Cette thèse est consacrée à l'analyse théorique de problèmes non supervisés impliquant des séries temporelles hautement dépendantes. Plus particulièrement, nous abordons les deux problèmes fondamentaux que sont le problème d'estimation des points de rupture et le partitionnement de séries temporelles. Ces problèmes sont abordés dans un cadre extrêmement général oùles données sont générées par des processus stochastiques ergodiques stationnaires. Il s'agit de l'une des hypothèses les plus faibles en statistiques, comprenant non seulement, les hypothèses de modèles et les hypothèses paramétriques habituelles dans la littérature scientifique, mais aussi des hypothèses classiques d'indépendance, de contraintes sur l'espace mémoire ou encore des hypothèses de mélange. En particulier, aucune restriction n'est faite sur la forme ou la nature des dépendances, de telles sortes que les échantillons peuvent être arbitrairement dépendants. Pour chaque problème abordé, nous proposons de nouvelles méthodes non paramétriques et nous prouvons de plus qu'elles sont, dans ce cadre, asymptotiquement consistantes. Pour l'estimation de points de rupture, la consistance asymptotique se rapporte à la capacité de l'algorithme à produire des estimations des points de rupture qui sont asymptotiquement arbitrairement proches des vrais points de rupture. D'autre part, un algorithme de partitionnement est asymptotiquement consistant si le partitionnement qu'il produit, restreint à chaque lot de séquences, coïncides, à partir d'un certain temps et de manière consistante, avec le partitionnement cible. Nous montrons que les algorithmes proposés sont implémentables efficacement, et nous accompagnons nos résultats théoriques par des évaluations expérimentales. L'analyse statistique dans le cadre stationnaire ergodique est extrêmement difficile. De manière générale, il est prouvé que les vitesses de convergence sont impossibles à obtenir. Dès lors, pour deux échantillons générés indépendamment par des processus ergodiques stationnaires, il est prouvé qu'il est impossible de distinguer le cas où les échantillons sont générés par le même processus de celui où ils sont générés par des processus différents. Ceci implique que des problèmes tels le partitionnement de séries temporelles sans la connaissance du nombre de partitions ou du nombre de points de rupture ne peut admettre de solutions consistantes. En conséquence, une tâche difficile est de découvrir les formulations du problème qui en permettent une résolution dans ce cadre général. La principale contribution de cette thèse est de démontrer (par construction) que malgré ces résultats d'impossibilités théoriques, des formulations naturelles des problèmes considérés existent et admettent des solutions consistantes dans ce cadre général. Ceci inclut la démonstration du fait que le nombre de points de rupture corrects peut être trouvé, sans recourir à des hypothèses plus fortes sur les processus stochastiques. Il en résulte que, dans cette formulation, le problème des points de rupture peut être réduit à du partitionnement de séries temporelles. Les résultats présentés dans ce travail formulent les fondations théoriques pour l'analyse des données séquentielles dans un espace d'applications bien plus large.

