Providing theoretical learning guarantees to Deep Learning Networks

Deep Learning (DL) is one of the most common subjects when Machine Learning and Data Science approaches are considered. There are clearly two movements related to DL: the first aggregates researchers in quest to outperform other algorithms from literature, trying to win contests by considering often small decreases in the empirical risk; and the second investigates overfitting evidences, questioning the learning capabilities of DL classifiers. Motivated by such opposed points of view, this paper employs the Statistical Learning Theory (SLT) to study the convergence of Deep Neural Networks, with particular interest in Convolutional Neural Networks. In order to draw theoretical conclusions, we propose an approach to estimate the Shattering coefficient of those classification algorithms, providing a lower bound for the complexity of their space of admissible functions, a.k.a. algorithm bias. Based on such estimator, we generalize the complexity of network biases, and, next, we study AlexNet and VGG16 architectures in the point of view of their Shattering coefficients, and number of training examples required to provide theoretical learning guarantees. From our theoretical formulation, we show the conditions which Deep Neural Networks learn as well as point out another issue: DL benchmarks may be strictly driven by empirical risks, disregarding the complexity of algorithms biases.Comment: Submitted to JML

Generalization of feature embeddings transferred from different video anomaly detection domains

Detecting anomalous activity in video surveillance often involves using only normal activity data in order to learn an accurate detector. Due to lack of annotated data for some specific target domain, one could employ existing data from a source domain to produce better predictions. Hence, transfer learning presents itself as an important tool. But how to analyze the resulting data space? This paper investigates video anomaly detection, in particular feature embeddings of pre-trained CNN that can be used with non-fully supervised data. By proposing novel cross-domain generalization measures, we study how source features can generalize for different target video domains, as well as analyze unsupervised transfer learning. The proposed generalization measures are not only a theorical approach, but show to be useful in practice as a way to understand which datasets can be used or transferred to describe video frames, which it is possible to better discriminate between normal and anomalous activity