Related papers: Normalizing Constant Estimation with Gaussianized …
Normalizing flows (NFs) provide uncorrelated samples from complex distributions, making them an appealing tool for parameter estimation. However, the practical utility of NFs remains limited by their tendency to collapse to a single mode of…
Importance Sampling (IS) is a method for approximating expectations under a target distribution using independent samples from a proposal distribution and the associated importance weights. In many applications, the target distribution is…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
An essential problem in statistics and machine learning is the estimation of expectations involving PDFs with intractable normalizing constants. The self-normalized importance sampling (SNIS) estimator, which normalizes the IS weights, has…
Score based learning (SBL) is a promising approach for learning Bayesian networks in the discrete domain. However, when employing SBL in the continuous domain, one is either forced to move the problem to the discrete domain or use metrics…
Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners…
Normalizing flows (NF) use a continuous generator to map a simple latent (e.g. Gaussian) distribution, towards an empirical target distribution associated with a training data set. Once trained by minimizing a variational objective, the…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…
We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and…
Continuous normalizing flows (CNFs) learn the probability path between a reference distribution and a target distribution by modeling the vector field generating said path using neural networks. Recently, Lipman et al. (2022) introduced a…
Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…
The marginal likelihood, or Bayesian evidence, is a crucial quantity for Bayesian model comparison but its computation can be challenging for complex models, even in parameters space of moderate dimension. The learned harmonic mean…
Gaussian Belief Propagation (BP) algorithm is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density…
We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such…
Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…
In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…
Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…
This paper presents a novel non-Gaussian inference algorithm, Normalizing Flow iSAM (NF-iSAM), for solving SLAM problems with non-Gaussian factors and/or non-linear measurement models. NF-iSAM exploits the expressive power of neural…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…