arXiv subjects

Alexandra Suvorikova

Publications and source records attributed to Alexandra Suvorikova.

12 recordsLinked to original sources

arXiv2026

Generalized bootstrap in the Bures-Wasserstein space

This study proposes a bootstrap-based method for uncertainty quantification in two important statistical scenarios. First, we approximate the sampling distribution of empirical barycenters under the Bures--Wasserstein metric using a reweighted estimator. Our theoretical results guarantee the accuracy of this approximation and enable the construction of data-driven confidence sets. The methodology is validated through experiments on graph-structured data, including stochastic block models and brain connectomes. Additionally, we compare bootstrap-based confidence sets with the asymptotic confidence sets obtained in arXiv:1901.00226v2, evaluating both their statistical performance and computational complexity. Second, we investigate the generalized bootstrap framework for $M$-estimators without requiring a specific resampling scheme, thus covering both weighted and resampling methods under mild conditions. Both contributions rely on a novel Gaussian approximation result for $M$-estimators.

math.ST↗

arXiv2026

Wall-Clock Complexity for Zeroth-Order Optimization with Tunable Oracle Fidelity

Zeroth-order (black-box) optimization is applied when gradients are unavailable and objective evaluations rely on expensive simulations. In many such applications, the oracle fidelity is tunable: higher-accuracy queries reduce noise but incur higher computational costs. To capture this trade-off, we study an accuracy-aware wall-clock model where each query with fidelity $δ$ has a cost $c(δ)$, and we minimize the total time $T_{\mathrm{total}} = \sum_{k=1}^{N} c(δ_k)$, subject to a target accuracy constraint. We show how the choice of oracle type, noise model, and optimization scheme induces explicit wall-clock-optimal choices for the algorithmic parameters. For instance, we demonstrate that accelerated methods can be wall-clock inferior to non-accelerated schemes. Furthermore, we characterize the conditions under which a constant fidelity strategy is optimal in the Big-O sense. Our framework provides a unified methodology to translate convergence guarantees into practical fidelity and batching recommendations.

math.OC↗

arXiv2026

Diffusion & Adversarial Schrödinger Bridges via Iterative Proportional Markovian Fitting

The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and the reciprocal class, successfully solves the Schrödinger Bridge (SB) problem. However, an efficient practical implementation requires a heuristic modification -- alternating between fitting forward and backward time diffusion at each iteration. This modification is crucial for stabilizing training and achieving reliable results in applications such as unpaired domain translation. Our work reveals a close connection between the modified version of IMF and the Iterative Proportional Fitting (IPF) procedure -- a foundational method for the SB problem, also known as Sinkhorn's algorithm. Specifically, we demonstrate that the heuristic modification of the IMF effectively integrates both IMF and IPF procedures. We refer to this combined approach as the Iterative Proportional Markovian Fitting (IPMF) procedure. Through theoretical and empirical analysis, we establish the convergence of the IPMF procedure under various settings, contributing to developing a unified framework for solving SB problems. Moreover, from a practical standpoint, the IPMF procedure enables a flexible trade-off between image similarity and generation quality, offering a new mechanism for tailoring models to specific tasks.

cs.LG↗

arXiv2026

SLDP: Semi-Local Differential Privacy for Density-Adaptive Analytics

Density-adaptive domain discretization is essential for high-utility privacy-preserving analytics but remains challenging under Local Differential Privacy (LDP) due to the privacy-budget costs associated with iterative refinement. We propose a novel framework, Semi-Local Differential Privacy (SLDP), that assigns a privacy region to each user based on local density and defines adjacency by the potential movement of a point within its privacy region. We present an interactive $(\varepsilon, δ)$-SLDP protocol, orchestrated by an honest-but-curious server over a public channel, to estimate these regions privately. Crucially, our framework decouples the privacy cost from the number of refinement iterations, allowing for high-resolution grids without additional privacy budget cost. We experimentally demonstrate the framework's effectiveness on estimation tasks across synthetic and real-world datasets.

cs.LG↗

arXiv2026

friends.test: rank-based method for feature selection in interaction matrices

The analysis of the interaction matrix between two distinct sets is essential across diverse fields, from pharmacovigilance to transcriptomics. Not all interactions are equally informative: a marker gene associated with a few specific biological processes is more informative than a highly expressed non-specific gene associated with most observed processes. Identifying these interactions is challenging due to background connections. Furthermore, data heterogeneity across sources precludes universal identification criteria. To address this challenge, we introduce \textsf{friends.test}, a method for identifying specificity by detecting structural breaks in entity interactions. Rank-based representation of the interaction matrix ensures invariance to heterogeneous data and allows for integrating data from diverse sources. To automatically locate the boundary between specific interactions and background activity, we employ model fitting. We demonstrate the applicability of \textsf{friends.test} on the GSE112026 -- transnational data from head and neck cancer. A computationally efficient \textsf{R} implementation is available at https://github.com/favorov/friends.test.

