Uncertainty
On the Convergence of Black-Box Variational Inference
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.
Training Energy-Based Normalizing Flow with Score-Matching Objectives Chen-Hao Chao 1, Wei-Fang Sun 1,2, Y en-Chang Hsu
Our experimental results demonstrate that this approach significantly improves the training efficiency as compared to maximum likelihood training.
A Proof of Theorem
In this section, we provide proof for the disentanglement identifiability of the inferred exogenous variable. Our proof consists of three main components. Then we have ( f, T, λ) ( f, T, λ) . The conditional V AE, in this case, inherits all the properties of maximum likelihood estimation. The following proof is based on the reduction to absurdity.
Efficient Robust Bayesian Optimization for Arbitrary Uncertain inputs
In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such as machining errors, execution noise, or contextual variability.
Differentiable and Stable Long-Range Tracking of Multiple Posterior Modes
But, they are limited to unimodal, Gaussian approximations of state uncertainty.
Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data
Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when the underlying graph involving the multivariate functions may have cycles.