L’apprentissage supervisé de réseaux hiérarchiques à grande échelle connaît présentement un succès fulgurant. Malgré cette effervescence, l’apprentissage non-supervisé représente toujours, selon plusieurs chercheurs, un élément clé de l’Intelligence Artificielle, où les agents doivent apprendre à partir d’un nombre potentiellement limité de données. Cette thèse s’inscrit dans cette pensée et aborde divers sujets de recherche liés au problème d’estimation de densité par l’entremise des machines de Boltzmann (BM), modèles graphiques probabilistes au coeur de l’apprentissage profond. Nos contributions touchent les domaines de l’échantillonnage, l’estimation de fonctions de partition, l’optimisation ainsi que l’apprentissage de représentations invariantes. Cette thèse débute par l’exposition d’un nouvel algorithme d'échantillonnage adaptatif, qui ajuste (de fa ̧con automatique) la température des chaînes de Markov sous simulation, afin de maintenir une vitesse de convergence élevée tout au long de l’apprentissage. Lorsqu’utilisé dans le contexte de l’apprentissage par maximum de vraisemblance stochastique (SML), notre algorithme engendre une robustesse accrue face à la sélection du taux d’apprentissage, ainsi qu’une meilleure vitesse de convergence. Nos résultats sont présent ́es dans le domaine des BMs, mais la méthode est générale et applicable à l’apprentissage de tout modèle probabiliste exploitant l’échantillonnage par chaînes de Markov. Tandis que le gradient du maximum de vraisemblance peut-être approximé par échantillonnage, l’évaluation de la log-vraisemblance nécessite un estimé de la fonction de partition. Contrairement aux approches traditionnelles qui considèrent un modèle donné comme une boîte noire, nous proposons plutôt d’exploiter la dynamique de l’apprentissage en estimant les changements successifs de log-partition encourus à chaque mise à jour des paramètres. Le problème d’estimation est reformulé comme un problème d’inférence similaire au filtre de Kalman, mais sur un graphe bi-dimensionnel, où les dimensions correspondent aux axes du temps et au paramètre de température. Sur le thème de l’optimisation, nous présentons également un algorithme permettant d’appliquer, de manière efficace, le gradient naturel à des machines de Boltzmann comportant des milliers d’unités. Jusqu’à présent, son adoption était limitée par son haut coût computationel ainsi que sa demande en mémoire. Notre algorithme, Metric-Free Natural Gradient (MFNG), permet d’éviter le calcul explicite de la matrice d’information de Fisher (et son inverse) en exploitant un solveur linéaire combiné à un produit matrice-vecteur efficace. L’algorithme est prometteur: en terme du nombre d’évaluations de fonctions, MFNG converge plus rapidement que SML. Son implémentation demeure malheureusement inefficace en temps de calcul. Ces travaux explorent également les mécanismes sous-jacents à l’apprentissage de représentations invariantes. À cette fin, nous utilisons la famille de machines de Boltzmann restreintes “spike & slab” (ssRBM), que nous modifions afin de pouvoir modéliser des distributions binaires et parcimonieuses. Les variables latentes binaires de la ssRBM peuvent être rendues invariantes à un sous-espace vectoriel, en associant à chacune d’elles, un vecteur de variables latentes continues (dénommées “slabs”). Ceci se traduit par une invariance accrue au niveau de la représentation et un meilleur taux de classification lorsque peu de données étiquetées sont disponibles. Nous terminons cette thèse sur un sujet ambitieux: l’apprentissage de représentations pouvant séparer les facteurs de variations présents dans le signal d’entrée. Nous proposons une solution à base de ssRBM bilinéaire (avec deux groupes de facteurs latents) et formulons le problème comme l’un de “pooling” dans des sous-espaces vectoriels complémentaires. / Despite the current widescale success of deep learning in training large scale hierarchical models through supervised learning, unsupervised learning promises to play a crucial role towards solving general Artificial Intelligence, where agents are expected to learn with little to no supervision. The work presented in this thesis tackles the problem of unsupervised feature learning and density estimation, using a model family at the heart of the deep learning phenomenon: the Boltzmann Machine (BM). We present contributions in the areas of sampling, partition function estimation, optimization and the more general topic of invariant feature learning. With regards to sampling, we present a novel adaptive parallel tempering method which dynamically adjusts the temperatures under simulation to maintain good mixing in the presence of complex multi-modal distributions. When used in the context of stochastic maximum likelihood (SML) training, the improved ergodicity of our sampler translates to increased robustness to learning rates and faster per epoch convergence. Though our application is limited to BM, our method is general and is applicable to sampling from arbitrary probabilistic models using Markov Chain Monte Carlo (MCMC) techniques. While SML gradients can be estimated via sampling, computing data likelihoods requires an estimate of the partition function. Contrary to previous approaches which consider the model as a black box, we provide an efficient algorithm which instead tracks the change in the log partition function incurred by successive parameter updates. Our algorithm frames this estimation problem as one of filtering performed over a 2D lattice, with one dimension representing time and the other temperature. On the topic of optimization, our thesis presents a novel algorithm for applying the natural gradient to large scale Boltzmann Machines. Up until now, its application had been constrained by the computational and memory requirements of computing the Fisher Information Matrix (FIM), which is square in the number of parameters. The Metric-Free Natural Gradient algorithm (MFNG) avoids computing the FIM altogether by combining a linear solver with an efficient matrix-vector operation. The method shows promise in that the resulting updates yield faster per-epoch convergence, despite being slower in terms of wall clock time. Finally, we explore how invariant features can be learnt through modifications to the BM energy function. We study the problem in the context of the spike & slab Restricted Boltzmann Machine (ssRBM), which we extend to handle both binary and sparse input distributions. By associating each spike with several slab variables, latent variables can be made invariant to a rich, high dimensional subspace resulting in increased invariance in the learnt representation. When using the expected model posterior as input to a classifier, increased invariance translates to improved classification accuracy in the low-label data regime. We conclude by showing a connection between invariance and the more powerful concept of disentangling factors of variation. While invariance can be achieved by pooling over subspaces, disentangling can be achieved by learning multiple complementary views of the same subspace. In particular, we show how this can be achieved using third-order BMs featuring multiplicative interactions between pairs of random variables.

