Related papers: Optimal Approximate Sampling from Discrete Probabi…
Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as…
Given a linear dynamical system, we consider the problem of constructing an approximate system using only a subset of the sensors out of the total set such that the observability Gramian of the new system is approximately equal to that of…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…
We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
In this note, we develop a novel algorithm for generating random numbers from a distribution with a probability density function proportional to $\sin^k(x)$, $x \in (0,\pi)$ and $k \geq 1$. Our algorithm is highly efficient and is based on…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\mathcal{H} = \{H_1, \ldots, H_n\}$, and samples from an unknown distribution $P$, both over a domain…
We show a connection between sampling and optimization on discrete domains. For a family of distributions $\mu$ defined on size $k$ subsets of a ground set of elements that is closed under external fields, we show that rapid mixing of…
To efficiently evaluate system reliability based on Monte Carlo simulation, importance sampling is used widely. The optimal importance sampling density was derived in 1950s for the deterministic simulation model, which maps an input to an…
In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…
Hypothesis Selection is a fundamental distribution learning problem where given a comparator-class $Q=\{q_1,\ldots, q_n\}$ of distributions, and a sampling access to an unknown target distribution $p$, the goal is to output a distribution…
We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…