Timothy L.H. Wee

Kline Tower, Rm 1261

219 Prospect Street

New Haven, CT 06511

I am a PhD student in the statistics department at Yale University, advised by Sekhar Tatikonda. I am broadly interested in high-dimensional probability and statistics, as well as statistical physics, in particular spin glasses and disordered systems. To elaborate, I am interested in the following topics:

Understanding dependence structures, phase transitions, and the efficacy of message-passing algorithms in diluted and mean-field models. I am especially interested in elucidating the underlying mechanisms behind variational principles for free energies.
Statistical physics techniques in planted models, leading to insights about the fundamental limits of inference and algorithm design.
Chaining frameworks for bounding suprema of stochastic processes—especially algorithms and explicit constructions of majorizing measures or weighted partitions and their applications in statistics or computer science problems.

Feel free to reach out if you would like to chat about any of these subjects. Otherwise I’m sure we can find something interesting to discuss!

selected publications

Asymptotic mutual information in quadratic estimation problems over compact groups

Kaylee Y Yang, Timothy LH Wee, and Zhou Fan

arXiv preprint arXiv:2404.10169, 2024

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Motivated by applications to group synchronization and quadratic assignment on random data, we study a general problem of Bayesian inference of an unknown “signal” belonging to a high-dimensional compact group, given noisy pairwise observations of a featurization of this signal. We establish a quantitative comparison between the signal-observation mutual information in any such problem with that in a simpler model with linear observations, using interpolation methods. For group synchronization, our result proves a replica formula for the asymptotic mutual information and Bayes-optimal mean-squared-error. Via analyses of this replica formula, we show that the conjectural phase transition threshold for computationally-efficient weak recovery of the signal is determined by a classification of the real-irreducible components of the observed group representation(s), and we fully characterize the information-theoretic limits of estimation in the example of angular/phase synchronization over \mathbbSO(2)/\mathbbU(1). For quadratic assignment, we study observations given by a kernel matrix of pairwise similarities and a randomly permutated and noisy counterpart, and we show in a bounded signal-to-noise regime that the asymptotic mutual information coincides with that in a Bayesian spiked model with i.i.d. signal prior.
@article{yang2024asymptotic, title = {Asymptotic mutual information in quadratic estimation problems over compact groups}, author = {Yang, Kaylee Y and Wee, Timothy LH and Fan, Zhou}, journal = {arXiv preprint arXiv:2404.10169}, year = {2024}, }
Random projections beyond zero overlap

Timothy LH Wee, and Sekhar Tatikonda

arXiv preprint arXiv:2312.01248, 2023

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A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections imply these hypotheses. This extends and unites several existing results in geometric functional analysis and spin glasses. Applications include a large-system characterization of the joint law of cavity fields in the Sherrington-Kirkpatrick model.
@article{wee2023random, title = {Random projections beyond zero overlap}, author = {Wee, Timothy LH and Tatikonda, Sekhar}, journal = {arXiv preprint arXiv:2312.01248}, year = {2023}, }
Local independence in mean-field spin glasses

Timothy LH Wee, and Sekhar Tatikonda

arXiv preprint arXiv:2212.14851, 2022

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We present a new approach to local independence in spin glasses, i.e. the phenomenon that any fixed subset of coordinates is asymptotically independent in the thermodynamic limit. The approach generalizes the rigorous cavity method from Talagrand by considering multiple cavity sites. Under replica-symmetric conditions of thin-shell and overlap concentration, the cavity fields are revealed to be asymptotically independent, conditionally on the disorder, which in turn leads to local independence. Conversely, it is shown that local independence implies those replica-symmetric properties. The framework is general enough to encompass the classical and soft spin ([-1,1]) Sherrington-Kirkpatrick models, as well as the Gardner spin glasses.
@article{wee2022local, title = {Local independence in mean-field spin glasses}, author = {Wee, Timothy LH and Tatikonda, Sekhar}, journal = {arXiv preprint arXiv:2212.14851}, year = {2022}, }