arXiv research

Unified framework for sparse logistic regression with nonconvex regularization.

The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its application to high dimensional data still poses significant challenges. In this paper…

We introduce Graph-Sparse Logistic Regression, a new algorithm for classification for the case in which the support should be sparse but connected on a graph. We val- idate this algorithm against synthetic data and benchmark it against L1-regularized Logistic Regression. We then explore our technique in the bioinformat…

Improved VB algorithm for high-dimensional logistic regression with theoretical guarantees.

Safe screening rules reduce computation time in logistic regression with $\ell_0-\ell_2$ regularization.

Sparse multinomial logistic regression for multiclass classification with feature selection.

Multinomial Logistic Regression is a well-studied tool for classification and has been widely used in fields like image processing, computer vision and, bioinformatics, to name a few. Under a supervised classification scenario, a Multinomial Logistic Regression model learns a weight vector to differentiate between any …

Proposes efficient Bayesian logistic regression for large sparse datasets.

Flexible Bayesian approach for generalized linear models, especially for sparse logistic regression.

The paper examines logistic regression in sparse network settings, improving inference under varying degrees of dyadic dependence.

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\ell_1$ norm. For a cl…

Improved CRT for sparse logistic regression in high dimensions.

Optimal sketching bounds for sparse linear regression under various loss functions are established.

We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic bounds for the resulting misclassification excess risk. The bounds can be reduc…

A neural network solves logistic regression with $\ell_1$ regularization efficiently.

$L_1$ 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 too many features and that so-called false positives are unavoidable. In this pape…

The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic regression problem. In this way, many insights and optimization procedures for sparse logistic…

New algorithm learns sparse GLMs for binary outcomes efficiently.

Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic regression are well understood. Recently, Sur and Candes have studied logistic regre…

New weighted Lasso estimates improve logistic regression performance with measurement error.

Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is the LASSO problem, where the l1 norm regularizes a quadratic function. A multil…

Multi-task learning has shown to significantly enhance the performance of multiple related learning tasks in a variety of situations. We present the fused logistic regression, a sparse multi-task learning approach for binary classification. Specifically, we introduce sparsity inducing penalties over parameter differenc…

New method for multiclass classification reduces error bounds.

Fast classification for sparse models, even with correlated features.

New algorithm solves $\ell_0$-norm constrained multilinear logistic regression for tensor data.

A new method for Bayesian neural networks using probabilistic backpropagation.

New algorithm recovers sparse binary vectors from generalized linear measurements efficiently.

Picasso is a new library for sparse learning problems in R and Python.

Logistic regression models with $n$ observations and $q$ linearly-independent covariates are shown to have Fisher information volumes which are bounded below by $π^q$ and above by ${n \choose q} π^q$. This is proved with a novel generalization of the classical theorems of Pythagoras and de Gua, which is of independent …

For the problem of multi-class linear classification and feature selection, we propose approximate message passing approaches to sparse multinomial logistic regression (MLR). First, we propose two algorithms based on the Hybrid Generalized Approximate Message Passing (HyGAMP) framework: one finds the maximum a posterio…

ACOWA improves distributed sparse classification with extra communication round.

Improved Frank-Wolfe algorithm speeds up training of differentially private LASSO models.

A fast method for Lasso and Logistic Lasso problems.

We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms $x_i$ and up to $p^2$ quadratic terms $x_i x_j$. Quadratic terms enable prediction/modeling of higher-order effects between features and the target, but when incorporated naively may involve solvi…

We propose a combined model, which integrates the latent factor model and the logistic regression model, for the citation network. It is noticed that neither a latent factor model nor a logistic regression model alone is sufficient to capture the structure of the data. The proposed model has a latent (i.e., factor anal…

We present a method for training multi-label, massively multi-class image classification models, that is faster and more accurate than supervision via a sigmoid cross-entropy loss (logistic regression). Our method consists in embedding high-dimensional sparse labels onto a lower-dimensional dense sphere of unit-normed …

Developed efficient distributed logistic regression for large datasets.

New method uses nuclear and ℓ1 penalties for matrix regression, improving brain disorder detection.

In this paper, we present a differential privacy version of convex and nonconvex sparse classification approach. Based on alternating direction method of multiplier (ADMM) algorithm, we transform the solving of sparse problem into the multistep iteration process. Then we add exponential noise to stable steps to achieve…

The generalized linear model (GLM) plays a key role in regression analyses. In high-dimensional data, the sparse GLM has been used but it is not robust against outliers. Recently, the robust methods have been proposed for the specific example of the sparse GLM. Among them, we focus on the robust and sparse linear regre…

In this paper, we study the information-theoretic limits of learning the structure of Bayesian networks (BNs), on discrete as well as continuous random variables, from a finite number of samples. We show that the minimum number of samples required by any procedure to recover the correct structure grows as $Ω(m)$ and $Ω…

Proposes a convex model for mixed logit to handle individual heterogeneity.

Rotation invariant algorithms fail with hard labels sampled from sparse targets.

The paper forecasts corporate distress using a novel MIDAS logistic regression method.

We study the problem of estimating high dimensional models with underlying sparse structures while preserving the privacy of each training example. We develop a differentially private high-dimensional sparse learning framework using the idea of knowledge transfer. More specifically, we propose to distill the knowledge …

Model predicts higher education dropout risk with interpretable parameters.

Paper finds a lower bound for estimating low-rank matrices in logistic regression.

Hybrid machine learning improves gallstone risk prediction.