PAC-Bayesian Domain Adaptation Bounds for Multi-view learning

This paper presents a series of new results for domain adaptation in the multi-view learning setting. The incorporation of multiple views in the domain adaptation was paid little attention in the previous studies. In this way, we propose an analysis of generalization bounds with Pac-Bayesian theory to consolidate the two paradigms, which are currently treated separately. Firstly, building on previous work by Germain et al., we adapt the distance between distribution proposed by Germain et al. for domain adaptation with the concept of multi-view learning. Thus, we introduce a novel distance that is tailored for the multi-view domain adaptation setting. Then, we give Pac-Bayesian bounds for estimating the introduced divergence. Finally, we compare the different new bounds with the previous studies.Comment: arXiv admin note: text overlap with arXiv:2004.11829 by other author

PAC-Bayes and Domain Adaptation

We provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different, but related, target distribution. Firstly, we propose an improvement of the previous approach we proposed in Germain et al. (2013), which relies on a novel distribution pseudodistance based on a disagreement averaging, allowing us to derive a new tighter domain adaptation bound for the target risk. While this bound stands in the spirit of common domain adaptation works, we derive a second bound (introduced in Germain et al., 2016) that brings a new perspective on domain adaptation by deriving an upper bound on the target risk where the distributions' divergence-expressed as a ratio-controls the trade-off between a source error measure and the target voters' disagreement. We discuss and compare both results, from which we obtain PAC-Bayesian generalization bounds. Furthermore, from the PAC-Bayesian specialization to linear classifiers, we infer two learning algorithms, and we evaluate them on real data.Comment: Neurocomputing, Elsevier, 2019. arXiv admin note: substantial text overlap with arXiv:1503.0694

Learning via Wasserstein-Based High Probability Generalisation Bounds

Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) -- this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of interest in recent years, a limitation of the PAC-Bayesian framework is that most bounds involve a Kullback-Leibler (KL) divergence term (or its variations), which might exhibit erratic behavior and fail to capture the underlying geometric structure of the learning problem -- hence restricting its use in practical applications. As a remedy, recent studies have attempted to replace the KL divergence in the PAC-Bayesian bounds with the Wasserstein distance. Even though these bounds alleviated the aforementioned issues to a certain extent, they either hold in expectation, are for bounded losses, or are nontrivial to minimize in an SRM framework. In this work, we contribute to this line of research and prove novel Wasserstein distance-based PAC-Bayesian generalisation bounds for both batch learning with independent and identically distributed (i.i.d.) data, and online learning with potentially non-i.i.d. data. Contrary to previous art, our bounds are stronger in the sense that (i) they hold with high probability, (ii) they apply to unbounded (potentially heavy-tailed) losses, and (iii) they lead to optimizable training objectives that can be used in SRM. As a result we derive novel Wasserstein-based PAC-Bayesian learning algorithms and we illustrate their empirical advantage on a variety of experiments.Comment: Accepted to NeurIPS 202

PAC-Bayesian Analysis for a two-step Hierarchical Multiview Learning Approach

Long version : https://arxiv.org/abs/1606.07240International audienceWe study a two-level multiview learning with more than two views under the PAC-Bayesian framework. This approach, sometimes referred as late fusion, consists in learning sequentially multiple view-specific classifiers at the first level, and then combining these view-specific classifiers at the second level. Our main theoretical result is a generalization bound on the risk of the majority vote which exhibits a term of diversity in the predictions of the view-specific classifiers. From this result it comes out that controlling the trade-off between diversity and accuracy is a key element for multiview learning, which complements other results in multiview learning. Finally, we experiment our principle on multiview datasets extracted from the Reuters RCV1/RCV2 collection

Analyzing Granger causality in climate data with time series classification methods

Attribution studies in climate science aim for scientifically ascertaining the influence of climatic variations on natural or anthropogenic factors. Many of those studies adopt the concept of Granger causality to infer statistical cause-effect relationships, while utilizing traditional autoregressive models. In this article, we investigate the potential of state-of-the-art time series classification techniques to enhance causal inference in climate science. We conduct a comparative experimental study of different types of algorithms on a large test suite that comprises a unique collection of datasets from the area of climate-vegetation dynamics. The results indicate that specialized time series classification methods are able to improve existing inference procedures. Substantial differences are observed among the methods that were tested

