arXiv Machine Learning
Extending Pathwise Gradients to Discrete Random Variables via Finite-Order Relaxation
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arXiv Machine Learning
Oct 2
The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Sampling
The paper develops a rigorous framework for computing the Normalized Maximum Likelihood (NML) codelength for regular path‑differentiable Lipschitz (PDL) estimators, which include non‑smooth models such as Lasso and Sparse SVMs. By leveraging geometric measure theory and a novel Propose‑and‑Project Metropolis‑Hastings sampler, the authors provide a method to exactly evaluate the stochastic complexity for these non‑smooth estimators and demonstrate its scalability to high‑dimensional settings. The study shows that the exact NML criterion can match cross‑validation performance while being more data‑efficient, offering a theoretically grounded alternative for model selection in modern machine learning.
arXiv Machine Learning
Jul 10
GradInf: Gradient Estimation as Probabilistic Inference
arXiv:2607. 07840v1 Announce Type: cross Abstract: Gradient estimation -- the task of computing the gradient of the expected value of a probabilistic program -- has diverse applications in scientific computing, but is notoriously difficult because of issues such as high-dimensional integration, discrete random choices, and complex stochastic dependencies.
arXiv Machine Learning
Aug 13
Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size
arXiv:2608. 12009v1 Announce Type: cross Abstract: Bregman proximal stochastic gradient (BPSG) methods bring variance-reduced composite optimization to objectives whose geometry is poorly captured by Euclidean smoothness.
arXiv AI
Oct 12
Variance-Reduced Policy Gradient is Nearly Minimax-Optimal
The paper introduces Loopless Variance-Reduced Policy Gradient (LVR-PG), a framework that unifies first‑order estimators combining recursive updates with defensive importance sampling, such as PAGE-PG and STORM-PG. It proves that LVR-PG achieves a ∫O(ε⁻²) last‑iterate global convergence rate under weak gradient domination for general parametric policies, using only first‑order updates and minimal assumptions. By extending lower bounds to continuous parametric policies, the authors show an Ω(ε⁻²) sample complexity limit, establishing that LVR-PG is minimax‑optimal up to logarithmic factors and horizon terms.
arXiv Machine Learning
Oct 16
Acceleration and its Limits in Gaussian Variational Inference
The paper investigates whether momentum-based acceleration can improve Gaussian variational inference (GVI) for strongly log-concave, log-smooth targets. With exact Gaussian expectations, GVI achieves the classic accelerated √κ convergence rate, but when only pointwise derivatives are available, the authors construct targets that force any randomized algorithm to use κ^{1-o(1)} queries, showing curvature alone does not guarantee acceleration. They identify additional structure—specifically a Hessian-Lipschitz condition with small Hessian variation—under which variance-reduced stochastic methods can achieve accelerated guarantees, and demonstrate empirical speedups on real datasets.
arXiv Machine Learning
Jul 7
A Gradient Flow Perspective on Minimum MMD Estimation
arXiv:2607. 03871v1 Announce Type: new Abstract: Minimum maximum mean discrepancy (MMD) estimation has emerged as a robust and likelihood-free alternative to maximum likelihood estimation for parameter estimation.