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We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the…
We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…
In this study, we evaluated the performance of the state-of-the-art sequence tagging grammar error detection and correction model (SeqTagger) using Japanese university students' writing samples. With an automatic annotation toolkit, ERRANT,…
Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…
Large Language Models (LLMs) show promise in code generation tasks. However, their code-writing abilities are often limited in scope: while they can successfully implement simple functions, they struggle with more complex tasks. A…
Many different metrics exist for evaluating parsing results, including Viterbi, Crossing Brackets Rate, Zero Crossing Brackets Rate, and several others. However, most parsing algorithms, including the Viterbi algorithm, attempt to optimize…
We revisit the problem of \textit{online linear optimization} in case the set of feasible actions is accessible through an approximated linear optimization oracle with a factor $\alpha$ multiplicative approximation guarantee. This setting…
Sparse dictionary learning (SDL) is a fundamental technique that is useful for many image processing tasks. As an example we consider here image recovery, where SDL can be cast as a nonsmooth optimization problem. For this kind of problems,…
We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + \lambda xx^\top$ with $W$ drawn from…
Speech applications dealing with conversations require not only recognizing the spoken words but also determining who spoke when. The task of assigning words to speakers is typically addressed by merging the outputs of two separate systems,…
Automatic prompt engineering aims to enhance the generation quality of large language models (LLMs). Recent works utilize feedbacks generated from erroneous cases to guide the prompt optimization. During inference, they may further retrieve…
Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…
We study dynamic regret minimization in unconstrained adversarial linear bandit problems. In this setting, a learner must minimize the cumulative loss relative to an arbitrary sequence of comparators…
Large language models (LLMs) augmented with retrieval exhibit robust performance and extensive versatility by incorporating external contexts. However, the input length grows linearly in the number of retrieved documents, causing a dramatic…
This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact…
Spaced repetition systems are fundamental to efficient learning and memory retention, but existing algorithms often struggle with semantic interference and personalized adaptation. We present LECTOR (\textbf{L}LM-\textbf{E}nhanced…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
We present a fast and effective framework for analysing and designing syndrome-extraction circuits (SECs). Our approach is based on left-right circuits, a general design for SECs which maintain low depth by staggering $X$ and $Z$ checks…