Classification tree methods for panel data using wavelet-transformed time series

Subgroup State Prediction under Different Noise Levels Using MODWT and XGBoost

In medical states prediction, the observations of different individuals are generally assumed to follow an identical distribution, whereas precision medicine has a rigorous requirement for accurate subgroup analysis. In this research, an aggregated method is proposed by means of combining the results generated from different subgroup models and is compared with the original method for different denoising levels as well as the prediction gaps. The results using real data demonstrate the effectiveness of the aggregated method exhibiting superior performance such as 0.95 in AUC, 0.87 in F1, and 0.82 in sensitivity, particularly for the denoising level that is set to be 2. With respect to the variable importance, it is shown that some variables such as heart rate and lactate arterial become more important when the denoising level increases.

Drug Treatment Effect Model Based on MODWT and Hawkes Self-Exciting Point Process

In precision medicine, especially in the pharmacodynamic area, the lack of an adequate long-term drug effect monitoring model leads to a quite low robustness to the instant drug treatment. Modelling the effect of drug based on the monitoring variables is essential to measure the drug benefit and its side effect preciously. In order to model the complex drug behavior in the context of time series, a sin function is selected to describe the basic trend of heart rate variable that is medically monitored. A Hawkes self-exciting point process model is chosen to describe the effect caused by multiple and sequential drug usage at different time points. The model considers the time lag between the drug given time and the drug effect during the whole drug emission period. A cumulative Gamma distribution is employed to describe the time lag effect. Simulation results demonstrate the established model effectively when describing the baseline trend and the drug effect with low noise levels, where the maximal overlap discrete wavelet transformation is utilized for the information decomposition in the frequency zone. The real data of the variables heart rate and drug liquemin from a medical database is analyzed. Instead of the original time series, scale variable s4 is selected according to the Granger cointegration test. The results show that the model accurately characterizes the cumulative drug effect with the Pearson correlation test value as 0.22, which is more significant for the value under 0.1. In the future, the model can be extended to more complicated scenarios through taking into account multiple monitoring variables and different kinds of drugs.

2011-2020 trends of urban and regional ammonia in and around Barcelona, NE Spain

It is well established that in environments where NH₃ abundance is limiting in secondary PM_2.5 generation, a reduction of NH₃ emissions can result in an important contribution to air quality control. However, as deduced from open data published by the European Environmental Agency, the availability of measurements of NH₃ concentrations is very scarce, with very few countries in Europe reporting data consistently for extensive periods, this being especially true for urban background sites. In this framework, simultaneous multi-site measurements were carried out in NE (Northeast) Spain from 2011 to 2020, using diffusion tubes. The highest NH₃ concentrations were recorded at the traffic site (5.3 μgm^-3 on average), followed by those measured at the urban background site (2.1 μgm^-3). Mean concentrations at the mountain site were 1.6 μgm^-3, while the lowest concentrations were recorded at the regional site (0.9 μgm^-3). This comparison highlights traffic emissions as an important source of NH₃. A statistically significant time trend of this pollutant was observed at the urban background site, increasing by 9.4% per year. A season-separated analysis also revealed a significant increasing trend at the mountain site during summer periods, probably related with increasing emissions from agricultural/livestock activities. These increases in NH₃ concentrations were hypothesized to be responsible for the lack of a decreasing trend of NO₃^- concentrations at the monitoring sites, in spite of a markedly reduction of NO₂ during the period, especially at the urban background. Thus, this would in turn affect the effectiveness of current action plans to abate fine aerosols, largely made up of secondary compounds. Actions to reduce NH₃ concentrations at urban backgrounds are challenging though, as predicting NH₃ is subjected to a high uncertainty and complexity due to its dependence on a variety of factors. This complexity was clearly indicated by the application of a decision tree algorithm to find the parameters better predicting NH₃ at the urban background under study. O₃, NO, NO₂, CO, SO₂ and OM + EC concentrations, together with meteorological indicators, were used as independent variables, obtaining no combination of parameters evidently able to predict significant differences in NH₃ concentrations, with a coefficient of determination between real and predicted measurements lower than 0.50. This emphasizes the need for highly temporally and spatially resolved NH₃ measurements for an accurate design of abatement actions.

Splitting Choice and Computational Complexity Analysis of Decision Trees

Some theories are explored in this research about decision trees which give theoretical support to the applications based on decision trees. The first is that there are many splitting criteria to choose in the tree growing process. The splitting bias that influences the criterion chosen due to missing values and variables with many possible values has been studied. Results show that the Gini index is superior to entropy information as it has less bias regarding influences. The second is that noise variables with more missing values have a better chance to be chosen while informative variables do not. The third is that when there are many noise variables involved in the tree building process, it influences the corresponding computational complexity. Results show that the computational complexity increase is linear to the number of noise variables. So methods that decompose more information from the original data but increase the variable dimension can also be considered in real applications.