Related papers: Probabilistic analysis of arithmetic coding showin…
Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each…
We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
We give an efficient algorithm for learning a binary function in a given class C of bounded VC dimension, with training data distributed according to P and test data according to Q, where P and Q may be arbitrary distributions over X. This…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected…
We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has $k$ data packets to broadcast, and it suffices that a large fraction of the network…
We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
In classical statistics and distribution testing, it is often assumed that elements can be sampled from some distribution $P$, and that when an element $x$ is sampled, the probability $P$ of sampling $x$ is also known. Recent work in…
In this paper, we study the problem of relaying a single bit of information across a series of binary symmetric channels, and the associated trade-off between the number of hops $m$, the transmission time $n$, and the error probability. We…
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…
We propose a new algorithm to compute numerically the distribution function of the sum of $d$ dependent, non-negative random variables with given joint distribution.
The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the…
We study the problem of robustly estimating the parameter $p$ of an Erd\H{o}s-R\'enyi random graph on $n$ nodes, where a $\gamma$ fraction of nodes may be adversarially corrupted. After showing the deficiencies of canonical estimators, we…
This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective…
We give an efficient algorithm to generate a graph from a distribution $\epsilon$-close to $G(n,p)$, in the sense of total variation distance. In particular, if $p$ is represented with $O(\log n)$-bit accuracy, then, with high probability,…
We describe a dynamic programming algorithm for computing the marginal distribution of discrete probabilistic programs. This algorithm takes a functional interpreter for an arbitrary probabilistic programming language and turns it into an…