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Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-10-11T17:36:54Z No. of bitstreams: 1 DissVAK.pdf: 4608619 bytes, checksum: 3022034b9035e4e8caf1195902d24581 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-21T13:03:21Z (GMT) No. of bitstreams: 1 DissVAK.pdf: 4608619 bytes, checksum: 3022034b9035e4e8caf1195902d24581 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-21T13:03:27Z (GMT) No. of bitstreams: 1 DissVAK.pdf: 4608619 bytes, checksum: 3022034b9035e4e8caf1195902d24581 (MD5) / Made available in DSpace on 2016-10-21T13:03:34Z (GMT). No. of bitstreams: 1 DissVAK.pdf: 4608619 bytes, checksum: 3022034b9035e4e8caf1195902d24581 (MD5) Previous issue date: 2016-08-12 / Não recebi financiamento / Cluster analysis is the organization of a collection of patterns into clusters based on similarity which is determined by using properties of data. Clustering techniques can be useful in a variety of knowledge domains such as biotechnology, computer vision, document retrieval and many others. An interesting area of biology involves the concept of microRNAs (miRNAs) that are approximately 22 nucleotide-long non-coding RNA molecules that play important roles in gene regulation. Clustering miRNA sequences can help to understand and explore sequences belonging to the same cluster that has similar biological functions. This research work investigates and explores seven unsupervised clustering algorithms based on graphs that can be divided into three categories: algorithm based on region of influence, algorithm based on minimum spanning tree and spectral algorithm. To assess the contribution of the proposed algorithms, data from miRNA families stored in the online miRBase database were used in the conducted experiments. The results of these experiments were presented, analysed and evaluated using clustering validation indexes as well as visual analysis. / A análise de agrupamento é uma organização de coleção de padrões em grupos, baseando-se na similaridade das propriedades pertencentes aos dados. A técnica de agrupamento pode ser utilizado em muitas áreas de conhecimento como biotecnologia, visão computacional, recuperação de documentos, entre outras. Uma área interessante da biologia envolve o conceito de microRNAs (miRNAs), que são moléculas não-codificadas de RNA com aproximadamente 22 nucleotídeos e que desempenham um papel importante na regulação dos genes. O agrupamento de sequências de miRNA podem ajudar em sua exploração e entendimento, pois as sequências que pertencem ao mesmo grupo possuem uma função biológica similar. Esse trabalho explora e investiga sete algoritmos de agrupamentos não-supervisionados baseados em grafos que podem ser divididos em três categorias: algoritmos baseados em região de influência, algoritmos baseados em árvore spanning minimal e algoritmo espectral. Para avaliar a contribuição dos algoritmos propostos, os experimentos conduzidos utilizaram os dados das famílias de miRNAs disponíveis no banco de dados denominado miRBase. Os resultados dos experimentos foram apresentados, analisados e avaliados usando índices de validação de agrupamento e análise visual.

