Related papers: Robust and Sparse Regression in GLM by Stochastic …
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…
We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line…
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…
Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…
Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…
We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use…
High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
As datasets grow larger, they are often distributed across multiple machines that compute in parallel and communicate with a central machine through short messages. In this paper, we focus on sparse regression and propose a new procedure…
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…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…