Variable Importance Assessment Research Articles

Моделювання поширення видів засобами MaxEnt: огляд і перспективи

Niche modelling of species has become increasingly important in the context of accelerating climate change and anthropogenic impacts on the biosphere. One such tool for predicting the potential distribution of species is the maximum entropy method (MaxEnt). This method is particularly valuable when working with biodiversity data collected from herbaria and museum collections, as such data typically only contain information about where a species has been recorded, rather than where it is absent. It is precisely this feature of MaxEnt that makes it an indispensable tool for biodiversity research based on historical data. This allows for the reconstruction of historical species ranges, the detection of changes in their distribution, and the forecasting of future trends, namely the prediction of potential ranges, the assessment of the impact of climate change and anthropogenic pressure, and the development of effective biodiversity conservation strategies. This article provides a brief overview of the MaxEnt software’s operating principle, its capabilities, and limitations. In particular, it analyses the impact of data quality on modelling results and considers various approaches to assessing the importance of ecological factors for species distribution. One of the key issues discussed in the article is the problem of sampling bias. Sampling bias arises because data on the presence of species are often collected non-randomly and depend on the accessibility of the locality, the interests of researchers, and other factors. This can lead to distortions in modelling results. Various methods can be used to correct these biases, such as the bias grid method and the background points method. Another important aspect is the choice of the territory for the background sample. It should be taken into account that when using projections where cells have different areas, MaxEnt may give incorrect results. The article also emphasises the need for cautious interpretation of modelling results. Assessing niche models solely based on AUC (area under ROC curve) can be misleading, therefore, for a more reliable assessment of variable importance, it is worth supplementing it with permutation importance and the jackknife method. Examples of modelling for various groups, including mammals of the Ukrainian fauna, were considered.

A Novel Traffic Speed Prediction for Road Weaving Sections: Incorporating Traffic Flow Characteristics

Weaving sections on roads are crucial areas with high concentrations of mandatory lane changes, which can increase the likelihood of traffic accidents. Speed is a key factor in determining traffic safety, and the development of an accurate speed prediction method is essential for improving safety in weaving sections. While current methods are effective in predicting speeds in straightforward situations, they face challenges in more complex scenarios such as weaving sections. This study presents a refined traffic speed prediction approach specifically designed for weaving sections in order to tackle the aforementioned issue. Initially, novel variables were formulated to capture the unique traffic flow attributes present in weaving sections, which distinguish them from standard road segments. Subsequently, supplementary empirical variables that are known to impact speed were incorporated. We conducted a variable importance assessment to ascertain the extent and direction of each variable’s contribution. Lastly, variables with significant positive effects were chosen as inputs for three machine learning algorithms: Random Forest (RF), Backpropagation Neural Network optimised with Genetic Algorithm (BPNN-GA) and Support Vector Regression (SVR). This method was evaluated using aerial footage from five distinct weaving sections in China, maintaining an approximately 3 km/h prediction error. In addition, the study also finds that the speed distribution in weaving sections is negatively correlated with the number of lane-changing. Vehicles experience deceleration at both on-ramp and off-ramp, with a more significant deceleration occurring at the on-ramp. Speed is significantly affected by short length, number of lanes and proportion of large vehicles. The proposed method can be embedded into intelligent traffic systems for safe speeds of autonomous vehicles in weaving sections. Reconstructing spatiotemporal patterns of traffic congestion, predicting traffic accidents and implementing active traffic management strategies in weaving sections could be investigated in the future.

Utilizing GaoFen-2 derived urban green space information to predict local surface temperature