Extracting useful knowledge from data sets is a key concept in modern information systems. Consequently, the need of efficient techniques to extract the desired knowledge has been growing over time. Machine learning is a research field dedicated to the development of techniques capable of enabling a machine to \"learn\" from data. Many techniques have been proposed so far, but there are still issues to be unveiled specially in interdisciplinary research. In this thesis, we explore the advantages of network data representation to develop machine learning techniques based on dynamical processes on networks. The network representation unifies the structure, dynamics and functions of the system it represents, and thus is capable of capturing the spatial, topological and functional relations of the data sets under analysis. We develop network-based techniques for the three machine learning paradigms: supervised, semi-supervised and unsupervised. The random walk dynamical process is used to characterize the access of unlabeled data to data classes, configuring a new heuristic we call ease of access in the supervised paradigm. We also propose a classification technique which combines the high-level view of the data, via network topological characterization, and the low-level relations, via similarity measures, in a general framework. Still in the supervised setting, the modularity and Katz centrality network measures are applied to classify multiple observation sets, and an evolving network construction method is applied to the dimensionality reduction problem. The semi-supervised paradigm is covered by extending the ease of access heuristic to the cases in which just a few labeled data samples and many unlabeled samples are available. A semi-supervised technique based on interacting forces is also proposed, for which we provide parameter heuristics and stability analysis via a Lyapunov function. Finally, an unsupervised network-based technique uses the concepts of pinning control and consensus time from dynamical processes to derive a similarity measure used to cluster data. The data is represented by a connected and sparse network in which nodes are dynamical elements. Simulations on benchmark data sets and comparisons to well-known machine learning techniques are provided for all proposed techniques. Advantages of network data representation and dynamical processes for machine learning are highlighted in all cases / A extração de conhecimento útil a partir de conjuntos de dados é um conceito chave em sistemas de informação modernos. Por conseguinte, a necessidade de técnicas eficientes para extrair o conhecimento desejado vem crescendo ao longo do tempo. Aprendizado de máquina é uma área de pesquisa dedicada ao desenvolvimento de técnicas capazes de permitir que uma máquina \"aprenda\" a partir de conjuntos de dados. Muitas técnicas já foram propostas, mas ainda há questões a serem reveladas especialmente em pesquisas interdisciplinares. Nesta tese, exploramos as vantagens da representação de dados em rede para desenvolver técnicas de aprendizado de máquina baseadas em processos dinâmicos em redes. A representação em rede unifica a estrutura, a dinâmica e as funções do sistema representado e, portanto, é capaz de capturar as relações espaciais, topológicas e funcionais dos conjuntos de dados sob análise. Desenvolvemos técnicas baseadas em rede para os três paradigmas de aprendizado de máquina: supervisionado, semissupervisionado e não supervisionado. O processo dinâmico de passeio aleatório é utilizado para caracterizar o acesso de dados não rotulados às classes de dados configurando uma nova heurística no paradigma supervisionado, a qual chamamos de facilidade de acesso. Também propomos uma técnica de classificação de dados que combina a visão de alto nível dos dados, por meio da caracterização topológica de rede, com relações de baixo nível, por meio de medidas de similaridade, em uma estrutura geral. Ainda no aprendizado supervisionado, as medidas de rede modularidade e centralidade Katz são aplicadas para classificar conjuntos de múltiplas observações, e um método de construção evolutiva de rede é aplicado ao problema de redução de dimensionalidade. O paradigma semissupervisionado é abordado por meio da extensão da heurística de facilidade de acesso para os casos em que apenas algumas amostras de dados rotuladas e muitas amostras não rotuladas estão disponíveis. É também proposta uma técnica semissupervisionada baseada em forças de interação, para a qual fornecemos heurísticas para selecionar parâmetros e uma análise de estabilidade mediante uma função de Lyapunov. Finalmente, uma técnica não supervisionada baseada em rede utiliza os conceitos de controle pontual e tempo de consenso de processos dinâmicos para derivar uma medida de similaridade usada para agrupar dados. Os dados são representados por uma rede conectada e esparsa na qual os vértices são elementos dinâmicos. Simulações com dados de referência e comparações com técnicas de aprendizado de máquina conhecidas são fornecidos para todas as técnicas propostas. As vantagens da representação de dados em rede e de processos dinâmicos para o aprendizado de máquina são evidenciadas em todos os casos

