The paper introduces a unified framework for measuring divergences between conditional distributions using kernel embeddings, termed conditional maximum mean discrepancy (CMMD). It defines a family of CMMD metrics—CMMD_0, CMMD_1, and CMMD_2—each based on different RKHS embeddings, and generalizes them to a level‑s CMMD with clear assumptions and operator‑based smoothing connections. Additionally, the authors present a novel doubly robust estimator for CMMD and demonstrate through experiments that the metric captures complex conditional dependencies for statistical testing.
arXiv:2602. 13362v2 Announce Type: replace-cross Abstract: A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty.
arXiv:2507. 12843v3 Announce Type: replace Abstract: Are two distributions close to each other with statistical significance?
The paper introduces a Conditional Kernel Stein Discrepancy (CKSD) that extends traditional Kernel Stein Discrepancies to evaluate goodness‑of‑fit for conditional distributions. By employing an operator‑valued kernel on the covariate space, the authors lift unconditional KSDs to settings where only a conditional target model and joint samples are available, covering both smooth manifolds and discrete spaces. They prove that the CKSD statistic vanishes exactly when the conditional model matches the true conditional distribution for almost all covariates, and demonstrate its practical effectiveness through experiments on level, power, and runtime.
arXiv:2607. 24235v1 Announce Type: cross Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others.
arXiv:2607. 20119v1 Announce Type: cross Abstract: We introduce the Directional Kernel Mean Difference (DKMD), a signed statistic for univariate distribution comparison that preserves the direction of distributional shifts.
arXiv:2501. 18897v4 Announce Type: replace-cross Abstract: Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification.
arXiv:2601. 08379v2 Announce Type: replace-cross Abstract: Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data.
arXiv:2603.05575v2 Announce Type: replace-cross Abstract: We study prediction-powered conditional inference in the setting where labeled data are scarce, unlabeled covariates are abundant, and a blac...
arXiv:2601.18952v3 Announce Type: replace Abstract: We propose Kernel Embedding Distributional Reinforcement Learning (KE-DRL) an offline method to estimate kernel mean embeddings of conditional mult...
arXiv:2610.09731v1 Announce Type: cross Abstract: Kernel methods are among the most powerful tools in machine learning and statistics, with a large number of successful applications. Their immense su...
The paper addresses the challenge of estimating joint probability distributions in high-dimensional settings by factorizing them autoregressively and using nonparametric conditional estimators. It establishes theoretical convergence bounds that link the difficulty of joint estimation to the hardest factor in the factorization, especially when conditional estimators adapt to sparsity in an undirected dependence graph. Empirical results show that an autoregressive estimator built with parallel gradient boosting achieves competitive performance on simulated and real datasets, even without optimizing factorization order.
arXiv:2608. 06155v1 Announce Type: cross Abstract: Conditional expectation operators (CEOs) and their associated conditional mean embeddings (CMEs) play a central role across applied mathematics and machine learning, appearing in nonparametric regression, Bayesian inverse problems, and Koopman operator theory.