Related papers: Multiclass classification by sparse multinomial lo…
While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification has remained open. The appropriate complexity parameter…
Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…
An important problem in the analysis of high-dimensional omics data is to identify subsets of molecular variables that are associated with a phenotype of interest. This requires addressing the challenges of high dimensionality, strong…
We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is…
We consider the problem of multi-class classification and a stochastic opti- mization approach to it. We derive risk bounds for stochastic mirror descent algorithm and provide examples of set geometries that make the use of the algorithm…
We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$…
We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…
Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing,…
Latent class models are widely used for identifying unobserved subgroups from multivariate categorical data in social sciences, with binary data as a particularly popular example. However, accurately recovering individual latent class…
In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the…
Variable selection is an old and pervasive problem in regression analysis. One solution is to impose a lasso penalty to shrink parameter estimates toward zero and perform continuous model selection. The lasso-penalized mixture of linear…
It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications…
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…
High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands…
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…
Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric. Traditional approaches to model-based clustering often fail for high dimensional data, e.g., due to…
This paper addresses the challenge of forecasting corporate distress, a problem marked by three key statistical hurdles: (i) right censoring, (ii) high-dimensional predictors, and (iii) mixed-frequency data. To overcome these complexities,…
Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…