Related papers: Theoretical and Practical Analysis of Fr\'echet Re…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…
Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general…
Matching is a popular approach in causal inference to estimate treatment effects by pairing treated and control units that are most similar in terms of their covariate information. However, classic matching methods completely ignore the…
Recently there was an increasing interest in applications of graph neural networks in non-Euclidean geometry; however, are non-Euclidean representations always useful for graph learning tasks? For different problems such as node…
In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…
Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing…
We develop algorithms for performing semiparametric regression analysis in real time, with data processed as it is collected and made immediately available via modern telecommunications technologies. Our definition of semiparametric…
Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
Heterogeneity is a hallmark of complex diseases. Regression-based heterogeneity analysis, which is directly concerned with outcome-feature relationships, has led to a deeper understanding of disease biology. Such an analysis identifies the…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
Data taking value on a Riemannian manifold and observed over a complex spatial domain are becoming more frequent in applications, e.g. in environmental sciences and in geoscience. The analysis of these data needs to rely on local models to…
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…
This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon…
Regression with random data objects is becoming increasingly common in modern data analysis. Unfortunately, this novel regression method is not immune to the trouble caused by unusual observations. A metric Cook's distance extending the…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…
Model merging aims to combine multiple models into one without additional training. Na\"ive parameter-space averaging can be fragile under architectural symmetries, as their geometry does not take them into account. In this work we show…
We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…