Learning and inference with Wasserstein metrics

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Brain and Cognitive Sciences, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 131-143).This thesis develops new approaches for three problems in machine learning, using tools from the study of optimal transport (or Wasserstein) distances between probability distributions. Optimal transport distances capture an intuitive notion of similarity between distributions, by incorporating the underlying geometry of the domain of the distributions. Despite their intuitive appeal, optimal transport distances are often difficult to apply in practice, as computing them requires solving a costly optimization problem. In each setting studied here, we describe a numerical method that overcomes this computational bottleneck and enables scaling to real data. In the first part, we consider the problem of multi-output learning in the presence of a metric on the output domain. We develop a loss function that measures the Wasserstein distance between the prediction and ground truth, and describe an efficient learning algorithm based on entropic regularization of the optimal transport problem. We additionally propose a novel extension of the Wasserstein distance from probability measures to unnormalized measures, which is applicable in settings where the ground truth is not naturally expressed as a probability distribution. We show statistical learning bounds for both the Wasserstein loss and its unnormalized counterpart. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data image tagging problem, outperforming a baseline that doesn't use the metric. In the second part, we consider the probabilistic inference problem for diffusion processes. Such processes model a variety of stochastic phenomena and appear often in continuous-time state space models. Exact inference for diffusion processes is generally intractable. In this work, we describe a novel approximate inference method, which is based on a characterization of the diffusion as following a gradient flow in a space of probability densities endowed with a Wasserstein metric. Existing methods for computing this Wasserstein gradient flow rely on discretizing the underlying domain of the diffusion, prohibiting their application to problems in more than several dimensions. In the current work, we propose a novel algorithm for computing a Wasserstein gradient flow that operates directly in a space of continuous functions, free of any underlying mesh. We apply our approximate gradient flow to the problem of filtering a diffusion, showing superior performance where standard filters struggle. Finally, we study the ecological inference problem, which is that of reasoning from aggregate measurements of a population to inferences about the individual behaviors of its members. This problem arises often when dealing with data from economics and political sciences, such as when attempting to infer the demographic breakdown of votes for each political party, given only the aggregate demographic and vote counts separately. Ecological inference is generally ill-posed, and requires prior information to distinguish a unique solution. We propose a novel, general framework for ecological inference that allows for a variety of priors and enables efficient computation of the most probable solution. Unlike previous methods, which rely on Monte Carlo estimates of the posterior, our inference procedure uses an efficient fixed point iteration that is linearly convergent. Given suitable prior information, our method can achieve more accurate inferences than existing methods. We additionally explore a sampling algorithm for estimating credible regions.by Charles Frogner.Ph. D

Automatic non-linear video editing for home video collections

The video editing process consists of deciding what elements to retain, delete, or combine from various video sources so that they come together in an organized, logical, and visually pleasing manner. Before the digital era, non-linear editing involved the arduous process of physically cutting and splicing video tapes, and was restricted to the movie industry and a few video enthusiasts. Today, when digital cameras and camcorders have made large personal video collections commonplace, non-linear video editing has gained renewed importance and relevance. Almost all available video editing systems today are dependent on considerable user interaction to produce coherent edited videos. In this work, we describe an automatic non-linear video editing system for generating coherent movies from a collection of unedited personal videos. Our thesis is that computing image-level visual similarity in an appropriate manner forms a good basis for automatic non-linear video editing. To our knowledge, this is a novel approach to solving this problem. The generation of output video from the system is guided by one or more input keyframes from the user, which guide the content of the output video. The output video is generated in a manner such that it is non-repetitive and follows the dynamics of the input videos. When no input keyframes are provided, our system generates "video textures" with the content of the output chosen at random. Our system demonstrates promising results on large video collections and is a first step towards increased automation in non-linear video editin

Robust density modelling using the student's t-distribution for human action recognition

The extraction of human features from videos is often inaccurate and prone to outliers. Such outliers can severely affect density modelling when the Gaussian distribution is used as the model since it is highly sensitive to outliers. The Gaussian distribution is also often used as base component of graphical models for recognising human actions in the videos (hidden Markov model and others) and the presence of outliers can significantly affect the recognition accuracy. In contrast, the Student's t-distribution is more robust to outliers and can be exploited to improve the recognition rate in the presence of abnormal data. In this paper, we present an HMM which uses mixtures of t-distributions as observation probabilities and show how experiments over two well-known datasets (Weizmann, MuHAVi) reported a remarkable improvement in classification accuracy. © 2011 IEEE

