-2021) and in 2022 his The Viral Tempest, a double vinyl LP of new audio work. In 2025, he joined the roster of artists/musicians at Table of the Elements with two CD/book releases: Selected Sound Works (1981-2021) and The Marriage of Orlando and Artaud, Even. From 1999 to 2013, Nechvatal taught art theories of immersive virtual reality and the viractual at the School of Visual Arts in New York City (SVA). A book of his collected essays entitled Towards an Immersive Intelligence: Essays on the Work of Art in the Age of Computer Technology and Virtual Reality (1993–2006) was published by Edgewise Press in 2009. Also in 2009, his virtual reality art theory and art history book Immersive Ideals / Critical Distances was published. In 2011, his book Immersion Into Noise was published by Open Humanities Press in conjunction with the University of Michigan Library's Scholarly Publishing Office. Nechvatal has also published three books with Punctum Books: Minóy (noise music—ed.—2014), Destroyer of Naivetés (poetry—2015), and Styling Sagaciousness (poetry—2022). In 2023 his art theory cybersex farce novella venus©~Ñ~vibrator, even was published by Orbis Tertius Press The Joseph Nechvatal archive is housed at The Fales Library Downtown Collection at the NYU Special Collections Library in New York City. === Viractualism === Viractualism is an art theory concept developed by Nechvatal in 1999 from Ph.D. research Nechvatal conducted at the Planetary Collegium at University of Wales, Newport. There he developed his concept of the viractual, which strives to create an interface between the actual and the virtual.

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  • WomanStats Project

    WomanStats Project

    The WomanStats Project is a donor-funded research and database project housed at Brigham Young University that "seeks to collect detailed statistical data on the status of women around the world, and to connect that data with data on the security of states." The WomanStats Database aims to provide a comprehensive compilation of information on the status of women in the world. Coders comb the extant literature and conduct expert interviews to find qualitative and quantitative information on over 300 indicators of women's status in 174 countries with populations of at least 200,000. Access to the online database is free. == History and structure == WomanStats began as an outgrowth of a paper Dr. Valerie M. Hudson (of the Brigham Young University Political Science department) and one of her graduate students, Andrea den Boer, published in International Security on the association between national security and the abnormal sex ratio in Asia. After the success and influence of their first article, (later added as one of their top twenty national security articles of that journal of all time), Hudson and den Boer did further research on the connection between the status of women and national security, but found that there was no single database that covered the range of topics that they needed for their research. Consequently, they began compiling information on variables regarding the status of women around the world. The database was officially formed in 2001 and grew exponentially as it later added more variables. The Project went live on the Internet in July 2007. The principal investigators are: Valerie M. Hudson (International Relations), Bonnie Ballif-Spanvill (Psychology, emeritus), and Chad F. Emmett (Geography) all from Brigham Young University, Mary Caprioli from the University of Minnesota, Duluth (International Relations), Rose McDermott from Brown University (International Relations), Andrea Den Boer from the University of Kent at Canterbury in the United Kingdom (International Relations) and S. Matthew Stearmer from the Ohio State University (Sociology; doctoral student). Approximately a dozen undergraduate and graduate students at Brigham Young University and Texas A&M University work at any one time as coders for the project. The coders take the raw quantitative and qualitative data collected in government reports, news articles, research papers, etc. and sort the applicable information on women into categories. They may also implement scales developed by the principal investigators, or that they (the students) themselves have developed. == Database == As of February 2011, the database has 307 variables, covers 174 nations with populations over 200,000, uses 18,015 sources and contains over 111,000 individual data points. All data is referenced to original sources. Not every variable has information for each country; similarly, not all countries have information for each variable: overall, about 70% of country-variable combinations have information. These database coding gaps exist where information is not available or is incomplete, or variables are not collected and reported by governments or international organizations. At times, information from different sources may be contradictory, and the WomanStats Database records this discrepant information for triangulation purposes. == Users and role of the database == The database is meant to help fill a hole in the extant data on the situation of women around the world. WomanStats data and research has been vetted and/or used by the United Nations, the United States Department of Defense, the Central Intelligence Agency, and the World Bank. Their data and research were also used by the United States Senate Committee on Foreign Relations in crafting the International Violence Against Women’s Act. The Inter-Agency Network on Women and Gender Equality (IANWGE) of the United Nations has stated that the WomanStats project "filled a major gap in the availability of data on women" (2007). Victor Asal and Mitchell Brown, researchers not affiliated with WomanStats, stated in an article published in Politics and Policy that "one of the most significant challenges of cross-national empirical studies of the prevalence of interpersonal violence is the paucity of available data, particularly reliable data," and that "WomanStats has allowed for an important first glimpse at analyzing the factors related to interpersonal violence." They conclude by stating that "Our findings suggest that, in the same way that larger disciplinary resources have invested in interstate and intrastate war, disciplinary resources need to be expended in creating a data set exploring interpersonal violence. Until the rights and the lives of women and children are taken as seriously as the survival of states by more proactively collaborating on projects like WomanStats, we will continue to only have a small lens through which to understand problems like this." Princeton University professor Evan S. Liberman wrote, "Although data on political regimes and group conflict have been in far greater demand by political scientists than data on gender politics and policies, two gender-related databases provide...examples of innovative HIRDs. Both the Womanstats database project (Hudson et al. 2009) and the Research Network on Gender Politics and the State (RNGS) project (McBride et al. 2008) are well-integrated presentations of quantitative and qualitative data characterizing the quality of gender relations around the world and, in particular, analytic descriptions of the treatment of women."." == Research == The research component of WomanStats focuses on exploring the relationship between the situation of women and the behavior and security of states. Current research initiatives include: Exploring the relationship between violent instability and inequity and family law. Examining the effect of polygyny and marriage market dislocations on the rise of suicide terrorism. Documenting discrepancies between laws on the books and cultural practices on the ground concerning gender issues. Investigating how well the situation of women predicts the peacefulness of nations-states, compared to their variables such as democracy, wealth, and civilization. The Project has published articles in International Security, International Studies Quarterly, Peace and Conflict, Journal of Peace Research, Political Psychology, Cumberland Law Review, and World Political Review, and has a forthcoming book from Columbia University Press.

