Section: New Results
Statistical analysis of time series
Non-negative Spectral Learning for Linear Sequential Systems 
Method of moments (MoM) has recently become an appealing alternative to standard iterative approaches like Expectation Maximization (EM) to learn latent variable models. In addition, MoM-based algorithms come with global convergence guarantees in the form of finite sample bounds. However, given enough computation time, by using restarts and heuristics to avoid local optima, iterative approaches often achieve better performance. We believe that this performance gap is in part due to the fact that MoM-based algorithms can output negative probabilities. By constraining the search space, we propose a non-negative spectral algorithm (NNSpectral) avoiding computing negative probabilities by design. NNSpectral is compared to other MoM-based algorithms and EM on synthetic problems of the PAutomaC challenge. Not only, NNSpectral outperforms other MoM-based algorithms, but also, achieves very competitive results in comparison to EM.
Learning of scanning strategies for electronic support using predictive state representations 
In Electronic Support, a receiver must monitor a wide frequency spectrum in which threatening emitters operate. A common approach is to use sensors with high sensitivity but a narrow band-width. To maintain surveillance over the whole spectrum, the sensor has to sweep between frequency bands but requires a scanning strategy. Search strategies are usually designed prior to the mission using an approximate knowledge of illumination patterns. This often results in open-loop policies that cannot take advantage of previous observations. As pointed out in past researches, these strategies lack of robustness to the prior. We propose a new closed loop search strategy that learns a stochastic model of each radar using predic-tive state representations. The learning algorithm benefits from the recent advances in spectral learning and rank minimization using nuclear norm penalization.
Spectral learning with proper probabilities for finite state automation 
Probabilistic Finite Automaton (PFA), Probabilistic Finite State Transducers (PFST) and Hidden Markov Models (HMM) are widely used in Automatic Speech Recognition (ASR), Text-to-Speech (TTS) systems and Part Of Speech (POS) tagging for language mod-eling. Traditionally, unsupervised learning of these latent variable models is done by Expectation-Maximization (EM)-like algorithms, as the Baum-Welch algorithm. In a recent alternative line of work, learning algorithms based on spectral properties of some low order moments matrices or tensors were proposed. In comparison to EM, they are orders of magnitude faster and come with theoretical convergence guarantees. However, returned models are not ensured to compute proper distributions. They often return negative values that do not sum to one, limiting their applicability and preventing them to serve as an initialization to EM-like algorithms. In this paper, we propose a new spectral algorithm able to learn a large range of models constrained to return proper distributions. We assess its performances on synthetic problems from the PAutomaC challenge and real datasets extracted from Wikipedia. Experiments show that it outperforms previous spectral approaches as well as the Baum-Welch algorithm with random restarts, in addition to serve as an efficient initialization step to EM-like algorithms.