Related papers: Understanding and mitigating difficulties in poste…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
While deep learning has demonstrated impressive progress, it remains a daunting challenge to learn from hard samples as these samples are usually noisy and intricate. These hard samples play a crucial role in the optimal performance of deep…
Recent research has focused on designing neural samplers that amortize the process of sampling from unnormalized densities. However, despite significant advancements, they still fall short of the state-of-the-art MCMC approach, Parallel…
We consider the problem of approximate Bayesian parameter inference in non-linear state-space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is one approach to approximate the…
We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in…
Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step…
In recent years, the shortcomings of Bayesian posteriors as inferential devices have received increased attention. A popular strategy for fixing them has been to instead target a Gibbs measure based on losses that connect a parameter of…
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
The generality and robustness of inference algorithms is critical to the success of widely used probabilistic programming languages such as Stan, PyMC, Pyro, and Turing.jl. When designing a new general-purpose inference algorithm, whether…
Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods…
Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…
Neural likelihood estimation methods for simulation-based inference can suffer from performance degradation when the modeled data is very high-dimensional or lies along a lower-dimensional manifold, which is due to the inability of the…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional…
We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…
Approximate Bayesian computation (ABC) methods can be used to sample from posterior distributions when the likelihood function is unavailable or intractable, as is often the case in biological systems. ABC methods suffer from inefficient…
We derive the optimal proposal density for Approximate Bayesian Computation (ABC) using Sequential Monte Carlo (SMC) (or Population Monte Carlo, PMC). The criterion for optimality is that the SMC/PMC-ABC sampler maximise the effective…
Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…
Encoding domain knowledge into the prior over the high-dimensional weight space of a neural network is challenging but essential in applications with limited data and weak signals. Two types of domain knowledge are commonly available in…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…