Related papers: Statistical Inference using the Morse-Smale Comple…

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…

Covariance estimation is essential yet underdeveloped for analyzing multivariate functional data. We propose a fast covariance estimation method for multivariate sparse functional data using bivariate penalized splines. The tensor-product…

Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts,…

Motivated by applications in geomorphology, the aim of this paper is to extend Morse-Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3-dimensional…

We introduce a probabilistic framework for two-sample comparison based on a nonparametric process taking the form of a Markov model that transitions between a "divide" and a "merge" state on a multi-resolution partition tree of the sample…

A class of evolution equations with nonlocal diffusion is considered in this work. These are integro-differential equations arising as models of propagation phenomena in continuum media with nonlocal interactions including neural tissue,…

In this paper, we develop a method for unsupervised clustering of two-way (matrix) data by combining two recent innovations from different fields: the Sparse Subspace Clustering (SSC) algorithm [10], which groups points coming from a union…

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…

Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…

Subsampling is a widely used and effective approach for addressing the computational challenges posed by massive datasets. Substantial progress has been made in developing non-uniform, probability-based subsampling schemes that prioritize…

Many signal and image processing applications have benefited remarkably from the fact that the underlying signals reside in a low dimensional subspace. One of the main models for such a low dimensionality is the sparsity one. Within this…

This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…

This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…

This study proposes a low-complexity interpretable classification system. The proposed system contains three main modules including feature extraction, feature reduction, and classification. All of them are linear. Thanks to the linear…

A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…

We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…

The comparison of subnational areas is ubiquitous but survey samples of these areas are often biased or prohibitively small. Researchers turn to methods such as multilevel regression and poststratification (MRP) to improve the efficiency of…

Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit models to making only one attempt at a problem. Here, we explore inference compute…

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the…