Related papers: A Strong Direct Sum Theorem for Distributional Que…
The direct sampling method proposed by Walker et al. (JCGS 2011) can generate draws from weighted distributions possibly having intractable normalizing constants. The method may be of interest as a useful tool in situations which require…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
We prove a factorization theorem for heavy-to-light form factors. Our result differs in several important ways from previous proposals. A proper separation of scales gives hard kernels that are free of endpoint singularities. A general…
Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…
A precise estimation of the computational complexity in Shor's factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large scale feature selection problems. Identifying the knockoff distribution requires solving a large scale…
Consider the following Online Boolean Matrix-Vector Multiplication problem: We are given an $n\times n$ matrix $M$ and will receive $n$ column-vectors of size $n$, denoted by $v_1,\ldots,v_n$, one by one. After seeing each vector $v_i$, we…
In the last three decades, the $k$-SUM hypothesis has emerged as a satisfying explanation of long-standing time barriers for a variety of algorithmic problems. Yet to this day, the literature knows of only few proven consequences of a…
Marcinkiewicz strong law of large numbers, ${n^{-\frac1p}}\sum_{k=1}^{n} (d_{k}- d)\rightarrow 0\ $ almost surely with $p\in(1,2)$, are developed for products $d_k=\prod_{r=1}^s x_k^{(r)}$, where the $x_k^{(r)} =…
Jeffery's equation with diffusion is widely used to predict the motion of concentrated fiber suspensions in flows with low Reynold's numbers. Unfortunately, the evaluation of the fiber orientation distribution can require excessive…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method…
We initiate a systematic study of the computational complexity of property testing, focusing on the relationship between query and time complexity. While traditional work in property testing has emphasized query complexity, relatively…
This paper proposes a standard way to represent sparse tensors. A broad theoretical framework for tensor data scattering methods used in various deep learning frameworks is established. This paper presents a theorem that is very important…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
For zero-error function computation over directed acyclic networks, existing upper and lower bounds on the computation capacity are known to be loose. In this work we consider the problem of computing the arithmetic sum over a specific…
Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when…
In this paper we study QCD and power corrections to sum rules which show up in deep inelastic lepton-hadron scattering. Furthermore we will make a distinction between fundamental sum rules which can be derived from quantum field theory and…
The three standard products (the Cartesian, the direct and the strong product) of undirected graphs have been wellinvestigated, unique prime factor decomposition (PFD) are known and polynomial time algorithms have been established for…