arXiv subjects

David Alvarez-Melis

Publications and source records attributed to David Alvarez-Melis.

71 records · Page 4Linked to original sources

arXiv2020

Unsupervised Hierarchy Matching with Optimal Transport over Hyperbolic Spaces

This paper focuses on the problem of unsupervised alignment of hierarchical data such as ontologies or lexical databases. This is a problem that appears across areas, from natural language processing to bioinformatics, and is typically solved by appeal to outside knowledge bases and label-textual similarity. In contrast, we approach the problem from a purely geometric perspective: given only a vector-space representation of the items in the two hierarchies, we seek to infer correspondences across them. Our work derives from and interweaves hyperbolic-space representations for hierarchical data, on one hand, and unsupervised word-alignment methods, on the other. We first provide a set of negative results showing how and why Euclidean methods fail in this hyperbolic setting. We then propose a novel approach based on optimal transport over hyperbolic spaces, and show that it outperforms standard embedding alignment techniques in various experiments on cross-lingual WordNet alignment and ontology matching tasks.

cs.LG↗

arXiv2020

Probabilistic Bias Mitigation in Word Embeddings

It has been shown that word embeddings derived from large corpora tend to incorporate biases present in their training data. Various methods for mitigating these biases have been proposed, but recent work has demonstrated that these methods hide but fail to truly remove the biases, which can still be observed in word nearest-neighbor statistics. In this work we propose a probabilistic view of word embedding bias. We leverage this framework to present a novel method for mitigating bias which relies on probabilistic observations to yield a more robust bias mitigation algorithm. We demonstrate that this method effectively reduces bias according to three separate measures of bias while maintaining embedding quality across various popular benchmark semantic tasks

cs.CL↗

arXiv2020

Geometric Dataset Distances via Optimal Transport

The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks, and many are architecture-dependent, relying on task-specific optimal parameters (e.g., require training a model on each dataset). In this work we propose an alternative notion of distance between datasets that (i) is model-agnostic, (ii) does not involve training, (iii) can compare datasets even if their label sets are completely disjoint and (iv) has solid theoretical footing. This distance relies on optimal transport, which provides it with rich geometry awareness, interpretable correspondences and well-understood properties. Our results show that this novel distance provides meaningful comparison of datasets, and correlates well with transfer learning hardness across various experimental settings and datasets.

cs.LG↗

arXiv2019

Weight of Evidence as a Basis for Human-Oriented Explanations

Interpretability is an elusive but highly sought-after characteristic of modern machine learning methods. Recent work has focused on interpretability via $\textit{explanations}$, which justify individual model predictions. In this work, we take a step towards reconciling machine explanations with those that humans produce and prefer by taking inspiration from the study of explanation in philosophy, cognitive science, and the social sciences. We identify key aspects in which these human explanations differ from current machine explanations, distill them into a list of desiderata, and formalize them into a framework via the notion of $\textit{weight of evidence}$ from information theory. Finally, we instantiate this framework in two simple applications and show it produces intuitive and comprehensible explanations.

cs.LG↗

arXiv2019

Towards Robust, Locally Linear Deep Networks

Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to explain (obtain coordinate relevance for) a prediction. One key challenge is that such derivatives are themselves inherently unstable. In this paper, we propose a new learning problem to encourage deep networks to have stable derivatives over larger regions. While the problem is challenging in general, we focus on networks with piecewise linear activation functions. Our algorithm consists of an inference step that identifies a region around a point where linear approximation is provably stable, and an optimization step to expand such regions. We propose a novel relaxation to scale the algorithm to realistic models. We illustrate our method with residual and recurrent networks on image and sequence datasets.

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arXiv2019

Learning Generative Models across Incomparable Spaces

Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension). In this work, we propose an approach to learn generative models across such incomparable spaces, and demonstrate how to steer the learned distribution towards target properties. A key component of our model is the Gromov-Wasserstein distance, a notion of discrepancy that compares distributions relationally rather than absolutely. While this framework subsumes current generative models in identically reproducing distributions, its inherent flexibility allows application to tasks in manifold learning, relational learning and cross-domain learning.

cs.LG↗

arXiv2019

Towards Optimal Transport with Global Invariances

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of objects can be represented in the same space, or at least distances between them can be directly evaluated. Unfortunately neither requirement is likely to hold when object representations are learned from data. Indeed, automatically derived representations such as word embeddings are typically fixed only up to some global transformations, for example, reflection or rotation. As a result, pairwise distances across two such instances are ill-defined without specifying their relative transformation. In this work, we propose a general framework for optimal transport in the presence of latent global transformations. We cast the problem as a joint optimization over transport couplings and transformations chosen from a flexible class of invariances, propose algorithms to solve it, and show promising results in various tasks, including a popular unsupervised word translation benchmark.

stat.ML↗

arXiv2019

Functional Transparency for Structured Data: a Game-Theoretic Approach

We provide a new approach to training neural models to exhibit transparency in a well-defined, functional manner. Our approach naturally operates over structured data and tailors the predictor, functionally, towards a chosen family of (local) witnesses. The estimation problem is setup as a co-operative game between an unrestricted predictor such as a neural network, and a set of witnesses chosen from the desired transparent family. The goal of the witnesses is to highlight, locally, how well the predictor conforms to the chosen family of functions, while the predictor is trained to minimize the highlighted discrepancy. We emphasize that the predictor remains globally powerful as it is only encouraged to agree locally with locally adapted witnesses. We analyze the effect of the proposed approach, provide example formulations in the context of deep graph and sequence models, and empirically illustrate the idea in chemical property prediction, temporal modeling, and molecule representation learning.

