Related papers: Local Procrustes for Manifold Embedding: A Measure…
Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
1. Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative…
Metric embeddings into structured spaces, particularly hierarchically well-separated trees (HSTs), are a fundamental tool in the design of online algorithms. In the classical online embedding setting, points arrive sequentially and must be…
Probabilistic metric embedding into trees is a powerful technique for designing online algorithms. The standard approach is to embed the entire underlying metric into a tree metric and then solve the problem on the latter. The overhead in…
Embedding techniques have become essential components of large databases in the deep learning era. By encoding discrete entities, such as words, items, or graph nodes, into continuous vector spaces, embeddings facilitate more efficient…
Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
Machine learning models can generalize well on real-world datasets. According to the manifold hypothesis, this is possible because datasets lie on a latent manifold with small intrinsic dimension (ID). There exist many methods for ID…
Compressing word embeddings is important for deploying NLP models in memory-constrained settings. However, understanding what makes compressed embeddings perform well on downstream tasks is challenging---existing measures of compression…
Optimal Transport (OT) provides a useful geometric framework to estimate the permutation matrix under unsupervised cross-lingual word embedding (CLWE) models that pose the alignment task as a Wasserstein-Procrustes problem. However, linear…
We consider the task of aligning two sets of points in high dimension, which has many applications in natural language processing and computer vision. As an example, it was recently shown that it is possible to infer a bilingual lexicon,…
This paper discusses the challenges of evaluating deblurring-methods quality and proposes a reduced-reference metric based on machine learning. Traditional quality-assessment metrics such as PSNR and SSIM are common for this task, but not…
High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands…
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…
In this paper, we adopt the Universal Manifold Embedding (UME) framework for the estimation of rigid transformations and extend it, so that it can accommodate scenarios involving partial overlap and differently sampled point clouds. UME is…
Dense depth maps have been used as a key element of visual perception tasks. There have been tremendous efforts to enhance the depth quality, ranging from optimization-based to learning-based methods. Despite the remarkable progress for a…