Related papers: Complexity Analysis of Normalizing Constant Estima…
Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma Z_i$ and $Y_i$ and $Z_i$ are independent. Assume that unobservable $Y$'s are distributed as a random variable $UV,$ where $U$ and $V$ are independent, $U$ has a Bernoulli…
The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples from more than one probability…
Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sam- pling in the framework of diffusion process and consider the change…
The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $\mathbb{P}(\sum_{i=1}^{N}{X_i} \leq \gamma)$, via importance sampling (IS). We…
Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…
Assume that we would like to estimate the expected value of a function $F$ with respect to an intractable density $\pi$, which is specified up to some unknown normalising constant. We prove that if $\pi$ is close enough under KL divergence…
Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in…
We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which is an adaptive importance technique useful to sample multimodal target distributions. The importance function is based on the weights (namely the…
The Metropolis-Hastings algorithm allows one to sample asymptotically from any probability distribution $\pi$. There has been recently much work devoted to the development of variants of the MH update which can handle scenarios where such…
We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of integration is…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete…
The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density $\pi$, when we are only able to estimate an unnormalized version of $\pi$…
Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
We present a method to obtain the average and the typical value of the number of critical points of the empirical risk landscape for generalized linear estimation problems and variants. This represents a substantial extension of previous…
We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…
This work studies certain notions of entropy that can be associated to (i) a representation of a separable, unital C*-algebra $\mathfrak{A}$ and (ii) an auxiliary random sequence $(\pi_n)_{n\ge 1}$ of finite-dimensional representations of…
In this paper we refine the procedure proposed by Lin et al. (2015) to estimate the density at a given quantile based on a resampling method. The approach consists on generating multiple samples of the zero-mean Gaussian variable from which…