cs.LG↗

arXiv2018

Towards Robust Interpretability with Self-Explaining Neural Networks

Most recent work on interpretability of complex machine learning models has focused on estimating $\textit{a posteriori}$ explanations for previously trained models around specific predictions. $\textit{Self-explaining}$ models where interpretability plays a key role already during learning have received much less attention. We propose three desiderata for explanations in general -- explicitness, faithfulness, and stability -- and show that existing methods do not satisfy them. In response, we design self-explaining models in stages, progressively generalizing linear classifiers to complex yet architecturally explicit models. Faithfulness and stability are enforced via regularization specifically tailored to such models. Experimental results across various benchmark datasets show that our framework offers a promising direction for reconciling model complexity and interpretability.

cs.LG↗

arXiv2018

Gromov-Wasserstein Alignment of Word Embedding Spaces

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. Current state-of-the-art methods, however, involve multiple steps, including heuristic post-hoc refinement strategies. In this paper, we cast the correspondence problem directly as an optimal transport (OT) problem, building on the idea that word embeddings arise from metric recovery algorithms. Indeed, we exploit the Gromov-Wasserstein distance that measures how similarities between pairs of words relate across languages. We show that our OT objective can be estimated efficiently, requires little or no tuning, and results in performance comparable with the state-of-the-art in various unsupervised word translation tasks.

cs.CL↗

arXiv2018

Game-Theoretic Interpretability for Temporal Modeling

Interpretability has arisen as a key desideratum of machine learning models alongside performance. Approaches so far have been primarily concerned with fixed dimensional inputs emphasizing feature relevance or selection. In contrast, we focus on temporal modeling and the problem of tailoring the predictor, functionally, towards an interpretable family. To this end, we propose a co-operative game between the predictor and an explainer without any a priori restrictions on the functional class of the predictor. The goal of the explainer is to highlight, locally, how well the predictor conforms to the chosen interpretable family of temporal models. Our co-operative game is setup asymmetrically in terms of information sets for efficiency reasons. We develop and illustrate the framework in the context of temporal sequence models with examples.

cs.LG↗

arXiv2018

On the Robustness of Interpretability Methods

We argue that robustness of explanations---i.e., that similar inputs should give rise to similar explanations---is a key desideratum for interpretability. We introduce metrics to quantify robustness and demonstrate that current methods do not perform well according to these metrics. Finally, we propose ways that robustness can be enforced on existing interpretability approaches.

cs.LG↗

arXiv2017

Structured Optimal Transport

Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground metric" is limited. In this work, we develop a nonlinear generalization of (discrete) optimal transport that is able to reflect much additional structure. We demonstrate how to leverage the geometry of this new model for fast algorithms, and explore connections and properties. Illustrative experiments highlight the benefit of the induced structured couplings for tasks in domain adaptation and natural language processing.

stat.ML↗

arXiv2017

A causal framework for explaining the predictions of black-box sequence-to-sequence models

We interpret the predictions of any black-box structured input-structured output model around a specific input-output pair. Our method returns an "explanation" consisting of groups of input-output tokens that are causally related. These dependencies are inferred by querying the black-box model with perturbed inputs, generating a graph over tokens from the responses, and solving a partitioning problem to select the most relevant components. We focus the general approach on sequence-to-sequence problems, adopting a variational autoencoder to yield meaningful input perturbations. We test our method across several NLP sequence generation tasks.

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arXiv2017

Distributional Adversarial Networks

We propose a framework for adversarial training that relies on a sample rather than a single sample point as the fundamental unit of discrimination. Inspired by discrepancy measures and two-sample tests between probability distributions, we propose two such distributional adversaries that operate and predict on samples, and show how they can be easily implemented on top of existing models. Various experimental results show that generators trained with our distributional adversaries are much more stable and are remarkably less prone to mode collapse than traditional models trained with pointwise prediction discriminators. The application of our framework to domain adaptation also results in considerable improvement over recent state-of-the-art.

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arXiv2015

A translation of "The characteristic function of a random phenomenon" by Bruno de Finetti

This article is a translation of Bruno de Finetti's paper "Funzione Caratteristica di un fenomeno aleatorio" which appeared in Atti del Congresso Internazionale dei Matematici, Bologna 3-10 Settembre 1928, Tomo VI, pp. 179-190, originally published by Nicola Zanichelli Editore S.p.A. The translation was made as close as possible to the original in form and style, except for apparent mistakes found in the original document, which were corrected and are mentioned as footnotes. Most of these were resolved by comparing against a longer version of this work by de Finetti, published shortly after this one under the same titlea. The interested reader is highly encouraged to consult this other version for a more detailed treatment of the topics covered here. Footnotes regarding the translation are labeled with letters to distinguish them from de Finetti's original footnotes.

math.ST↗

arXiv2015

Word, graph and manifold embedding from Markov processes

Continuous vector representations of words and objects appear to carry surprisingly rich semantic content. In this paper, we advance both the conceptual and theoretical understanding of word embeddings in three ways. First, we ground embeddings in semantic spaces studied in cognitive-psychometric literature and introduce new evaluation tasks. Second, in contrast to prior work, we take metric recovery as the key object of study, unify existing algorithms as consistent metric recovery methods based on co-occurrence counts from simple Markov random walks, and propose a new recovery algorithm. Third, we generalize metric recovery to graphs and manifolds, relating co-occurence counts on random walks in graphs and random processes on manifolds to the underlying metric to be recovered, thereby reconciling manifold estimation and embedding algorithms. We compare embedding algorithms across a range of tasks, from nonlinear dimensionality reduction to three semantic language tasks, including analogies, sequence completion, and classification.

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