Related papers: Bias-corrected estimator for intrinsic dimension a…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a…
Given the variety of the visual world there is not one true scale for recognition: objects may appear at drastically different sizes across the visual field. Rather than enumerate variations across filter channels or pyramid levels, dynamic…
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…
Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve…
Dimension reduction and data visualization aim to project a high-dimensional dataset to a low-dimensional space while capturing the intrinsic structures in the data. It is an indispensable part of modern data science, and many dimensional…
Quantification of the number of variables needed to locally explain complex data is often the first step to better understanding it. Existing techniques from intrinsic dimension estimation leverage statistical models to glean this…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…
Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
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…
The estimation of viewpoints and keypoints effectively enhance object detection methods by extracting valuable traits of the object instances. While the output of both processes differ, i.e., angles vs. list of characteristic points, they…
The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID)…
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…
The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are…
Estimating the dimensionality of the latent representation needed for prediction -- the task-relevant dimension -- is a difficult, largely unsolved problem with broad scientific applications. We cast it as an Information Bottleneck…