Machine Annotation of Traditional Irish Dance Music

The work presented in this thesis is validated in experiments using 130 realworld field recordings of traditional music from sessions, classes, concerts and commercial recordings. Test audio includes solo and ensemble playing on a variety of instruments recorded in real-world settings such as noisy public sessions. Results are reported using standard measures from the field of information retrieval (IR) including accuracy, error, precision and recall and the system is compared to alternative approaches for CBMIR common in the literature

Dissimilarity-based learning for complex data

Mokbel B. Dissimilarity-based learning for complex data. Bielefeld: Universität Bielefeld; 2016.Rapid advances of information technology have entailed an ever increasing amount of digital data, which raises the demand for powerful data mining and machine learning tools. Due to modern methods for gathering, preprocessing, and storing information, the collected data become more and more complex: a simple vectorial representation, and comparison in terms of the Euclidean distance is often no longer appropriate to capture relevant aspects in the data. Instead, problem-adapted similarity or dissimilarity measures refer directly to the given encoding scheme, allowing to treat information constituents in a relational manner. This thesis addresses several challenges of complex data sets and their representation in the context of machine learning. The goal is to investigate possible remedies, and propose corresponding improvements of established methods, accompanied by examples from various application domains. The main scientific contributions are the following: (I) Many well-established machine learning techniques are restricted to vectorial input data only. Therefore, we propose the extension of two popular prototype-based clustering and classification algorithms to non-negative symmetric dissimilarity matrices. (II) Some dissimilarity measures incorporate a fine-grained parameterization, which allows to configure the comparison scheme with respect to the given data and the problem at hand. However, finding adequate parameters can be hard or even impossible for human users, due to the intricate effects of parameter changes and the lack of detailed prior knowledge. Therefore, we propose to integrate a metric learning scheme into a dissimilarity-based classifier, which can automatically adapt the parameters of a sequence alignment measure according to the given classification task. (III) A valuable instrument to make complex data sets accessible are dimensionality reduction techniques, which can provide an approximate low-dimensional embedding of the given data set, and, as a special case, a planar map to visualize the data's neighborhood structure. To assess the reliability of such an embedding, we propose the extension of a well-known quality measure to enable a fine-grained, tractable quantitative analysis, which can be integrated into a visualization. This tool can also help to compare different dissimilarity measures (and parameter settings), if ground truth is not available. (IV) All techniques are demonstrated on real-world examples from a variety of application domains, including bioinformatics, motion capturing, music, and education

Effective and efficient visual description based on local binary patterns and gradient distribution for object recognition

