The generative paradigm has become increasingly important in machine learning and deep slearning models. Among popular generative models are normalizing flows, which enable exact likelihood estimation by transforming a base distribution through diffeomorphic transformations. Extending the normalizing flow framework to handle time-indexed flows provided dynamic normalizing flows, a powerful tool to model time series, stochastic processes, and neural stochastic differential equations (SDEs). In this work, we propose a novel variant of dynamic normalizing flows, a Time-Changed Normalizing Flow (TCNF), based on time deformation of a Brownian motion which constitutes a versatile and extensive family of Gaussian processes. This approach enables us to effectively model some SDEs that cannot be modeled otherwise, including standard ones such as the well-known Ornstein-Uhlenbeck process, generalizes prior methodologies, and leads to improved results and better inference and prediction capability.

Finding good measures of robustness – i.e. the ability to correctly classify corrupted input signals – of a trained classifier is an important question for sensitive practical applications. In this paper, we point out that averaging the radius of robustness of samples in a validation set is a statistically weak measure. We propose instead to weight the importance of samples depending on their difficulty. We motivate the proposed score by a theoretical case study using logistic regression. We also empirically demonstrate the ability of the proposed score to measure robustness of classifiers with little dependence on the choice of samples in more complex settings, including deep convolutional neural networks and real datasets.

Transfer learning using deep neural networks as feature extractors has become increasingly popular over the past few years. It allows to obtain state-of-the-art accuracy on datasets too small to train a deep neural network on its own, and it provides cutting edge descriptors that, combined with nonparametric learning methods, allow rapid and flexible deployment of performing solutions in computationally restricted settings. In this paper, we are interested in showing that the features extracted using deep neural networks have specific properties which can be used to improve accuracy of downstream nonparametric learning methods. Namely, we demonstrate that for some distributions where information is embedded in a few coordinates, segmenting feature vectors can lead to better accuracy. We show how this model can be applied to real datasets by performing experiments using three mainstream deep neural network feature extractors and four databases, in vision and audio.

In this correspondence, we study a lightly loaded code-division multiple-access (CDMA) system with and without multistage hard- and soft-decision parallel interference cancelation (HD-PIC and SD-PIC). Throughout this paper we will only consider the situation of a noiseless channel, equal powers and random spreading codes. For the system with no or a fixed number of steps of interference cancelation, we give a lower bound on the maximum number of users such that the probability for the system to have no bit-errors converges to one. Moreover, we investigate when the matched filter system, where parallel interference cancelation is absent, has bit errors with probability converging to one. This implies that the use of HD-PIC and SD-PIC significantly enhances the number of users the system can serve