Urban green spaces (UGS) significantly influence the distribution of surface heat and play a crucial role in regulating surface temperature. However, the quantitative relationship between UGS and surface temperature remains unclear, necessitating further research. This study aims to predict surface temperature based on green space information from GaoFen-2 satellite data. To achieve this, GaoFen-2 data were utilized to obtain spatial distribution and vegetation growth status in Urumqi, Xinjiang. Three machine learning models such as Support Vector Machine (SVM), Random Forest (RF), and Gradient Boosting Regression Tree (GBRT) were constructed to predict surface temperature. Results indicated that UGS information extracted from GaoFen-2 data using the U-Net semantic segmentation model successfully predicted surface temperature. Among the three machine learning models, GBRT exhibited the highest predictive accuracy with an Radj2 of 0.81, RMSE of 0.44, and RPD of 2.29, followed by RF (Radj2 of 0.80, RMSE of 0.45, and RPD of 2.22), and SVM (Radj2of 0.79, RMSE of 0.47, and RPD of 2.15), In addition, a variable importance assessment reduced the original 44 variables to 28, maintaining predictive accuracy with the GBRT model achieving an Radj2 of 0.81, RMSE of 0.43, and RPD of 2.3. Our study demonstrates the effectiveness of using vegetation information derived from GaoFen-2 to predict surface temperature. This approach provides valuable recommendations for the layout of UGS in urban areas and serves as a comprehensive reference for urban planning and real estate development.

Variable importance analysis with interpretable machine learning for fair risk prediction.

Machine learning (ML) methods are increasingly used to assess variable importance, but such black box models lack stability when limited in sample sizes, and do not formally indicate non-important factors. The Shapley variable importance cloud (ShapleyVIC) addresses these limitations by assessing variable importance from an ensemble of regression models, which enhances robustness while maintaining interpretability, and estimates uncertainty of overall importance to formally test its significance. In a clinical study, ShapleyVIC reasonably identified important variables when the random forest and XGBoost failed to, and generally reproduced the findings from smaller subsamples (n = 2500 and 500) when statistical power of the logistic regression became attenuated. Moreover, ShapleyVIC reasonably estimated non-significant importance of race to justify its exclusion from the final prediction model, as opposed to the race-dependent model from the conventional stepwise model building. Hence, ShapleyVIC is robust and interpretable for variable importance assessment, with potential contribution to fairer clinical risk prediction.

Unveiling the drivers of atmospheric methane variability in Iran: A 20-year exploration using spatiotemporal modeling and machine learning

Understanding the factors controlling spatial and temporal variability of atmospheric methane concentration (XCH4) is crucial for mitigating its impacts and implementing emission reduction strategies. This study comprehensively investigates XCH4 and its driving factors (environmental, meteorological, and anthropogenic activity) across Iran over 20 years, from 2003 to 2022. It combines multi-source satellite observations, advanced spatiotemporal modeling techniques, correlation analysis, and machine learning algorithms. The spatiotemporal analysis showed notable spatial variation, with high XCH4 levels in central, southern, and eastern Iran and lower levels in the northwest and north. Moreover, distinct seasonal cycles emerged, with maximum XCH4 occurring during summer (August-September) and minimum levels in spring (April-May). Correlation analysis and variable importance assessment were developed to elucidate the key drivers governing XCH4 dynamics. Correlation analysis revealed that vegetation cover, precipitation, and soil moisture were negatively correlated with XCH4, while temperature indices showed a positive correlation, exhibiting the highest correlation in time dispersion and quantity among the studied variables. The Permutation Importance technique, used with a Random Forest classifier, a machine learning-based approach that considers the role of all variables together, showed that land surface temperature, wind speed, soil moisture, and vegetation cover are the dominant controls, with their importance ranked respectively. Surprisingly, anthropogenic emissions played a relatively minor role in shaping XCH4 distributions at the regional scale. These findings highlight the significant influence of meteorological variables and ecosystem processes on XCH4 modulation, revealing intricate Earth system feedbacks that inform targeted mitigation strategies and predictive models for curbing greenhouse gas emissions and mitigating climate change impacts.

Projection of future carbon benefits by photovoltaic power potential in China using CMIP6 statistical downscaling data

