Related papers: Extracting Weighted Automata for Approximate Minim…
In this paper we introduce a new type of approximate state reductions where the behaviors of the reduced and the original automaton do not have to be identical, but they must match on all words of length less than or equal to some given…
The rank minimization problem is to find the lowest-rank matrix in a given set. Nuclear norm minimization has been proposed as an convex relaxation of rank minimization. Recht, Fazel, and Parrilo have shown that nuclear norm minimization…
We present a novel approach for black-box VI that bypasses the difficulties of stochastic gradient ascent, including the task of selecting step-sizes. Our approach involves using a sequence of sample average approximation (SAA) problems.…
Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling…
We describe an algorithm for sampling a low-rank random matrix $Q$ that best approximates a fixed target matrix $P\in\mathbb{C}^{n\times m}$ in the following sense: $Q$ is unbiased, i.e., $\mathbb{E}[Q] = P$; $\mathsf{rank}(Q)\leq r$; and…
Arbitrary-shaped text detection is an important and challenging task in computer vision. Most existing methods require heavy data labeling efforts to produce polygon-level text region labels for supervised training. In order to reduce the…
Training or finetuning large-scale language models (LLMs) such as GPT-3 requires substantial computation resources, motivating recent efforts to explore parameter-efficient adaptation to downstream tasks. One practical area of research is…
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…
We provide a minimax optimal estimation procedure for F and W in matrix valued linear models Y = F W + Z where the parameter matrix W and the design matrix F are unknown but the latter takes values in a known finite set. The proposed finite…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset…
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…
Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a…
Consider the finite regular language L_n = {w0 : w \in {0,1}^*, |w| \le n}. It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum…
Matrix low rank approximation including the classical PCA and the robust PCA (RPCA) method have been applied to solve the background modeling problem in video analysis. Recently, it has been demonstrated that a special weighted low rank…
In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…
Large language models have demonstrated remarkable performance; however, their massive parameter counts make deployment highly expensive. Low-rank approximation offers a promising compression solution, yet existing approaches have two main…
Automatic Speech Assessment (ASA) has seen notable advancements with the utilization of self-supervised features (SSL) in recent research. However, a key challenge in ASA lies in the imbalanced distribution of data, particularly evident in…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…