Related papers: Information-Theoretic Quality Metric of Low-Dimens…
In this paper, we study the Empirical Risk Minimization (ERM) problem in the non-interactive Local Differential Privacy (LDP) model. Previous research on this problem \citep{smith2017interaction} indicates that the sample complexity, to…
Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN)…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
In some memory-constrained settings like IoT devices and over-the-network data pipelines, it can be advantageous to have smaller contextual embeddings. We investigate the efficacy of projecting contextual embedding data (BERT) onto a…
While data selection methods have been studied extensively in active learning, data pruning, and data augmentation settings, there is little evidence for the efficacy of these methods in industry scale settings, particularly in low-resource…
In this paper, an efficient Minkowski Distance based Metric (MDM) for no-reference (NR) quality assessment of contrast distorted images is proposed. It is shown that higher orders of Minkowski distance and entropy provide accurate quality…
Diffusion models perform remarkably well on high-dimensional data such as images, often using only a modest number of reverse-time steps. Despite this practical success, existing convergence theory does not fully explain why such samplers…
Deep metric learning aims to construct an embedding space where samples of the same class are close to each other, while samples of different classes are far away from each other. Most existing deep metric learning methods attempt to…
Instruction-based image editing, which aims to modify the image faithfully according to the instruction while preserving irrelevant content unchanged, has made significant progress. However, there still lacks a comprehensive metric for…
Dimension reduction, widely used in science, maps high-dimensional data into low-dimensional space. We investigate a basic mathematical model underlying the techniques of stochastic neighborhood embedding (SNE) and its popular variant…
This work constructs Jonson-Lindenstrauss embeddings with best accuracy, as measured by variance, mean-squared error and exponential concentration of the length distortion. Lower bounds for any data and embedding dimensions are determined,…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
Randomized dimensionality reduction has been recognized as one of the fundamental techniques in handling high-dimensional data. Starting with the celebrated Johnson-Lindenstrauss Lemma, such reductions have been studied in depth for the…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Point convolution operations rely on different embedding mechanisms to encode the neighborhood information of each point in order to detect patterns in 3D space. However, as convolutions are usually evaluated as a whole, not much work has…
We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of…
Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…
Unsupervised homogeneous network embedding (NE) represents every vertex of networks into a low-dimensional vector and meanwhile preserves the network information. Adjacency matrices retain most of the network information, and directly…
A classic problem in unsupervised learning and data analysis is to find simpler and easy-to-visualize representations of the data that preserve its essential properties. A widely-used method to preserve the underlying hierarchical structure…
Self-referential learning -- training a model on data it generated itself -- promises boundless scalability but chronically suffers from model collapse: language models degenerate into repetitive text, GANs drop modes, and…