In this work, we investigate an alternative setting for tuning regularization parameters, namely data-driven algorithm design, following the previous line of work by Balcan et al. [

Neural Information Processing Systems http://nips.cc/

Selecting subsets of features that differentiate between two conditions is a key task inabroad range ofscientific domains.

Using the enhanced mixture model, we can extract generalizable insights for a target model through a global approximation.

Neural Information Processing Systems http://nips.cc/

In this work, we investigate an alternative setting for tuning regularization parameters, namely data-driven algorithm design, following the previous line of work by Balcan et al. [

The recent technological advances in digitalization have revolutionized the industrial sector. Leveraging data analytics has now enabled the collection of deep insights into the performance and, as a result, the optimization of assets. Industrial drives, for example, already accumulate all the necessary information to control electric machines. These signals include but are not limited to currents, frequency, and temperature. Integrating machine learning (ML) models responsible for predicting the evolution of those directly collected or implicitly derived parameters enhances the smartness of industrial systems even further. In this article, data already residing in most modern electric drives has been used to develop a data-driven thermal model of a power module. A test bench has been designed and used specifically for training and validating the thermal digital twin undergoing various static and dynamic operating profiles. Different approaches, from traditional linear models to deep neural networks, have been implemented to emanate the best ML model for estimating the case temperature of a power module. Several evaluation metrics were then used to assess the investigated methods' performance and implementation in industrial embedded systems.

In many practical applications, regression models are employed to uncover relationships between predictors and a response variable, yet the common assumption of constant error variance is frequently violated. This issue is further compounded in high-dimensional settings where the number of predictors exceeds the sample size, necessitating regularization for effective estimation and variable selection. To address this problem, we propose the Heteroscedastic Double Bayesian Elastic Net (HDBEN), a novel framework that jointly models the mean and log-variance using hierarchical Bayesian priors incorporating both $\ell_1$ and $\ell_2$ penalties. Our approach simultaneously induces sparsity and grouping in the regression coefficients and variance parameters, capturing complex variance structures in the data. Theoretical results demonstrate that proposed HDBEN achieves posterior concentration, variable selection consistency, and asymptotic normality under mild conditions which justifying its behavior. Simulation studies further illustrate that HDBEN outperforms existing methods, particularly in scenarios characterized by heteroscedasticity and high dimensionality.