相关论文: Practical and Matching Gradient Variance Bounds fo…
We present VBPI-Mixtures, an algorithm designed to enhance the accuracy of phylogenetic posterior distributions, particularly for tree-topology and branch-length approximations. Despite the Variational Bayesian Phylogenetic Inference…
Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator - often…
This study investigates leveraging stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We propose weak and strong regularity conditions for the target operator to depict its intrinsic structure and…
We study the implementation of Automatic Differentiation Variational inference (ADVI) for Bayesian inference on regression models with bridge penalization. The bridge approach uses $\ell_{\alpha}$ norm, with $\alpha \in (0, +\infty)$ to…
Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new…
Importance sampling has become an indispensable strategy to speed up optimization algorithms for large-scale applications. Improved adaptive variants - using importance values defined by the complete gradient information which changes…
Stochastic gradient methods for minimizing nonconvex composite objective functions typically rely on the Lipschitz smoothness of the differentiable part, but this assumption fails in many important problem classes like quadratic inverse…
Understanding the convergence performance of asynchronous stochastic gradient descent method (Async-SGD) has received increasing attention in recent years due to their foundational role in machine learning. To date, however, most of the…
Software systems exhibit distinct behaviors based on input characteristics, and failures often occur at the boundaries between input domains. Traditional Boundary Value Analysis (BVA) relies on manual heuristics, while automated Boundary…
Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein…
Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…
Current state-of-the-art optimizers are adaptive gradient-based optimization methods such as Adam. Recently, there has been an increasing interest in formulating gradient-based optimizers in a probabilistic framework for better modeling the…
The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…
In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…
Semi-implicit variational inference (SIVI) is introduced to expand the commonly used analytic variational distribution family, by mixing the variational parameter with a flexible distribution. This mixing distribution can assume any density…
We introduce a new one-parameter family of divergence measures, called bounded Bhattacharyya distance (BBD) measures, for quantifying the dissimilarity between probability distributions. These measures are bounded, symmetric and positive…
We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…
One of the defining properties of deep learning is that models are chosen to have many more parameters than available training data. In light of this capacity for overfitting, it is remarkable that simple algorithms like SGD reliably return…
We develop a new variational approach on level sets aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. With this new approach,…
Practitioners apply neural networks to increasingly complex problems in natural language processing, such as syntactic parsing and semantic role labeling that have rich output structures. Many such structured-prediction problems require…