A Brief Review of Random Forests for Water Scientists and Practitioners and Their Recent History in Water Resources
Abstract
:1. Introduction
2. Random Forests
2.1. How Random Forests Work
2.1.1. Supervised Learning
2.1.2. Classification and Regression Trees
2.1.3. Bagging
2.1.4. Random Forests
2.2. Properties of Random Forests
2.3. Variable Importance Metrics
2.4. Parameters
2.5. Variable Selection
2.6. Interactions
2.7. Uncertainty, Time Series Forecasting, Spatial and Spatiotemporal Modeling
2.8. What to Expect and Not Expect from Random Forests
2.8.1. Twenty Two Reasons towards the Use of Random Forests
- 1.1.
- 1.2.
- They can capture non-linear dependencies between predictor and dependent variables (see e.g., Boulesteix et al. [16]).
- 1.3.
- They are non-parametric; i.e., no parametric statistical model needs to be defined for their use (see e.g., Boulesteix et al. [16]).
- 1.4.
- They are fast compared to other machine learning algorithms (see e.g., Ziegler and König [17]) and, also, they can operate in parallel computing mode.
- 1.5.
- They can be applied to large-scale problems (see e.g., Biau and Scornet [2]).
- 1.6.
- 1.7.
- They do not overfit (see e.g., Díaz-Uriarte and De Andres [80]).
- 1.8.
- 1.9.
- The number of model parameters is small, and the default values in corresponding software implementations are properly set and the algorithm is robust to changes of the parameters (see Section 2.4, and Biau and Scornet [2], Díaz-Uriarte and De Andres [80]).
- 1.10.
- They are robust to the inclusion of noisy predictor variables (see e.g., Díaz-Uriarte and De Andres [80]).
- 1.11.
- 1.12.
- They can operate successfully when interactions (see Section 2.6) are present (see e.g., Boulesteix et al. [16], Ziegler and König [17], Díaz-Uriarte and De Andres [80], Boulesteix et al. [83]).
- 1.13.
- 1.14.
- They permit ranking of the relative significance of predictor variables, through variable importance metrics (VIMs; see Section 2.3 and Biau and Scornet [2], Ziegler and König [17], Díaz-Uriarte and De Andres [80]).
- 1.15.
- Variable selection procedures, based on VIMs, can be combined with other machine learning algorithms (see e.g., Ziegler and König [17]).
- 1.16.
- They can effectively handle small sample sizes (see e.g., Biau and Scornet [2]).
- 1.17.
- 1.18.
- They can simultaneously incorporate continuous and categorical variables (see e.g., Díaz-Uriarte and De Andres [80]).
- 1.19.
- They can be used to solve problems with many classes of the response variable (see e.g., Díaz-Uriarte and De Andres [80]).
- 1.20.
- They are invariant to monotone transformations of the predictor variables (see e.g., Díaz-Uriarte and De Andres [80]).
- 1.21.
- They can effectively handle missing data (see e.g., Biau and Scornet [2]).
- 1.22.
- There exist free software implementations of RF algorithms (see e.g., Díaz-Uriarte and De Andres [80]), with most variants and extensions been available as contributed packages in the R programming language.
2.8.2. Why the Practicing Hydrologist Should Use Random Forests with Caution
- 2.1.
- The theoretical properties of random forests are not fully understood, and they are usually interpreted based on simplified/stylized versions of the algorithm (see e.g., Biau and Scornet [2], Ziegler and König [17], and Section 2.2).
- 2.2.
- Random forests cannot extrapolate outside the training range; see Hengl et al. [47] for an example.
- 2.3.
- 2.4.
- Random forests are harder to interpret/understand compared to single trees (see e.g., Ziegler and König [17]).
- 2.5.
- The automation of random forests may result in a slight decrease of their predictive performance compared to e.g., highly parameterized tree-based boosting (see e.g., Efron and Hastie [3], p. 324).
- 2.6.
- They cannot adequately model datasets with imbalanced data (i.e., datasets in which the number of observations of the response variable belonging to one class differs significantly compared to other classes, [91]).
- 2.7.
3. Random Forest Variants
4. R Software
5. Random Forests in a Published Case Study
6. Application of Random Forests and Related Algorithms in Water Sciences
6.1. Literature Search Results
6.2. More in-Depth Analysis on the Use of Random Forests
- Ability to model non-linear relationships (reason 1.2), and ability to model interactions (reason 1.12).
