Visualizing and Understanding Sum-Product Networks

Sum-Product Networks (SPNs) are recently introduced deep tractable probabilistic models by which several kinds of inference queries can be answered exactly and in a tractable time. Up to now, they have been largely used as black box density estimators, assessed only by comparing their likelihood scores only. In this paper we explore and exploit the inner representations learned by SPNs. We do this with a threefold aim: first we want to get a better understanding of the inner workings of SPNs; secondly, we seek additional ways to evaluate one SPN model and compare it against other probabilistic models, providing diagnostic tools to practitioners; lastly, we want to empirically evaluate how good and meaningful the extracted representations are, as in a classic Representation Learning framework. In order to do so we revise their interpretation as deep neural networks and we propose to exploit several visualization techniques on their node activations and network outputs under different types of inference queries. To investigate these models as feature extractors, we plug some SPNs, learned in a greedy unsupervised fashion on image datasets, in supervised classification learning tasks. We extract several embedding types from node activations by filtering nodes by their type, by their associated feature abstraction level and by their scope. In a thorough empirical comparison we prove them to be competitive against those generated from popular feature extractors as Restricted Boltzmann Machines. Finally, we investigate embeddings generated from random probabilistic marginal queries as means to compare other tractable probabilistic models on a common ground, extending our experiments to Mixtures of Trees.Comment: Machine Learning Journal paper (First Online), 24 page

Adaptive Multipath Key Reinforcement for Energy Harvesting Wireless Sensor Networks

AbstractEnergy Harvesting - Wireless Sensor Networks (EH-WSNs) constitute systems of networked sensing nodes that are capable of extracting energy from the environment and that use the harvested energy to operate in a sustainable state. Sustainability, seen as design goal, has a significant impact on the design of the security protocols for such networks, as the nodes have to adapt and optimize their behaviour according to the available energy. Traditional key management schemes do not take energy into account, making them not suitable for EH-WSNs. In this paper we propose a new multipath key reinforcement scheme specifically designed for EH-WSNs. The proposed scheme allows each node to take into consideration and adapt to the amount of energy available in the system. In particular, we present two approaches, one static and one fully dynamic, and we discuss some experimental results

Cosmic-ray propagation with DRAGON2: II. Nuclear interactions with the interstellar gas

Understanding the isotopic composition of cosmic rays (CRs) observed near Earth represents a milestone towards the identification of their origin. Local fluxes contain all the known stable and long-lived isotopes, reflecting the complex history of primaries and secondaries as they traverse the interstellar medium. For that reason, a numerical code which aims at describing the CR transport in the Galaxy must unavoidably rely on accurate modelling of the production of secondary particles. In this work we provide a detailed description of the nuclear cross sections and decay network as implemented in the forthcoming release of the galactic propagation code DRAGON2. We present the secondary production models implemented in the code and we apply the different prescriptions to compute quantities of interest to interpret local CR fluxes (e.g., nuclear fragmentation timescales, secondary and tertiary source terms). In particular, we develop a nuclear secondary production model aimed at accurately computing the light secondary fluxes (namely: Li, Be, B) above 1 GeV/n. This result is achieved by fitting existing empirical or semi-empirical formalisms to a large sample of measurements in the energy range 100 MeV/n to 100 GeV/n and by considering the contribution of the most relevant decaying isotopes up to iron. Concerning secondary antiparticles (positrons and antiprotons), we describe a collection of models taken from the literature, and provide a detailed quantitative comparison.Comment: 22 pages, 12 figure