Solar photovoltaic (PV) systems is an affordable solution that significantly contribute to climate adaptation and resilience, energy security and greenhouse gas abatement with respect to fossil fuel electricity generation. Currently, available studies on the benefits of PV power generation only consider the electricity consumption and do not account for the possible future benefits from carbon trading under the combined impacts of pollution emissions and socio-economic. In this study, the downscaling and bias correction were applied to the Coupled Model Inter-comparison Project Phase 6 (CMIP6) multi-model mean data based on the historical data from the China Meteorological Administration (CMA) stations. The corrected measurements of meteorology were used to explore the PV power potential and the environmental and economic benefits offset by solar power generation under SSP126, SSP245 and SSP585 in China during 2023–2100. We found that the annual mean PV power potential across mainland China ranged from 1 to 37 Wm−2 and demonstrated a decreasing trend in the Northwest China and an increasing trend in the Southeast China. Compared to thermal power generation, electricity from solar energy will counteract the total emissions of annual mean 139.54 × 105 t CO2, 1702 t SO2, 2562 t NO X and 3710 t dust in China in SSP126 scenario. The results of variable importance assessment showed that the West Texas Intermediate crude oil price (47.77%), coal price (41.76%), natural gas price (6.65%) and gross domestic product (2.44%) contribute the most to the carbon emissions allowances (CEAs) price. Against a ‘carbon peak’ background in China, the CEA price will reach 80 CNY/t CO2 by 2030 in China, with the carbon trading value potential ranging from 20 billion to 200 billion CNY of each pixel (10 km × 10 km) by 2030. This study would have important implications for the environmental construction and future investment and construction of PV systems in China.

Ecological Niche Models using MaxEnt in Google Earth Engine: Evaluation, guidelines and recommendations

Google Earth Engine (GEE) has revolutionized geospatial analyses by fast-processing formerly demanding analyses from multiple research areas. Recently, maximum entropy (MaxEnt), the most commonly used method in ecological niche models (ENMs), was integrated into GEE. This integration can significantly enhance modeling efficiency and encourage multidisciplinary approaches of ENMs, but an evaluation assessment of MaxEnt in GEE is lacking. Herein, we present the first MaxEnt models in GEE, as well as its first statistical and spatial evaluation. We also identify the limitations of the approach, providing guidelines and recommendations for its easier applicability in GEE.We tested MaxEnt in GEE using 11 case studies. For each case, we used species of different taxa (insects, amphibians, reptiles, birds and mammals) distributed across global and regional extents. Each species occupied habitats with distinct environmental characteristics (nine terrestrial and two marine species) and within divergent ecoregions across five continents. The models were performed in GEE and Maxent software, and both approaches were contrasted for their model discrimination performance (assessed by eight evaluation metrics) and spatial consistency (correlation analyses and two measures of niche overlap/equivalency).MaxEnt in GEE allows setting several parameters, but important analyses and outputs are unavailable, such as automatic selection of background data, model replicates, and analyses of variable importance (concretely, jackknife analyses and response curves). GEE provided MaxEnt models with high discrimination performance (area under the curve mean between all species models of 0.90) and with spatial equivalency in relation to Maxent software outputs (Hellinger's I mean between all species models >0.90).Our work demonstrates the first application and assessment of MaxEnt in GEE at global and regional scales. We conclude that the GEE modeling method provides ENMs with high performance and reliable spatial predictions, comparable to the widely used Maxent software. We also acknowledge important limitations that should be integrated into GEE in the future, particularly those related to the assessment of variable importance. We expect that our guidelines, recommendations and potential solutions to surpass the identified limitations could help researchers easily apply MaxEnt in GEE across different research fields.

Abstract 802: Identifying factors that affect barriers to lymphoma treatment during the COVID - 19 pandemic

