Related papers: A Wiener Process Perspective on Local Intrinsic Di…

High-dimensional datasets often exhibit low-dimensional geometric structures, as suggested by the manifold hypothesis, which implies that data lie on a smooth manifold embedded in a higher-dimensional ambient space. While this insight…

In recent years, neural network-based anomaly detection methods have attracted considerable attention in the hyperspectral remote sensing domain due to the powerful reconstruction ability compared with traditional methods. However, actual…

Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of…

Likelihood-based deep generative models (DGMs) have gained significant attention for their ability to approximate the distributions of high-dimensional data. However, these models lack a performance guarantee in assigning higher likelihood…

Advances in deep generative and density models have shown impressive capacity to model complex probability density functions in lower-dimensional space. Also, applying such models to high-dimensional image data to model the PDF has shown…

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…

Robust local feature representations are essential for spatial intelligence tasks such as robot navigation and augmented reality. Establishing reliable correspondences requires descriptors that provide both high discriminative power and…

The formalism of Wiener filtering is developed here for the purpose of reconstructing the large scale structure of the universe from noisy, sparse and incomplete data. The method is based on a linear minimum variance solution, given data…

Intrinsic image decomposition (IID) is the task that decomposes a natural image into albedo and shade. While IID is typically solved through supervised learning methods, it is not ideal due to the difficulty in observing ground truth albedo…

Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions. More recent generative models…

Density level sets are mainly estimated using one of three methodologies: plug-in, excess mass, or a hybrid approach. The plug-in methods are based on replacing the unknown density by some nonparametric estimator, usually the kernel. Thus,…

An additive autoencoder for dimension reduction, which is composed of a serially performed bias estimation, linear trend estimation, and nonlinear residual estimation, is proposed and analyzed. Computational experiments confirm that an…

The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…

In recent years there has been increased interest in understanding the interplay between deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses on understanding the reasons why commonly-used DGMs succeed or…

Variational Autoencoders (VAEs) have gained significant popularity among researchers as a powerful tool for understanding unknown distributions based on limited samples. This popularity stems partly from their impressive performance and…

Out-of-distribution (OOD) detection is critical for ensuring the reliability of deep learning systems, particularly in safety-critical applications. Likelihood-based deep generative models have historically faced criticism for their…

Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical…

We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…