Related papers: Classification by sparse generalized additive mode…

Generalized additive models (GAMs) are a well-established statistical tool for modeling complex nonlinear relationships between covariates and a response assumed to have a conditional distribution in the exponential family. In this article,…

Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…

Sharpness-Aware Minimization (SAM) is a recent training method that relies on worst-case weight perturbations which significantly improves generalization in various settings. We argue that the existing justifications for the success of SAM…

The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…

We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random…

We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models. I-LAMM is a two-stage…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…

We propose a new model for supervised learning to rank. In our model, the relevance labels are assumed to follow a categorical distribution whose probabilities are constructed based on a scoring function. We optimize the training objective…

Support Vector Machines (SVM) with $\ell_1$ penalty became a standard tool in analysis of highdimensional classification problems with sparsity constraints in many applications including bioinformatics and signal processing. Although SVM…

In this paper, we propose an adaptive sieving (AS) strategy for solving general sparse machine learning models by effectively exploring the intrinsic sparsity of the solutions, wherein only a sequence of reduced problems with much smaller…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…

Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to obtain accurate classification performance when the feature distributions in the different classes are complex, with nonlinear,…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…

Given a training sample of size $m$ from a $d$-dimensional population, we wish to allocate a new observation $Z\in \R^d$ to this population or to the noise. We suppose that the difference between the distribution of the population and that…

We show that a new design criterion, i.e., the least squares on subband errors regularized by a weighted norm, can be used to generalize the proportionate-type normalized subband adaptive filtering (PtNSAF) framework. The new criterion…

Sparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model's performance, but they are…