arXiv Machine Learning
Jun 18
Wasserstein Policy Learning for Distributional Outcomes
arXiv:2606. 19117v1 Announce Type: cross Abstract: Offline policy learning has received growing attention in causal inference.
Minimax Rates for Conditional Generative Learning under Wasserstein Loss
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arXiv Machine Learning
Jun 2
Theoretical Analysis of Engression and Reverse Markov Engression
arXiv:2606. 01002v1 Announce Type: cross Abstract: Engression is a recently proposed and effective framework for conditional distribution learning.
arXiv Machine Learning
Sep 24
Robustness of Diffusion Models under Distribution Shift
arXiv:2609.27546v1 Announce Type: cross Abstract: Score-based diffusion models are increasingly considered in settings where the underlying data distribution may differ from the training distribution...
arXiv Statistics ML
1d ago
On the Error Analysis of Triangular Transport Maps for Conditional Generation via MMD-based Objectives
arXiv:2610.33610v1 Announce Type: new Abstract: Conditional generative models parameterized by triangular transport maps are widely used for conditional sampling, yet theoretical guarantees on the qu...
arXiv Machine Learning
6d ago
Near Minimax Rate for Quantile Distributional Reinforcement Learning
The paper investigates quantile distributional policy evaluation by approximating the return distribution under a policy with a quantile Bellman fixed point. It constructs an estimator from an empirical Markov decision process and derives non‑asymptotic error bounds in Wasserstein distances, achieving root‑n rates that are independent of the quantile resolution for a wide range of Wasserstein orders. The authors also characterize the exact local asymptotic minimax risk and show that their estimator attains this optimal rate, while examining how the risk depends on resolution in simple state‑space examples.
arXiv Statistics ML
Oct 16
Optimal score function estimation via derivatives constraints
The paper develops a statistical framework showing that empirical score matching can achieve minimax optimal performance for diffusion generative models when data lie on a low‑dimensional manifold. It establishes convergence rates for empirical risk minimization over constrained Sobolev classes and demonstrates that the resulting score estimators yield minimax optimal Wasserstein‑1 rates for the generated distribution, up to logarithmic factors. The analysis reveals that the statistical rates depend on the intrinsic dimension of the data manifold rather than its ambient dimension, providing conditions under which score‑based generative modeling generalizes rather than overfits.
arXiv Machine Learning
6d ago
Generalization Bounds via Vector-Valued $L_p$ Correlation $V_\alpha$
arXiv:2610. 29425v1 Announce Type: new Abstract: Understanding generalization of randomized learning algorithms remains a central challenge.
arXiv Machine Learning
Oct 12
Minimax Rates for Estimating Powered Sliced Wasserstein Functionals
arXiv:2610. 12740v1 Announce Type: cross Abstract: We study the two-sample estimation of the powered Sliced Wasserstein functional under projected $r$-th moment assumptions.
arXiv Machine Learning
Jun 9
Conditional Random Ordered Transport Spaces
arXiv:2606. 08113v1 Announce Type: new Abstract: A small Wasserstein distance does not certify that a transformation is admissible.
arXiv AI
Jun 8
A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space
arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.
arXiv Machine Learning
Aug 13
Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows
arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.
arXiv Machine Learning
Jul 17
Distributionally Robust Optimization via Iterative Algorithms in Continuous Probability Spaces
arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.