Computationally intensive, distributed and decentralised machine learning: from theory to applications

Machine learning (ML) is currently one of the most important research fields, spanning computer science, statistics, pattern recognition, data mining, and predictive analytics. It plays a central role in automatic data processing and analysis in numerous research domains owing to widely distributed and geographically scattered data sources, powerful computing clouds, and high digitisation requirements. However, aspects such as the accuracy of methods, data privacy, and model explainability remain challenging and require additional research. Therefore, it is necessary to analyse centralised and distributed data processing architectures, and to create novel computationally intensive explainable and privacy-preserving ML methods, to investigate their properties, to propose distributed versions of prospective ML baseline methods, and to evaluate and apply these in various applications. This thesis addresses the theoretical and practical aspects of state-of-the-art ML methods. The contributions of this thesis are threefold. In Chapter 2, novel non-distributed, centralised, computationally intensive ML methods are proposed, their properties are investigated, and state-of-the-art ML methods are applied to real-world data from two domains, namely transportation and bioinformatics. Moreover, algorithms for ‘black-box’ model interpretability are presented. Decentralised ML methods are considered in Chapter 3. First, we investigate data processing as a preliminary step in data-driven, agent-based decision-making. Thereafter, we propose novel decentralised ML algorithms that are based on the collaboration of the local models of agents. Within this context, we consider various regression models. Finally, the explainability of multiagent decision-making is addressed. In Chapter 4, we investigate distributed centralised ML methods. We propose a distributed parallelisation algorithm for the semi-parametric and non-parametric regression types, and implement these in the computational environment and data structures of Apache SPARK. Scalability, speed-up, and goodness-of-fit experiments using real-world data demonstrate the excellent performance of the proposed methods. Moreover, the federated deep-learning approach enables us to address the data privacy challenges caused by processing of distributed private data sources to solve the travel-time prediction problem. Finally, we propose an explainability strategy to interpret the influence of the input variables on this federated deep-learning application. This thesis is based on the contribution made by 11 papers to the theoretical and practical aspects of state-of-the-art and proposed ML methods. We successfully address the stated challenges with various data processing architectures, validate the proposed approaches in diverse scenarios from the transportation and bioinformatics domains, and demonstrate their effectiveness in scalability, speed-up, and goodness-of-fit experiments with real-world data. However, substantial future research is required to address the stated challenges and to identify novel issues in ML. Thus, it is necessary to advance the theoretical part by creating novel ML methods and investigating their properties, as well as to contribute to the application part by using of the state-of-the-art ML methods and their combinations, and interpreting their results for different problem setting

Marginal integration for nonparametric causal inference

We consider the problem of inferring the total causal effect of a single variable intervention on a (response) variable of interest. We propose a certain marginal integration regression technique for a very general class of potentially nonlinear structural equation models (SEMs) with known structure, or at least known superset of adjustment variables: we call the procedure S-mint regression. We easily derive that it achieves the convergence rate as for nonparametric regression: for example, single variable intervention effects can be estimated with convergence rate $n^{-2/5}$ assuming smoothness with twice differentiable functions. Our result can also be seen as a major robustness property with respect to model misspecification which goes much beyond the notion of double robustness. Furthermore, when the structure of the SEM is not known, we can estimate (the equivalence class of) the directed acyclic graph corresponding to the SEM, and then proceed by using S-mint based on these estimates. We empirically compare the S-mint regression method with more classical approaches and argue that the former is indeed more robust, more reliable and substantially simpler.Comment: 40 pages, 14 figure

Accounting for variance and hyperparameter optimization in machine learning benchmarks

