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Class of statistical models
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing
Generalized_linear_model
statistics, the generalized linear array model (GLAM) is used for analyzing data sets with array structures. It based on the generalized linear model with the
Generalized linear array model
Generalized_linear_array_model
Topics referred to by the same term
county of Wales and formerly used as a postal abbreviation. Generalized linear array model, 2006, in statistics Glam metal, 1970s, a subgenre of heavy
Glam
Least squares approximation of linear functions to data
in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least
Linear_least_squares
Mathematical operation on matrices
\mathbf {c} } and d {\displaystyle \mathbf {d} } are vectors. Generalized linear array model Hadamard product (matrices) Kronecker coefficient Weisstein
Kronecker_product
Applying operations to whole sets of values simultaneously
languages that support array programming (also known as vector or multidimensional languages) have been engineered specifically to generalize operations on scalars
Array_programming
Several equations of degree 1 to be solved simultaneously
can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively
System_of_linear_equations
robustness. Given a linear time-invariant (LTI) system represented by a nonsingular matrix G {\displaystyle \mathrm {G} } , the relative gain array (RGA) is defined
Relative_gain_array
Branch of mathematics
models for many physical phenomena; it's also useful in many areas of computing, and is thus applied to most sciences. For nonlinear systems, linear algebra
Linear_algebra
Generalized inverse Gaussian distribution Generalized least squares Generalized linear array model Generalized linear mixed model Generalized linear model
List_of_statistics_articles
Data structure holding key/value pairs
In computer science, an associative array, key-value store, map, symbol table, or dictionary is an abstract data type that stores a collection of key/value
Associative_array
Type of mathematical array
generalized to Latin cubes and hypercubes, and orthogonal Latin cubes and hypercubes by Kishen (1942). Rao (1946) generalized these results to arrays
Orthogonal_array
Type of product of matrices
popular Natural Language Processing models, and hypergraph models of similarity, Generalized linear array model in statistics Two- and multidimensional
Khatri–Rao_product
Mathematical descriptions of the properties of certain cells in the nervous system
related to linear-nonlinear-Poisson cascade models (also called Generalized Linear Model). The estimation of parameters of probabilistic neuron models such
Biological_neuron_model
replication allows the estimation and testing of an interaction term in the linear model (without making parametric assumptions about a normal distribution for
Generalized randomized block design
Generalized_randomized_block_design
Process of calculating the causal factors that produced a set of observations
the case of a linear forward map and when we deal with a finite number of model parameters, the forward map can be written as a linear system d=Fp where
Inverse_problem
Problem in computational complexity theory
{\displaystyle n} real numbers contains three elements that sum to zero. A generalized version, k {\displaystyle k} -SUM, asks the same question on k {\displaystyle
3SUM
Nonlinear transduction mechanism
primary fields generated by linear sources in the medium. This formalism has been applied not only to parametric arrays, but also to other nonlinear
Parametric_array
Type of machine learning model
bigger models on various tasks, when plotted on a log–log scale, appears as a linear extrapolation of performance achieved by smaller models. However
Large_language_model
Soviet and Ukrainian scientist
properties used for multidimensional smoothing with P-splines and Generalized linear array model in the statistic in two- and multidimensional approximations
Vadym_Slyusar
Array of numbers
of linear algebra, but soon grew to include subjects related to graph theory, algebra, combinatorics and statistics. A matrix is a rectangular array of
Matrix_(mathematics)
Search algorithm used in sorted arrays
elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary
Binary_search
Geometric property of a pair of sets of points in Euclidean geometry
generalizes to higher-dimensional Euclidean spaces if the line is replaced by a hyperplane. The problem of determining if a pair of sets is linearly separable
Linear_separability
Algebraic object with geometric applications
multidimensional array. For example, a linear operator is represented in a basis as a two-dimensional square n × n array. The numbers in the multidimensional array are
Tensor
Regression models that combine parametric and nonparametric models
methods are the partially linear, index and varying coefficient models. A partially linear model is given by Y i = X i ′ β + g ( Z i ) + u i , i = 1 , … , n
Semiparametric_regression
library for manipulating sets and relations of integer points bounded by linear constraints. The following operations are supported: intersection, union
Integer_set_library
Family of power series in mathematics
defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation. The generalized hypergeometric
Generalized hypergeometric function
Generalized_hypergeometric_function
Algorithm for modelling sequential data
vision-language model composed of a language model (Vicuna-13B) and a vision model (ViT-L/14), connected by a linear layer. Only the linear layer is finetuned
Transformer_(deep_learning)
Topics referred to by the same term
behavior is not expressible as a linear function of its inputs Non-linear transformation matrix, (n+1)×(n+1) array that can represent affine and projective
Nonlinearity_(disambiguation)
Problem of determining if a Boolean formula could be made true
