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This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
In this paper we present a technique for using the bootstrap to estimate the operating characteristics and their variability for certain types of ensemble methods. Bootstrapping a model can require a huge amount of work if the training data…
This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…
Quantifying the complexity and irregularity of time series data is a primary pursuit across various data-scientific disciplines. Sample entropy (SampEn) is a widely adopted metric for this purpose, but its reliability is sensitive to the…
The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a test-piece. Various methods…
This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…
The problem of estimating a high-dimensional sparse vector $\boldsymbol{\theta} \in \mathbb{R}^n$ from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features,…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
The standard empirical risk minimization (ERM) can underperform on certain minority groups (i.e., waterbirds in lands or landbirds in water) due to the spurious correlation between the input and its label. Several studies have improved the…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
Classification is one of the main applications of supervised learning. Recent advancement in developing quantum computers has opened a new possibility for machine learning on such machines. Due to the noisy performance of near-term quantum…
A greedy algorithm called Bayesian multiple matching pursuit (BMMP) is proposed to estimate a sparse signal vector and its support given $m$ linear measurements. Unlike the maximum a posteriori (MAP) support detection, which was proposed by…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Large language models (LLMs) have demonstrated remarkable capabilities in generating programs from natural language descriptions, yet ensuring their correctness without an external oracle remains a critical challenge. To solve the…
Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…
Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from…
Reliable detection and quantification of quantum entanglement, particularly in high-spin or many-body systems, present significant computational challenges for traditional methods. This study examines the effectiveness of ensemble machine…
Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do…