La récente révolution de l'apprentissage automatique s'est fortement appuyée sur l'utilisation de bancs de test standardisés. Ces derniers sont au centre de la méthodologie scientifique en apprentissage automatique, fournissant des cibles et mesures indéniables des améliorations des algorithmes d'apprentissage. Ils ne garantissent cependant pas la validité des résultats ce qui implique que certaines conclusions scientifiques sur les avancées en intelligence artificielle peuvent s'avérer erronées. Nous abordons cette question dans cette thèse en soulevant d'abord la problématique (Chapitre 5), que nous étudions ensuite plus en profondeur pour apporter des solutions (Chapitre 6) et finalement developpons un nouvel outil afin d'amélioration la méthodologie des chercheurs (Chapitre 7). Dans le premier article, chapitre 5, nous démontrons la problématique de la reproductibilité pour des bancs de test stables et consensuels, impliquant que ces problèmes sont endémiques aussi à de grands ensembles d'applications en apprentissage automatique possiblement moins stable et moins consensuels. Dans cet article, nous mettons en évidence l'impact important de la stochasticité des bancs de test, et ce même pour les plus stables tels que la classification d'images. Nous soutenons d'après ces résultats que les solutions doivent tenir compte de cette stochasticité pour améliorer la reproductibilité des bancs de test. Dans le deuxième article, chapitre 6, nous étudions les différentes sources de variation typiques aux bancs de test en apprentissage automatique, mesurons l'effet de ces variations sur les méthodes de comparaison d'algorithmes et fournissons des recommandations sur la base de nos résultats. Une contribution importante de ce travail est la mesure de la fiabilité d'estimateurs peu coûteux à calculer mais biaisés servant à estimer la performance moyenne des algorithmes. Tel qu'expliqué dans l'article, un estimateur idéal implique plusieurs exécution d'optimisation d'hyperparamètres ce qui le rend trop coûteux à calculer. La plupart des chercheurs doivent donc recourir à l'alternative biaisée, mais nous ne savions pas jusqu'à présent la magnitude de la dégradation de cet estimateur. Sur la base de nos résultats, nous fournissons des recommandations pour la comparison d'algorithmes sur des bancs de test avec des budgets de calculs limités. Premièrement, les sources de variations devraient être randomisé autant que possible. Deuxièmement, la randomization devrait inclure le partitionnement aléatoire des données pour les ensembles d'entraînement, de validation et de test, qui s'avère être la plus importante des sources de variance. Troisièmement, des tests statistiques tel que la version du Mann-Withney U-test présenté dans notre article devrait être utilisé plutôt que des comparisons sur la simple base de moyennes afin de prendre en considération l'incertitude des mesures de performance. Dans le chapitre 7, nous présentons un cadriciel d'optimisation d'hyperparamètres développé avec principal objectif de favoriser les bonnes pratiques d'optimisation des hyperparamètres. Le cadriciel est conçu de façon à privilégier une interface simple et intuitive adaptée aux habitudes de travail des chercheurs en apprentissage automatique. Il inclut un nouveau système de versionnage d'expériences afin d'aider les chercheurs à organiser leurs itérations expérimentales et tirer profit des résultats antérieurs pour augmenter l'efficacité de l'optimisation des hyperparamètres. L'optimisation des hyperparamètres joue un rôle important dans les bancs de test, les hyperparamètres étant un facteur confondant significatif. Fournir aux chercheurs un instrument afin de bien contrôler ces facteurs confondants est complémentaire aux recommandations pour tenir compte des sources de variation dans le chapitre 6. Nos recommendations et l'outil pour l'optimisation d'hyperparametre offre une base solide pour une méthodologie robuste et fiable.The recent revolution in machine learning has been strongly based on the use of standardized benchmarks. Providing clear target metrics and undeniable measures of improvements of learning algorithms, they are at the center of the scientific methodology in machine learning. They do not ensure validity of results however, therefore some scientific conclusions based on flawed methodology may prove to be wrong. In this thesis we address this question by first raising the issue (Chapter 5), then we study it to find solutions and recommendations (Chapter 6) and build tools to help improve the methodology of researchers (Chapter 7). In first article, Chapter 5, we demonstrate the issue of reproducibility in stable and consensual benchmarks, implying that these issues are endemic to a large ensemble of machine learning applications that are possibly less stable or less consensual. We raise awareness of the important impact of stochasticity even in stable image classification tasks and contend that solutions for reproducible benchmarks should account for this stochasticity. In second article, Chapter 6, we study the different sources of variation that are typical in machine learning benchmarks, measure their effect on comparison methods to benchmark algorithms and provide recommendations based on our results. One important contribution of this work is that we measure the reliability of a cheaper but biased estimator for the average performance of algorithms. As explained in the article, an ideal estimator involving multiple rounds of hyperparameter optimization is too computationally expensive. Most researchers must resort to use the biased alternative, but it has been unknown until now how serious a degradation of the quality of estimation this leads to. Our investigations provides guidelines for benchmarks on practical budgets. First, as many sources of variations as possible should be randomized. Second, the partitioning of data in training, validation and test sets should be randomized as well, since this is the most important source of variation. Finally, statistical tests should be used instead of ad-hoc average comparisons so that the uncertainty of performance estimation can be accounted for when comparing machine learning algorithms. In Chapter 7, we present a framework for hyperparameter optimization that has been developed with the main goal of encouraging best practices for hyperparameter optimization. The framework is designed to favor a simple and intuitive interface adapted to the workflow of machine learning researchers. It includes a new version control system for experiments to help researchers organize their rounds of experimentations and leverage prior results for more efficient hyperparameter optimization. Hyperparameter optimization plays an important role in benchmarking, with the effect of hyperparameters being a serious confounding factor. Providing an instrument for researchers to properly control this confounding factor is complementary to our guidelines to account for sources of variation in Chapter 7. Our recommendations together with our tool for hyperparameter optimization provides a solid basis for a reliable methodology in machine learning benchmarks

Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data

pre-printThis paper proposes an original approach for the statistical analysis of longitudinal shape data. The proposed method allows the characterization of typical growth patterns and subject-specific shape changes in repeated time-series observations of several subjects. This can be seen as the extension of usual longitudinal statistics of scalar measurements to high-dimensional shape or image data. The method is based on the estimation of continuous subject-specific growth trajectories and the comparison of such temporal shape changes across subjects. Differences between growth trajectories are decomposed into morphological deformations, which account for shape changes independent of the time, and time warps, which account for different rates of shape changes over time. Given a longitudinal shape data set, we estimate a mean growth scenario representative of the population, and the variations of this scenario both in terms of shape changes and in terms of change in growth speed. Then, intrinsic statistics are derived in the space of spatiotemporal deformations, which characterize the typical variations in shape and in growth speed within the studied population. They can be used to detect systematic developmental delays across subjects. In the context of neuroscience, we apply this method to analyze the differences in the growth of the hippocampus in children diagnosed with autism, developmental delays and in controls. Result suggest that group differences may be better characterized by a different speed of maturation rather than shape differences at a given age. In the context of anthropology, we assess the differences in the typical growth of the endocranium between chimpanzees and bonobos. We take advantage of this study to show the robustness of the method with respect to change of parameters and perturbation of the age estimates

Bayesian plug & play methods for inverse problems in imaging.

