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Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs) is a fundamental yet computationally challenging problem arising in domains such as diagnosis, planning, and structured prediction. In many practical…

The early solution path, which tracks the first few variables that enter the model of a selection procedure, is of profound importance to scientific discoveries. In practice, it is often statistically hopeless to identify all the important…

We present a novel sparsity-based space-time adaptive processing (STAP) technique based on the alternating direction method to overcome the severe performance degradation caused by array gain/phase (GP) errors. The proposed algorithm…

Many statistical methods require solutions to optimization problems. When the global solution is hard to attain, statisticians always use the better if there are two solutions for chosen, where the word "better" is understood in the sense…

The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…

The paradigm of worst-group loss minimization has shown its promise in avoiding to learn spurious correlations, but requires costly additional supervision on spurious attributes. To resolve this, recent works focus on developing weaker…

There has been a rise in the popularity of algebraic methods for graph algorithms given the development of the GraphBLAS library and other sparse matrix methods. An exemplar for these approaches is Breadth-First Search (BFS). The algebraic…

Neural architecture search (NAS) recently attracts much research attention because of its ability to identify better architectures than handcrafted ones. However, many NAS methods, which optimize the search process in a discrete search…

Machine learning and artificial intelligence algorithms typically require large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden…

We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because the best existing exact algorithm becomes numerically unstable for sample sizes…

This work presents the convergence rate analysis of stochastic variants of the broad class of direct-search methods of directional type. It introduces an algorithm designed to optimize differentiable objective functions $f$ whose values can…

Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…

While experimental design often focuses on selecting the single best alternative from a finite set (e.g., in ranking and selection or best-arm identification), many pure-exploration problems pursue richer goals. Given a specific goal,…

Learning causal structure from observational data is especially challenging when latent variables or selection bias are present. The Fast Causal Inference (FCI) algorithm addresses this setting but performs exhaustive conditional…

The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…

Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…

SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an…

Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…

Recently Neural Architecture Search (NAS) has aroused great interest in both academia and industry, however it remains challenging because of its huge and non-continuous search space. Instead of applying evolutionary algorithm or…

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…