- Speed (reason 1.4), and small number of parameters (reason 1.9).
- Simplicity (reason 1.6), and small number of parameters (reason 1.9).
- Flexibility of the algorithm (reason 1.13), and reliability of VIMs (reason 2.3).
- Ability to process small samples (reason 1.16), and free software implementation (reason 1.22).
- Ability to solve problems with many classes (reason 1.19), and free software implementation (reason 1.22).
7. Concluding Remarks and Take-Home Considerations
- Contrary to the general class of data-driven models, which focus mostly on forecasting and prediction over interpretation and understanding, random forests allow for explicit interpretation of the obtained results through variable importance metrics (VIMs); see Introduction.
- Important considerations regarding the implementation of data-driven models in water science, such as splitting of the dataset into training and testing periods, preprocessing of variables, and variable selection, are explicitly dealt with by random forests. For example, tuning of the algorithm is commonly performed using OOB (out-of-bag) data (see Section 2.1.4 and Section 2.5), preprocessing has generally small influence on the predictive performance of the algorithm (see reason 1.20 in Section 2.8.1), while there are many automatic variable selection procedures based on VIMs (see reason 1.15 in Section 2.8.1).
- In 33% of the reviewed water-related studies (i.e., 67 out of 203) random forests were not the algorithm of focus but, rather, they were used to complement other modeling approaches to improve inference. This highlights their usefulness in water science.
- The role of random forests as a useful complementary tool in water resources applications is related to their benchmarking nature (see e.g., the comment by Efron and Hastie [3] (pp. 347, 348) in Section 2.8.1, and reason 1.1), as well as their simplicity and ease of use (see Section 2.8.1). Other important properties of RF algorithms are their speed, and the fact that little (or no) tuning of their parameters is required to reach an acceptable predictive performance; see Section 6.1.
- While some attractive properties of random forests are also shared by other data-driven methods (e.g., non-linear and non-parametric modeling), their selection is driven mostly by their increased predictive performance, their capability to capture non-linear dependencies and interactions of variables, as well as their speed, parsimonious parameterization, ease of use, and ability to handle big datasets; see Section 6.1 and Section 6.2, and Figure 8. The use of VIMs for interpretation and variable selection is also noteworthy, as they are not commonly implemented by data-driven models other than random forests.
- The large potential of random forests in water resources applications has been exploited only to a small degree. Perhaps, this is related to the fact that many RF-variants were introduced very recently, while the properties of the algorithm are not fully understood; see Section 6.1. Thus, the potential for further uses and improvements is large, including variants specializing in clustering, modeling of interactions, heteroscedasticity, survival analysis, computation of VIMs and more. The added value of random forests is also confirmed by a wide range of applications in diverse areas of research, such as streamflow modeling, imputation of missing values, water quality, hydrological signatures, ecology, land cover, urban water, floods, and soil properties among other applications; see Section 6.1 for further details.