Thèse de Doctorat de Mathématiques Appliquées (Université de Paris)Tesis de Doctorado en Ingeniería Eléctrica (Universidad de la República)This thesis deals with Bayesian methods for solving ill-posed inverse problems in imaging with learnt image priors. The first part of this thesis (Chapter 3) concentrates on two particular problems, namely joint denoising and decompression and multi-image super-resolution. After an extensive study of the noise statistics for these problem in the transformed (wavelet or Fourier) domain, we derive two novel algorithms to solve this particular inverse problem. One of them is based on a multi-scale self-similarity prior and can be seen as a transform-domain generalization of the celebrated non-local bayes algorithm to the case of non-Gaussian noise. The second one uses a neural-network denoiser to implicitly encode the image prior, and a splitting scheme to incorporate this prior into an optimization algorithm to find a MAP-like estimator. The second part of this thesis concentrates on the Variational AutoEncoder (VAE) model and some of its variants that show its capabilities to explicitly capture the probability distribution of high-dimensional datasets such as images. Based on these VAE models, we propose two ways to incorporate them as priors for general inverse problems in imaging : • The first one (Chapter 4) computes a joint (space-latent) MAP estimator named Joint Posterior Maximization using an Autoencoding Prior (JPMAP). We show theoretical and experimental evidence that the proposed objective function satisfies a weak bi-convexity property which is sufficient to guarantee that our optimization scheme converges to a stationary point. Experimental results also show the higher quality of the solutions obtained by our JPMAP approach with respect to other non-convex MAP approaches which more often get stuck in spurious local optima. • The second one (Chapter 5) develops a Gibbs-like posterior sampling algorithm for the exploration of posterior distributions of inverse problems using multiple chains and a VAE as image prior. We showhowto use those samples to obtain MMSE estimates and their corresponding uncertainty.Cette thèse traite des méthodes bayésiennes pour résoudre des problèmes inverses mal posés en imagerie avec des distributions a priori d’images apprises. La première partie de cette thèse (Chapitre 3) se concentre sur deux problèmes partic-uliers, à savoir le débruitage et la décompression conjoints et la super-résolutionmulti-images. Après une étude approfondie des statistiques de bruit pour ces problèmes dans le domaine transformé (ondelettes ou Fourier), nous dérivons deuxnouveaux algorithmes pour résoudre ce problème inverse particulie. L’un d’euxest basé sur une distributions a priori d’auto-similarité multi-échelle et peut êtrevu comme une généralisation du célèbre algorithme de Non-Local Bayes au cas dubruit non gaussien. Le second utilise un débruiteur de réseau de neurones pourcoder implicitement la distribution a priori, et un schéma de division pour incor-porer cet distribution dans un algorithme d’optimisation pour trouver un estima-teur de type MAP. La deuxième partie de cette thèse se concentre sur le modèle Variational Auto Encoder (VAE) et certaines de ses variantes qui montrent ses capacités à capturer explicitement la distribution de probabilité d’ensembles de données de grande dimension tels que les images. Sur la base de ces modèles VAE, nous proposons deuxmanières de les incorporer comme distribution a priori pour les problèmes inverses généraux en imagerie: •Le premier (Chapitre 4) calcule un estimateur MAP conjoint (espace-latent) nommé Joint Posterior Maximization using an Autoencoding Prior (JPMAP). Nous montrons des preuves théoriques et expérimentales que la fonction objectif proposée satisfait une propriété de bi-convexité faible qui est suffisante pour garantir que notre schéma d’optimisation converge vers un pointstationnaire. Les résultats expérimentaux montrent également la meilleurequalité des solutions obtenues par notre approche JPMAP par rapport à d’autresapproches MAP non convexes qui restent le plus souvent bloquées dans desminima locaux. •Le second (Chapitre 5) développe un algorithme d’échantillonnage a poste-riori de type Gibbs pour l’exploration des distributions a posteriori de problèmes inverses utilisant des chaînes multiples et un VAE comme distribution a priori. Nous montrons comment utiliser ces échantillons pour obtenir desestimations MMSE et leur incertitude correspondante.En esta tesis se estudian métodos bayesianos para resolver problemas inversos mal condicionados en imágenes usando distribuciones a priori entrenadas. La primera parte de esta tesis (Capítulo 3) se concentra en dos problemas particulares, a saber, el de eliminación de ruido y descompresión conjuntos, y el de superresolución a partir de múltiples imágenes. Después de un extenso estudio de las estadísticas del ruido para estos problemas en el dominio transformado (wavelet o Fourier),derivamos dos algoritmos nuevos para resolver este problema inverso en particular. Uno de ellos se basa en una distribución a priori de autosimilitud multiescala y puede verse como una generalización al dominio wavelet del célebre algoritmo Non-Local Bayes para el caso de ruido no Gaussiano. El segundo utiliza un algoritmo de eliminación de ruido basado en una red neuronal para codificar implícitamente la distribución a priori de las imágenes y un esquema de relajación para incorporar esta distribución en un algoritmo de optimización y así encontrar un estimador similar al MAP. La segunda parte de esta tesis se concentra en el modelo Variational AutoEncoder (VAE) y algunas de sus variantes que han mostrado capacidad para capturar explícitamente la distribución de probabilidad de conjuntos de datos en alta dimensión como las imágenes. Basándonos en estos modelos VAE, proponemos dos formas de incorporarlos como distribución a priori para problemas inversos genéricos en imágenes : •El primero (Capítulo 4) calcula un estimador MAP conjunto (espacio imagen y latente) llamado Joint Posterior Maximization using an Autoencoding Prior (JPMAP). Mostramos evidencia teórica y experimental de que la función objetivo propuesta satisface una propiedad de biconvexidad débil que es suficiente para garantizar que nuestro esquema de optimización converge a un punto estacionario. Los resultados experimentales también muestran la mayor calidad de las soluciones obtenidas por nuestro enfoque JPMAP con respecto a otros enfoques MAP no convexos que a menudo se atascan en mínimos locales espurios. •El segundo (Capítulo 5) desarrolla un algoritmo de muestreo tipo Gibbs parala exploración de la distribución a posteriori de problemas inversos utilizando múltiples cadenas y un VAE como distribución a priori. Mostramos cómo usar esas muestras para obtener estimaciones de MMSE y su correspondiente incertidumbr

