Approaches based on point processes provide a principled statistical framework for modeling neural spiking activity.

However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo.

Logical Credal Networks or LCNs were recently introduced as a powerful probabilistic logic framework for representing and reasoning with imprecise knowledge.

The fundamental building block for drug discovery is molecule geometry and thus, the molecule's geometrical

Specifically, we lay the foundation within the Bayesian framework.

Recent work [Ma et al., 2019] shows that in the non-convex case, sampling

Graphical models are widely used to compactly model the conditional interdependence among multiple random variables Lauritzen [1996] and Pearl [2009]. The vertices of the graph represent the random variables (RVs), while the edges encode the inter-dependence among the RVs. The complete structure of the graph is analytically captured by the joint probability distribution of the random variables. Graphical models offer effective and tractable solutions to various inferential and decision-making solutions in different domains, e.g., computer vision Won and Derin [1992], genetics Chen et al. [2013], Fang et al. [2016], Dobra et al. [2004], social networks Jacob et al. [2014], and power systems Dvijotham et al. [2017].

We provide the first convergence guarantee for black-box variational inference (BBVI) with the reparameterization gradient. While preliminary investigations worked on simplified versions of BBVI ( e.g., bounded domain, bounded support, only optimizing for the scale, and such), our setup does not need any such algorithmic modifications. Our results hold for log-smooth posterior densities with and without strong log-concavity and the location-scale variational family. Notably, our analysis reveals that certain algorithm design choices commonly employed in practice, such as nonlinear parameterizations of the scale matrix, can result in suboptimal convergence rates. Fortunately, running BBVI with proximal stochastic gradient descent fixes these limitations and thus achieves the strongest known convergence guarantees. We evaluate this theoretical insight by comparing proximal SGD against other standard implementations of BBVI on large-scale Bayesian inference problems.