arXiv subjects

Kirill Sokolov

Publications and source records attributed to Kirill Sokolov.

6 recordsLinked to original sources

arXiv2026

Markovization of Randomized Stopping Times

We study randomized stopping times for a Markov process, described by a progressively measurable intensity $α_t(ω)$. We prove that every admissible intensity has a Markovian representative $λ(t,X_t)$, explicitly obtained from the observed measure and the surviving occupation measure. This representative preserves both the family of surviving mass measures and the joint distribution of the stopping time and the state at stopping. Whenever the relative entropy with respect to a reference intensity $r(t,x)$ is finite, we prove an exact decomposition showing that Markovization does not increase the entropy. As a consequence, variational problems in which a randomized stopping time enters only through its observed measure and an entropy penalty can be reduced to optimization over Markovian intensities $λ(t,x)$. For every observed measure admitting a finite-entropy representative, there is a unique minimum-entropy randomized stopping time, and it is Markovian. We discuss the connection with optimal Skorokhod embedding and prove a finite-constraint realization result for Brownian stopping. We also approximate arbitrary observed measures by those generated by bounded Markovian intensities.

math.PR↗

arXiv2026

Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputation

Missing values are ubiquitous in heterogeneous data mining, where numerical, categorical, and binary variables often coexist. Many imputation methods, especially diffusion-based ones, treat discrete variables through continuous surrogates such as one-hot relaxations rather than modeling them natively. This creates a mismatch between the model state space and the mixed discrete and continuous structure of the data. We propose Impute-EM, an Expectation Maximization style framework that alternates between imputing missing entries with the current model and refitting a diffusion backbone on completed data. We instantiate Impute-EM with native mixed-state diffusion backbones for heterogeneous data, combining Gaussian and masked categorical components without one-hot relaxations. In exact settings, we characterize the update and show that the observed mask-indexed marginals match the targets at the limit, while making explicit that the full data distribution is generally non-identifiable from incomplete observations alone. Empirically, Impute-EM delivers the best distributional fidelity on mixed-type tabular imputation, on which downstream modeling relies, with text imputation serving as a controlled validation of the native discrete backbone.

cs.LG↗

arXiv2026

Duality for a Martingale Transport Problem with Moment Constraints

We consider a weak martingale optimal transport problem related to the martingale analogue of the Benamou--Brenier formula. In contrast to the classical setting, the second marginal is not given, but specified only through a finite number of moment constraints of a particular form. For this problem, we derive a finite-dimensional dual formulation and prove the absence of a duality gap under the specified interiority condition on the constraint vector. In addition, we describe the structure of the optimal martingale coupling and its relation to Bass martingales.

math.PR↗

arXiv2026

Variational Entropic Optimal Transport

Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem. In practice, recent approaches optimize a weak dual EOT objective depending on a single potential, but doing so is computationally not efficient due to the intractable log-partition term. Existing methods typically resolve this obstacle in one of two ways: by significantly restricting the transport family to obtain closed-form normalization (via Gaussian-mixture parameterizations), or by using general neural parameterizations that require simulation-based training procedures. We propose Variational Entropic Optimal Transport (VarEOT), based on an exact variational reformulation of the log-partition $\log \mathbb{E}[\exp(\cdot)]$ as a tractable minimization over an auxiliary log-normalizer. This yields a differentiable learning objective optimized with stochastic gradients and avoids the necessity of MCMC simulations during the training. We provide theoretical guarantees, including finite-sample generalization bounds and approximation results under universal function approximation. Experiments on synthetic data and unpaired image-to-image translation demonstrate competitive or improved translation quality, while comparisons within the solvers that use the same weak dual EOT objective support the benefit of the proposed optimization principle. The code for our solver can be found at https://github.com/DrEternity/VarEOT .

cs.LG↗

arXiv2025

Exponential convergence rate for Iterative Markovian Fitting

We consider the discrete-time Schrödinger bridge problem on a finite state space. Although it has been known that the Iterative Markovian Fitting (IMF) algorithm converges in Kullback-Leibler divergence to the ground truth solution, the speed of that convergence remained unquantified. In this work, we establish for the first time that IMF exhibits exponential convergence with an explicit contraction factor.

cs.IT↗

arXiv2024

On a problem of optimal mixing

We consider the simultaneous optimal transportation of measures, where the target marginal is not necessarily fixed. For this problem, we prove the existence of a solution for completely regular spaces and investigate the structure of the discrete problem. We establish a connection between the Monge problem and the Kantorovich problem by showing that their functionals are equal and that the solutions coincide in Euclidean space.

math.PR↗