We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise are carried out using distinct (but interacting) methods. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure with alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the current estimate of the noise power. A complete Bayesian study over the model parameters and the scale parameter can also be performed. Numerical experiments show the benefits of the proposed approach.

In recent years, there has been a growing interest in establishing bridges between statistics and neural networks. This article focuses on the adaptation of the widely used lasso algorithm within the context of neural networks. To accomplish this, the network configuration is first designed. After that, in order to estimate the network weights, three optimization algorithms are considered. The first one, called standard neural lasso, employs the conventional procedure for training neural networks. The second optimization algorithm, termed restricted neural lasso, mimics traditional lasso to establish a connection between statistics and machine learning. Finally, a third optimization algorithm, called voting neural lasso was developed. Voting neural lasso offers a novel way of estimating weights by considers the significance of variables across the cross-validation scenarios. Results showed that the conventional approach of training neural networks resulted in a lower performance when the validation set is not sufficiently representative. It was also observed that restricted neural lasso and the traditional lasso obtained equivalent results, which shows the convergence of the neural technique with the statistical one. Finally, the developed voting neural lasso algorithm outperformed the traditional lasso. These results were obtained across diverse training sets, encompassing observations ranging from as few as 47 to as many as 4000, with the number of predictors varying from 9 to 200.

Volatility estimation and quantile regression are relevant active research areas in statistics, machine learning and econometrics. In this work, we propose two procedures to estimate the local variances in generic regression problems by using kernel smoothers. The proposed schemes can be applied in multidimensional scenarios (not just for time series analysis) and easily in a multi-output framework as well. Moreover, they enable the possibility of providing uncertainty estimation using a generic kernel smoother technique. Several numerical experiments show the benefits of the proposed methods, even compared with the benchmark techniques. One of these experiments involves a real dataset analysis.

Approximately one in seven people worldwide is affected by a mental disorder, making early identification crucial for preventing symptom progression and chronicity. However, diagnosis remains challenging, with discrepancies between referring physicians’ initial assessments and specialist psychiatric diagnoses reported in approximately half of cases. In recent years, machine learning has shown promising results in mental health assessment, with supervised techniques such as decision trees, random forests, and support vector machines among the most widely used approaches. However, these methods require large and representative datasets to capture the substantial heterogeneity of mental disorders, which can be difficult to obtain due to stigma, disease severity, and limited access to mental healthcare. This work investigates the feasibility of identifying mental disorders using data exclusively from a non-psychiatric population. The underlying hypothesis is that this population exhibits greater homogeneity and can therefore be characterized using a variational autoencoder with a Gaussian latent space. The proposed approach uses reconstruction errors from the non-psychiatric training population as a reference, with substantially higher errors in new observations indicating a potential mental disorder. Results show that the proposed VAE achieves performance comparable to that of the three aforementioned supervised techniques in the two dataset used. For the first dataset, the accuracy, sensitivity, specificity and ROC-AUC of the VAE were 0.88, 0.90, 0.85 and 0.95. These performance measures were 0.83, 0.86, 0.80, and 0.88 for decision trees; 0.88, 0.91, 0.85 and 0.94 for random forest; and 0.88, 0.91, 0.85 and 0.95 for support vector machines. Similar results were obtained for the second dataset. Moreover, the progressive increase in reconstruction errors across populations may reflect greater deviations from the patterns observed in the non-psychiatric population in groups with greater clinical complexity, supporting its potential use as a screening tool.