to define the notion of a generalized conjunctive normal form formula, viz. as a conjunction of arbitrarily many generalized clauses, the latter being
Boolean satisfiability problem
Boolean_satisfiability_problem
Representation of a type of random process
sources. The model specifies output variables that are dependent linearly on their own previous values on a stochastic basis. The model is in the form
Autoregressive_model
Musical keyboards with regular arrangements of keys
810-key models that can be programmed and the key surfaces organized into generalized as well as many other arrangements. Isomorphic keyboard Linear temperament
Generalized_keyboard
In mathematical biology, the community matrix is the linearization of a generalized Lotka–Volterra equation at an equilibrium point. The eigenvalues of
Community_matrix
Correlation of a signal with a time-shifted copy of itself, as a function of shift
with k degrees of freedom. Responses to nonzero autocorrelation include generalized least squares and the Newey–West HAC estimator (Heteroskedasticity and
Autocorrelation
Coordinate system that is defined by points instead of vectors
point not having unique generalized barycentric coordinates except when P {\displaystyle P} is a simplex. Dual to generalized barycentric coordinates
Barycentric_coordinate_system
Algorithm that arranges lists in order
sort is a divide-and-conquer sorting algorithm that generalizes counting sort by partitioning an array into a finite number of buckets. Each bucket is then
Sorting_algorithm
Topics referred to by the same term
models using matrices Generalized linear model (GLM), a flexible generalization of ordinary linear regression that allows the linear model to be related to
Linear_(disambiguation)
Algorithm that estimates unknowns from a series of measurements over time
In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed
Kalman_filter
Python package
provides an interface to build and solve Bayesian generalized (non-)linear multivariate multilevel models. Bambi is an open source project, developed by
Bambi_(software)
Adjustment of color intensities in photography
can be described as a linear model with N basis terms, the proper color transformation will be the weighted sum of N fixed linear transformations, not
Color_balance
Special arrangement of permanent magnets
independently invented the Halbach array to focus particle accelerator beams. The magnetic flux distribution of a linear Halbach array may seem somewhat counter-intuitive
Halbach_array
Collection of microscopic DNA spots attached to a solid surface
designed, RNA-Seq can also be used for new model organisms whose genome has not been sequenced yet. An array or slide is a collection of features spatially
DNA_microarray
Programming language for statistics
support for various statistical techniques (such as linear, generalized linear and nonlinear modeling, classical statistical tests, spatial analysis, time-series
R_(programming_language)
Concepts from linear algebra
normal form and therefore admits a basis of generalized eigenvectors and a decomposition into generalized eigenspaces. In the Hermitian case, eigenvalues
Eigenvalues_and_eigenvectors
Collection of statistical models
produce a derived linear model, very similar to the textbook model discussed previously. The test statistics of this derived linear model are closely approximated
Analysis_of_variance
Algorithm for supervised learning of binary classifiers
perceptron model is the Receptron that incorporates non-linear interactions between inputs. A single receptron is able to classify non-linear Boolean functions
Perceptron
Statistical concept
&{\mathcal {N}}(\mu _{z_{i}},\sigma _{z_{i}}^{2})\end{array}}} A Bayesian version of a Gaussian mixture model is as follows: K , N = as above ϕ i = 1 … K , ϕ
Mixture_model
Sequence in computer science
frequencies to calculate the position of each key in the sorted output array. It runs in linear time for integer keys that are smaller than the number of items
Prefix_sum
Logical problem studied in computer science
theories of arrays and list structures (useful for modeling and verifying computer programs), and the theory of bit vectors (useful in modeling and verifying
Satisfiability modulo theories
Satisfiability_modulo_theories
Statistical modeling technique
"quantreg: Quantile Regression". R Project. 2018-12-18. "gbm: Generalized Boosted Regression Models". R Project. 2019-01-14. "quantregForest: Quantile Regression
Quantile_regression
Regularization method for artificial neural networks
unique case. If the neural net is processed by a high-performance digital array-multiplicator, then it is likely more effective to drive the value to zero
Dropout_(neural_networks)
Optimization problem
solving geometric programs (GPs) and generalized geometric programs (GGPs). CVXPY is a Python-embedded modeling language for specifying and solving convex
Geometric_programming
Method for generating heightmaps for computer graphics
in a generalized algorithm introduced by J.P. Lewis. In this variant the weights on the neighboring points are obtained by solving a small linear system
Diamond-square_algorithm
Generalization of the one-dimensional normal distribution to higher dimensions
multiple linear regression. Since the log likelihood of a normal vector is a quadratic form of the normal vector, it is distributed as a generalized chi-squared
Multivariate normal distribution
Multivariate_normal_distribution
Statistical model
discriminate between the fixed and the random effects models. Consider the linear unobserved effects model for N {\displaystyle N} observations and T {\displaystyle
Fixed_effects_model
Elementwise product of two matrices
"Matrix differential calculus with applications in the multivariate linear model and its diagnostics". Journal of Multivariate Analysis. 188 104849. doi:10
Hadamard_product_(matrices)
Abstract data type
access structure is the priority queue, which is not a linear structure. The deque can be generalized by the addition of some operations: a deque with heap
