Related papers: Logistic regression geometry
Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors $X_1,\ldots, X_p$ (for example: $Y = 1$ if the outcome occurred and $Y = 0$…
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…
The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Convergence bounds are one of the main tools to obtain information on the performance of a distributed machine learning task, before running the task itself. In this work, we perform a set of experiments to assess to which extent, and in…
Spin glass models, such as the Sherrington-Kirkpatrick, Hopfield and Ising models, are all well-studied members of the exponential family of discrete distributions, and have been influential in a number of application domains where they are…
Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…
Psychiatric neuroscience is increasingly aware of the need to define psychopathology in terms of abnormal neural computation. The central tool in this endeavour is the fitting of computational models to behavioural data. The most prominent…
We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory,…
Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…
In observational studies, researchers must select a method to control for confounding. Options include propensity score methods and regression. It remains unclear how dataset characteristics (size, overlap in propensity scores, exposure…
In the well known logistic map, the parameter of interest is weighted by a coefficient that decreases linearly when this parameter increases. Since such a linear decrease forms a specific case, we consider the more general case where this…
In this work, we introduce a modified (rescaled) likelihood for imbalanced logistic regression. This new approach makes easier the use of exponential priors and the computation of lasso regularization path. Precisely, we study a limiting…
Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…
Naive maximum likelihood estimation of binary logit models with fixed effects leads to unreliable inference due to the incidental parameter problem. We study the case of three-dimensional panel data, where the model includes three sets of…
The slope coefficient in a rank-rank regression is a popular measure of intergenerational mobility. In this article, we first show that commonly used inference methods for this slope parameter are invalid. Second, when the underlying…
This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…
We propose a generalisation of the logistic regression model, that aims to account for non-linear main effects and complex interactions, while keeping the model inherently explainable. This is obtained by starting with log-odds that are…
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…
Random-effects models are frequently used to synthesise information from different studies in meta-analysis. While likelihood-based inference is attractive both in terms of limiting properties and of implementation, its application in…