Related papers: Extending Sheldon M. Ross's Method for Efficient L…
Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…
We study the problem of minimizing the average of a large number of smooth convex functions penalized with a strongly convex regularizer. We propose and analyze a novel primal-dual method (Quartz) which at every iteration samples and…
We introduce a new algorithm, extended regularized dual averaging (XRDA), for solving regularized stochastic optimization problems, which generalizes the regularized dual averaging (RDA) method. The main novelty of the method is that it…
Large Language Model or LLM inference has two phases, the prompt (or prefill) phase to output the first token and the extension (or decoding) phase to the generate subsequent tokens. In this work, we propose an efficient parallelization…
Anderson acceleration (AA) is a well-known method for accelerating the convergence of iterative algorithms, with applications in various fields including deep learning and optimization. Despite its popularity in these areas, the…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
Speculative data-parallel algorithms for language recognition have been widely experimented for various types of finite-state automata (FA), deterministic (DFA) and nondeterministic (NFA), often derived from regular expressions (RE). Such…
We consider the problem of correctly identifying the \textit{mode} of a discrete distribution $\mathcal{P}$ with sufficiently high probability by observing a sequence of i.i.d. samples drawn from $\mathcal{P}$. This problem reduces to the…
Covariate shift has been shown to sharply degrade both predictive accuracy and the calibration of uncertainty estimates for deep learning models. This is worrying, because covariate shift is prevalent in a wide range of real world…
Prior authorization (PA) requires interpretation of complex and fragmented coverage policies, yet existing retrieval-augmented systems rely on static top-$K$ strategies with fixed numbers of retrieved sections. Such fixed retrieval can be…
The progressive hedging algorithm (PHA) is a cornerstone among algorithms for large-scale stochastic programming problems. However, its traditional implementation is hindered by some limitations, including the requirement to solve all…
We present an easily implemented, fast, and accurate method for approximating extreme quantiles of compound loss distributions (frequency+severity) as are commonly used in insurance and operational risk capital models. The Interpolated…
Retrieval-Augmented Generation (RAG) improves model output accuracy by leveraging external knowledge bases, serving as an effective solution to address hallucination issues and knowledge-update delays in Large Language Models (LLMs).…
We propose PESA, a novel approach combining Particle Swarm Optimisation (PSO), Evolution Strategy (ES), and Simulated Annealing (SA) in a hybrid Algorithm, inspired from reinforcement learning. PESA hybridizes the three algorithms by…
Large Language Models (LLMs) have made significant strides in natural language processing and generation, yet their ability to handle long-context input remains constrained by the quadratic complexity of attention computation and…
Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how…
In this article, we present a new Nested Cross Approximation (NNCA) for constructing H2 matrices. It differs from the existing NCAs~\cite{bebendorf2012constructing, zhao2019fast} in the technique of choosing pivots, a key part of the…
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…
We present fastrerandomize, an R package for fast, scalable rerandomization in experimental design. Rerandomization improves precision by discarding treatment assignments that fail a prespecified covariate-balance criterion, but existing…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…