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Linear function of explanatory variables used to predict a dependent variable
In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables
Linear_predictor_function
Statistical modeling method
variables is a multiple linear regression. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters
Linear_regression
Class of statistical models
observed values (predictors). This implies that a constant change in a predictor leads to a constant change in the response variable (i.e. a linear-response model)
Generalized_linear_model
Algorithm for supervised learning of binary classifiers
classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector. The artificial
Perceptron
Regression for more than two discrete outcomes
techniques, is to construct a linear predictor function that constructs a score from a set of weights that are linearly combined with the explanatory
Multinomial logistic regression
Multinomial_logistic_regression
Method used in statistics, pattern recognition, and other fields
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization
Linear_discriminant_analysis
Statistical model for a binary dependent variable
generalized linear model, which predicts variables with various types of probability distributions by fitting a linear predictor function of the above
Logistic_regression
Type of statistical model
linear model Generalized linear model Linear predictor function Linear system Linear regression Statistical model Priestley, M.B. (1988) Non-linear and
Linear_model
Statistical method
Multiple linear regression, also known as multivariable linear regression, is a generalization of simple linear regression to the case of more than one
Multiple_linear_regression
Artificial neural network node function
performance, activation functions also have different mathematical properties: Nonlinear When the activation function is non-linear, then a two-layer neural
Activation_function
Advanced method of process control
satisfying a set of constraints. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system
Model_predictive_control
Smooth approximation of one-hot arg max
discriminant analysis, the input to the function is the result of K distinct linear functions, and the predicted probability for the j-th class given a
Softmax_function
Topics referred to by the same term
fitting a tangent to the graph and extending the line Linear predictor function, a linear function (linear combination) of a set of coefficients and explanatory
Linear_(disambiguation)
Linear regression model with a single explanatory variable
finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent
Simple_linear_regression
Statistical model
family with its expectation related to the linear predictor X β + Z u {\textstyle X\beta +Zu} via a link function g {\textstyle g} : g ( E [ y | u ] ) = X
Generalized linear mixed model
Generalized_linear_mixed_model
Digital circuit
conditional jump can be predicted easily with a simple counter. A loop predictor is part of a hybrid predictor where a meta-predictor detects whether the
Branch_predictor
denoted the linear predictor function. It is generally assumed that the modeled relationship is monotone convex (delivering monotone convex function) or monotone
Response_modeling_methodology
Measurable property or characteristic
such as linear regression. Feature vectors are often combined with weights using a dot product in order to construct a linear predictor function that is
Feature_(machine_learning)
Mathematical operation that predicts future values of a discrete-time signal
Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In
Linear_prediction
Least squares approximation of linear functions to data
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems
Linear_least_squares
Moving average and polynomial regression method for smoothing data
intended for smoothing scatterplots. This implements local linear fitting with a single predictor variable, and also introduces robustness downweighting to
Local_regression
Categorization of data using statistics
product. The predicted category is the one with the highest score. This type of score function is known as a linear predictor function and has the following
Statistical_classification
System where changes of output are not proportional to changes of input
known linear functions appear in the equations. In particular, a differential equation is linear if it is linear in terms of the unknown function and its derivatives
Nonlinear_system
Method for estimating the unknown parameters in a linear regression model
input dataset and the output of the (linear) function of the independent variable. Some sources consider OLS to be linear regression. Geometrically, this is
Ordinary_least_squares
Overview of and topical guide to machine learning
Learnable function class Least squares support vector machine Leslie P. Kaelbling Linear genetic programming Linear predictor function Linear separability
Outline_of_machine_learning
Mathematical model for stochastic processes
response variable to a linear predictor, which in case of GFLM is obtained by forming the scalar product of the random predictor function X {\displaystyle X}
