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The linearized Bregman method is a method to calculate sparse solutions to systems of linear equations. We formulate this problem as a split feasibility problem, propose an algorithmic framework based on Bregman projections and prove a…

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…

Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual…

Inspired by biological vision systems, the over-complete local features with huge cardinality are increasingly used for face recognition during the last decades. Accordingly, feature selection has become more and more important and plays a…

Although extreme learning machine (ELM) has been successfully applied to a number of pattern recognition problems, it fails to pro-vide sufficient good results in hyperspectral image (HSI) classification due to two main drawbacks. The first…

With the prevalence of pre-training-fine-tuning paradigm, how to efficiently adapt the pre-trained model to the downstream tasks has been an intriguing issue. Parameter-Efficient Fine-Tuning (PEFT) methods have been proposed for low-cost…

Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…

With the rapid proliferation of Natural Language Processing (NLP), especially Large Language Models (LLMs), generating adversarial examples to jailbreak LLMs remains a key challenge for understanding model vulnerabilities and improving…

Representation learning is critical to the empirical and theoretical success of reinforcement learning. However, many existing methods are induced from model-learning aspects, misaligning them with the RL task in hand. This work introduces…

Structured output prediction is an important machine learning problem both in theory and practice, and the max-margin Markov network (\mcn) is an effective approach. All state-of-the-art algorithms for optimizing \mcn\ objectives take at…

Effective features can improve the performance of a model, which can thus help us understand the characteristics and underlying structure of complex data. Previous feature selection methods usually cannot keep more local structure…

We introduce a dynamic sparse training algorithm based on linearized Bregman iterations / mirror descent that exploits the naturally incurred sparsity by alternating between periods of static and dynamic sparsity pattern updates. The key…

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…

The problem of automatic software generation is known as Machine Programming. In this work, we propose a framework based on genetic algorithms to solve this problem. Although genetic algorithms have been used successfully for many problems,…

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…

This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…

Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern…