Neural ODEs with stochastic vector field mixtures

It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to the set that baseline methods cannot solve, and proposes mixtures of stochastic vector fields as a model class that is capable of solving these essential problems. Dynamic vector field selection is of critical importance for our model, and our approach is to propagate component uncertainty over the integration interval with a technique based on forward filtering. We also formalise several loss functions that encourage desirable properties on the trajectory paths, and of particular interest are those that directly encourage fewer expected function evaluations. Experimentally, we demonstrate that our model class is capable of capturing the natural dynamics of human behaviour; a notoriously volatile application area. Baseline approaches cannot adequately model this problem

Kernel bandwidth estimation for moving object detection in non-stabilized cameras

The evolution of the television market is led by 3DTV technology, and this tendency can accelerate during the next years according to expert forecasts. However, 3DTV delivery by broadcast networks is not currently developed enough, and acts as a bottleneck for the complete deployment of the technology. Thus, increasing interest is dedicated to ste-reo 3DTV formats compatible with current HDTV video equipment and infrastructure, as they may greatly encourage 3D acceptance. In this paper, different subsampling schemes for HDTV compatible transmission of both progressive and interlaced stereo 3DTV are studied and compared. The frequency characteristics and preserved frequency content of each scheme are analyzed, and a simple interpolation filter is specially designed. Finally, the advantages and disadvantages of the different schemes and filters are evaluated through quality testing on several progressive and interlaced video sequences

Conditional t-SNE: Complementary t-SNE embeddings through factoring out prior information

Dimensionality reduction and manifold learning methods such as t-Distributed Stochastic Neighbor Embedding (t-SNE) are routinely used to map high-dimensional data into a 2-dimensional space to visualize and explore the data. However, two dimensions are typically insufficient to capture all structure in the data, the salient structure is often already known, and it is not obvious how to extract the remaining information in a similarly effective manner. To fill this gap, we introduce \emph{conditional t-SNE} (ct-SNE), a generalization of t-SNE that discounts prior information from the embedding in the form of labels. To achieve this, we propose a conditioned version of the t-SNE objective, obtaining a single, integrated, and elegant method. ct-SNE has one extra parameter over t-SNE; we investigate its effects and show how to efficiently optimize the objective. Factoring out prior knowledge allows complementary structure to be captured in the embedding, providing new insights. Qualitative and quantitative empirical results on synthetic and (large) real data show ct-SNE is effective and achieves its goal

Cost-sensitive classification based on Bregman divergences

The main object of this PhD. Thesis is the identification, characterization and study of new loss functions to address the so-called cost-sensitive classification. Many decision problems are intrinsically cost-sensitive. However, the dominating preference for cost-insensitive methods in the machine learning literature is a natural consequence of the fact that true costs in real applications are di fficult to evaluate. Since, in general, uncovering the correct class of the data is less costly than any decision error, designing low error decision systems is a reasonable (but suboptimal) approach. For instance, consider the classification of credit applicants as either being good customers (will pay back the credit) or bad customers (will fail to pay o part of the credit). The cost of classifying one risky borrower as good could be much higher than the cost of classifying a potentially good customer as bad. Our proposal relies on Bayes decision theory where the goal is to assign instances to the class with minimum expected cost. The decision is made involving both costs and posterior probabilities of the classes. Obtaining calibrated probability estimates at the classifier output requires a suitable learning machine, a large enough representative data set as well as an adequate loss function to be minimized during learning. The design of the loss function can be aided by the costs: classical decision theory shows that cost matrices de ne class boundaries determined by posterior class probability estimates. Strictly speaking, in order to make optimal decisions, accurate probability estimates are only required near the decision boundaries. It is key to point out that the election of the loss function becomes especially relevant when the prior knowledge about the problem is limited or the available training examples are somehow unsuitable. In those cases, different loss functions lead to dramatically different posterior probabilities estimates. We focus our study on the set of Bregman divergences. These divergences offer a rich family of proper losses that has recently become very popular in the machine learning community [Nock and Nielsen, 2009, Reid and Williamson, 2009a]. The first part of the Thesis deals with the development of a novel parametric family of multiclass Bregman divergences which captures the information in the cost matrix, so that the loss function is adapted to each specific problem. Multiclass costsensitive learning is one of the main challenges in cost-sensitive learning and, through this parametric family, we provide a natural framework to successfully overcome binary tasks. Following this idea, two lines are explored: Cost-sensitive supervised classification: We derive several asymptotic results. The first analysis guarantees that the proposed Bregman divergence has maximum sensitivity to changes at probability vectors near the decision regions. Further analysis shows that the optimization of this Bregman divergence becomes equivalent to minimizing the overall cost regret in non-separable problems, and to maximizing a margin in separable problems. Cost-sensitive semi-supervised classification: When labeled data is scarce but unlabeled data is widely available, semi-supervised learning is an useful tool to make the most of the unlabeled data. We discuss an optimization problem relying on the minimization of our parametric family of Bregman divergences, using both labeled and unlabeled data, based on what is called the Entropy Minimization principle. We propose the rst multiclass cost-sensitive semi-supervised algorithm, under the assumption that inter-class separation is stronger than intra-class separation. The second part of the Thesis deals with the transformation of this parametric family of Bregman divergences into a sequence of Bregman divergences. Work along this line can be further divided into two additional areas: Foundations of sequences of Bregman divergences: We generalize some previous results about the design and characterization of Bregman divergences that are suitable for learning and their relationship with convexity. In addition, we aim to broaden the subset of Bregman divergences that are interesting for cost-sensitive learning. Under very general conditions, we nd sequences of (cost-sensitive) Bregman divergences, whose minimization provides minimum (cost-sensitive) risk for non-separable problems and some type of maximum margin classifiers in separable cases. Learning with example-dependent costs: A strong assumption is widespread through most cost-sensitive learning algorithms: misclassification costs are the same for all examples. In many cases this statement is not true. We claim that using the example-dependent costs directly is more natural and will lead to the production of more accurate classifiers. For these reasons, we consider the extension of cost-sensitive sequences of Bregman losses to example-dependent cost scenarios to generate finely tuned posterior probability estimates

