Measure transport with kernel mean embeddings

Kalman filters constitute a scalable and robust methodology for approximate Bayesian inference, matching first and second order moments of the target posterior. To improve the accuracy in nonlinear and non-Gaussian settings, we extend this principle to include more or different characteristics, based on kernel mean embeddings (KMEs) of probability measures into their corresponding Hilbert spaces. Focusing on the continuous-time setting, we develop a family of interacting particle systems (termed $\textit{KME-dynamics}$) that bridge between the prior and the posterior, and that include the Kalman-Bucy filter as a special case. A variant of KME-dynamics has recently been derived from an optimal transport perspective by Maurais and Marzouk, and we expose further connections to (kernelised) diffusion maps, leading to a variational formulation of regression type. Finally, we conduct numerical experiments on toy examples and the Lorenz-63 model, the latter of which show particular promise for a hybrid modification (called Kalman-adjusted KME-dynamics).Comment: 21 pages, 5 figure

Multi-class Gaussian Process Classification with Noisy Inputs

It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly accurate. If this input noise is not taken into account, a supervised machine learning method is expected to perform sub-optimally. In this paper, we focus on multi-class classification problems and use Gaussian processes (GPs) as the underlying classifier. Motivated by a data set coming from the astrophysics domain, we hypothesize that the observed data may contain noise in the inputs. Therefore, we devise several multi-class GP classifiers that can account for input noise. Such classifiers can be efficiently trained using variational inference to approximate the posterior distribution of the latent variables of the model. Moreover, in some situations, the amount of noise can be known before-hand. If this is the case, it can be readily introduced in the proposed methods. This prior information is expected to lead to better performance results. We have evaluated the proposed methods by carrying out several experiments, involving synthetic and real data. These include several data sets from the UCI repository, the MNIST data set and a data set coming from astrophysics. The results obtained show that, although the classification error is similar across methods, the predictive distribution of the proposed methods is better, in terms of the test log-likelihood, than the predictive distribution of a classifier based on GPs that ignores input noiseWe would like to thank M. A. Sanchez-Conde, J. Coronado and V. Gammaldi for pointing our attention to the data set that motivated this work, as well as for the discussions concerning the data extraction. We thank as well E. Fernandez-Martınez, A. Suarez and C. M. Alaız-Gudin for useful discussions and feedback about the work. BZ especially acknowledges the hospitality of the Machine Learning group of UAM during the development of this project. BZ is supported by the Programa Atraccion de Talento de la Comunidad de Madrid under grant n. 2017-T2/TIC-5455, from the Spanish MINECO’s “Centro de Excelencia Severo Ochoa” Programme via grant SEV-2016-0597, and from the Comunidad de Madrid project SI1-PJI-2019-00294, of which BZ is the P.I. The authors gratefully acknowledge the use of the facilities of Centro de Computacion Cientıfica (CCC) at Universidad Autonoma de Madrid. The authors also acknowledge financial support from Spanish Plan Nacional I+D+i, grants TIN2016-76406-P. Finally, the authors acknowledge financial support from PID2019-106827GB-I00/AEI/10.13039/50110001103