Abstract Introduction: Barriers to therapy for patients with lymphoma are an essential topic. The Lymphoma Coalition biennial global patient survey collects data on patient experiences, including challenges or limitations patients face in seeking medical attention or access to treatment. Due to Covid-19, patients with lymphoma have experienced high barriers. This study aims to rank the influence of core demographic variables in their ability to predict barriers to lymphoma treatment in 2020 and 2022. Methods: The survey was deployed globally to lymphoma patients and caregivers in 2020 & 2022. The outcome variable was the identification of any barrier to receiving lymphoma treatment. Logit regression was used to model the outcome against core demographics. Variable importance was quantified with independent Monte Carlo resampling. Results: Barriers were significantly elevated in all regions in 2022 (p<0.0001). Those who are of older age were found to have fewer barriers to treatment: Unit OR = 0.965; 95%CI [0.962 - 0.968]. Age was consistently a variable of high importance across most regions in both survey years (Table 1). In 2022, treatment delay due to concerns over COVID-19 was the second-ranked variable of importance in three regions. Conclusions: Barriers to treatment for patients with lymphoma increased dramatically across all regions from 2020-2022. Increased barriers to treatment in those of younger age were an unexpected finding. Heterogeneity in the impact of variables that influence access to treatment appears to be enhanced by participants' psychosocial impacts due to the pandemic. Policymakers and providers should actively rectify access disparities in their respective regions. Table 1. Assessment of variable importance for encountering barriers to lymphoma treatment with the top two contributors to the model for each region displayed in bold. Global Patient Survey 2020 Variables Asia-Pacific Europe Middle East & Africa North America South America N 2116 2476 30 820 99 Percent with barrier 50.3% 11.7% 40.0% 18.9% 13.1% Age 0.473 0.286 0.087 0.493 0.309 Education 0.148 0.029 0.322 0.011 0.004 Household Status 0.006 0.432 0.074 0.157 0.149 Indolent/Aggressive 0.014 0.126 0.199 0.189 0.150 Local Area 0.353 0.112 0.316 0.059 0.483 Sex/Gender 0.052 0.047 0.104 0.011 0.074 Global Patient Survey 2022 Variables Asia-Pacific Europe Middle East & Africa North America South America N 1573 2224 32 871 52 Percent with barrier 85.7% 46.7% 88.9% 54.7% 76.1% Age 0.720 0.465 0.001 0.320 0.067 COVID Delay 0.157 0.386 0.002 0.145 0.294 Education 0.001 0.008 0.195 0.046 0.033 Household Status 0.003 0.014 0.173 0.069 0.182 Indolent/Aggressive 0.052 0.007 0.546 0.053 0.312 Local Area 0.141 0.058 0.304 0.375 0.256 Sex/Gender 0.026 0.056 0.152 0.013 0.023 Age is treated as a continuous variable. COVID delay represents a deliberate delay in seeking lymphoma treatment due to fear of contracting COVID-19. Education was binary with the cut-point between secondary and post-secondary. Household status refers to those who are either single or with a partner. Indolent/Aggressive refers to typical clinical behaviour of a lymphoma subtype. Local Area refers to whether a respondent lives in an urban, suburban, or rural setting. Sex/Gender refers to biological sex in the absence of stated gender. Citation Format: Cherie D. Bates, Steve E. Kalloger, Lorna E. Warwick. Identifying factors that affect barriers to lymphoma treatment during the COVID - 19 pandemic [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 802.

Monitoring of Drought Stress in Chinese Forests Based on Satellite Solar-Induced Chlorophyll Fluorescence and Multi-Source Remote Sensing Indices

Greenhouse gas emissions have largely changed the global climate, leading to an increase in the frequency and extent of droughts. Forests are essential natural resources, and they play an important role in maintaining ecological security. Effectively monitoring drought stress in forests can help promote sustainable forestry development. Solar-induced chlorophyll fluorescence is a spectral signal released by vegetation photosynthesis after light absorption. In this study, we used solar-induced chlorophyll fluorescence data (SIF), canopy fluorescence yield (SIFyield) data, vegetation indices (NDVI, EVI), leaf area index (LAI), and fraction of absorbed photosynthetically active radiation (fPAR) to study forest drought stress in the Yunnan, Fujian, Shaanxi, and Heilongjiang provinces in China, respectively. The temporal and spatial ranges of drought stress indicated by the Standardized Precipitation-Evapotranspiration Index (SPEI) values were used as a reference (SPEI ≤ −0.5 indicates the occurrence of drought). Firstly, the standardized anomalous values of SIF, SIFyield, NDVI, EVI, LAI, and fPAR were calculated. The temporal and spatial response abilities of each variable to drought stress were analyzed. Secondly, the correlation between each variable and the drought indicator SPEI was quantified. Finally, the validity and variability of SIF and other variables for drought monitoring were analyzed and verified with a random forest classification model. The results showed that on a temporal scale, SIFyield showed an earlier response to drought stress than other variables and the abnormal change of SIFyield was higher than other variables by 10% or more. Spatially, the range of drought areas indicated by SIFyield and SPEI had more coincident areas than other variables. The overall correlation between SIFyield and SPEI was also higher during the drought period, especially during late drought periods when other variables showed negative correlations. For SIFyield, the correlation coefficients of the Yunnan, Fujian, Shaanxi, and Heilongjiang provinces were 0.57, 0.43, 0.32, and 0.49, respectively. Additionally, the variable importance assessment using a random forest model also indicated that SIFyield is more sensitive to forest droughts. We concluded that SIFyield is an effective tool for monitoring forest drought stress in various regions of China and that it can provide a scientific basis for forest drought monitoring.

