Related papers: Supervised dimension reduction for ordinal predict…
We study the generalization performance of gradient methods in the fundamental stochastic convex optimization setting, focusing on its dimension dependence. First, for full-batch gradient descent (GD) we give a construction of a learning…
Linear discriminant analysis is a widely used method for classification. However, the high dimensionality of predictors combined with small sample sizes often results in large classification errors. To address this challenge, it is crucial…
This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of…
Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…
Sufficient dimension reduction reduces the dimensionality of data while preserving relevant regression information. In this article, we develop Minimum Average Deviance Estimation (MADE) methodology for sufficient dimension reduction. It…
A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the…
In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…
In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme…
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a…
In high-dimensional prediction problems, where the number of features may greatly exceed the number of training instances, fully Bayesian approach with a sparsifying prior is known to produce good results but is computationally challenging.…
Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…
In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…
High-dimensional count data poses significant challenges for statistical analysis, necessitating effective methods that also preserve explainability. We focus on a low rank constrained variant of the Poisson log-normal model, which relates…
In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…
We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…
For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…