- Another important aspect is that most RF-variants have been implemented in the R programming language, and are freely available; see Table 3. This facilitates reproducibility of the results, research advancements, as well as further uses of the algorithm.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
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Paper | Algorithms | General Theme | Topics Examined |
---|---|---|---|
[21] | Artificial neural networks | Rainfall-runoff modeling and flood forecasting | Preprocessing, variable selection, training, testing, modeling practices |
[22,23] | Artificial neural networks | Water resources applications | Methods for variable selection |
[20] | Artificial neural networks, genetic programming, evolutionary regression, fuzzy-rule based systems, support vector machines, chaos theory, instance-based learning, regression trees | River flow forecasting, river basin flow prediction, contaminant transport | Testing, human expertise, uncertainty estimation, hybrid models |
[24] | Artificial neural networks | Rainfall-runoff modeling | Variable selection, training, testing, hybrid models, extrapolation |
[25] | Artificial neural networks | Flow, salinity, level, nitrate, SO4, drought index, sediment, volume, turbidity, specific conductance, DO, pH, water temperature, concentration of tracer, runoff, river discharge, Secchi depth, Chl a, phosphorus, ammonia, fecal coliform, water supply, debris flow, dam inflow | Variable selection, training, testing, model architecture |
[26] | Bayesian networks | Environmental modeling | Preprocessing, training, testing, software |
[27] | Artificial neural networks | Rainfall-runoff, river flow forecasting | Model architecture, preprocessing, variable selection, training, testing, physical interpretation, modular solutions, ensemble learning, hybrid models, benchmark datasets, diagnostics, operational models, uncertainty estimation |
[28] | Wavelet-Artificial intelligence models | Precipitation modeling, flow forecasting, rainfall-runoff modeling, sediment modeling, groundwater modeling, hydroclimatologic applications | Reviews of data-driven models, testing, usefulness of hybrid wavelet-based models |
[29] | Support vector machine | Rainfall forecasting, runoff forecasting, streamflow forecasting, sediment yield forecasting, evaporation and evapotranspiration forecasting, lake and water level forecasting, flood forecasting, drought forecasting, groundwater level forecasting, soil moisture estimation, groundwater quality assessment | Mostly comparison of studies |
[30] | Ant colony optimization | Optimization, reservoir operation and surface water management, water distribution systems, drainage and wastewater engineering, groundwater systems including remediation, monitoring, and management, Environmental and Watershed Management Problems, other applications | Analysis of the literature |
[31] | Artificial neural networks, fuzzy logic networks, genetic algorithms, genetic programming, particle swarm optimization, honey-bee mating, artificial bee colony | Inflow forecasting, reservoir management optimization | General evaluation of the algorithms |
[32] | Artificial neural networks, support vector machine, fuzzy logic, evolutionary computing, wavelet-artificial intelligence model | Streamflow forecasting | General evaluation of the algorithms |
[33] | Artificial neural networks, adaptive neuro fuzzy inference system, other algorithms, wavelet-artificial intelligence model | Sediment transport | General evaluation of the algorithms |
[34] | Bayesian belief networks | Environmental applications | Geographic distribution of papers, data sources, testing, climate change related issues, water resources management, integration with other models |
[35] | Artificial neural networks | Forecasting of water related variables, uncertainty estimation | General evaluation of methods for uncertainty estimation, testing |
[36] | Genetic programming | Rainfall-runoff modeling, streamflow forecasting, water quality variables modeling, groundwater modeling, soil properties modeling, sediment transport, reservoir flow prediction, pipeline flow prediction, open channel flow, wave height prediction, statistical downscaling, precipitation, evaporation, evapotranspiration, solar radiation, drought forecasting, temperature | Evaluation of the applications, selection of parameters |
[37] | Deep learning | Water resources related problems | General discussion |
[38] | ARIMA, ARMAX, linear regression, support vector machine, genetic programming, fuzzy logic, hybrid models | Univariate streamflow forecasting | General evaluation of the algorithms |
Variant | Reference | Characteristic |
---|---|---|
Quantile regression forests | [85] | Quantile regression |
Extremely randomized trees | [103] | They split nodes by choosing cut-points fully at random and use the full learning sample to grow the trees. It corresponds to a lower parametric version of random forests |
Enriched random forests | [104] | Weighted random selection of predictor variables as candidates for splitting. |
Rotation forests | [105] | Combines splitting of the predictor variables set with principal component analysis for improved accuracy |
Conditional inference forests | [71,100,106,107,108] | Unbiased variable importance measures in the case of correlated or mixed type (i.e., continuous and categorical) predictor variables. |