Multi-Feature-Based Identification of Subtropical Evergreen Tree Species Using Gaofen-2 Imagery and Algorithm Comparison

The species and distribution of trees in a forest are critical to the understanding of forest ecosystem processes and the development of forest management strategies. Subtropical forest landscapes feature a complex canopy structure and high stand density. Studies on the effects of classification algorithms on the remote sensing-based identification of tree species are few. GF-2 is the first satellite in China with sub-meter accuracy which has the high resolution and short replay cycle. Here, we considered three representative tree types (Masson pine, Chinese fir, and broadleaved evergreen trees) in the southern subtropical evergreen broadleaved forest region of China as research objects. We quantitatively compared the effects of five machine learning algorithms, including the backpropagation neural network, k-nearest neighbour, polytomous logistic regression, random forest (RF) and support vector machine (SVM), and four features (vegetation index, band reflectance, textural features, and topographic factors) on tree species identification using Gaofen-2 panchromatic and multispectral remote sensing images and field survey data. All five classification algorithms could effectively identify major tree species in subtropical forest areas (overall accuracy [OA] > 87.40%, kappa coefficient > 81.08%). The SVM model exhibited the best identification ability (OA = 90.27%, kappa coefficient = 85.37%), followed by RF (OA = 88.90%, Kappa coefficient = 83.30%). The combination of band reflectance, vegetation index, and the topographic factor performed exhibited the best, followed by the combination of band reflectance, vegetation index, textural feature, and topographic factor. In addition, we find that the classifier constructed by a single feature is not as effective as the combination of multiple feature factors. The addition of topographic factors can significantly improve the ability of tree species identification. According to the results of the five classifiers, the separability of the three tree species was good. The producer’s accuracy and user’s accuracy of Masson pine were more than 90%, and the evergreen broad-leaved tree and Chinese fir were more than 80%. The commission errors and omission errors of the three tree species were evergreen broadleaved tree > Chinese fir > Masson pine. The variable importance assessment results showed that the normalized difference greenness index, altitude, and the modified soil-adjusted vegetation index were the key variables. The results of this study used GF-2 to accurately identify the main tree species of subtropical evergreen forests in China, which can help forest managers to regularly monitor tree species composition and provide theoretical support for forest managers to formulate policies, monitor sustainable plans for wood mining, and forest conservation and management measures.

A novel interpretable machine learning system to generate clinical risk scores: An application for predicting early mortality or unplanned readmission in a retrospective cohort study.

Risk scores are widely used for clinical decision making and commonly generated from logistic regression models. Machine-learning-based methods may work well for identifying important predictors to create parsimonious scores, but such 'black box' variable selection limits interpretability, and variable importance evaluated from a single model can be biased. We propose a robust and interpretable variable selection approach using the recently developed Shapley variable importance cloud (ShapleyVIC) that accounts for variability in variable importance across models. Our approach evaluates and visualizes overall variable contributions for in-depth inference and transparent variable selection, and filters out non-significant contributors to simplify model building steps. We derive an ensemble variable ranking from variable contributions across models, which is easily integrated with an automated and modularized risk score generator, AutoScore, for convenient implementation. In a study of early death or unplanned readmission after hospital discharge, ShapleyVIC selected 6 variables from 41 candidates to create a well-performing risk score, which had similar performance to a 16-variable model from machine-learning-based ranking. Our work contributes to the recent emphasis on interpretability of prediction models for high-stakes decision making, providing a disciplined solution to detailed assessment of variable importance and transparent development of parsimonious clinical risk scores.