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  • Ordination (statistics)

    Ordination (statistics)

    Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near each other share attributes (i.e., are similar to some degree), and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes or latent variables, are then characterized numerically and/or graphically in a biplot. The first ordination method, principal components analysis, was suggested by Karl Pearson in 1901. == Methods == Ordination methods can broadly be categorized in eigenvector-, algorithm-, or model-based methods. Many classical ordination techniques, including principal components analysis, correspondence analysis (CA) and its derivatives (detrended correspondence analysis, canonical correspondence analysis, and redundancy analysis, belong to the first group). The second group includes some distance-based methods such as non-metric multidimensional scaling, and machine learning methods such as T-distributed stochastic neighbor embedding and nonlinear dimensionality reduction. The third group includes model-based ordination methods, which can be considered as multivariate extensions of Generalized Linear Models. Model-based ordination methods are more flexible in their application than classical ordination methods, so that it is for example possible to include random-effects. Unlike in the aforementioned two groups, there is no (implicit or explicit) distance measure in the ordination. Instead, a distribution needs to be specified for the responses as is typical for statistical models. These and other assumptions, such as the assumed mean-variance relationship, can be validated with the use of residual diagnostics, unlike in other ordination methods. == Applications == Ordination can be used on the analysis of any set of multivariate objects. It is frequently used in several environmental or ecological sciences, particularly plant community ecology. It is also used in genetics and systems biology for microarray data analysis and in psychometrics.

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  • Sufficient dimension reduction