Cette thèse est consacrée au problème de la reconnaissance visuelle des objets basé sur l'ordinateur, qui est devenue un sujet de recherche très populaire et important ces dernières années grâce à ses nombreuses applications comme l'indexation et la recherche d'image et de vidéo , le contrôle d'accès de sécurité, la surveillance vidéo, etc. Malgré beaucoup d'efforts et de progrès qui ont été fait pendant les dernières années, il reste un problème ouvert et est encore considéré comme l'un des problèmes les plus difficiles dans la communauté de vision par ordinateur, principalement en raison des similarités entre les classes et des variations intra-classe comme occlusion, clutter de fond, les changements de point de vue, pose, l'échelle et l'éclairage. Les approches populaires d'aujourd'hui pour la reconnaissance des objets sont basé sur les descripteurs et les classiffieurs, ce qui généralement extrait des descripteurs visuelles dans les images et les vidéos d'abord, et puis effectue la classification en utilisant des algorithmes d'apprentissage automatique sur la base des caractéristiques extraites. Ainsi, il est important de concevoir une bonne description visuelle, qui devrait être à la fois discriminatoire et efficace à calcul, tout en possédant certaines propriétés de robustesse contre les variations mentionnées précédemment. Dans ce contexte, l objectif de cette thèse est de proposer des contributions novatrices pour la tâche de la reconnaissance visuelle des objets, en particulier de présenter plusieurs nouveaux descripteurs visuelles qui représentent effectivement et efficacement le contenu visuel d image et de vidéo pour la reconnaissance des objets. Les descripteurs proposés ont l'intention de capturer l'information visuelle sous aspects différents. Tout d'abord, nous proposons six caractéristiques LBP couleurs de multi-échelle pour traiter les défauts principaux du LBP original, c'est-à-dire, le déffcit d'information de couleur et la sensibilité aux variations des conditions d'éclairage non-monotoniques. En étendant le LBP original à la forme de multi-échelle dans les différents espaces de couleur, les caractéristiques proposées non seulement ont plus de puissance discriminante par l'obtention de plus d'information locale, mais possèdent également certaines propriétés d'invariance aux différentes variations des conditions d éclairage. En plus, leurs performances sont encore améliorées en appliquant une stratégie de l'image division grossière à fine pour calculer les caractéristiques proposées dans les blocs d'image afin de coder l'information spatiale des structures de texture. Les caractéristiques proposées capturent la distribution mondiale de l information de texture dans les images. Deuxièmement, nous proposons une nouvelle méthode pour réduire la dimensionnalité du LBP appelée la combinaison orthogonale de LBP (OC-LBP). Elle est adoptée pour construire un nouveau descripteur local basé sur la distribution en suivant une manière similaire à SIFT. Notre objectif est de construire un descripteur local plus efficace en remplaçant l'information de gradient coûteux par des patterns de texture locales dans le régime du SIFT. Comme l'extension de notre première contribution, nous étendons également le descripteur OC-LBP aux différents espaces de couleur et proposons six descripteurs OC-LBP couleurs pour améliorer la puissance discriminante et la propriété d'invariance photométrique du descripteur basé sur l'intensité. Les descripteurs proposés capturent la distribution locale de l information de texture dans les images. Troisièmement, nous introduisons DAISY, un nouveau descripteur local rapide basé sur la distribution de gradient, dans le domaine de la reconnaissance visuelle des objets. [...]This thesis is dedicated to the problem of machine-based visual object recognition, which has become a very popular and important research topic in recent years because of its wide range of applications such as image/video indexing and retrieval, security access control, video monitoring, etc. Despite a lot of e orts and progress that have been made during the past years, it remains an open problem and is still considered as one of the most challenging problems in computer vision community, mainly due to inter-class similarities and intra-class variations like occlusion, background clutter, changes in viewpoint, pose, scale and illumination. The popular approaches for object recognition nowadays are feature & classifier based, which typically extract visual features from images/videos at first, and then perform the classification using certain machine learning algorithms based on the extracted features. Thus it is important to design good visual description, which should be both discriminative and computationally efficient, while possessing some properties of robustness against the previously mentioned variations. In this context, the objective of this thesis is to propose some innovative contributions for the task of visual object recognition, in particular to present several new visual features / descriptors which effectively and efficiently represent the visual content of images/videos for object recognition. The proposed features / descriptors intend to capture the visual information from different aspects. Firstly, we propose six multi-scale color local binary pattern (LBP) features to deal with the main shortcomings of the original LBP, namely deficiency of color information and sensitivity to non-monotonic lighting condition changes. By extending the original LBP to multi-scale form in different color spaces, the proposed features not only have more discriminative power by obtaining more local information, but also possess certain invariance properties to different lighting condition changes. In addition, their performances are further improved by applying a coarse-to-fine image division strategy for calculating the proposed features within image blocks in order to encode spatial information of texture structures. The proposed features capture global distribution of texture information in images. Secondly, we propose a new dimensionality reduction method for LBP called the orthogonal combination of local binary patterns (OC-LBP), and adopt it to construct a new distribution-based local descriptor by following a way similar to SIFT.Our goal is to build a more efficient local descriptor by replacing the costly gradient information with local texture patterns in the SIFT scheme. As the extension of our first contribution, we also extend the OC-LBP descriptor to different color spaces and propose six color OC-LBP descriptors to enhance the discriminative power and the photometric invariance property of the intensity-based descriptor. The proposed descriptors capture local distribution of texture information in images. Thirdly, we introduce DAISY, a new fast local descriptor based on gradient distribution, to the domain of visual object recognition.LYON-Ecole Centrale (690812301) / SudocSudocFranceF

Bayesian methods in music modelling

This thesis presents several hierarchical generative Bayesian models of musical signals designed to improve the accuracy of existing multiple pitch detection systems and other musical signal processing applications whilst remaining feasible for real-time computation. At the lowest level the signal is modelled as a set of overlapping sinusoidal basis functions. The parameters of these basis functions are built into a prior framework based on principles known from musical theory and the physics of musical instruments. The model of a musical note optionally includes phenomena such as frequency and amplitude modulations, damping, volume, timbre and inharmonicity. The occurrence of note onsets in a performance of a piece of music is controlled by an underlying tempo process and the alignment of the timings to the underlying score of the music. A variety of applications are presented for these models under differing inference constraints. Where full Bayesian inference is possible, reversible-jump Markov Chain Monte Carlo is employed to estimate the number of notes and partial frequency components in each frame of music. We also use approximate techniques such as model selection criteria and variational Bayes methods for inference in situations where computation time is limited or the amount of data to be processed is large. For the higher level score parameters, greedy search and conditional modes algorithms are found to be sufficiently accurate. We emphasize the links between the models and inference algorithms developed in this thesis with that in existing and parallel work, and demonstrate the effects of making modifications to these models both theoretically and by means of experimental results