Generalized functional linear model
Generalized_functional_linear_model
Set of statistical processes for estimating the relationships among variables
regression, regression in which the predictor variables are measured with error, regression with more predictor variables than observations, and causal
Regression_analysis
Type of statistical model
the Level 2 predictor. γ 01 {\displaystyle \gamma _{01}} and γ 11 {\displaystyle \gamma _{11}} refer to the effect of the Level 2 predictor on the Level
Multilevel_model
Linear optimal control technique
dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the
Linear–quadratic_regulator
Family of functions to transform data
technique used to assess and correct non-linearity between predictor variables and the logit in a generalized linear model, particularly in logistic regression
Power_transform
Approximation method in statistics
least squares, depending on whether or not the model functions are linear in all unknowns. The linear least-squares problem occurs in statistical regression
Least_squares
Flaw in mathematical modelling
training data for y can be adequately predicted by a linear function of two independent variables. Such a function requires only three parameters (the intercept
Overfitting
Statistics models class
is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some predictor variables, and interest
Generalized_additive_model
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) gives the relative merit of various statistical models for describing a data set. Often the
Likelihood_function
Mathematical relation assigning a probability event to a cost
applied using linear regression theory, which is based on the quadratic loss function. The quadratic loss function is also used in linear-quadratic optimal
Loss_function
Indicator for how well data points fit a line or curve
rather a measure of how good a predictor might be constructed from the modeled values (by creating a revised predictor of the form α + βƒi). According
Coefficient_of_determination
Process of calculating the causal factors that produced a set of observations
the components of the unknown function but only in sub-unknowns that are the images of the unknown function by a linear operator. These approaches are
Inverse_problem
Method of machine learning
to update the best predictor for future data at each step, as opposed to batch learning techniques which generate the best predictor by learning on the
Online_machine_learning
Statistical modeling technique
estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median (or other
Quantile_regression
Method of statistical analysis
of y i {\displaystyle y_{i}} given a k × 1 {\displaystyle k\times 1} predictor vector x i {\displaystyle \mathbf {x} _{i}} : y i = x i T β + ε i , {\displaystyle
Bayesian_linear_regression
Type of feedforward neural network
with nonlinear activation functions, organized in layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks
Multilayer_perceptron
Statistical estimation technique
the predictor values are placed in the design matrix,𝐗≡(1x12x13⋯x1k1x22x23⋯x2k⋮⋮⋮⋱⋮1xn2xn3⋯xnk), where each row is a vector of the k predictor variables
Generalized_least_squares
Fundamental principle of physics
B) produces response (X + Y). A function F(x) that satisfies the superposition principle is called a linear function. Superposition can be defined by
Superposition_principle
Mathematical function conceived as a crude model
they may also take the form of other nonlinear functions, piecewise linear functions, or step functions. They are also often monotonically increasing,
Artificial_neuron
occurs if the predictor (or a linear combination of some subset of the predictors) is associated with only one outcome value when the predictor range is split
Separation_(statistics)
Concept in mathematical modeling, statistical modeling and experimental sciences
Depending on the context, an independent variable is sometimes called a "predictor variable", "regressor", "covariate", "manipulated variable", "explanatory
Dependent and independent variables
Dependent_and_independent_variables
Type of shift register in computing
linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function
Linear-feedback shift register
Linear-feedback_shift_register
Regression models accounting for possible errors in independent variables
}}_{x}} is a consistent estimator of the parameter required for a best linear predictor of y {\displaystyle y} given the observed x t {\displaystyle x_{t}}
Errors-in-variables_model
Method of data analysis
linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data are linearly
Principal_component_analysis
Type of differential equation
PDE is called linear if it is linear in the unknown and its derivatives. For example, for a function u of x and y, a second order linear PDE is of the
Partial_differential_equation
Topics referred to by the same term
interacting elements whose behavior is not expressible as a linear function of its inputs Non-linear transformation matrix, (n+1)×(n+1) array that can represent
Nonlinearity_(disambiguation)
Statistical model for count data