Density estimation of plankton size spectra: a reanalysis of IronEx II data

Many critical processes of ecosystem function, including trophic relationships between predators and prey and maximum rates of photosynthesis and growth, are size-dependent. Size spectral data are therefore precious to modellers because they can constrain model predictions of size-dependent processes. Here we illustrate a multi-step statistical approach to create size spectra based on a reanalysis of plankton size data from the IronEx II experiment, where iron was added to a marked patch of water and changes in productivity and community structure were followed. First, bootstrapping was applied to resample original size measurements and cell counts. Kernel density estimation was then used to provide nonparametric descriptions of density versus size. Finally, parametric distributions were used to obtain parameter estimates that can more easily be applied in models. A major advantage of this approach is that it provides confidence envelopes for the density distributions. Our analyses suggest three basic distributional patterns of cell concentration versus logarithm of equivalent spherical diameter for individual taxa. Composite size-densities of heterotrophs and photoautotrophs reveal important aspects of the coupling between protist grazing and the phytoplankton community

Nonparametric Stochastic Generation of Daily Precipitation and Other Weather Variables

Traditional stochastic approaches for synthetic generation of weather variables often assume a prior functional form for the stochastic process, are often not capable of reproducing the probabilistic structure present in the data, and may not be uniformly applicable across sites. In an attempt to find a general framework for stochastic generation of weather variables, this study marks a unique departure from the traditional approaches, and ushers in the use of data-driven nonparametric techniques and demonstrates their utility. Precipitation is one of the key variables that drive hydrologic systems and hence warrants more focus . In this regard, two major aspects of precipitation modeling were considered: (I) resampling traces under the assumption of stationarity in the process, or with some treatment of the seasonality, and (2) investigations into interannual and secular trends in precipitation and their likely implications. A nonparametric seasonal wet/dry spell model was developed for the generation of daily precipitation. In this the probability density functions of interest are estimated using non parametric kernel density estimators. In the course of development of this model, various nonparametric density estimators for discrete and continuous data were reviewed, tested, and documented, which resulted in the development of a nonparametric estimator for discrete probability estimation. Variations in seasonality of precipitation as a function of latitude and topographic factors were seen through the non parametric estimation of the time-varying occurrence frequency. Nonparametric spectral analysis, performed on monthly precipitation, revealed significant interannual frequencies and coherence with known atmospheric oscillations. Consequently, a non parametric, nonhomogeneous Markov chain for modeling daily precipitation was developed that obviated the need to divide the year into seasons. Multivariate nonparametric resampling technique from the nonparametrically fitted probability density functions, which can be likened to a smoothed bootstrap approach, was developed for the simulation of other weather variables (solar radiation, maximum and minimum temperature, average dew point temperature, and average wind speed). In this technique the vector of variables on a day is generated by conditioning on the vector of these variables on the preceding day and the precipitation amount on the current day generated from the wet/dry spell model

Data-based decision rules about the convexity of the support of a distribution

Given n independent, identically distributed random vectors in R-d, drawn from a common density f, one wishes to find out whether the support of f is convex or not. In this paper we describe a decision rule which decides correctly for sufficiently largen, with probability 1, whenever f is bounded away from zero in its compact support. We also show that the assumption of boundedness is necessary. The rule is based on a statistic that is a second-orde U-statistic with a random kernel. Moreover, we suggest a way of approximating the distribution of the statistic under the hypothesis of convexity of the support. The performance of the proposed method is illustrated on simulated data sets. As an example of its potential statistical implications, the decision rule is used to automatically choose the tuning parameter of ISOMAP, a nonlinear dimensionality reduction method.Peer ReviewedPostprint (published version

