7 accepted papers
We propose to study and promote the robustness of a model as per its performance on a continuous geodesic interpolation of subpopulations, e.g., a class of samples in a classification problem. Specifically, (1) we augment the data by finding the worst-case Wasserstein barycenter on the geodesic conn…
Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the under…
Learning and understanding heterogeneous patterns in complex spatio-temporal data is an important and challenging task across domains in science and engineering. In this work, we develop a model for learning heterogeneous and dynamic patterns of velocity field data, motivated by applications in the…
Optimal transport (OT) measures distances between distributions in a way that depends on the geometry of the sample space. In light of recent advances in computational OT, OT distances are widely used as loss functions in machine learning. Despite their prevalence and advantages, OT loss functions c…
We propose Dirichlet Simplex Nest, a class of probabilistic models suitable for a variety of data types, and develop fast and provably accurate inference algorithms by accounting for the model’s convex geometry and low dimensional simplicial structure. By exploiting the connection to Voronoi tessell…
We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses.…
We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex hull of vertices representing the latent topics. Our algori…