Related papers: Intrinsic Dimensionality Estimation within Tight L…
The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in…
Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE…
One of the most common methods for statistical inference is the maximum likelihood estimator (MLE). The MLE needs to compute the normalization constant in statistical models, and it is often intractable. Using unnormalized statistical…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Cybersecurity has emerged as a critical global concern. Intrusion Detection Systems (IDS) play a critical role in protecting interconnected networks by detecting malicious actors and activities. Machine Learning (ML)-based behavior analysis…
In this paper, we evaluate dimensionality reduction methods in terms of difficulty in estimating visual information on original images from dimensionally reduced ones. Recently, dimensionality reduction has been receiving attention as the…
The ability to detect out-of-distribution (OOD) inputs is critical to guarantee the reliability of classification models deployed in an open environment. A fundamental challenge in OOD detection is that a discriminative classifier is…
Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…
In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weighted sums of $2\times 2$ configuration counts. For Boolean models with balls as grains,…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be…
The overarching goals in image-based localization are scale, robustness and speed. In recent years, approaches based on local features and sparse 3D point-cloud models have both dominated the benchmarks and seen successful realworld…
We introduce Locally Linear Embedding (LLE) to the astronomical community as a new classification technique, using SDSS spectra as an example data set. LLE is a nonlinear dimensionality reduction technique which has been studied in the…
The problem of explaining deep learning models, and model predictions generally, has attracted intensive interest recently. Many successful approaches forgo global approximations in order to provide more faithful local interpretations of…
Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually…
Intrinsic Image Decomposition (IID) is a challenging and interesting computer vision problem with various applications in several fields. We present novel semantic priors and an integrated approach for single image IID that involves…
Estimating the location where an image was taken based solely on the contents of the image is a challenging task, even for humans, as properly labeling an image in such a fashion relies heavily on contextual information, and is not as…
Monocular Metric Depth Estimation (MMDE) is essential for physically intelligent systems, yet accurate depth estimation for underrepresented classes in complex scenes remains a persistent challenge. To address this, we propose RAD, a…