arXiv subjects

Vadim O. Sokolov

Publications and source records attributed to Vadim O. Sokolov.

5 recordsLinked to original sources

arXiv2026

An Old Look at Empirical Bayes

Dennis Lindley once said that there is only one thing worse than a frequentist, and that is an empirical Bayesian. The quip has the air of caricature, but its technical content is serious: empirical Bayes uses the same data twice, conflates levels of a hierarchy, and produces posterior-shaped summaries whose uncertainty quantification differs from what a fully hierarchical model delivers. David Blei's 2026 IMS Medallion Lecture, "A Fresh Look at Empirical Bayes," revives the program under three new banners: empirical Bayes via probabilistic symmetries (rebranded "Bayesian empirical Bayes"), empirical Bayes with implicit likelihoods through simulation-based inference, and empirical Bayes for combining experimental and observational data through calibration studies. This is a continuation of Blei and Kucukelbir's earlier "population empirical Bayes" (PopEB, 2015). We argue, in the spirit of Lindley, I. J. Good, William DuMouchel, Thomas Louis, and our own recent work with Datta, that Blei's machinery targets inferential objects distinct from the posterior conditional on the realized data, and that the cost of maintaining the full hierarchical discipline has fallen low enough that the computational trade-off no longer favors the shortcut. The case study is the Tweedie formula. Efron's f-modeling empirical Bayes plugs an estimated score function into a posterior-mean identity, but a smoothed score need not arise from any prior. The horseshoe Tweedie formula does. We conclude by recommending that the impressive computational machinery of modern empirical Bayes (variational inference, neural amortization, simulation-based inference) be redeployed in service of properly hierarchical Bayes.

stat.ME↗

arXiv2022

Data Augmentation for Bayesian Deep Learning

Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and largely unexplored. Data augmentation techniques are a natural approach to provide uncertainty quantification and to incorporate stochastic Monte Carlo search into stochastic gradient descent (SGD) methods. The purpose of our paper is to show that training DL architectures with data augmentation leads to efficiency gains. We use the theory of scale mixtures of normals to derive data augmentation strategies for deep learning. This allows variants of the expectation-maximization and MCMC algorithms to be brought to bear on these high dimensional nonlinear deep learning models. To demonstrate our methodology, we develop data augmentation algorithms for a variety of commonly used activation functions: logit, ReLU, leaky ReLU and SVM. Our methodology is compared to traditional stochastic gradient descent with back-propagation. Our optimization procedure leads to a version of iteratively re-weighted least squares and can be implemented at scale with accelerated linear algebra methods providing substantial improvement in speed. We illustrate our methodology on a number of standard datasets. Finally, we conclude with directions for future research.

stat.ML↗

arXiv2020

Eco-Mobility-on-Demand Fleet Control with Ride-Sharing

Shared Mobility-on-Demand using automated vehicles can reduce energy consumption and cost for future mobility. However, its full potential in energy saving has not been fully explored. An algorithm to minimize fleet fuel consumption while satisfying customers travel time constraints is developed in this paper. Numerical simulations with realistic travel demand and route choice are performed, showing that if fuel consumption is not considered, the MOD service can increase fleet fuel consumption due to increased empty vehicle mileage. With fuel consumption as part of the cost function, we can reduce total fuel consumption by 7 percent while maintaining a high level of mobility service.

stat.AP↗

arXiv2018

Deep Learning

Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we review the state-of-the-art of deep learning from a modeling and algorithmic perspective. We provide a list of successful areas of applications in Artificial Intelligence (AI), Image Processing, Robotics and Automation. Deep learning is predictive in its nature rather then inferential and can be viewed as a black-box methodology for high-dimensional function estimation.

stat.ML↗

arXiv2018

Deep Learning for Spatio-Temporal Modeling: Dynamic Traffic Flows and High Frequency Trading

Deep learning applies hierarchical layers of hidden variables to construct nonlinear high dimensional predictors. Our goal is to develop and train deep learning architectures for spatio-temporal modeling. Training a deep architecture is achieved by stochastic gradient descent (SGD) and drop-out (DO) for parameter regularization with a goal of minimizing out-of-sample predictive mean squared error. To illustrate our methodology, we predict the sharp discontinuities in traffic flow data, and secondly, we develop a classification rule to predict short-term futures market prices as a function of the order book depth. Finally, we conclude with directions for future research.

stat.ML↗