Related papers: Self-concordant analysis for logistic regression

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

We develop an improvement to conditional logistic regression (CLR) in the setting where the parameter of interest is the additive effect of binary treatment effect on log-odds of the positive level in the binary response. Our improvement is…

We consider the problem of nonparametric estimation of a convex regression function $\phi_0$. We study the risk of the least squares estimator (LSE) under the natural squared error loss. We show that the risk is always bounded from above by…

The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

We study an $\ell_{1}$-regularized generalized least-squares (GLS) estimator for high-dimensional regressions with autocorrelated errors. Specifically, we consider the case where errors are assumed to follow an autoregressive process,…

We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…

Generalized linear regressions, such as logistic regressions or Poisson regressions, are long-studied regression analysis approaches, and their applications are widely employed in various classification problems. Our study considers a…

We study a family of sparse estimators defined as minimizers of some empirical Lipschitz loss function -- which include the hinge loss, the logistic loss and the quantile regression loss -- with a convex, sparse or group-sparse…

This paper revisits the special type of a neural network known under two names. In the statistics and machine learning community it is known as a multi-class logistic regression neural network. In the neural network community, it is simply…

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…

The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…

Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine…

A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under controlled circumstances. Now, linear regression models are commonly used to analyze observational…

We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing…

In this paper, we develop a new optimization framework for the least squares learning problem via fully connected neural networks or physics-informed neural networks. The gradient descent sometimes behaves inefficiently in deep learning…

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…

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…

We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and…

We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…