Related papers: Minimum Sample Size for Developing a Multivariable…
Clinical prediction models must be developed using sufficiently large datasets to minimise overfitting and ensure robust predictive performance. Existing sample size calculations assume complete predictor data for all included participants,…
We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…
We propose a new family of regression models for analyzing categorical responses, called multinomial link models. It consists of four classes, namely, mixed-link models that generalize existing multinomial logistic models and their…
Model selection is often performed by empirical risk minimization. The quality of selection in a given situation can be assessed by risk bounds, which require assumptions both on the margin and the tails of the losses used. Starting with…
Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…
The selection of essential variables in logistic regression is vital because of its extensive use in medical studies, finance, economics and related fields. In this paper, we explore four main typologies (test-based, penalty-based,…
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…
We investigate the complexity of logistic regression models which is defined by counting the number of indistinguishable distributions that the model can represent (Balasubramanian, 1997). We find that the complexity of logistic models with…
Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid…
Linear model prediction with a large number of potential predictors is both statistically and computationally challenging. The traditional approaches are largely based on shrinkage selection/estimation methods, which are applicable even…
Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…
We propose a penalized likelihood method to fit the bivariate categorical response regression model. Our method allows practitioners to estimate which predictors are irrelevant, which predictors only affect the marginal distributions of the…
We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration…
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted…
The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…
Predictive modelling is vital to guide preventive efforts. Whilst large-scale prospective cohort studies and a diverse toolkit of available machine learning (ML) algorithms have facilitated such survival task efforts, choosing the…
Given a sample of size $N$, it is often useful to select a subsample of smaller size $n<N$ to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the…
The logistic regression estimator is known to inflate the magnitude of its coefficients if the sample size $n$ is small, the dimension $p$ is (moderately) large or the signal-to-noise ratio $1/\sigma$ is large (probabilities of observing a…
The objective of many high-dimensional microarray and RNA-seq studies is to develop a classifier of cancer patients based on characteristics of their disease. The germinal center B-cell (GCB) classifier study in lymphoma and the National…
A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with…