Generalized Linear Models

By Eric R. Ziegel. 2002

18,919 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges (2021, methodology): “Generalized additive models (GAMs) were introduced to present a flexible extension of generalized linear models (GLMs) (Nelder and Wedderburn, 1972), allowing for arbitrary functions for modeling the influence of each feature on a response (Hastie and Tibshirani 1990 see also Wood 2017).”
Differentially-Private "Draw and Discard" Machine Learning (2018, methodology): “In GLMs [40], the outcome or response variable Y is assumed to be generated from a particular distribution in the exponential family that includes normal (regular linear model), binomial (logistic regression) and Poisson (Poisson regression) distributions, among many others.”
Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “Generalized linear models (GLMs) [119] allow more flexibility in the response variable through the introduction of a link function.”
Predictive Multiplicity in Classification (2019, background): “Several works mention that prediction problems can exhibit multiplicity [see 34, 36], but only few discuss its practical implications, or provide concrete recommendations.”
Sparse Partially Linear Additive Models (2014, methodology): “Generalized partially linear additive models (GPLAMs) [1] provide an attractive middle ground between the simplicity of generalized linear models (GLMs) [2] and the flexibility of generalized additive models (GAMs) [3].”
How Powerful are Graph Neural Networks? (2018, methodology): “Nonetheless, many existing GNNs instead use a 1-layer perceptron σ (Nelder & Wedderburn, 1972).”
Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, background): “Let P = (Pw, w ∈ Υ ) be an exponential family with a canonical parametrization; see e.g. McCullagh and Nelder (1989).”
Kernel methods in machine learning (2007, neutral): “(71) This is a generalized linear model (GLM) (McCullagh and Nelder [97]) with a canonical link, that is, the canonical parameters depend linearly on the covariates Φ(x).”
From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification (2016, methodology): “The softmax transformation is a key component of several statistical learning models, encompassing multinomial logistic regression (McCullagh & Nelder, 1989), action selection in reinforcement learning (Sutton & Barto, 1998), and neural networks for multi-class classification (Bridle, 1990;…”
An Online Learning Approach to Generative Adversarial Networks (2017, methodology): “…the sigmoid activation function, but it also holds for other choices of activation, e.g. cumulative gaussian distribution, i.e. Note that the logarithm of h v ( x ) for the sigmoid and cumulative gaussian activations correspond to the well known logit and probit models, McCullagh and Nelder (1989).”
Deep Exponential Families (2014, positive): “Similar to the literature on generalized linear models [26], we call it the link function.”
The functional linear array model (2015, methodology): “Examples for exponential family distributions used for generalized linear models (GLMs) include binomial, Poisson, log-normal and Gamma distributions (Nelder and Wedderburn, 1972).”
The Eﬀects of Data Quality on Machine Learning Performance (2022, methodology): “We included two linear classiﬁcation models: Logistic regression (LogR) [46] and support vector machine (SVM) [16]; a tree-based model: Decision tree (DT) [11]; a k-nearest neighbors (KNN) classiﬁer [3]; and ﬁnally a neural network-based multi-layer perceptron (MLP) [68].”
Double logistic curve in regression modeling (2010, methodology): “Introduction Logistic sigmoid functions are widely used in applied research for nonlinear regressions, neural networking, binary response, and multiple choice modeling [2,7,18,19,22,24,27].”
Modelling and predicting fungal distribution patterns using herbarium data (2008, methodology): “With binary presence/absence data, generalized linear models (GLM) with binomial distribution and logistic link (logistic regression) are commonly used (McCullagh & Nelder, 1989; Meyer et al., 2002; Venables & Ripley, 2002; Crawley, 2005).”
Measuring the relative effect of factors affecting species distribution model predictions (2014, methodology): “…simulate virtual species distributions (see Miller 2014): proposed approaches include simulating from a model (e.g. a generalized linear model, GLM; McCullagh & Nelder 1989) fitted to real data (as in Wisz & Guisan 2009; Albert et al. 2010), defining theoretical response functions (e.g. Hirzel…”