12 accepted papers
Flow matching has proven to be a powerful density estimator, yet it often fails to explicitly capture the rich inherent latent structure of complex data. To address this limitation, we introduce Structured Flow Autoencoders (SFA), a family of probabilistic models that augments Continuous Normalizing…
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…
As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being deviated from the known estimate by a mixture distribution. To mo…
Conventional machine learning algorithms cannot be applied until a data matrix is available to process. When the data matrix needs to be obtained from a relational database via a feature extraction query, the computation cost can be prohibitive, as the data matrix may be (much) larger than the total…
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…
We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of interactions among the predictors, while the interaction selection is g…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over severa…
We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the…