Related papers: Dimension Estimation Using Random Connection Model…
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
Large-scale datasets with count outcome variables are widely present in various applications, and the Poisson regression model is among the most popular models for handling count outcomes. This paper considers the high-dimensional sparse…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…
Many privacy mechanisms reveal high-level information about a data distribution through noisy measurements. It is common to use this information to estimate the answers to new queries. In this work, we provide an approach to solve this…
Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points…
We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset $X$ of $\mathbb{R}^d$ from a set $Y$ that is close in the Hausdorff distance. This estimator enjoys a linear rate of convergence as…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of…
High-dimensional dense embeddings have become central to modern Information Retrieval, but many dimensions are noisy or redundant. Recently proposed DIME (Dimension IMportance Estimation), provides query-dependent scores to identify…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Distance measures are part and parcel of many computer vision algorithms. The underlying assumption in all existing distance measures is that feature elements are independent and identically distributed. However, in real-world settings,…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…