Advances in unsupervised learning and deep neural networks have led to increased performance in a number of domains, and to the ability to draw strong comparisons between the biological method of self-organization conducted by the brain and computational mechanisms. This thesis aims to use real-world data to tackle two areas in the domain of computer vision which have biological equivalents: feature detection and motion tracking. The aforementioned advances have allowed efficient learning of feature representations directly from large sets of unlabeled data instead of using traditional handcrafted features. The first part of this thesis evaluates such representations by comparing regularization and preprocessing methods which incorporate local neighbouring information during training on a single-layer neural network. The networks are trained and tested on the Hollywood2 video dataset, as well as the static CIFAR-10, STL-10, COIL-100, and MNIST image datasets. The induction of topography or simple image blurring via Gaussian filters during training produces better discriminative features as evidenced by the consistent and notable increase in classification results that they produce. In the visual domain, invariant features are desirable such that objects can be classified despite transformations. It is found that most of the compared methods produce more invariant features, however, classification accuracy does not correlate to invariance. The second, and paramount, contribution of this thesis is a biologically-inspired model to explain the emergence of motion tracking behaviour in early development using unsupervised learning. The model’s self-organization is biased by an original concept called retinal constancy, which measures how similar visual contents are between successive frames. In the proposed two-layer deep network, when exposed to real-world video, the first layer learns to encode visual motion, and the second layer learns to relate that motion to gaze movements, which it perceives and creates through bi-directional nodes. This is unique because it uses general machine learning algorithms, and their inherent generative properties, to learn from real-world data. It also implements a biological theory and learns in a fully unsupervised manner. An analysis of its parameters and limitations is conducted, and its tracking performance is evaluated. Results show that this model is able to successfully follow targets in real-world video, despite being trained without supervision on real-world video.

Machine learning is evidenced as a research area with the main purpose of developing computational methods that are capable of learning with their previously acquired experiences. Although a large amount of machine learning techniques has been proposed and successfully applied in real systems, there are still many challenging issues, which need be addressed. In the last years, an increasing interest in techniques based on complex networks (large-scale graphs with nontrivial connection patterns) has been verified. This emergence is explained by the inherent advantages provided by the complex network representation, which is able to capture the spatial, topological and functional relations of the data. In this work, we investigate the new features and possible advantages offered by complex networks in the machine learning domain. In fact, we do show that the network-based approach really brings interesting features for supervised, semisupervised, and unsupervised learning. Specifically, we reformulate a previously proposed particle competition technique for both unsupervised and semisupervised learning using a stochastic nonlinear dynamical system. Moreover, an analytical analysis is supplied, which enables one to predict the behavior of the proposed technique. In addition to that, data reliability issues are explored in semisupervised learning. Such matter has practical importance and is found to be of little investigation in the literature. With the goal of validating these techniques for solving real problems, simulations on broadly accepted databases are conducted. Still in this work, we propose a hybrid supervised classification technique that combines both low and high orders of learning. The low level term can be implemented by any classification technique, while the high level term is realized by the extraction of features of the underlying network constructed from the input data. Thus, the former classifies the test instances by their physical features, while the latter measures the compliance of the test instances with the pattern formation of the data. Our study shows that the proposed technique not only can realize classification according to the semantic meaning of the data, but also is able to improve the performance of traditional classification techniques. Finally, it is expected that this study will contribute, in a relevant manner, to the machine learning area / Aprendizado de máquina figura-se como