Related papers: Statistical Inference for Manifold Similarity and …

Flow-based models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data space that they natively reside in, rather inhabiting a…

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…

Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This paper introduces a class of models 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…

High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…

Heterogeneous data pose serious challenges to data analysis tasks, including exploration and visualization. Current techniques often utilize dimensionality reductions, aggregation, or conversion to numerical values to analyze heterogeneous…

High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…

In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to…

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…

This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…

Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…

We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are…

Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary…

In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…

The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of…

We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

With the emergence of dynamic multiplex networks, corresponding to graphs where multiple types of edges evolve over time, a key inferential task is to determine whether the layers associated with different edge types differ in their…

This paper proposes a method for estimating a surface that contains a given set of points from noisy measurements. More precisely, by assuming that the surface is described by the zero set of a function in the span of a given set of…