Online Feature Selection for Activity Recognition using Reinforcement Learning with Multiple Feedback

Recent advances in both machine learning and Internet-of-Things have attracted attention to automatic Activity Recognition, where users wear a device with sensors and their outputs are mapped to a predefined set of activities. However, few studies have considered the balance between wearable power consumption and activity recognition accuracy. This is particularly important when part of the computational load happens on the wearable device. In this paper, we present a new methodology to perform feature selection on the device based on Reinforcement Learning (RL) to find the optimum balance between power consumption and accuracy. To accelerate the learning speed, we extend the RL algorithm to address multiple sources of feedback, and use them to tailor the policy in conjunction with estimating the feedback accuracy. We evaluated our system on the SPHERE challenge dataset, a publicly available research dataset. The results show that our proposed method achieves a good trade-off between wearable power consumption and activity recognition accuracy

Statistical moving object detection for mobile devices with camera

A novel and high-quality system for moving object detection in sequences recorded with moving cameras is proposed. This system is based on the collaboration between an automatic homography estimation module for image alignment, and a robust moving object detection using an efficient spatiotemporal nonparametric background modeling

Versatile Bayesian classifier for moving object detection by non-parametric background-foreground modeling

Along the recent years, several moving object detection strategies by non-parametric background-foreground modeling have been proposed. To combine both models and to obtain the probability of a pixel to belong to the foreground, these strategies make use of Bayesian classifiers. However, these classifiers do not allow to take advantage of additional prior information at different pixels. So, we propose a novel and efficient alternative Bayesian classifier that is suitable for this kind of strategies and that allows the use of whatever prior information. Additionally, we present an effective method to dynamically estimate prior probability from the result of a particle filter-based tracking strategy

Adaptable Bayesian classifier for spatiotemporal nonparametric moving object detection strategies

Electronic devices endowed with camera platforms require new and powerful machine vision applications, which commonly include moving object detection strategies. To obtain high-quality results, the most recent strategies estimate nonparametrically background and foreground models and combine them by means of a Bayesian classifier. However, typical classifiers are limited by the use of constant prior values and they do not allow the inclusion of additional spatiodependent prior information. In this Letter, we propose an alternative Bayesian classifier that, unlike those reported before, allows the use of additional prior information obtained from any source and depending on the spatial position of each pixel

Sampling Based On Natural Image Statistics Improves Local Surrogate Explainers

Many problems in computer vision have recently been tackled using models whose predictions cannot be easily interpreted, most commonly deep neural networks. Surrogate explainers are a popular post-hoc interpretability method to further understand how a model arrives at a particular prediction. By training a simple, more interpretable model to locally approximate the decision boundary of a non-interpretable system, we can estimate the relative importance of the input features on the prediction. Focusing on images, surrogate explainers, e.g., LIME, generate a local neighbourhood around a query image by sampling in an interpretable domain. However, these interpretable domains have traditionally been derived exclusively from the intrinsic features of the query image, not taking into consideration the manifold of the data the non-interpretable model has been exposed to in training (or more generally, the manifold of real images). This leads to suboptimal surrogates trained on potentially low probability images. We address this limitation by aligning the local neighbourhood on which the surrogate is trained with the original training data distribution, even when this distribution is not accessible. We propose two approaches to do so, namely (1) altering the method for sampling the local neighbourhood and (2) using perceptual metrics to convey some of the properties of the distribution of natural images.Comment: 12 pages, 7 figure