Apprentissage automatique avec garanties de généralisation à l'aide de méthodes d'ensemble maximisant le désaccord

Nous nous intéressons au domaine de l’apprentissage automatique, une branche de l’intelligence artificielle. Pour résoudre une tâche de classification, un algorithme d’apprentissage observe des données étiquetées et a comme objectif d’apprendre une fonction qui sera en mesure de classifier automatiquement les données qui lui seront présentées dans le futur. Plusieurs algorithmes classiques d’apprentissage cherchent à combiner des classificateurs simples en construisant avec ceux-ci un classificateur par vote de majorité. Dans cette thèse, nous explorons l’utilisation d’une borne sur le risque du classificateur par vote de majorité, nommée la C-borne. Celle-ci est définie en fonction de deux quantités : la performance individuelle des votants, et la corrélation de leurs erreurs (leur désaccord). Nous explorons d’une part son utilisation dans des bornes de généralisation des classificateurs par vote de majorité. D’autre part, nous l’étendons de la classification binaire vers un cadre généralisé de votes de majorité. Nous nous en inspirons finalement pour développer de nouveaux algorithmes d’apprentissage automatique, qui offrent des performances comparables aux algorithmes de l’état de l’art, en retournant des votes de majorité qui maximisent le désaccord entre les votants, tout en contrôlant la performance individuelle de ceux-ci. Les garanties de généralisation que nous développons dans cette thèse sont de la famille des bornes PAC-bayésiennes. Nous généralisons celles-ci en introduisant une borne générale, à partir de laquelle peuvent être retrouvées les bornes de la littérature. De cette même borne générale, nous introduisons des bornes de généralisation basées sur la C-borne. Nous simplifions également le processus de preuve des théorèmes PAC-bayésiens, nous permettant d’obtenir deux nouvelles familles de bornes. L’une est basée sur une différente notion de complexité, la divergence de Rényi plutôt que la divergence Kullback-Leibler classique, et l’autre est spécialisée au cadre de l’apprentissage transductif plutôt que l’apprentissage inductif. Les deux algorithmes d’apprentissage que nous introduisons, MinCq et CqBoost, retournent un classificateur par vote de majorité maximisant le désaccord des votants. Un hyperparamètre permet de directement contrôler leur performance individuelle. Ces deux algorithmes étant construits pour minimiser une borne PAC-bayésienne, ils sont rigoureusement justifiés théoriquement. À l’aide d’une évaluation empirique, nous montrons que MinCq et CqBoost ont une performance comparable aux algorithmes classiques de l’état de l’art.We focus on machine learning, a branch of artificial intelligence. When solving a classification problem, a learning algorithm is provided labelled data and has the task of learning a function that will be able to automatically classify future, unseen data. Many classical learning algorithms are designed to combine simple classifiers by building a weighted majority vote classifier out of them. In this thesis, we extend the usage of the C-bound, bound on the risk of the majority vote classifier. This bound is defined using two quantities : the individual performance of the voters, and the correlation of their errors (their disagreement). First, we design majority vote generalization bounds based on the C-bound. Then, we extend this bound from binary classification to generalized majority votes. Finally, we develop new learning algorithms with state-of-the-art performance, by constructing majority votes that maximize the voters’ disagreement, while controlling their individual performance. The generalization guarantees that we develop in this thesis are in the family of PAC-Bayesian bounds. We generalize the PAC-Bayesian theory by introducing a general theorem, from which the classical bounds from the literature can be recovered. Using this same theorem, we introduce generalization bounds based on the C-bound. We also simplify the proof process of PAC-Bayesian theorems, easing the development of new families of bounds. We introduce two new families of PAC-Bayesian bounds. One is based on a different notion of complexity than usual bounds, the Rényi divergence, instead of the classical Kullback-Leibler divergence. The second family is specialized to transductive learning, instead of inductive learning. The two learning algorithms that we introduce, MinCq and CqBoost, output a majority vote classifier that maximizes the disagreement between voters. An hyperparameter of the algorithms gives a direct control over the individual performance of the voters. These two algorithms being designed to minimize PAC-Bayesian generalization bounds on the risk of the majority vote classifier, they come with rigorous theoretical guarantees. By performing an empirical evaluation, we show that MinCq and CqBoost perform as well as classical stateof- the-art algorithms