Related papers: From Soft-Minoration to Information-Constrained Op…
This paper deals with parameter estimation from extreme measurements. While being a special case of parameter estimation from partial data, in scenarios where only one sample from a given set of K measurements can be extracted, choosing…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
Graph summarization is the problem of producing smaller graph representations of an input graph dataset, in such a way that the smaller compressed graphs capture relevant structural information for downstream tasks. There is a recent graph…
We derive a universal bound on the efficiency with which "dissipated" work can generate distinguishable changes in a quantum many-body state at a finite temperature, as quantified by the quantum Fisher information. The bound follows solely…
We study the convergence of an $N$-particle Markovian controlled system to the solution of a family of stochastic McKean-Vlasov control problems, either with a finite horizon or Schr\"odinger type cost functional. Specifically, under…
In this thesis, I study the minimax oracle complexity of distributed stochastic optimization. First, I present the "graph oracle model", an extension of the classic oracle complexity framework that can be applied to study distributed…
We study robust testing and estimation of discrete distributions in the strong contamination model. We consider both the "centralized setting" and the "distributed setting with information constraints" including communication and local…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
We study an information-theoretic minimax problem for finite multivariate Markov chains on $d$-dimensional product state spaces. Given a family $\mathcal B=\{P_1,\ldots,P_n\}$ of $\pi$-stationary transition matrices and a class $\mathcal F…
The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs,…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets -- tasks ubiquitous in data science and machine learning. Because…
We consider deterministic homogenization for discrete-time fast-slow systems of the form $$ X_{k+1} = X_k + n^{-1}a_n(X_k,Y_k) + n^{-1/2}b_n(X_k,Y_k)\;, \quad Y_{k+1} = T_nY_k\;$$ and give conditions under which the dynamics of the slow…
Consider two correlated sources $X$ and $Y$ generated from a joint distribution $p_{X,Y}$. Their G\'acs-K\"orner Common Information, a measure of common information that exploits the combinatorial structure of the distribution $p_{X,Y}$,…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…
Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…
We consider the problem of noiseless and noisy low-rank tensor completion from a set of random linear measurements. In our derivations, we assume that the entries of the tensor belong to a finite field of arbitrary size and that…
We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…
We study geodesic equations for a family of right-invariant Riemannian metrics on the group of diffeomorphisms of a compact manifold. The metrics descend to Fisher's information metric on the space of smooth probability densities. The right…
We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are available. For the non-smooth non-convex setting, we establish an…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…