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Training Generative Models from Privatized Data via Entropic Optimal Transport
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsOther Conference Item -
Gromov–Wasserstein Alignment: Statistical and Computational Advancements via Duality
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsThe Gromov-Wasserstein (GW) distance quantifies dissimilarity between metric measure (mm) spaces and provides a natural correspondence between them. As such, it serves as a figure of merit for applications involving alignment of heterogeneous datasets, including object matching, single-cell genomics, and language models translation. While various heuristic methods for approximately evaluating the GW distance from data have been developed, ...Other Conference Item -
Bounds on Transport Maps via Diffusion Processes
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsGlobally lipschitz transport maps have found many applications in the study of probabilistic functional inequalities such as logarithmic Sobolev and Poincaré inequalities, by transporting an inequality from a nice reference measure to another one. For example, a theorem of Caffarelli states that optimal transport maps from the standard Gaussian measure onto uniformly log-concave measures are 1-lipschitz. This then recovers the sharp bounds ...Other Conference Item -
The Shifted Composition Rule
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsOther Conference Item -
Functional Representation Lemma: Algorithms and Applications
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsFunctional Representation Lemma (FRL) is an information-theoretic technique that fixes a correlated ‘reference’ information source, and extracts a ‘residual’ information about the original source. Recently, there has been a lot of interest in FRL since variants of this technique appear across different problems in information theory, and data science more broadly. In this tutorial talk we overview the FRL problem. We highlight some of its ...Other Conference Item -
Quantitative Group Testing and Pooled Data with Sublinear Number of Tests
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsIn the pooled data problem, the goal is to identify the categories associated with a large collection of items via a sequence of pooled tests. Each pooled test reveals the number of items of each category within the pool. A prominent special case is quantitative group testing (QGT), which is the case of pooled data with two categories. We consider these problems in the linear regime, where the fraction of items in each category is of ...Other Conference Item -
A Representation-Learning Game for Classes of Prediction Tasks
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsWe propose a game-theoretic formulation for learn ing dimensionality-reducing representations of feature vectors, when a prior knowledge on future prediction tasks is available. We analytically find the value of the game and optimal mixed (randomized) strategies for the case of linear representations, tasks, and the mean squared error loss, and propose an algorithm for general classes of representations, tasks, and loss functions.Other Conference Item -
Neural Compression with Lattice Transform Coding
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsOther Conference Item -
The Sample Complexity of Simple Binary Hypothesis Testing
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsThe sample complexity of simple binary hypothesis testing is the smallest number of i.i.d. samples required to distinguish between two distributions p and q such that the Type-I and Type-II errors are smaller than some pre-specified thresholds α and β, respectively. Our main contribution is deriving, under mild technical conditions, a formula for the sample complexity in terms of parameters p, q, α, and βOther Conference Item -
The Out-of-Sample Prediction Error of the Square-Root-LASSO and Related Estimator
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsOther Conference Item