Related papers: Fast Witness Counting
Span programs are a model of computation that have been used to design quantum algorithms, mainly in the query model. For any decision problem, there exists a span program that leads to an algorithm with optimal quantum query complexity,…
Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a…
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as…
We propose a new fast word embedding technique using hash functions. The method is a derandomization of a new type of random projections: By disregarding the classic constraint used in designing random projections (i.e., preserving pairwise…
Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of \emph{feature selection} in which only a subset of the predictors $X_t$ are dependent on the…
The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…
The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
The transformer has revolutionized modern AI across language, vision, and beyond. It consists of $L$ layers, each running $H$ attention heads in parallel and feeding the combined output to the subsequent layer. In attention, the input…
Multidimensional packing problems generalize the classical packing problems such as Bin Packing, Multiprocessor Scheduling by allowing the jobs to be $d$-dimensional vectors. While the approximability of the scalar problems is well…
We present new, faster pseudopolynomial time algorithms for the $k$-Subset Sum problem, defined as follows: given a set $Z$ of $n$ positive integers and $k$ targets $t_1, \ldots, t_k$, determine whether there exist $k$ disjoint subsets…
We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to $k$-uniform CNF formulas where each variable appears at most $d$ times. For any $k$ and $d$ satisfying $kd<n^{o(1)}$ and $k\ge 20\log…
The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k…
Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
In this paper we advance the state-of-the-art for crowd counting in high density scenes by further exploring the idea of a fully convolutional crowd counting model introduced by (Zhang et al., 2016). Producing an accurate and robust crowd…
The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…