Abstract: Variational inference (VI) is a scalable method for sampling from intractable posterior distributions that arise in Bayesian inference. Normalizing flows have been used to aid VI in sampling from complex, multimodal posteriors. Despite its impact as an expressive alternative to mean-field and structured VI, theoretical studies on the approximate posterior from normalizing flows VI are limited. The computational cost of normalizing flows VI varies with the flow transformation, but there is no work quantifying the nature of the variational posterior at a particular complexity of the flow. In this talk we address these questions within the context of Bayesian linear regression. Assuming a Gaussian prior and inverse auto-regressive flows; we relate loss in accurate recovery of posterior samples from VI, to eigenvalues of the true posterior covariance matrix. Specifically, we derive the optimal KL divergence and loss in credible interval coverage from the variational approximation as functions of these eigenvalues, across the range of flow complexities. We find, given sufficient complexity of the flow, there is no loss in coverage from normalizing flows VI, while even for the 2 predictor case, the loss for mean-field VI increases with the magnitude of correlation between predictors. I will end this talk with a brief overview on my transition from academia to industry research, and contrast the differences in the two research environments.  

Abstract: A central problem in quantum information theory is determining how much information can be reliably transmitted through a noisy quantum channel, known as the "quantum capacity." Unlike classical channels, computing quantum capacity is notoriously difficult due to a phenomenon called non-additivity: using multiple copies of a channel together can sometimes achieve higher rates per channel copy than with a single copy of a channel. This leads to an optimization problem over an exponentially large space. In this talk, I'll introduce the quantum capacity problem and explain why additivity (or lack thereof) makes it computationally intractable. I'll then present joint work with Felix Leditzky (arXiv:2508.09978) where we exploit permutation symmetry to make progress. When the input to many channel copies is symmetric under permutations, the output can be efficiently described using the representation theory of the symmetric group. This reduces an optimization problem that scales exponentially in the number of qubits to something tractable, allowing us to evaluate the relevant figure of merit for up to 100 channel copies. Applying this to several physically motivated noise models, we obtain improved lower bounds on the quantum capacity and identify a surprisingly effective family of input states resembling repetition codes.

Abstract: MUC5B is a major component of mucus in the human airway and plays a significant role in removing pathogens and debris out of the lungs. However, a genetic variant in the MUC5B gene is enriched in a rare disease called idiopathic pulmonary fibrosis (IPF) which led to its discovery. It is still unknown why the variant is enriched in IPF. Interestingly however, while IPF remains rare even in those with the genetic variant, the variant is common in the northwestern region of the globe (about ~1/5 people have at least one variant). Why is this variant so common? Could it have a beneficial effect? In this talk, we use survival analysis techniques with data from the All of Us database to show that the MUC5B variant is protective against COVID-19 hospitalization, perhaps suggesting some protective effect against viral respiratory pathogens. Further results will suggest a trend toward a protective effect against all-cause mortality.