models are generalized linear models with the logarithm as the (canonical) link function, and the Poisson distribution function as the assumed probability
Poisson_regression
In regression analysis, an interval predictor model (IPM) is an approach to regression where bounds on the function to be approximated are obtained. This
Interval_predictor_model
Statistical measure in mathematical model
that predictor variable is 2.3 times larger than if that predictor variable had 0 correlation with the other predictor variables. vif function in the
Variance_inflation_factor
Smooth function in statistics
variance in their errors, at every predictor level. This assumption works well when the response variable and the predictor variable are jointly normal. As
Variance_function
Class of algorithms for pattern analysis
to get linear learning algorithms to learn a nonlinear function or decision boundary. For all 𝐱 and 𝐱′ in the input space 𝒳, certain functions k(𝐱,𝐱′)
Kernel_method
Statistical concept
correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between
Coefficient of multiple correlation
Coefficient_of_multiple_correlation
Measure of the error of an estimator
the standard error. The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random
Mean_squared_error
Sequence of data points over time
the autocorrelation function Hjorth parameters FFT parameters Autoregressive model parameters Mann–Kendall test Univariate non-linear measures Measures
Time_series
shape-flexible, has simple closed forms, and can be parameterized with data using linear least squares. The Marchenko–Pastur distribution is important in the theory
List of probability distributions
List_of_probability_distributions
Mathematical description of quantum state
advantages to understanding wave functions as representing elements of an abstract vector space: All the powerful tools of linear algebra can be used to manipulate
Wave_function
Statistical technique to aid interpretation of data
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to
Linear_trend_estimation
Algorithms for solving convex optimization problems
where f is a convex function and G is a convex set. Without loss of generality, we can assume that the objective f is a linear function. Usually, the convex
Interior-point_method
Statistical linear model
The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models
General_linear_model
Form of modelling that uses statistics to predict outcomes
(e.g. Linear regression). The usage of predictive modelling in business decision making is often referred to as predictive analytics. Predictive modelling
Predictive_modelling
quasi-linearization, which is the approximation of the non-linear system under investigation by a linear time-invariant (LTI) transfer function that depends
Describing_function
Method for model fitting in statistics
squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the
Weighted_least_squares
Regression analysis
_{1}x}{\beta _{2}+x}}} This function, which is a rectangular hyperbola, is nonlinear because it cannot be expressed as a linear combination of the two β
Nonlinear_regression
Type of regression analysis
conditional mean; Link function g connecting the conditional mean and the linear predictor through μ=g(η). Functional data analysis Functional principal component
Functional_regression
Statistical model used in time series analysis
the series depends linearly on its own past values (lags), while the MA component specifies that the current value depends on a linear combination of past
Autoregressive moving-average model
Autoregressive_moving-average_model
Concept in statistics
the relationship between a linear predictor and a parameter of the distribution. There are many commonly used link functions, and their choice can be somewhat
Vector generalized linear model
Vector_generalized_linear_model
Process of using data analysis for predicting population data from sample data
datasets are generated by 'simple' random sampling. The family of generalized linear models is a widely used and flexible class of parametric models. Non-parametric:
Statistical_inference
Concept in statistical analysis
corresponding predicted y-values of each data point. A bivariate correlation is a measure of whether and how two variables covary linearly, that is, whether
Bivariate_analysis
Measure of linear correlation
{\hat {Y}})^{2}} is the proportion of variance in Y explained by a linear function of X. In the derivation above, the fact that ∑ i ( Y i − Y ^ i ) (
Pearson correlation coefficient
Pearson_correlation_coefficient
Category of regression analysis
deterministic function. Linear regression is a restricted case of nonparametric regression where m ( x ) {\displaystyle m(x)} is assumed to be a linear function of
Nonparametric_regression
Non-linear regression method
in the context of link equation choice. If a power of a fitted mean/linear predictor is used as a covariate and it results in a better model than the same
Beta_regression
Machine learning paradigm
non-linearities. If each of the features makes an independent contribution to the output, then algorithms based on linear functions (e.g., linear regression
Supervised_learning
