Related papers: Posterior contraction in group sparse logit models…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
This article focuses on inference in logistic regression for high-dimensional binary outcomes. A popular approach induces dependence across the outcomes by including latent factors in the linear predictor. Bayesian approaches are useful for…
We analyze the posterior contraction rates of parameters in Bayesian models via the Langevin diffusion process, in particular by controlling moments of the stochastic process and taking limits. Analogous to the non-asymptotic analysis of…
In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…
Bayesian model selection, with precedents in George and McCulloch (1993) and Abramovich et al. (1998), support credibility measures that relate model uncertainty, but computation can be costly when sparse priors are approximate. We design…
Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize…
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…
Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…
We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either…
This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical…
In this paper, we propose a general framework for combining evidence of varying quality to estimate underlying binary latent variables in the presence of restrictions imposed to respect the scientific context. The resulting algorithms…
Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are…
We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically…
We present two sets of theoretical results on the grouped lasso with overlap of Jacob, Obozinski and Vert (2009) in the linear regression setting. This method allows for joint selection of predictors in sparse regression, allowing for…
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.…
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…
We study the posterior contraction behavior of the latent population structure that arises in admixture models as the amount of data increases. We adopt the geometric view of admixture models - alternatively known as topic models - as a…
We study frequentist properties of Bayesian and $L_0$ model selection, with a focus on (potentially non-linear) high-dimensional regression. We propose a construction to study how posterior probabilities and normalized $L_0$ criteria…