Double-ended_queue
Problem in computer science
contiguous subarray with the largest sum, within a given one-dimensional array A[1...n] of numbers. It can be solved in O ( n ) {\displaystyle O(n)} time
Maximum_subarray_problem
Mathematical relation defining a sequence
combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference
Linear recurrence with constant coefficients
Linear_recurrence_with_constant_coefficients
regular and nonregular designs. In doing this, Ye established generalized resolution and generalized minimum aberration. Whereas regular designs are designs
Robust_parameter_design
Statistical methods to improve the quality of manufactured goods
least squares estimators have minimum variance among all mean-unbiased linear estimators. The emphasis on comparisons of means also draws (limiting) comfort
Taguchi_methods
Overview of and topical guide to deep learning
ONNX OpenVINO TensorFlow Hub Backpropagation Conjugate gradient method Generalized Hebbian algorithm Gradient descent Levenberg–Marquardt algorithm Perceptron
Outline_of_deep_learning
Categorization of data using statistics
undertaken by Fisher, in the context of two-group problems, leading to Fisher's linear discriminant function as the rule for assigning a group to a new observation
Statistical_classification
real tridiagonal, generalized real, and generalized real symmetric matices. LINPACK is a software library for performing numerical linear algebra on digital
List_of_numerical_libraries
Broad concept generalizing scalars in mathematics and physics
Vectorization (mathematics), a linear transformation that converts a matrix into a column vector Vector autoregression, an econometric model used to capture the
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Statistical test used on paired nominal data
Rimarcik.com. Retrieved 2012-11-22. Sun, Xuezheng; Yang, Zhao (2008). "Generalized McNemar's Test for Homogeneity of the Marginal Distributions" (PDF).
McNemar's_test
Software for working with quantitative decision models
quantitative decision models. It combines hierarchical influence diagrams to visually create and view models, intelligent arrays to work with multidimensional
Analytica_(software)
Feature detection algorithm in computer vision
procedure in which a linear least squares solution is performed for the parameters of the affine transformation relating the model to the image. The affine
Scale-invariant feature transform
Scale-invariant_feature_transform
Type of artificial neural network
a linear projection, defined by P(x)=Mx where M is a m×n matrix. The matrix is trained via backpropagation, as is any other parameter of the model. The
Residual_neural_network
General linear model that blends ANOVA and regression
Analysis of covariance (ANCOVA) is a general linear model that blends ANOVA and regression. ANCOVA evaluates whether the means of a dependent variable
Analysis_of_covariance
Design of tasks
Douglas C.; Vining, G. Geoffrey; Robinson, Timothy J. (2010). Generalized linear models: with applications in engineering and the sciences (2 ed.). Hoboken
Design_of_experiments
Format for presentation of quantitative data
{\displaystyle {\begin{array}{r|l}{\text{Stem}}&{\text{Leaf}}\\\hline 4&4~6~7~9\\5&\\6&3~4~6~8~8\\7&2~2~5~6\\8&1~4~8\\9&\\10&6\end{array}}} Key: 6 ∣ 3 = 63
Stem-and-leaf_display
Mathematical analysis technique
used in some form of mathematical relationship ("model") to calculate that derived quantity. The model used to convert the measurements into the derived
Experimental uncertainty analysis
Experimental_uncertainty_analysis
Measure of variation in statistics
− 5 ) 2 = ( − 1 ) 2 = 1 ( 9 − 5 ) 2 = 4 2 = 16. {\displaystyle {\begin{array}{lll}(2-5)^{2}=(-3)^{2}=9&&(5-5)^{2}=0^{2}=0\\(4-5)^{2}=(-1)^{2}=1&&(5-
Standard_deviation
Dependence of the state of a system on its history
such as OpenSees. Hysteretic models may have a generalized displacement u {\displaystyle u} as input variable and a generalized force f {\displaystyle f}
Hysteresis
Type of chart
Instead, the star-shaped figures are usually arranged in a rectangular array on the page. It is somewhat easier to see patterns in the data if the observations
Radar_chart
Statistical approach
model, and their biased linear-models estimated the gradient to be zero. Box's design reduced the costs of experimentation so that a quadratic model could
Response_surface_methodology
Type of Monte Carlo algorithms for signal processing and statistical inference
solve Hidden Markov Model (HMM) and nonlinear filtering problems. With the notable exception of linear-Gaussian signal-observation models (Kalman filter)
Particle_filter
Sequence of data points over time
predictions derived from non-linear models, over those from linear models, as for example in nonlinear autoregressive exogenous models. Further references on
Time_series
Mathematical concept
dynamical systems is to linearize the system, and then compute its eigenvalues and eigenvectors. The eigenvectors (and generalized eigenvectors if they occur)
Center_manifold
Experimental design framework
design depends on the particular utility criterion chosen. If the model is linear, the prior probability density function (PDF) is homogeneous and observational
Bayesian_experimental_design
Degradation of solder due to deformation under cyclic loading
loading schemes, Miner's linear superposition damage law is employed to calculate accumulated damage. The generalized Coffin–Manson model considers the elastic
Solder_fatigue
Pattern defining an infinite sequence of numbers
function of an integral. Many homogeneous linear recurrence relations may be solved by means of the generalized hypergeometric series. Special cases of
Recurrence_relation
Table that displays the frequency of variables
ISBN 978-0-262-02113-5. MR 0381130. Christensen, Ronald (1997). Log-linear models and logistic regression. Springer Texts in Statistics (Second ed.).
