Abstract: The shape of the fluctuations as heat approaches equilibrium in an insulated body are governed by the first Neumann eigenfunction of the Laplacian. Rauch's hot spots conjecture states that […]
Abstract: It is common to use adjuvants in immunotherapeutic regimens to strengthen the immune response. However, multiple dosages are required making it inconvenient for the patient. Hydrogels have been proposed […]
Abstract: Earlier work has shown that similarity-based predictive models can improve upon predictive performance, as compared to using the entire training data to help build models, particular regarding model discrimination for binary responses. My collaborators and I have some updated results to share, regarding similarity-based modeling for joint consideration of model calibration and discrimination, as […]
Abstract: Modern machine learning is ultimately a simple process: We iteratively update the weights of machine learning models to minimize a problem-specific loss. When it works well, we deploy the model in human-facing domains like healthcare, finance, or the justice system. But even though we know how models are trained, we don't understand why they […]
Abstract: Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This talk focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson-Picard (AAP) method. Despite introducing more `slow' Picard iterations, this method has been […]
Abstract: Transparency is vital for efficiency in social systems, yet individuals with critical information often strategically postpone disclosure, even when required, to benefit themselves. To study this behavior, we introduce […]
Abstract: The problem of classification in machine learning has often been approached in terms of function approximation. In this talk, we propose an alternative approach for classification in arbitrary compact […]
Abstract: Modern machine learning and scientific computing pose optimization challenges of unprecedented scale and complexity, demanding fundamental advances in both theory and algorithmic design for nonconvex optimization. This talk presents […]
Abstract: The talk introduces a conjecture on the first exit time of fractional Brownian motion: the upper-tail probability for a fractional Brownian motion to first exit a positive-valued barrier over time […]
Abstract: A proper coloring of a graph is an assignment of colors from \( \{1, 2, \ldots, k\} \) to each node of a graph such that no two nodes […]
Abstract: Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal attribution that is motivated by the concept of genetic heritability in twin studies. Counterfactual explainability extends methods for global sensitivity analysis (including the functional analysis […]
Abstract: We present a new approach for deriving structure-preserving numerical discretizations of Fokker-Planck equations by establishing a connection between the Fokker-Planck equation and its semi-discrete master equation at the level of the energy-dissipation law. We determine the transition rate in the master equation via the detailed balance condition and the spatial discretization of the continuous […]
