arXiv Statistics ML
6d ago
Transitional Conditional Independence
arXiv:2104. 11547v5 Announce Type: replace-cross Abstract: Statistical models contain variables that are not random: parameters, treatments, environments, design points.
Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invariant Entropy, and Directional Degrees of Freedom
arXiv:2607. 07851v1 Announce Type: cross Abstract: We give mathematically self-contained formulations, in the complex-time (kime) representation, of three open problems from the foundations of classical mechanics: (I) the extension of the classical entropic uncertainty principle to non-canonical variables and to multiple degrees of freedom; (II) the characterization of coordinate-invariant measures and entropies, i.
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arXiv Machine Learning
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Toscani-Fourier Distance on Probability Measures: Wasserstein Control, Topological Equivalence on Model Classes, and Duality
arXiv:2609.23163v1 Announce Type: cross Abstract: Comparing probability measures in machine learning trades transport geometry against computational cost: Wasserstein distances encode the geometry of...
arXiv Machine Learning
Sep 10
A Note on Scaling in Randomly Rotated Quantization and Its Connection to the CDEF +1 Pythagorean Relation
arXiv:2609.08759v1 Announce Type: cross Abstract: Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction...
arXiv Machine Learning
Aug 11
Logarithmic-Free Moment and Generalization Bounds for Uniformly Stable Algorithms
arXiv:2608. 09870v1 Announce Type: cross Abstract: Uniform stability is a classical tool for controlling the generalization error of a learning algorithm.
arXiv Machine Learning
Sep 24
Theoretical Study on the Evidential Learning-based Variational Autoencoder
arXiv:2609. 27853v1 Announce Type: cross Abstract: A normal--inverse-gamma (NIG) latent hierarchy has four parameters, but its induced latent law does not identify all four.
arXiv Machine Learning
Sep 24
Exact Minimax One-Bit Unbiased Compression: Heavy-Tail Necessity and Finite-Randomness Approximation
arXiv:2609. 27860v1 Announce Type: new Abstract: A pointwise-unbiased one-bit compressor reconstructs every real input in expectation while transmitting one bit.
arXiv Machine Learning
Jun 11
Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization
arXiv:2606. 11255v1 Announce Type: new Abstract: Bernstein--Schur kernels are products of a finite-feature kernel (one with an explicit finite-dimensional feature map) and a completely monotone shift-invariant kernel: nonstationary kernels that fall between the shift-invariant and dot-product templates random features usually exploit, so in general neither Bochner sampling nor polynomial sketching applies to the full kernel directly.
arXiv AI
Sep 15
On the Equivalence of Stochastic Control and Path Space Formulations for Schr\"odinger Bridges over Compact Connected Lie Groups
arXiv:2609.13758v1 Announce Type: cross Abstract: We establish the equivalence between the stochastic optimal control and path space formulations of the Schr\"odinger bridge problem (SBP) for the kin...
arXiv Machine Learning
Jun 2
Generalized Guarantees for Variational Inference in the Presence of Even and Elliptical Symmetry
arXiv:2511. 01064v3 Announce Type: replace-cross Abstract: Variational inference (VI) approximates a target density $p$ by the best match $q$ in a family of tractable distributions.
arXiv Statistics ML
Sep 7
Simultaneous Pointwise Majorization for Mixed Tail Processes with Applications in Gaussian Chaos and Ergodic Diffusions
The paper introduces a new simultaneous pointwise majorization framework for Banach‑valued stochastic processes that possess finite‑metric mixed‑tail increments. By assuming an anchored process satisfies a tail bound involving multiple pseudo‑metrics and orders, the authors derive a high‑probability envelope that holds uniformly over the index set, with terms expressed through integrals of log‑covering numbers and distance functions. This result generalizes single‑metric sub‑Weibull bounds and, in the Gaussian case, improves existing pointwise upper bounds by removing extraneous logarithmic factors.
arXiv Machine Learning
Jun 11
Triangular-Reference Schr\"odinger Bridges for Time Series Generation
arXiv:2605. 27478v3 Announce Type: replace-cross Abstract: Schr\"odinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid.
arXiv AI
Sep 24
The Risk-Sensitive Schr\"odinger Bridge: Is Not a KL Projection
arXiv:2609.27250v1 Announce Type: cross Abstract: The Schr\"odinger bridge owes its computational power to a single structural fact: by Girsanov's theorem the controlled problem is a Kullback--Leible...