Feedforward deep architectures for classification and synthesis

Cette thèse par article présente plusieurs contributions au domaine de l'apprentissage de représentations profondes, avec des applications aux problèmes de classification et de synthèse d'images naturelles. Plus spécifiquement, cette thèse présente plusieurs nouvelles techniques pour la construction et l'entraînment de réseaux neuronaux profonds, ainsi q'une étude empirique de la technique de «dropout», une des approches de régularisation les plus populaires des dernières années. Le premier article présente une nouvelle fonction d'activation linéaire par morceau, appellée «maxout», qui permet à chaque unité cachée d'un réseau de neurones d'apprendre sa propre fonction d'activation convexe. Nous démontrons une performance améliorée sur plusieurs tâches d'évaluation du domaine de reconnaissance d'objets, et nous examinons empiriquement les sources de cette amélioration, y compris une meilleure synergie avec la méthode de régularisation «dropout» récemment proposée. Le second article poursuit l'examen de la technique «dropout». Nous nous concentrons sur les réseaux avec fonctions d'activation rectifiées linéaires (ReLU) et répondons empiriquement à plusieurs questions concernant l'efficacité remarquable de «dropout» en tant que régularisateur, incluant les questions portant sur la méthode rapide de rééchelonnement au temps de l´évaluation et la moyenne géometrique que cette méthode approxime, l'interprétation d'ensemble comparée aux ensembles traditionnels, et l'importance d'employer des critères similaires au «bagging» pour l'optimisation. Le troisième article s'intéresse à un problème pratique de l'application à l'échelle industrielle de réseaux neuronaux profonds au problème de reconnaissance d'objets avec plusieurs etiquettes, nommément l'amélioration de la capacité d'un modèle à discriminer entre des étiquettes fréquemment confondues. Nous résolvons le problème en employant la prédiction du réseau des sous-composantes dédiées à chaque sous-ensemble de la partition. Finalement, le quatrième article s'attaque au problème de l'entraînment de modèles génératifs adversariaux (GAN) récemment proposé. Nous présentons une procédure d'entraînment améliorée employant un auto-encodeur débruitant, entraîné dans un espace caractéristiques abstrait appris par le discriminateur, pour guider le générateur à apprendre un encodage qui s'aligne de plus près aux données. Nous évaluons le modèle avec le score «Inception» récemment proposé.This thesis by articles makes several contributions to the field of deep learning, with applications to both classification and synthesis of natural images. Specifically, we introduce several new techniques for the construction and training of deep feedforward networks, and present an empirical investigation into dropout, one of the most popular regularization strategies of the last several years. In the first article, we present a novel piece-wise linear parameterization of neural networks, maxout, which allows each hidden unit of a neural network to effectively learn its own convex activation function. We demonstrate improvements on several object recognition benchmarks, and empirically investigate the source of these improvements, including an improved synergy with the recently proposed dropout regularization method. In the second article, we further interrogate the dropout algorithm in particular. Focusing on networks of the popular rectified linear units (ReLU), we empirically examine several questions regarding dropout’s remarkable effectiveness as a regularizer, including questions surrounding the fast test-time rescaling trick and the geometric mean it approximates, interpretations as an ensemble as compared with traditional ensembles, and the importance of using a bagging-like criterion for optimization. In the third article, we address a practical problem in industrial-scale application of deep networks for multi-label object recognition, namely improving an existing model’s ability to discriminate between frequently confused classes. We accomplish this by using the network’s own predictions to inform a partitioning of the label space, and augment the network with dedicated discriminative capacity addressing each of the partitions. Finally, in the fourth article, we tackle the problem of fitting implicit generative models of open domain collections of natural images using the recently introduced Generative Adversarial Networks (GAN) paradigm. We introduce an augmented training procedure which employs a denoising autoencoder, trained in a high-level feature space learned by the discriminator, to guide the generator towards feature encodings which more closely resemble the data. We quantitatively evaluate our findings using the recently proposed Inception score

A novel transformer-based approach for soil temperature prediction

Soil temperature is one of the most significant parameters that plays a crucial role in glacier energy, dynamics of mass balance, processes of surface hydrological, coaction of glacier-atmosphere, nutrient cycling, ecological stability, the management of soil, water, and field crop. In this work, we introduce a novel approach using transformer models for the purpose of forecasting soil temperature prediction. To the best of our knowledge, the usage of transformer models in this work is the very first attempt to predict soil temperature. Experiments are carried out using six different FLUXNET stations by modeling them with five different transformer models, namely, Vanilla Transformer, Informer, Autoformer, Reformer, and ETSformer. To demonstrate the effectiveness of the proposed model, experiment results are compared with both deep learning approaches and literature studies. Experiment results show that the utilization of transformer models ensures a significant contribution to the literature, thence determining the new state-of-the-art