Mechanical property that measures stiffness of a solid material
a linear elastic material: ue(ε)=∫Eεdε=12Eε2, since the strain is defined ε≡ΔLL0. In a nonlinear elastic material the Young's modulus is a function of
Young's_modulus
Type of numerical analysis
constrained by any functional form, such as the linearity imposed by linear regression, as long as the function is monotonic increasing. Another application
Isotonic_regression
Linear dependency situation in a regression model
the collinearity of the predictor variables. Perfect multicollinearity refers to a situation where the predictors are linearly dependent (one can be written
Multicollinearity
Numerical measure of a statistical relationship between variables
coefficient is a numerical measure of some type of linear correlation, meaning a linear function between two variables. The variables may be two columns
Correlation_coefficient
Statement about a future event
A functional form, often linear, is hypothesized for the postulated causal relationship, and the parameters of the function are estimated from the data—that
Prediction
Diagnostic plot of binary classifier ability
Note that the output of a consistently bad predictor could simply be inverted to obtain a good predictor. Consider four prediction results from 100 positive
Receiver operating characteristic
Receiver_operating_characteristic
Measure for evaluating probabilistic forecasts
the expected score if the "correct" distributions are predicted. In the same way, scoring functions answer the question "how good is a point prediction
Scoring_rule
Statistical estimation method
is the linear probability model, which models the probability itself as a linear function of the explanatory variables. A drawback of the linear probability
Binary_regression
Type of artificial neural network
basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination
Radial_basis_function_network
Narrowband analog-to-digital conversion
sampling instant is predicted according to a linear function of the past values of the quantized signals. APC is related to linear predictive coding (LPC) in
Adaptive_predictive_coding
Application of a function to each point in a data set
transformations of both X (the predictor variables) and Y, such that the homoscedasticity assumption (in addition to the linearity assumption) holds true on
Data transformation (statistics)
Data_transformation_(statistics)
Approximation method in statistics
a function of constants, the independent variable and the parameters, so it changes from one iteration to the next. Thus, in terms of the linearized model
Non-linear_least_squares
Non-parametric regression technique
produced a kink in the predicted y to take into account non-linearity. The kink is produced by hinge functions. The hinge functions are the expressions starting
Multivariate adaptive regression spline
Multivariate_adaptive_regression_spline
Method of estimating the parameters of a statistical model, given observations
conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes
Maximum_likelihood_estimation
Statistical measure of fit
as a measure for goodness of fit and when a likelihood function is used to fit a model. In linear regression, the squared multiple correlation, R2 is used
Pseudo-R-squared
Set of methods for supervised statistical learning
not clear that SVMs have better predictive performance than other linear models, such as logistic regression and linear regression. Classifying data is
Support_vector_machine
Inferential psychometric model
probability of response is related to a linear combination of predictors by means of a sigmoid link function (e.g. probit, logit, etc.). Depending on
Psychometric_function
Statistical principle
sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion
Sufficient_statistic
Study of mathematical algorithms for optimization problems
of linear or convex quadratic programming. Linear programming (LP), a type of convex programming, studies the case in which the objective function f is
Mathematical_optimization
Model in digital signal processing
using a conventional DAC and some linear analog circuitry, to reconstruct the piecewise linear output for either predictive or delayed FOH. Even though this
First-order_hold
Statistical model validation technique
missed a critical predictor and/or included a confounded predictor. New evidence is that cross-validation by itself is not very predictive of external validity
Cross-validation_(statistics)
Statistical method
the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space
Partial least squares regression
Partial_least_squares_regression
Speech coding algorithm
Code-excited linear prediction (CELP) is a linear predictive speech coding algorithm originally proposed by Manfred R. Schroeder and Bishnu S. Atal in
Code-excited linear prediction
Code-excited_linear_prediction
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LINEAR PREDICTOR-FUNCTION
LINEAR PREDICTOR-FUNCTION
LINEAR PREDICTOR-FUNCTION
LINEAR PREDICTOR-FUNCTION
LINEAR PREDICTOR-FUNCTION
LINEAR PREDICTOR-FUNCTION
LINEAR PREDICTOR-FUNCTION
LINEAR PREDICTOR-FUNCTION
LINEAR PREDICTOR-FUNCTION
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