Gradient boosting in automatic machine learning: feature selection and hyperparameter optimization

Das Ziel des automatischen maschinellen Lernens (AutoML) ist es, alle Aspekte der Modellwahl in prädiktiver Modellierung zu automatisieren. Diese Arbeit beschäftigt sich mit Gradienten Boosting im Kontext von AutoML mit einem Fokus auf Gradient Tree Boosting und komponentenweisem Boosting. Beide Techniken haben eine gemeinsame Methodik, aber ihre Zielsetzung ist unterschiedlich. Während Gradient Tree Boosting im maschinellen Lernen als leistungsfähiger Vorhersagealgorithmus weit verbreitet ist, wurde komponentenweises Boosting im Rahmen der Modellierung hochdimensionaler Daten entwickelt. Erweiterungen des komponentenweisen Boostings auf multidimensionale Vorhersagefunktionen werden in dieser Arbeit ebenfalls untersucht. Die Herausforderung der Hyperparameteroptimierung wird mit Fokus auf Bayesianische Optimierung und effiziente Stopping-Strategien diskutiert. Ein groß angelegter Benchmark über Hyperparameter verschiedener Lernalgorithmen, zeigt den kritischen Einfluss von Hyperparameter Konfigurationen auf die Qualität der Modelle. Diese Daten können als Grundlage für neue AutoML- und Meta-Lernansätze verwendet werden. Darüber hinaus werden fortgeschrittene Strategien zur Variablenselektion zusammengefasst und eine neue Methode auf Basis von permutierten Variablen vorgestellt. Schließlich wird ein AutoML-Ansatz vorgeschlagen, der auf den Ergebnissen und Best Practices für die Variablenselektion und Hyperparameteroptimierung basiert. Ziel ist es AutoML zu vereinfachen und zu stabilisieren sowie eine hohe Vorhersagegenauigkeit zu gewährleisten. Dieser Ansatz wird mit AutoML-Methoden, die wesentlich komplexere Suchräume und Ensembling Techniken besitzen, verglichen. Vier Softwarepakete für die statistische Programmiersprache R sind Teil dieser Arbeit, die neu entwickelt oder erweitert wurden: mlrMBO: Ein generisches Paket für die Bayesianische Optimierung; autoxgboost: Ein AutoML System, das sich vollständig auf Gradient Tree Boosting fokusiert; compboost: Ein modulares, in C++ geschriebenes Framework für komponentenweises Boosting; gamboostLSS: Ein Framework für komponentenweises Boosting additiver Modelle für Location, Scale und Shape.The goal of automatic machine learning (AutoML) is to automate all aspects of model selection in (supervised) predictive modeling. This thesis deals with gradient boosting techniques in the context of AutoML with a focus on gradient tree boosting and component-wise gradient boosting. Both techniques have a common methodology, but their goal is quite different. While gradient tree boosting is widely used in machine learning as a powerful prediction algorithm, component-wise gradient boosting strength is in feature selection and modeling of high-dimensional data. Extensions of component-wise gradient boosting to multidimensional prediction functions are considered as well. Focusing on Bayesian optimization and efficient early stopping strategies the challenge of hyperparameter optimization for these algorithms is discussed. Difficulty in the optimization of these algorithms is shown by a large scale random search on hyperparameters for machine learning algorithms, that can build the foundation of new AutoML and metalearning approaches. Furthermore, advanced feature selection strategies are summarized and a new method based on shadow features is introduced. Finally, an AutoML approach based on the results and best practices for feature selection and hyperparameter optimization is proposed, with the goal of simplifying and stabilizing AutoML while maintaining high prediction accuracy. This is compared to AutoML approaches using much more complex search spaces and ensembling techniques. Four software packages for the statistical programming language R have been newly developed or extended as a part of this thesis: mlrMBO: A general framework for Bayesian optimization; autoxgboost: An automatic machine learning framework that heavily utilizes gradient tree boosting; compboost: A modular framework for component-wise boosting written in C++; gamboostLSS: A framework for component-wise boosting for generalized additive models for location scale and shape