    Sufficient dimension reduction

    In statistics, sufficient dimension reduction (SDR) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency. Dimension reduction has long been a primary goal of regression analysis. Given a response variable y and a p-dimensional predictor vector x {\displaystyle {\textbf {x}}} , regression analysis aims to study the distribution of y ∣ x {\displaystyle y\mid {\textbf {x}}} , the conditional distribution of y {\displaystyle y} given x {\displaystyle {\textbf {x}}} . A dimension reduction is a function R ( x ) {\displaystyle R({\textbf {x}})} that maps x {\displaystyle {\textbf {x}}} to a subset of R k {\displaystyle \mathbb {R} ^{k}} , k < p, thereby reducing the dimension of x {\displaystyle {\textbf {x}}} . For example, R ( x ) {\displaystyle R({\textbf {x}})} may be one or more linear combinations of x {\displaystyle {\textbf {x}}} . A dimension reduction R ( x ) {\displaystyle R({\textbf {x}})} is said to be sufficient if the distribution of y ∣ R ( x ) {\displaystyle y\mid R({\textbf {x}})} is the same as that of y ∣ x {\displaystyle y\mid {\textbf {x}}} . In other words, no information about the regression is lost in reducing the dimension of x {\displaystyle {\textbf {x}}} if the reduction is sufficient. == Graphical motivation == In a regression setting, it is often useful to summarize the distribution of y ∣ x {\displaystyle y\mid {\textbf {x}}} graphically. For instance, one may consider a scatterplot of y {\displaystyle y} versus one or more of the predictors or a linear combination of the predictors. A scatterplot that contains all available regression information is called a sufficient summary plot. When x {\displaystyle {\textbf {x}}} is high-dimensional, particularly when p ≥ 3 {\displaystyle p\geq 3} , it becomes increasingly challenging to construct and visually interpret sufficiency summary plots without reducing the data. Even three-dimensional scatter plots must be viewed via a computer program, and the third dimension can only be visualized by rotating the coordinate axes. However, if there exists a sufficient dimension reduction R ( x ) {\displaystyle R({\textbf {x}})} with small enough dimension, a sufficient summary plot of y {\displaystyle y} versus R ( x ) {\displaystyle R({\textbf {x}})} may be constructed and visually interpreted with relative ease. Hence sufficient dimension reduction allows for graphical intuition about the distribution of y ∣ x {\displaystyle y\mid {\textbf {x}}} , which might not have otherwise been available for high-dimensional data. Most graphical methodology focuses primarily on dimension reduction involving linear combinations of x {\displaystyle {\textbf {x}}} . The rest of this article deals only with such reductions. == Dimension reduction subspace == Suppose R ( x ) = A T x {\displaystyle R({\textbf {x}})=A^{T}{\textbf {x}}} is a sufficient dimension reduction, where A {\displaystyle A} is a p × k {\displaystyle p\times k} matrix with rank k ≤ p {\displaystyle k\leq p} . Then the regression information for y ∣ x {\displaystyle y\mid {\textbf {x}}} can be inferred by studying the distribution of y ∣ A T x {\displaystyle y\mid A^{T}{\textbf {x}}} , and the plot of y {\displaystyle y} versus A T x {\displaystyle A^{T}{\textbf {x}}} is a sufficient summary plot. Without loss of generality, only the space spanned by the columns of A {\displaystyle A} need be considered. Let η {\displaystyle \eta } be a basis for the column space of A {\displaystyle A} , and let the space spanned by η {\displaystyle \eta } be denoted by S ( η ) {\displaystyle {\mathcal {S}}(\eta )} . It follows from the definition of a sufficient dimension reduction that F y ∣ x = F y ∣ η T x , {\displaystyle F_{y\mid x}=F_{y\mid \eta ^{T}x},} where F {\displaystyle F} denotes the appropriate distribution function. Another way to express this property is y ⊥ ⊥ x ∣ η T x , {\displaystyle y\perp \!\!\!