Related papers: Metrics for Multivariate Dictionaries
In representation learning, there has been recent interest in developing algorithms to disentangle the ground-truth generative factors behind a dataset, and metrics to quantify how fully this occurs. However, these algorithms and metrics…
Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
Though there are some works on improving distributed word representations using lexicons, the improper overfitting of the words that have multiple meanings is a remaining issue deteriorating the learning when lexicons are used, which needs…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
One major deficiency of most semantic representation techniques is that they usually model a word type as a single point in the semantic space, hence conflating all the meanings that the word can have. Addressing this issue by learning…
Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a high dimensional space and, because of this high-dimensional structure, most algorithms are inefficient. The typical solution is to reduce the…
This paper presents a generalization of the Wasserstein distance for both persistence diagrams and merge trees [20], [66] that takes advantage of the regions of their topological features in the input domain. Specifically, we redefine the…
In traditional Distributional Semantic Models (DSMs) the multiple senses of a polysemous word are conflated into a single vector space representation. In this work, we propose a DSM that learns multiple distributional representations of a…
Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…
We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…
Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…
With the success of self-supervised representations, researchers seek a better understanding of the information encapsulated within a representation. Among various interpretability methods, we focus on classification-based linear probing.…
We derive closed-form expressions for the Bayes optimal decision boundaries in binary classification of high dimensional overlapping Gaussian mixture model (GMM) data, and show how they depend on the eigenstructure of the class covariances,…
Machine learning (ML) datasets, often perceived as neutral, inherently encapsulate abstract and disputed social constructs. Dataset curators frequently employ value-laden terms such as diversity, bias, and quality to characterize datasets.…
Cross-lingual or cross-domain correspondences play key roles in tasks ranging from machine translation to transfer learning. Recently, purely unsupervised methods operating on monolingual embeddings have become effective alignment tools.…
As a highlighting research topic in the multimedia area, cross-media retrieval aims to capture the complex correlations among multiple media types. Learning better shared representation and distance metric for multimedia data is important…