uma área de pesquisa que visa a desenvolver métodos computacionais capazes de aprender com a experiência. Embora uma grande quantidade de técnicas de aprendizado de máquina foi proposta e aplicada, com sucesso, em sistemas reais, existem ainda inúmeros problemas desafiantes que necessitam ser explorados. Nos últimos anos, um crescente interesse em técnicas baseadas em redes complexas (grafos de larga escala com padrões de conexão não triviais) foi verificado. Essa emergência é explicada pelas inerentes vantagens que a representação em redes complexas traz, sendo capazes de capturar as relações espaciais, topológicas e funcionais dos dados. Nesta tese, serão investigadas as possíveis vantagens oferecidas por redes complexas quando utilizadas no domínio de aprendizado de máquina. De fato, será mostrado que a abordagem por redes realmente proporciona melhorias nos aprendizados supervisionado, semissupervisionado e não supervisionado. Especificamente, será reformulada uma técnica de competição de partículas para o aprendizado não supervisionado e semissupervisionado por meio da utilização de um sistema dinâmico estocástico não linear. Em complemento, uma análise analítica de tal modelo será desenvolvida, permitindo o entendimento evolucional do modelo no tempo. Além disso, a questão de confiabilidade de dados será investigada no aprendizado semissupervisionado. Tal tópico tem importância prática e é pouco estudado na literatura. Com o objetivo de validar essas técnicas em problemas reais, simulações computacionais em bases de dados consagradas pela literatura serão conduzidas. Ainda nesse trabalho, será proposta uma técnica híbrica de classificação supervisionada que combina tanto o aprendizado de baixo como de alto nível. O termo de baixo nível pode ser implementado por qualquer técnica de classificação tradicional, enquanto que o termo de alto nível é realizado pela extração das características de uma rede construída a partir dos dados de entrada. Nesse contexto, aquele classifica as instâncias de teste segundo qualidades físicas, enquanto que esse estima a conformidade da instância de teste com a formação de padrões dos dados. Os estudos aqui desenvolvidos mostram que o método proposto pode melhorar o desempenho de técnicas tradicionais de classificação, além de permitir uma classificação de acordo com o significado semântico dos dados. Enfim, acredita-se que este estudo possa gerar contribuições relevantes para a área de aprendizado de máquina.

Humans' incredible capacity to model the complexity of the physical world is possible because they cast this complexity as the composition of simpler entities and rules to process them. Extensive work in cognitive science indeed shows that human perception and reasoning ability is structured around objects. Motivated by this observation, a growing number of recent work focused on entity-centric approaches to learning representation and their potential to facilitate downstream tasks. In the first contribution, we show how an entity-centric approach to learning a transition model allows us to extract meaningful visual entities and to learn transition rules that achieve better compositional generalization. In the second contribution, we show how an entity-centric approach to generating graphs allows us to design a model for conditional graph generation that permits direct optimisation of the graph properties. We investigate the performance of our model in a prototype-based molecular graph generation task. In this task, called lead optimization in drug discovery, we wish to adjust a few physico-chemical properties of a molecule that has proven efficient in vitro in order to make a drug out of it. / L'incroyable capacité des humains à modéliser la complexité du monde physique est rendue possible par la décomposition qu'ils en font en un ensemble d'entités et de règles simples. De nombreux travaux en sciences cognitives montre que la perception humaine et sa capacité à raisonner est essentiellement centrée sur la notion d'objet. Motivés par cette observation, de récents travaux se sont intéressés aux différentes approches d'apprentissage de représentations centrées sur des entités et comment ces représentations peuvent être utilisées pour résoudre plus facilement des tâches sous-jacentes. Dans la première contribution on montre comment une architecture centrée sur la notion d'entité va permettre d'extraire des entités visuelles interpretables et d'apprendre un modèle du monde plus robuste aux différentes configurations d'objets. Dans la deuxième contribution on s’intéresse à un modèle de génération de graphes dont l'architecture est également centrée sur la notion d'entités et comment cette architecture rend plus facile l'apprentissage d'une génération conditionelle à certaines propriétés du graphe. On s’intéresse plus particulièrement aux applications en découverte de médicaments. Dans cette tâche, on souhaite optimiser certaines propriétés physico-chmiques du graphe d'une molécule qui a été efficace in-vitro et dont on veut faire un médicament.

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