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Hyperparameter Tuning via Trajectory Predictions: Stochastic Prox-Linear Methods in Matrix Sensing
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsOther Conference Item -
Equivalence Principles for Nonlinear Random Matrices
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsNonlinear random matrices have significant applications in machine learning, statistics, and signal processing. Recent results in the field have pointed to an intriguing equivalence principle for these matrices. This principle shows that their asymptotic properties, including but not limited to their spectral characteristics, are asymptotically equivalent to those of simpler, noisy linear equivalent models. In my presentation, I will ...Other Conference Item -
Weak Decoding and Symmetries
(2024)International Zurich Seminar on Information and Communication (IZS 2024). ProceedingsTraditional channel coding theory requires a vanishing block error probability for the reliability criterion. In this note, we consider a weak decoding reliability criterion, requiring only the local error (i.e., decoding a bit incorrectly given the other noisy bits) to be non-trivial (i.e., bounded away from half). For this weak decoding criterion, we provide a simple general result: any linear transitive code achieves weak decoding below ...Other Conference Item -
Phase Transitions for Spectral Estimators in Generalized Linear Models via Approximate Message Passing
(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 -
Training Generative Models from Privatized Data via Entropic Optimal Transport
(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 -