Dans cette thèse, nous proposons des modèles de reconstruction de la structure curviligne fondée sur la modélisation stochastique et sur un système d’apprentissage structuré. Nous supposons que le réseau de lignes, dans sa totalité, peut être décomposé en un ensemble de segments de ligne avec des longueurs et orientations variables. Cette hypothèse nous permet de reconstituer des formes arbitraires de la structure curviligne pour différents types de jeux de données. Nous calculons les descripteurs des caractéristiques curvilignes fondés sur les profils des gradients d’image et les profils morphologiques. Pour le modèle stochastique, nous proposons des contraintes préalables qui définissent l'interaction spatiale des segments de ligne. Pour obtenir une configuration optimale correspondant à la structure curviligne latente, nous combinons plusieurs hypothèses de ligne qui sont calculées par échantillonnage MCMC avec différents jeux de paramètres. De plus, nous apprenons une fonction de classement qui prédit la correspondance du segment de ligne donné avec les structures curvilignes latentes. Une nouvelle méthode fondée sur les graphes est proposée afin d’inférer la structure sous-jacente curviligne en utilisant les classements de sortie des segments de ligne. Nous utilisons nos modèles pour analyser la structure curviligne sur des images statiques. Les résultats expérimentaux sur de nombreux types de jeux de données démontrent que les modèles de structure curviligne proposés surpassent les techniques de l'état de l'art. / In this dissertation, we propose curvilinear structure reconstruction models based on stochastic modeling and ranking learning system. We assume that the entire line network can be decomposed into a set of line segments with variable lengths and orientations. This assumption enables us to reconstruct arbitrary shapes of curvilinear structure for different types of datasets. We compute curvilinear feature descriptors based on the image gradient profiles and the morphological profiles. For the stochastic model, we propose prior constraints that define the spatial interaction of line segments. To obtain an optimal configuration corresponding to the latent curvilinear structure, we combine multiple line hypotheses which are computed by MCMC sampling with different parameter sets. Moreover, we learn a ranking function which predicts the correspondence of the given line segment and the latent curvilinear structures. A novel graph-based method is proposed to infer the underlying curvilinear structure using the output rankings of the line segments. We apply our models to analyze curvilinear structure on static images. Experimental results on wide types of datasets demonstrate that the proposed curvilinear structure modeling outperforms the state-of-the-art techniques.

Recurrent neural networks (RNNs) are state of the art sequential machine learning tools, but have difficulty learning sequences with long-range dependencies due to the exponential growth or decay of gradients backpropagated through the RNN. Some methods overcome this problem by modifying the standard RNN architecure to force the recurrent weight matrix W to remain orthogonal throughout training. The first half of this thesis presents a novel orthogonal RNN architecture that enforces orthogonality of W by parametrizing with a skew-symmetric matrix via the Cayley transform. We present rules for backpropagation through the Cayley transform, show how to deal with the Cayley transform's singularity, and compare its performance on benchmark tasks to other orthogonal RNN architectures. The second half explores two deep learning approaches to problems in RNA secondary structure inference and compares them to a standard structure inference tool, the nearest neighbor thermodynamic model (NNTM). The first uses RNNs to detect paired or unpaired nucleotides in the RNA structure, which are then converted into synthetic auxiliary data that direct NNTM structure predictions. The second method uses recurrent and convolutional networks to directly infer RNA base pairs. In many cases, these approaches improve over NNTM structure predictions by 20-30 percentage points.

Probabilistic graphical modeling is a framework which can be used to succinctly<br>represent multivariate probability distributions of time series in terms of each time<br>series’s dependence on others. In general, it is computationally prohibitive to sta-<br>tistically infer an arbitrary model from data. However, if we constrain the model to<br>have a tree topology, the corresponding learning algorithms become tractable. The<br>expressive power of tree-structured distributions are low, since only n − 1 dependen-<br>cies are explicitly encoded for an n node tree. One way to improve the expressive<br>power of tree models is to combine many of them in a mixture model. This work<br>presents and uses simulations to validate extensions of the standard mixtures of trees<br>model for i.i.d data to the setting of time series data. We also consider the setting<br>where the tree mixture itself forms a hidden Markov chain, which could be better<br>suited for approximating time-varying seasonal data in the real world. Both of these<br>are evaluated on artificial data sets.<br><br>