1 citations · 2 across the 24 of their papers we have counts for
25 papers
An Old Look at Empirical Bayes
Nicholas G. Polson, Vadim O. Sokolov, Daniel Zantedeschi
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…
Horseshoe Priors and MDP
Nick Polson, Vadim Sokolov, Daniel Zantedeschi
Carvalho (2010) established two foundational theorems for the horseshoe prior: tight two-sided logarithmic bounds on the marginal density near the origin (Theorem~1.1), and a super…
Bell's Inequality, Causal Bounds, and Quantum Bayesian Computation: A Unified Framework
Nick Polson, Vadim Sokolov, Daniel Zantedeschi
Bell inequalities characterize the boundary of the local-realist correlation polytope -- the set of joint probability distributions achievable by classical hidden-variable models.…
Bayes, E-values and Testing
Nicholas G. Polson, Vadim Sokolov, Daniel Zantedeschi
E-values and E-processes (nonnegative supermartingales) provide anytime-valid evidence for sequential testing via Ville's inequality, yet their connection to Bayesian reasoning, re…
Martingale Posterior Predictive Coherence: Hausdorff Moment Hierarchy
Nicholas G. Polson, Daniel Zantedeschi
For an exchangeable Bernoulli sequence with de Finetti mixing measure Pi, the k-step predictive probability P(X_{n+1}=...=X_{n+k}=0 | F_n) equals the posterior expectation E[(1-the…
Synthetic Priors
Nick Polson, Vadim Sokolov
Bayesian inference in generalized linear models requires a prior on the coefficient vector . Practitioners naturally reason about response probabilities at specific covariate va…
Generative Bayesian Computation as a Scalable Alternative to Gaussian Process Surrogates
Nick Polson, Vadim Sokolov
Gaussian process (GP) surrogates are the default tool for emulating expensive computer experiments, but cubic cost, stationarity assumptions, and Gaussian predictive distributions…
Photons = Tokens: The Physics of AI and the Economics of Knowledge
Alec Litowitz, Nick Polson, Vadim Sokolov
Debates about artificial intelligence capabilities and risks are often conducted without quantitative grounding. This paper applies the methodology of MacKay (2009) -- who reframed…
Fast Compute for ML Optimization
Nick Polson, Vadim Sokolov
We study optimization for losses that admit a variance-mean scale-mixture representation. Under this representation, each EM iteration is a weighted least squares update in which l…
Some Bayesian Perspectives on Clinical Trials
Alexandra Sokolova, Vadim Sokolov, Nick Polson
We examine three landmark clinical trials -- ECMO, CALGB~49907, and I-SPY~2 -- through a unified Bayesian framework connecting prior specification, sequential adaptation, and decis…
Bayesian Methods for the Navier-Stokes Equations
Nicholas Polson, Vadim Sokolov
We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier…
Horseshoe Mixtures-of-Experts (HS-MoE)
Nick Polson, Vadim Sokolov
Horseshoe mixtures-of-experts (HS-MoE) models provide a Bayesian framework for sparse expert selection in mixture-of-experts architectures. We combine the horseshoe prior's adaptiv…
Generative Bayesian Hyperparameter Tuning
Hedibert Lopes, Nick Polson, Vadim Sokolov
\noindent Hyper-parameter selection is a central practical problem in modern machine learning, governing regularization strength, model capacity, and robustness choices. Cross-vali…
Bayesian Global-Local Regularization
Jyotishka Datta, Nick Polson, Vadim Sokolov
We propose a unified framework for global-local regularization that bridges the gap between classical techniques -- such as ridge regression and the nonnegative garotte -- and mode…
Mixed Integer and Linear Programming
Nick Polson, Vadim Sokolov
In this paper, we design algorithms for Mixed Integer and Linear Programming. By expressing a constrained optimisation as one of simulation from a Boltzmann distribution, we…
Generative Quantile Bayesian Prediction
Maria Nareklishvili, Nick Polson, Vadim Sokolov
Prediction is a central task of machine learning. Our goal is to solve large scale prediction problems using Generative Quantile Bayesian Prediction (GQBP).By directly learning pre…
Bayesian Double Descent
Nick Polson, Vadim Sokolov
Double descent is a phenomenon of over-parameterized statistical models such as deep neural networks which have a re-descending property in their risk function. As the complexity o…
Generative Learner for Distributional Causal Effects
Maria Nareklishvili, Nicholas Polson, Vadim Sokolov
We propose a generative learner for estimating conditional average treatment effects and characterizing the full distribution of these effects. The learner takes the form of a mult…
Generative Modeling: A Review
Maria Nareklishvili, Nick Polson, Vadim Sokolov
We organize the generative-modeling literature around three classes of generators, corresponding to three distinct inferential tasks: estimating counterfactual outcome distribution…
Kramnik vs Nakamura: A Chess Scandal
Shiva Maharaj, Nick Polson, Vadim Sokolov
We provide a statistical analysis of the recent controversy between Vladimir Kramnik (ex chess world champion) and Hikaru Nakamura. Hikaru Nakamura is a chess prodigy and a five-ti…
Generative Bayesian Computation for Maximum Expected Utility
Nick Polson, Fabrizio Ruggeri, Vadim Sokolov
Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative…
Counting Queens
Nick Polson, Vadim Sokolov
Gauss proposed the problem of how to enumerate the number of solutions for placing queens on an chess board, so no two queens attack each other. The N-queen problem…
Negative Probability
Nick Polson, Vadim Sokolov
Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent va…
Generative AI for Bayesian Computation
Nicholas G. Polson, Vadim Sokolov
Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the paramet…