\perp {\textbf {x}}\mid \eta ^{T}{\textbf {x}},} or y {\displaystyle y} is conditionally independent of x {\displaystyle {\textbf {x}}} , given η T x {\displaystyle \eta ^{T}{\textbf {x}}} . Then the subspace S ( η ) {\displaystyle {\mathcal {S}}(\eta )} is defined to be a dimension reduction subspace (DRS). === Structural dimensionality === For a regression y ∣ x {\displaystyle y\mid {\textbf {x}}} , the structural dimension, d {\displaystyle d} , is the smallest number of distinct linear combinations of x {\displaystyle {\textbf {x}}} necessary to preserve the conditional distribution of y ∣ x {\displaystyle y\mid {\textbf {x}}} . In other words, the smallest dimension reduction that is still sufficient maps x {\displaystyle {\textbf {x}}} to a subset of R d {\displaystyle \mathbb {R} ^{d}} . The corresponding DRS will be d-dimensional. === Minimum dimension reduction subspace === A subspace S {\displaystyle {\mathcal {S}}} is said to be a minimum DRS for y ∣ x {\displaystyle y\mid {\textbf {x}}} if it is a DRS and its dimension is less than or equal to that of all other DRSs for y ∣ x {\displaystyle y\mid {\textbf {x}}} . A minimum DRS S {\displaystyle {\mathcal {S}}} is not necessarily unique, but its dimension is equal to the structural dimension d {\displaystyle d} of y ∣ x {\displaystyle y\mid {\textbf {x}}} , by definition. If S {\displaystyle {\mathcal {S}}} has basis η {\displaystyle \eta } and is a minimum DRS, then a plot of y versus η T x {\displaystyle \eta ^{T}{\textbf {x}}} is a minimal sufficient summary plot, and it is (d + 1)-dimensional. == Central subspace == If a subspace S {\displaystyle {\mathcal {S}}} is a DRS for y ∣ x {\displaystyle y\mid {\textbf {x}}} , and if S ⊂ S drs {\displaystyle {\mathcal {S}}\subset {\mathcal {S}}_{\text{drs}}} for all other DRSs S drs {\displaystyle {\mathcal {S}}_{\text{drs}}} , then it is a central dimension reduction subspace, or simply a central subspace, and it is denoted by S y ∣ x {\displaystyle {\mathcal {S}}_{y\mid x}} . In other words, a central subspace for y ∣ x {\displaystyle y\mid {\textbf {x}}} exists if and only if the intersection ⋂ S drs {\textstyle \bigcap {\mathcal {S}}_{\text{drs}}} of all dimension reduction subspaces is also a dimension reduction subspace, and that intersection is the central subspace S y ∣ x {\displaystyle {\mathcal {S}}_{y\mid x}} . The central subspace S y ∣ x {\displaystyle {\mathcal {S}}_{y\mid x}} does not necessarily exist because the intersection ⋂ S drs {\textstyle \bigcap {\mathcal {S}}_{\text{drs}}} is not necessarily a DRS. However, if S y ∣ x {\displaystyle {\mathcal {S}}_{y\mid x}} does exist, then it is also the unique minimum dimension reduction subspace. === Existence of the central subspace === While the existence of the central subspace S y ∣ x {\displaystyle {\mathcal {S}}_{y\mid x}} is not guaranteed in every regression situation, there are some rather broad conditions under which its existence follows directly. For example, consider the following proposition from Cook (1998): Let S 1 {\displaystyle {\mathcal {S}}_{1}} and S 2 {\displaystyle {\mathcal {S}}_{2}} be dimension reduction subspaces for y ∣ x {\displaystyle y\mid {\textbf {x}}} . If x {\displaystyle {\textbf {x}}} has density f ( a ) > 0 {\displaystyle f(a)>0} for all a ∈ Ω x {\displaystyle a\in \Omega _{x}} and f ( a ) = 0 {\displaystyle f(a)=0} everywhere else, where Ω x {\displaystyle \Omega _{x}} is convex, then the intersection S 1 ∩ S 2 {\displaystyle {\mathcal {S}}_{1}\cap {\mathcal {S}}_{2}} is also a dimension reduction subspace. It follows from this proposition that the central subspace S y ∣ x {\displaystyle {\mathcal {S}}_{y\mid x}} exists for such x {\displaystyle {\textbf {x}}} . == Methods for dimension reduction == There are many existing methods for dimension reduction, both graphical and numeric. For example, sliced inverse regression (SIR) and sliced average variance estimation (SAVE) were introduced in the 1990s and continue to be widely used. Although SIR was originally designed to estimate an effective dimension reducing subspace, it is now understood that it estimates only the central subspace, which is generally different. More recent methods for dimension reduction include likelihood-based sufficient dimension reduction, estimating the central subspace based on the inverse third moment (or kth moment), estimating the central solution space, graphical regression, envelope model, and the principal support vector machine. For more details on these and other methods, consult the statistical literature. Principal components analysis (PCA) and similar methods for dimension reduction are not based on the sufficiency principle. === Example: linear regression === Consider the regression model y = α + β T x + ε , where ε ⊥ ⊥ x . {\displaystyle y=\alpha +\beta ^{T}{\textbf {x}}+\varepsilon ,{\text{ where }}\varepsilon \perp \!\!\!\perp {\textbf {x}}.} Note that the distribution of y ∣ x {\displaystyle y\mid {\textbf {x}}} is the same as the distribution of y ∣ β T x {\displ

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