Related papers: Approximation algorithms for the normalizing const…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
We study algorithmic applications of a natural discretization for the hard-sphere model and the Widom-Rowlinson model in a region $\mathbb{V}\subset\mathbb{R}^d$. These models are used in statistical physics to describe mixtures of one or…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we introduce a notion of approximate majorization. For any distribution, and given a distance $\delta$,…
Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
We obtain some approximation results for the weights appearing in the exchangeable partition probability function identifying Gibbs partition models of parameter $\alpha \in (0,1)$, as introduced in Gnedin and Pitman (2006). We rely on…
Computing the partition function, $Z$, of an Ising model over a graph of $N$ \enquote{spins} is most likely exponential in $N$. Efficient variational methods, such as Belief Propagation (BP) and Tree Re-Weighted (TRW) algorithms, compute…
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…
We introduce and study the computational problem of determining statistical similarity between probability distributions. For distributions $P$ and $Q$ over a finite sample space, their statistical similarity is defined as…
This paper proposes an efficient numerical integration formula to compute the normalizing constant of Fisher--Bingham distributions. This formula uses a numerical integration formula with the continuous Euler transform to a Fourier-type…
We obtain order-exact estimates for uniform approximations by using Zygmund sums $Z^{s}_{n}$ of classes $C^{\psi}_{\beta,p}$ of $2\pi$-periodic continuous functions $f$ representable by convolutions of functions from unit balls of the space…
This work describes a method of approximating matrix permanents efficiently using belief propagation. We formulate a probability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this…
We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
In this short note we study uniform approximations to the normal distributions by Jacobi theta functions. We shall show that scaled theta functions approach to a normal distribution exponentially fast.
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…