Classifiers and machine learning techniques for image processing and computer vision

Orientador: Siome Klein GoldensteinTese (doutorado) - Universidade Estadual de Campinas, Instituto da ComputaçãoResumo: Neste trabalho de doutorado, propomos a utilizaçãoo de classificadores e técnicas de aprendizado de maquina para extrair informações relevantes de um conjunto de dados (e.g., imagens) para solução de alguns problemas em Processamento de Imagens e Visão Computacional. Os problemas de nosso interesse são: categorização de imagens em duas ou mais classes, detecçãao de mensagens escondidas, distinção entre imagens digitalmente adulteradas e imagens naturais, autenticação, multi-classificação, entre outros. Inicialmente, apresentamos uma revisão comparativa e crítica do estado da arte em análise forense de imagens e detecção de mensagens escondidas em imagens. Nosso objetivo é mostrar as potencialidades das técnicas existentes e, mais importante, apontar suas limitações. Com esse estudo, mostramos que boa parte dos problemas nessa área apontam para dois pontos em comum: a seleção de características e as técnicas de aprendizado a serem utilizadas. Nesse estudo, também discutimos questões legais associadas a análise forense de imagens como, por exemplo, o uso de fotografias digitais por criminosos. Em seguida, introduzimos uma técnica para análise forense de imagens testada no contexto de detecção de mensagens escondidas e de classificação geral de imagens em categorias como indoors, outdoors, geradas em computador e obras de arte. Ao estudarmos esse problema de multi-classificação, surgem algumas questões: como resolver um problema multi-classe de modo a poder combinar, por exemplo, caracteríisticas de classificação de imagens baseadas em cor, textura, forma e silhueta, sem nos preocuparmos demasiadamente em como normalizar o vetor-comum de caracteristicas gerado? Como utilizar diversos classificadores diferentes, cada um, especializado e melhor configurado para um conjunto de caracteristicas ou classes em confusão? Nesse sentido, apresentamos, uma tecnica para fusão de classificadores e caracteristicas no cenário multi-classe através da combinação de classificadores binários. Nós validamos nossa abordagem numa aplicação real para classificação automática de frutas e legumes. Finalmente, nos deparamos com mais um problema interessante: como tornar a utilização de poderosos classificadores binarios no contexto multi-classe mais eficiente e eficaz? Assim, introduzimos uma tecnica para combinação de classificadores binarios (chamados classificadores base) para a resolução de problemas no contexto geral de multi-classificação.Abstract: In this work, we propose the use of classifiers and machine learning techniques to extract useful information from data sets (e.g., images) to solve important problems in Image Processing and Computer Vision. We are particularly interested in: two and multi-class image categorization, hidden messages detection, discrimination among natural and forged images, authentication, and multiclassification. To start with, we present a comparative survey of the state-of-the-art in digital image forensics as well as hidden messages detection. Our objective is to show the importance of the existing solutions and discuss their limitations. In this study, we show that most of these techniques strive to solve two common problems in Machine Learning: the feature selection and the classification techniques to be used. Furthermore, we discuss the legal and ethical aspects of image forensics analysis, such as, the use of digital images by criminals. We introduce a technique for image forensics analysis in the context of hidden messages detection and image classification in categories such as indoors, outdoors, computer generated, and art works. From this multi-class classification, we found some important questions: how to solve a multi-class problem in order to combine, for instance, several different features such as color, texture, shape, and silhouette without worrying about the pre-processing and normalization of the combined feature vector? How to take advantage of different classifiers, each one custom tailored to a specific set of classes in confusion? To cope with most of these problems, we present a feature and classifier fusion technique based on combinations of binary classifiers. We validate our solution with a real application for automatic produce classification. Finally, we address another interesting problem: how to combine powerful binary classifiers in the multi-class scenario more effectively? How to boost their efficiency? In this context, we present a solution that boosts the efficiency and effectiveness of multi-class from binary techniques.DoutoradoEngenharia de ComputaçãoDoutor em Ciência da Computaçã