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Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

Wasserstein distances form a family of metrics on spaces of probability measures that have recently seen many applications. However, statistical analysis in these spaces is complex due to the nonlinearity of Wasserstein spaces. One…

Geometric data sets arising in modern applications are often very large and change dynamically over time. A popular framework for dealing with such data sets is the evolving data framework, where a discrete structure continuously varies…

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…

We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…

Metrics in Grassmannians, or distances between subspaces of same dimension, have many uses, and extending them to the Total Grassmannian of subspaces of different dimensions is an important problem, as usual extensions lack good properties…

Recently, deep metric learning techniques received attention, as the learned distance representations are useful to capture the similarity relationship among samples and further improve the performance of various of supervised or…

Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without linear structure. In such settings the classical additive error…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

Distributional ambiguity sets provide quantifiable ways to characterize the uncertainty about the true probability distribution of random variables of interest. This makes them a key element in data-driven robust optimization by exploiting…

In exploration, the goal is to build a map of an unknown environment. Most state-of-the-art approaches use map representations that require drift-free state estimates to function properly. Real-world state estimators, however, exhibit…

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

Learning task-specific representations of persistence diagrams is an important problem in topological data analysis and machine learning. However, current state of the art methods are restricted in terms of their expressivity as they are…

Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…

Dense Passage Retrieval (DPR) typically relies on Euclidean or cosine distance to measure query-passage relevance in embedding space, which is effective when embeddings lie on a linear manifold. However, our experiments across DPR…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

While generalized linear mixed models are a fundamental tool in applied statistics, many specifications, such as those involving categorical factors with many levels or interaction terms, can be computationally challenging to estimate due…

We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…