q-bio.QM↗

arXiv2026

UCB-type Algorithm for Budget-Constrained Expert Learning

In many modern applications, a system must dynamically choose between several adaptive learning algorithms that are trained online. Examples include model selection in streaming environments, switching between trading strategies in finance, and orchestrating multiple contextual bandit or reinforcement learning agents. At each round, a learner must select one predictor among $K$ adaptive experts to make a prediction, while being able to update at most $M \le K$ of them under a fixed training budget. We address this problem in the \emph{stochastic setting} and introduce \algname{M-LCB}, a computationally efficient UCB-style meta-algorithm that provides \emph{anytime regret guarantees}. Its confidence intervals are built directly from realized losses, require no additional optimization, and seamlessly reflect the convergence properties of the underlying experts. If each expert achieves internal regret $\tilde O(T^α)$, then \algname{M-LCB} ensures overall regret bounded by $\tilde O\!\Bigl(\sqrt{\tfrac{KT}{M}} \;+\; (K/M)^{1-α}\,T^α\Bigr)$. To our knowledge, this is the first result establishing regret guarantees when multiple adaptive experts are trained simultaneously under per-round budget constraints. We illustrate the framework with two representative cases: (i) parametric models trained online with stochastic losses, and (ii) experts that are themselves multi-armed bandit algorithms. These examples highlight how \algname{M-LCB} extends the classical bandit paradigm to the more realistic scenario of coordinating stateful, self-learning experts under limited resources.

cs.LG↗

arXiv2025

Bernstein-type and Bennett-type inequalities for unbounded matrix martingales

We derive explicit Bernstein-type and Bennett-type concentration inequalities for matrix-valued martingale processes with unbounded observations from the Hermitian space $\mathbb{H}(d)$. Specifically, we assume that the $ψ_α$-Orlicz (quasi-)norms of their difference process are bounded for some $α> 0$. Further, we generalize the obtained result by replacing the ambient dimension $d$ with the effective rank of the covariance of the observations. To illustrate the applicability of the results, we prove several corollaries, including an empirical version of Bernstein's inequality and an extension of the bounded difference inequality, also known as McDiarmid's inequality.

math.PR↗

arXiv2019

Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding

In this work, we investigate Gaussian Processes indexed by multidimensional distributions. While directly constructing radial positive definite kernels based on the Wasserstein distance has been proven to be possible in the unidimensional case, such constructions do not extend well to the multidimensional case as we illustrate here. To tackle the problem of defining positive definite kernels between multivariate distributions based on optimal transport, we appeal instead to Hilbert space embeddings relying on optimal transport maps to a reference distribution, that we suggest to take as a Wasserstein barycenter. We characterize in turn radial positive definite kernels on Hilbert spaces, and show that the covariance parameters of virtually all parametric families of covariance functions are microergodic in the case of (infinite-dimensional) Hilbert spaces. We also investigate statistical properties of our suggested positive definite kernels on multidimensional distributions, with a focus on consistency when a population Wasserstein barycenter is replaced by an empirical barycenter and additional explicit results in the special case of Gaussian distributions. Finally, we study the Gaussian process methodology based on our suggested positive definite kernels in regression problems with multidimensional distribution inputs, on simulation data stemming both from synthetic examples and from a mechanical engineering test case.

stat.ME↗

arXiv2019

Statistical inference for Bures-Wasserstein barycenters

In this work we introduce the concept of Bures-Wasserstein barycenter $Q_*$, that is essentially a Fréchet mean of some distribution $\mathbb{P}$ supported on a subspace of positive semi-definite Hermitian operators $\mathbb{H}_{+}(d)$. We allow a barycenter to be restricted to some affine subspace of $\mathbb{H}_{+}(d)$ and provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of $Q_*$ in both Frobenius norm and Bures-Wasserstein distance, and explain, how obtained results are connected to optimal transportation theory and can be applied to statistical inference in quantum mechanics.

math.ST↗

arXiv2018

Multivariate Brenier cumulative distribution functions and their application to non-parametric testing

In this work we introduce a novel approach of construction of multivariate cumulative distribution functions, based on cyclical-monotone mapping of an original measure $μ\in \mathcal{P}^{ac}_2(\mathbb{R}^d)$ to some target measure $ν\in \mathcal{P}^{ac}_2(\mathbb{R}^d)$ , supported on a convex compact subset of $\mathbb{R}^d$. This map is referred to as $ν$-Brenier distribution function ($ν$-BDF), whose counterpart under the one-dimensional setting $d = 1$ is an ordinary CDF, with $ν$ selected as $\mathcal{U}[0, 1]$, a uniform distribution on $[0, 1]$. Following one-dimensional frame-work, a multivariate analogue of Glivenko-Cantelli theorem is provided. A practical applicability of the theory is then illustrated by the development of a non-parametric pivotal two-sample test, that is rested on $2$-Wasserstein distance.

math.ST↗

arXiv2017

Construction of Non-asymptotic Confidence Sets in 2-Wasserstein Space

In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea further to construction of a non-parametric two-sample test that is then applied to the detection of structural breaks in data with complex geometry. Both procedures mainly rely on the idea of multiplier bootstrap (Spokoiny and Zhilova (2015), Chernozhukov et al. (2014)). The main focus lies on probability measures that have commuting covariance matrices and belong to the same scatter-location family: we proof the validity of a bootstrap procedure that allows to compute confidence sets and critical values for a Wasserstein-based two-sample test.

math.ST↗

arXiv2016

Universal method with inexact oracle and its applications for searching equillibriums in multistage transport problems

In this paper we propose a new efficient approach for numerical calculation of equillibriums in multistage transport problems. In the very core of our approach lies the proper combination of Universal Gradient Method proposed by Yu. Nesterov (2013) and conception of inexact oracle (Devolder--Glineur--Nesterov, 2011). In particular our technique allows us to calculate Wasserstein's Barycenter in a fast manner (this results generalized M. Cuturi et al. (2014)).

math.OC↗