Several epidemiological studies indicate that fine particulate matter$PM_{2.5}$affect human health, provoking cardiovascular and respiratory diseases, among other. It is therefore important to assess the spatial distribution of this pollutant. Air quality monitoring (AQM) networks are used to this end. However, they are usually spatially sparse due to their high costs, leaving large areas without monitoring. Numerical models have traditionally been proposed to infer the spatial distribution of air pollutants by simulating the diffusion and reaction process of air pollutants. However, such models usually need highly precise emission data and high-end computing hardware. In this paper, we propose a novel neural network architecture for$PM_{2.5}$spatial estimation. This model uses a recently proposed attention layer to build an structured graph of the AQM stations (nodes) and to weight the k nearest neighbors for certain nodes based on attention kernels. The learned attention layer can generate a transformed feature representation for a testing node, which is further processed by a fully connected neural network (FCNN) to infer the pollutant concentration. Results on data from Sao Paulo AQM network showed that our approach has better predictive performance than classical methods like Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and FCNN without attention layer, according to different performance metrics. Additionally, the normalized attention weights computed by our model showed that in some cases, the attention given to the nearest nodes is independent of their spatial distances. This shows that the model is more flexible, since it can learn to interpolate$PM_{2.5}$concentration levels based on the available data of the AQM network and some context information. As for this information we supply to the model different variables like vegetation index (NDVI), surface elevation data, Nighttime Lights (NTL) information and meteorological information.

MOTIVATION: Understanding the patterns of association between polymorphisms at different loci in a population (linkage disequilibrium, LD) is of fundamental importance in various genetic studies. Many coefficients were proposed for measuring the degree of LD, but they provide only a static view of the current LD structure. Generative models (GMs) were proposed to go beyond these measures, giving not only a description of the actual LD structure but also a tool to help understanding the process that generated such structure. GMs based in coalescent theory have been the most appealing because they link LD to evolutionary factors. Nevertheless, the inference and parameter estimation of such models is still computationally challenging. RESULTS: We present a more practical method to build GM that describe LD. The method is based on learning weighted Bayesian network structures from haplotype data, extracting equivalence structure classes and using them to model LD. The results obtained in public data from the HapMap database showed that the method is a promising tool for modeling LD. The associations represented by the learned models are correlated with the traditional measure of LD D'. The method was able to represent LD blocks found by standard tools. The granularity of the association blocks and the readability of the models can be controlled in the method. The results suggest that the causality information gained by our method can be useful to tell about the conservability of the genetic markers and to guide the selection of subset of representative markers. AVAILABILITY: The implementation of the method is available upon request by email.

This paper presents the Gaussian hierarchical Bayesian clustering algorithm (GHBC). A new method for agglomerative hierarchical clustering derived from the HBC algorithm. GHBC has several advantages over traditional agglomerative algorithms. (1) It reduces the limitations due time and memory complexity. (2) It uses a Bayesian posterior probability criterion to decide on merging clusters (modeling clusters as Gaussian distributions) rather than ad-hoc distance metrics. (3) It automatically finds the partition that most closely matches the data using Bayesian information criterion (BIC). Finally, experimental results on synthetic and real data show that GHBC can cluster data as the best classical agglomerative and partitional algorithms.