1,721,624 research outputs found
Optimal Transport between Gaussian Stationary Processes
No full textWe consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this article is to show that the corresponding solution leads to a weighted Hellinger distance between multivariate power spectral densities. Then, we propose a spectral estimation approach in the case of indirect measurements, which is based on this distance
Optimal Transport between Gaussian random fields
No full textWe consider the optimal transport problem between zero mean Gaussian stationary random fields both in the aperiodic and periodic case. We show that the solution corresponds to a weighted Hellinger distance between the multivariate and multidimensional power spectral densities of the random fields. Then, we show that such a distance defines a geodesic, which depends on the weight function, on the manifold of the multivariate and multidimensional power spectral densities
Robust fixed-lag smoothing under model perturbations
Full text linkA robust fixed-lag smoothing approach is proposed in the case there is a mismatch between the nominal model and the actual model. The resulting robust smoother is characterized by a dynamic game between two players: one player selects the least favorable model in a prescribed ambiguity set, while the other player selects the fixed-lag smoother minimizing the smoothing error with respect to least favorable model. We propose an efficient implementation of the proposed smoother. Moreover, we characterize the corresponding least favorable model over a finite time horizon. Finally, we test the robust fixed-lag smoother in two examples. The first one regards a target tracking problem, while the second one regards a parameter estimation problem
L'approccio moderno all'Intelligenza Artificiale e la rivoluzione del deep learning
No full textIn the past decade artificial intelligence research has achieved impressive results, mostly due to the creation of efficient machine learning algorithms. One of the most promising approaches is constituted by deep learning, which allows to build multi-layer artificial neural networks that can autonomously extract knowledge from large-scale data sets. In this review we will discuss the main theoretical and technological progresses underlying these achievements, also focusing on their relevance for psychology and cognitive neuroscience. We will also highlight some of the limits of deep learning models and possible research directions to overcome them
A generalized multidimensional circulant rational covariance and cepstral extension problem
Full text linkWe propose a general scenario to estimate the spectral density of an homogeneous random field from its moments. More precisely, we consider a multidimensional rational covariance and cepstral extension problem. The latter is usually solved by searching the spectral density maximizing the entropy rate while matching the moments. The generality of our mathematical formulation can be seen from the employed entropic index as well as the definition of cepstral coefficients. We characterize the solution in the circulant case. Finally, we apply our theory to a 2-d system identification problem
Low-rank Kalman filtering under model uncertainty
No full textWe consider a robust filtering problem where the nominal state space model is not reachable and different from the actual one. We propose a robust Kalman filter which solves a dynamic game: one player selects the least-favorable model in a given ambiguity set, while the other player designs the optimum filter for the least-favorable model. It turns out that the robust filter is governed by a low-rank risk sensitive-like Riccati equation. Finally, simulation results show the effectiveness of the proposed filter
Robust Kalman Filtering Under Model Uncertainty: The Case of Degenerate Densities
Full text linkIn this article, we consider a robust state-space filtering problem in the case that the transition probability density is unknown and possibly degenerate. The resulting robust filter has a Kalman-like structure and solves a minimax game: the nature selects the least favorable model in a prescribed ambiguity set, which also contains non-Gaussian probability densities, while the other player designs the optimum filter for the least favorable model. It turns out that the resulting robust filter is characterized by a Riccati-like iteration evolving on the cone of the positive-semidefinite matrices. Moreover, we study the convergence of such iteration in the case that the nominal model is with constant parameters on the basis of the contraction analysis in the same spirit of Bougerol. Finally, some numerical examples show that the proposed filter outperforms the standard Kalman filter
Nonparametric Identification of Kronecker Networks
Full text linkWe address the problem to estimate a dynamic network whose edges describe
Granger causality relations and whose topology has a Kronecker structure. Such
a structure arises in many real networks and allows to understand the
organization of complex networks. We proposed a kernel-based PEM method to
learn such networks. Numerical examples show the effectiveness of the proposed
method
Optimal link scheduling in millimeter wave multi-hop networks with MU-MIMO radios
Full text linkThis paper studies the maximum throughput achievable with optimal scheduling in multi-hop mmWave picocellular networks with Multi-user Multiple-Input Multiple-Output (MU-MIMO) radios. MU-MIMO enables simultaneous transmission to multiple receivers (Space Division Multiplexing) and simultaneous reception from multiple transmitters (Space Division Multiple Access). The main contribution is the extension to MU-MIMO of the Network Utility Maximization (NUM) scheduling framework for multi-hop networks. We generalize to MU-MIMO the classic proof that Maximum Back Pressure (MBP) scheduling is NUM optimal. MBP requires the solution of an optimization that becomes harder with MU-MIMO radios. In prior models with one-to-one transmission and reception, each valid schedule was a matching over a graph. However, with MU-MIMO each valid schedule is, instead, a Directed Bipartite SubGraph (DBSG). In the general case this prevents finding efficient algorithms to solve the scheduler. We make MU-MIMO MBP scheduling tractable by assuming fixed power allocation, so the optimal scheduler is the Maximum Weighted DBSG. The MWDBSG problem can be solved using standard Mixed Integer Linear Programing. We simulate multi-hop mmWave picocellular networks and show that a MU-MIMO MBP scheduler enables a 160% increase in network throughput versus the classic one-to-one MBP scheduler, while fair rate allocation mechanisms are used in both cases
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