Dimension Reduction Forests: Local Variable Importance Using Structured Random Forests

Random forests are one of the most popular machine learning methods due to their accuracy and variable importance assessment. However, random forests only provide variable importance in a global sense. There is an increasing need for such assessments at a local level, motivated by applications in personalized medicine, policy-making, and bioinformatics. We propose a new nonparametric estimator that pairs the flexible random forest kernel with local sufficient dimension reduction to adapt to a regression function’s local structure. This allows us to estimate a meaningful directional local variable importance measure at each prediction point. We develop a computationally efficient fitting procedure and provide sufficient conditions for the recovery of the splitting directions. We demonstrate significant accuracy gains of our proposed estimator over competing methods on simulated and real regression problems. Finally, we apply the proposed method to seasonal particulate matter concentration data collected in Beijing, China, which yields meaningful local importance measures. The methods presented here are available in the drforest Python package. Supplementary materials for this article are available online.

Rich cities, poor countryside? Social structure of the poor and poverty risks in urban and rural places in an affluent country.

This paper contributes to the field of regional poverty literature by using linked tax data to examine poverty in a large district in Switzerland with one million inhabitants and rural and urban parts. We measure poverty using income and asset-based approaches. Our regional comparison of the social structure of the poor shows that poor people in rural areas are more likely to be of retirement age. Among the workforce, the share of poor is larger for those who work in agriculture compared to those working in industry or the service sector. In urban areas, the poor are more often freelancers and people of foreign origin. Despite where they live, people with little education, single parents, and people working in gastronomy/tourism are disproportionately often poor. We then use a random forest based variable importance assessment to clarify whether the importance of poverty risks factors differs in urban and rural locations. It shows little regional differences among the major poverty risk factors, and it demonstrates that the opportunity structure, like density of workplaces or aggravated access in mountain areas, seem to be of minor importance compared to risk factors that relate to the immediate social situation.

A General Framework for Inference on Algorithm-Agnostic Variable Importance

In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response—in other words, to gauge the variable importance of features. Most recent work on variable importance assessment has focused on describing the importance of features within the confines of a given prediction algorithm. However, such assessment does not necessarily characterize the prediction potential of features, and may provide a misleading reflection of the intrinsic value of these features. To address this limitation, we propose a general framework for nonparametric inference on interpretable algorithm-agnostic variable importance. We define variable importance as a population-level contrast between the oracle predictiveness of all available features versus all features except those under consideration. We propose a nonparametric efficient estimation procedure that allows the construction of valid confidence intervals, even when machine learning techniques are used. We also outline a valid strategy for testing the null importance hypothesis. Through simulations, we show that our proposal has good operating characteristics, and we illustrate its use with data from a study of an antibody against HIV-1 infection. Supplementary materials for this article are available online.

286Collider-stratification bias when estimating variable importance using Random Forests

Abstract Background Advances in causal inference have helped explain the longstanding birthweight and obesity paradoxes: selection bias due to conditioning on a collider variable i.e. collider-stratification bias (CSB). The lessons learned have critical implications for the interpretation of machine learning (ML), including decision trees and random forests (RFs), that implicitly condition on input variables. RFs are a popular approach for identifying important “predictors” from large data through variable importance, defined by the average decrease in prediction accuracy. While CSB has become a recognized concern when estimating exposure-outcome effects, knowledge of its impact on ML’s variable importance measures (VIMs) is limited. Applying the causal inference framework, we investigated the accuracy of RFs’ VIMs in data-mechanisms prone to CSB. Methods A Monte Carlo simulation study was conducted, with binary outcome and collider variables generated from logistic models. Two exposure variables stochastically determined the outcome and a collider variable, independent of the outcome. VIMs from RFs were compared to the known causal relevance of the input variables on the outcome. Results While variable importance of true exposure variables was not systematically affected by CSB, validity of VIMs can be affected, leading to erroneous selection of collider variables, causally independent of the outcome, as outcome predictors. Conclusions In presence of CSB, VIMs are not valid measures of the causal relevance of variables and may mislead selection of truly important factors that affect the outcome. Key messages ML must consider causal data-generating mechanisms otherwise it may lead to erroneous assessment of variable importance regarding outcome prediction.

