Logistic regression is a fundamental and widely used statistical method for modeling binary outcomes based on covariates. However, the presence of missing data, particularly in settings involving hybrid covariates (a mix of discrete and continuous variables), poses significant challenges. In this paper, we propose a novel Expectation-Maximization based algorithm tailored for parameter estimation in logistic regression models with missing hybrid covariates. The proposed method is specifically designed to handle these complexities, delivering efficient parameter estimates. Through comprehensive simulations and real-world application, we demonstrate that our approach consistently outperforms traditional methods, achieving superior accuracy and reliability.

Like the Joint Diagonalization of a unique set of matrices, Generalized Joint Diagonalization is an algebraic problem encountered in different applications such as data fusion and blind source separation. This letter proposes a new generalized unitary joint diagonalization approach based on the Jacobi iterative scheme using Givens rotations and simplified criterion, introducing three approximations. These approximations allowed us to reach a simultaneous estimation of different parameters. The first appears in the simplified criterion composed of entries doubly affected by the Givens rotations. The second approximation is in the Givens parameter using a small amplitude angle. The last approximation resides in keeping only the first order of transformed entries. Numerical experiments, including examples of joint blind audio source separation, are provided. The results show the effectiveness of the developed algorithm as compared to existing ones. The simultaneous estimation of different Givens rotations improves the algorithm's computation complexity and convergence rate.

This letter deals with a hybrid joint diagonalization problem considering both Hermitian and transpose congruence. Such problem can be encountered in certain noncircular signal analysis applications including blind source separation. We introduce new Jacobi-like algorithms using Givens or a combination of Givens and hyperbolic rotations. These algorithms are compared with state-of-the-art methods and their performance gain, especially in the high dimensional case, is assessed through simulation experiments including examples related to blind separation of noncircular sources.

This letter proposes a novel technique for the blind separation of autoregressive (AR) sources. The latter relies on the joint diagonalization (JD) of appropriate AR matrix coefficients of the observed signals and can be applied to the separation of statistically dependent sources. The developed algorithm is referred to as `DARSS-JD' (for Dependent AR Source Separation using JD). Through the simulation experiments, DARSS-JD is shown to overcome existing second order separation methods with a relatively moderate computational cost.