Related papers: Gaussian Word Embedding with a Wasserstein Distanc…

A review of Word Embedding Models through a deconstructive approach reveals their several shortcomings and inconsistencies. These include instability of the vector representations, a distorted analogical reasoning, geometric incompatibility…

We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…

Data representation is a fundamental task in machine learning. The representation of data affects the performance of the whole machine learning system. In a long history, the representation of data is done by feature engineering, and…

Distributed word embeddings have yielded state-of-the-art performance in many NLP tasks, mainly due to their success in capturing useful semantic information. These representations assign only a single vector to each word whereas a large…

We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in…

The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian manifolds and generalizes the notion of hyperplanes. As several…

In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…

In this paper, we introduce personalized word embeddings, and examine their value for language modeling. We compare the performance of our proposed prediction model when using personalized versus generic word representations, and study how…

The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…

Most existing word embedding methods can be categorized into Neural Embedding Models and Matrix Factorization (MF)-based methods. However some models are opaque to probabilistic interpretation, and MF-based methods, typically solved using…

Word embedding, which encodes words into vectors, is an important starting point in natural language processing and commonly used in many text-based machine learning tasks. However, in most current word embedding approaches, the similarity…

The main objective of this study is to propose an optimal transport based semi-supervised approach to learn from scarce labelled image data using deep convolutional networks. The principle lies in implicit graph-based transductive…

One of the prime problems of computer science and machine learning is to extract information efficiently from large-scale, heterogeneous data. Text data, with its syntax, semantics, and even hidden information content, possesses an…

We present a simple yet effective approach for learning word sense embeddings. In contrast to existing techniques, which either directly learn sense representations from corpora or rely on sense inventories from lexical resources, our…

Word embeddings are a popular way to improve downstream performances in contemporary language modeling. However, the underlying geometric structure of the embedding space is not well understood. We present a series of explorations using…

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…

We introduce the cross-match test - an exact, distribution free, high-dimensional hypothesis test as an intrinsic evaluation metric for word embeddings. We show that cross-match is an effective means of measuring distributional similarity…