Probability density estimation from observed data constitutes a central task in statistics. In this brief, we focus on the problem of estimating the copula density associated with any observed data, as it fully describes the dependence between random variables. We separate univariate marginal distributions from the joint dependence structure in the data, the copula itself, and we model the latter with a neural network-based method referred to as copula density neural estimation (CODINE). Results show that the novel learning approach is capable of modeling complex distributions and can be applied for mutual information estimation and data generation.

In deep learning, classification tasks are formalized as optimization problems often solved via the minimization of the cross-entropy. However, recent advancements in the design of objective functions allow the usage of the $f$-divergence to generalize the formulation of the optimization problem for classification. We adopt a Bayesian perspective and formulate the classification task as a maximum a posteriori probability problem. We propose a class of objective functions based on the variational representation of the $f$-divergence. Furthermore, driven by the challenge of improving the state-of-the-art approach, we propose a bottom-up method that leads us to the formulation of an objective function corresponding to a novel $f$-divergence referred to as shifted log (SL). We theoretically analyze the objective functions proposed and numerically test them in three application scenarios: toy examples, image datasets, and signal detection/decoding problems. The analyzed scenarios demonstrate the effectiveness of the proposed approach and that the SL divergence achieves the highest classification accuracy in almost all the considered cases.

Estimating mutual information accurately is pivotal across diverse applications, from machine learning to communications and biology, enabling us to gain insights into the inner mechanisms of complex systems. Yet, dealing with high-dimensional data presents a formidable challenge, due to its size and the presence of intricate relationships. Recently proposed neural methods employing variational lower bounds on the mutual information have gained prominence. However, these approaches suffer from either high bias or high variance, as the sample size and the structure of the loss function directly influence the training process. In this paper, we propose a novel class of discriminative mutual information estimators based on the variational representation of the $f$-divergence. We investigate the impact of the permutation function used to obtain the marginal training samples and present a novel architectural solution based on derangements. The proposed estimator is flexible since it exhibits an excellent bias/variance trade-off. The comparison with state-of-the-art neural estimators, through extensive experimentation within established reference scenarios, shows that our approach offers higher accuracy and lower complexity.

In this article, we introduce a novel machine learning algorithm termed the S-parameters-based Human Detection Algorithm (S-PBHD). Designed to operate on radio frequency datasets transformed into an S-parameter multi-port channel matrix, our algorithm aims to detect human targets within indoor environments using distributed antennas. Central to the efficacy of this algorithm lies its preprocessing phase, which entails the extraction of critical components from the scattered radio field. This is achieved through the Para-Hermitian Eigenvalue Decomposition method, which effectively disentangles the complexities inherent in the S-parameter multi-port channel matrix.