Related papers: Principal Feature Detection via $\Phi$-Sobolev Ine…
Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. We introduce a method for identifying and approximating a target measure $\pi$ as a perturbation of a…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these…
We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…
Extraction of local feature descriptors is a vital stage in the solution pipelines for numerous computer vision tasks. Learning-based approaches improve performance in certain tasks, but still cannot replace handcrafted features in general.…
Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…
A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settings, the nature of this anisotropy may be…
Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching…
One-class anomaly detection aims to detect objects that do not belong to a predefined normal class. In practice training data lack those anomalous samples; hence state-of-the-art methods are trained to discriminate between normal and…
A feature-mapping framework for inverse reconstruction of density-based topology optimization results is proposed. Unlike SIMP, whose voxelized outputs are hard to interpret or reuse, the method represents designs with high-level geometric…
The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…
A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of…
The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…
Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally…
We present a novel feature matching algorithm that systematically utilizes the geometric properties of features such as position, scale, and orientation, in addition to the conventional descriptor vectors. In challenging scenes with the…
We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor…
In this paper we study the problem of content-based image retrieval. In this problem, the most popular performance measure is the top precision measure, and the most important component of a retrieval system is the similarity function used…
When pre-processing observational data via matching, we seek to approximate each unit with maximally similar peers that had an alternative treatment status--essentially replicating a randomized block design. However, as one considers a…