相关论文: Diamond Sampling for Approximate Maximum All-pairs…

We consider a class of optimization problems over stochastic variables where the algorithm can learn information about the value of any variable through a series of costly steps; we model this information acquisition process as a Markov…

Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…

We study coded distributed matrix multiplication from an approximate recovery viewpoint. We consider a system of $P$ computation nodes where each node stores $1/m$ of each multiplicand via linear encoding. Our main result shows that the…

Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both…

A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…

This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…

Motivated by comparative genomics, Chen et al. [9] introduced the Maximum Duo-preservation String Mapping (MDSM) problem in which we are given two strings $s_1$ and $s_2$ from the same alphabet and the goal is to find a mapping $\pi$…

This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…

In this paper, we study a sequential decision-making problem, called Adaptive Sampling for Discovery (ASD). Starting with a large unlabeled dataset, algorithms for ASD adaptively label the points with the goal to maximize the sum of…

We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting…

In this paper, we present a maximum likelihood estimation approach to determine the value vector in transformer models. We model the sequence of value vectors, key vectors, and the query vector as a sequence of Gaussian distributions. The…

Let $n_1,\dots,n_\ell,k_1,\dots,k_\ell$ be integers and let $V_1,\dots,V_\ell$ be disjoint sets with $|V_i|=n_i$ for $i=1,\dots,\ell$. Define $\sqcup_{i=1}^\ell \binom{V_i}{k_i}$ as the collection of all subsets $F$ of $\cup_{i=1}^\ell V_i$…

We consider the Demand Strip Packing problem (DSP), in which we are given a set of jobs, each specified by a processing time and a demand. The task is to schedule all jobs such that they are finished before some deadline $D$ while…

Comparing $K$-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we…

We propose an exact slice sampler for Hierarchical Dirichlet process (HDP) and its associated mixture models (Teh et al., 2006). Although there are existing MCMC algorithms for sampling from the HDP, a slice sampler has been missing from…

Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and…

We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…

Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…

We propose a coupled rejection-sampling method for sampling from couplings of arbitrary distributions. The method relies on accepting or rejecting coupled samples coming from dominating marginals. Contrary to existing acceptance-rejection…

Best-of-N (BoN) sampling, a common strategy for test-time scaling of Large Language Models (LLMs), relies on reward models to select the best candidate solution from multiple generations. However, traditional reward models often assign…