Contingency_table
Covariance and correlation
transform, etc. The kernel cross-correlation extends cross-correlation from linear space to kernel space. Cross-correlation is equivariant to translation;
Cross-correlation
Middle quantile of a data set or probability distribution
Hodges–Lehmann estimator has been generalized to multivariate distributions. The Theil–Sen estimator is a method for robust linear regression based on finding
Median
Taxonomy of statistical data elements
nearby variables. Multilevel models are subclasses of Bayes networks that can be thought of as having multiple levels of linear regression. Random trees These
Statistical_data_type
Abstract mathematical system of two types of objects and a relation between them
examples of incidence structures 1. Fano plane 2. Non-uniform structure 3. Generalized quadrangle 4. Möbius–Kantor configuration 5. Pappus configuration An
Incidence_structure
Ancient algorithm for generating prime numbers
multiples of p. This actually appears in the original algorithm. This can be generalized with wheel factorization, forming the initial list only from numbers
Sieve_of_Eratosthenes
Subset of artificial intelligence
were mostly perceptrons and other models that were later found to be reinventions of the generalised linear models of statistics. Probabilistic reasoning
Machine_learning
Spatial prediction technique
ISBN 978-0-387-95296-3. Goldberger, A.S. (1962). "Best Linear Unbiased Prediction in the Generalized Linear Regression Model". Journal of the American Statistical Association
Regression-kriging
Statistical distribution for dependence between random variables
F_{1}^{-1}(U_{1}),\ F_{2}^{-1}(U_{2}),\ \dots ,\ F_{d}^{-1}(U_{d})\ {\Bigr )}~.} The generalized inverses F i − 1 {\displaystyle \ F_{i}^{-1}\ } are unproblematic
Copula_(statistics)
Design of experiments to collect similar contexts together
Pre-publication chapters are available on-line. Bapat, R. B. (2000). Linear Algebra and Linear Models (Second ed.). Springer. ISBN 978-0-387-98871-9. Caliński T
Blocking_(statistics)
Nonlinear two-terminal fundamental circuit element
array built on a CMOS chip. According to the original 1971 definition, the memristor is the fourth fundamental circuit element, forming a non-linear relationship
Memristor
Involutive change of basis in linear algebra
transform) is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric, involutive, linear operation on a tuple of 2m
Hadamard_transform
Experimental design in statistics
of the Linear Model. Pacific Grove, CA: Wadsworth & Brooks/Cole. ISBN 0-87872-108-8. Hocking, Ronald R. (1985). The Analysis of Linear Models. Pacific
Factorial_experiment
software suite for non-linear statistical modeling based on C++ which uses automatic differentiation. AMPL is a mathematical modeling language for describing
List of numerical-analysis software
List_of_numerical-analysis_software
Statistical model validation technique
is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set
Cross-validation_(statistics)
Periodicity computation method
periodogram". He generalized this method to account for any systematic components beyond a simple mean, such as a "predicted linear (quadratic, exponential
Least-squares spectral analysis
Least-squares_spectral_analysis
Statistic for rank correlation
{\displaystyle \tau _{B}} are easily obtained in a single linear-time pass through the sorted arrays. Efficient algorithms for calculating the Kendall rank
Kendall rank correlation coefficient
Kendall_rank_correlation_coefficient
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GENERALIZED LINEAR-ARRAY-MODEL
GENERALIZED LINEAR-ARRAY-MODEL
GENERALIZED LINEAR-ARRAY-MODEL
GENERALIZED LINEAR-ARRAY-MODEL
GENERALIZED LINEAR-ARRAY-MODEL
GENERALIZED LINEAR-ARRAY-MODEL
GENERALIZED LINEAR-ARRAY-MODEL
GENERALIZED LINEAR-ARRAY-MODEL
GENERALIZED LINEAR-ARRAY-MODEL
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