Related papers: On nonnegative unbiased estimators
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation.…
We study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by Monte Carlo methods (and in particular Markov Chain Monte Carlo). We derive conditions on the step size and the Monte Carlo…
The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…
Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…
We study the problem of approximating an unknown function $f:\mathbb{R}\to\mathbb{R}$ by a degree-$d$ polynomial using as few function evaluations as possible, where error is measured with respect to a probability distribution $\mu$.…
Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…
We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no response $Y$. We do not make any sparsity assumptions on the vector of…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…
We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we…
Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to…
We propose a novel method for estimating nonseparable selection models. We show that, for a given selection function, the potential outcome distributions are nonparametrically identified from the selected outcome distributions and can be…
Models implicitly defined through a random simulator of a process have become widely used in scientific and industrial applications in recent years. However, simulation-based inference methods for such implicit models, like approximate…
Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically…
Computing partition functions, the normalizing constants of probability distributions, is often hard. Variants of importance sampling give unbiased estimates of a normalizer Z, however, unbiased estimates of the reciprocal 1/Z are harder to…
Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In…