Variable Selection with ABC Bayesian Forests

AbstractFew problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants thereof. In this work, we abandon the linear model framework, which can be quite detrimental when the covariates impact the outcome in a non-linear way, and turn to tree-based methods for variable selection. Such variable screening is traditionally done by pruning down large trees or by ranking variables based on some importance measure. Despite heavily used in practice, these ad hoc selection rules are not yet well understood from a theoretical point of view. In this work, we devise a Bayesian tree-based probabilistic method and show that it is consistent for variable selection when the regression surface is a smooth mix of p > n covariates. These results are the first model selection consistency results for Bayesian forest priors. Probabilistic assessment of variable importance is made feasible by a spike-and-slab wrapper around sum-of-trees priors. Sampling from posterior distributions over trees is inherently very difficult. As an alternative to Markov Chain Monte Carlo (MCMC), we propose approximate Bayesian computation (ABC) Bayesian forests, a new ABC sampling method based on data-splitting that achieves higher ABC acceptance rate. We show that the method is robust and successful at finding variables with high marginal inclusion probabilities. Our ABC algorithm provides a new avenue towards approximating the median probability model in non-parametric setups where the marginal likelihood is intractable.

Multiblock variable influence on orthogonal projections (MB-VIOP) for enhanced interpretation of total, global, local and unique variations in OnPLS models

BackgroundFor multivariate data analysis involving only two input matrices (e.g., X and Y), the previously published methods for variable influence on projection (e.g., VIPOPLS or VIPO2PLS) are widely used for variable selection purposes, including (i) variable importance assessment, (ii) dimensionality reduction of big data and (iii) interpretation enhancement of PLS, OPLS and O2PLS models. For multiblock analysis, the OnPLS models find relationships among multiple data matrices (more than two blocks) by calculating latent variables; however, a method for improving the interpretation of these latent variables (model components) by assessing the importance of the input variables was not available up to now.ResultsA method for variable selection in multiblock analysis, called multiblock variable influence on orthogonal projections (MB-VIOP) is explained in this paper. MB-VIOP is a model based variable selection method that uses the data matrices, the scores and the normalized loadings of an OnPLS model in order to sort the input variables of more than two data matrices according to their importance for both simplification and interpretation of the total multiblock model, and also of the unique, local and global model components separately. MB-VIOP has been tested using three datasets: a synthetic four-block dataset, a real three-block omics dataset related to plant sciences, and a real six-block dataset related to the food industry.ConclusionsWe provide evidence for the usefulness and reliability of MB-VIOP by means of three examples (one synthetic and two real-world cases). MB-VIOP assesses in a trustable and efficient way the importance of both isolated and ranges of variables in any type of data. MB-VIOP connects the input variables of different data matrices according to their relevance for the interpretation of each latent variable, yielding enhanced interpretability for each OnPLS model component. Besides, MB-VIOP can deal with strong overlapping of types of variation, as well as with many data blocks with very different dimensionality. The ability of MB-VIOP for generating dimensionality reduced models with high interpretability makes this method ideal for big data mining, multi-omics data integration and any study that requires exploration and interpretation of large streams of data.

VtNet: A neural network with variable importance assessment

The architectures of many neural networks rely heavily on the underlying grid associated with the variables, for instance, the lattice of pixels in an image. For general biomedical data without a grid structure, the multi‐layer perceptron (MLP) and deep belief network (DBN) are often used. However, in these networks, variables are treated homogeneously in the sense of network structure; and it is difficult to assess their individual importance. In this paper, we propose a novel neural network called Variable‐block tree Net (VtNet) whose architecture is determined by an underlying tree with each node corresponding to a subset of variables. The tree is learned from the data to best capture the causal relationships among the variables. VtNet contains a long short‐term memory (LSTM)‐like cell for every tree node. The input and forget gates of each cell control the information flow through the node, and they are used to define a significance score for the variables. To validate the defined significance score, VtNet is trained using smaller trees with variables of low scores removed. Hypothesis tests are conducted to show that variables of higher scores influence classification more strongly. Comparison is made with the variable importance score defined in Random Forest from the aspect of variable selection. Our experiments demonstrate that VtNet is highly competitive in classification accuracy and can often improve accuracy by removing variables with low significance scores.

Rejoinder to "Nonparametric variable importance assessment using machine learning techniques".

Rejoinder to "Nonparametric variable importance assessment using machine learning techniques".

Discussion on "Nonparametric variable importance assessment using machine learning techniques" by Brian D. Williamson, Peter B. Gilbert, Marco Carone, and Noah Simon.

Discussion on "Nonparametric variable importance assessment using machine learning techniques" by Brian D. Williamson, Peter B. Gilbert, Marco Carone, and Noah Simon.