Random survival forests | [98,109,110] | Survival analysis. |
Online forests, Mondrian forests. information forests | [111,112,113,114] | Handles training data arriving sequentially or continuously, changing the underlying distribution. |
Ranking forests | [115,116] | Ranking problems |
Random ferns | [117] | Same test parameters are used in all nodes of the same tree level. It corresponds to a lower parametric version of random forests. |
Bayesian additive regression trees | [94] | Aggregation of trees, but inference and fitting is accomplished using Bayesian methods. Conditional means and quantiles can be computed. |
Node harvest | [118] | Multiple single nodes. |
Density forests | [15] | Density estimation of unlabeled data. |
Manifold forests | [15] | Manifold learning (dimensionality reduction). |
Semi-supervised forests | [15] | Semi-supervised learning. |
Entangled forests | [119] | Entanglement of the tests applied at each tree node with other nodes in the forest. |
Decision tree fields | [99] | Combination of random forests and random fields. |
STAR model | [120] | They can be seen as single nodes equipped with one random projection and multiple decision thresholds |
Multivariate random forests | [97] | Predicts multiple dependent variables. |
Dynamic random forests | [121] | Inclusion of trees in the ensemble learner depending on previous outputs. |
Gradient forests | [122] | Use of alternative importance measures. |
Regularized random forests | [123,124] | Improvements on variable selection within trees. |
Cluster forests | [125] | Appropriate for clustering (unsupervised learning). |
Weighted random forests | [126] | Incorporates tree-level weights for more accurate prediction and computation of variable importance. |
Random intersection trees | [101] | High-order interaction discovery. |
Hyper-Ensemble Smote Undersampled Random Forests | [91] | Undersampling of the majority class and oversampling of the minority class to learn from highly imbalanced data. |
Integrated multivariate random forests | [127] | Integrated different data subtypes. |
Generalized random forests | [89] | Generalization of random forests for adaptive, local estimation. |
Iterative random forests | [102,128] | High-order interaction discovery. |
Heteroscedastic Bayesian additive regression trees | [95] | Bayesian additive regression trees for modeling heteroscedastic data. |
Local linear forests | [129] | They model smooth signals and fix boundary bias issues. They build on generalized random forests. |
Distributional regression forests | [96] | Version of generalized additive models for location, scale, and shape parameters (GAMLSS), using trees. |
Causal forests | [92] | Estimation of heterogeneous treatment effects. They can be used for statistical inference. |
Neural random forests | [130] | Reformulation of random forests in a neural network setting. |
R Package | Characteristics |
---|---|
abcrf | Combined with other methods |
AUCRF | Variable selection |
bartMachine | Variant |
Boruta | Variable selection |
CALIBERrfimpute | Imputation |
caret | Of general use |
edarf | Utilities |
extendedForest | Utilities |
forestControl | Variable selection |
forestFloor | Utilities |
funbarRF | Application |
ggRandomForests | Utilities |
gradientForest | Variant |
grf | Variant |
hyperSMURF | Variant |
IntegratedMRF | Variant |
IPMRF | Variable importance |
iRafNet | Variant |
iRF | Variant |
JRF | Variant |
m2b | Application |
MAVTgsa | Application |
metaforest | Application |
missForest | Imputation |
mlr | Of general use |
mobForest | Application |
ModelMap | Utilities |
MultivariateRandomForest | Variant |
obliqueRF | Variant |
OOBCurve | Utilities |
ParallelForest | Better programmed |
party | Variant |
partykit | Variant |
pRF | Variable importance |
quantregForest | Variant |
randomForest | Variant |
randomForestExplainer | Variable importance |
randomForestSRC | Variant |
ranger | Better programmed |
Rborist | Better programmed |
RFgroove | Variable importance |
RFmarkerDetector | Application |
rfPermute | Variable importance |
rfUtilities | Utilities |
roughrf | Imputation |
RRF | Variant |
snpRF | Variant |
Sstack | Application |
SuperLearner | Of general use |
trimTrees | Variant |
tuneRanger | Utilities |
varSelRF | Variable selection |
vita | Variable importance |
VSURF | Variable selection |
wsrf | Variant |
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Tyralis, H.; Papacharalampous, G.; Langousis, A. A Brief Review of Random Forests for Water Scientists and Practitioners and Their Recent History in Water Resources. Water 2019, 11, 910. https://doi.org/10.3390/w11050910
Tyralis H, Papacharalampous G, Langousis A. A Brief Review of Random Forests for Water Scientists and Practitioners and Their Recent History in Water Resources. Water. 2019; 11(5):910. https://doi.org/10.3390/w11050910
Chicago/Turabian StyleTyralis, Hristos, Georgia Papacharalampous, and Andreas Langousis. 2019. "A Brief Review of Random Forests for Water Scientists and Practitioners and Their Recent History in Water Resources" Water 11, no. 5: 910. https://doi.org/10.3390/w11050910
APA StyleTyralis, H., Papacharalampous, G., & Langousis, A. (2019). A Brief Review of Random Forests for Water Scientists and Practitioners and Their Recent History in Water Resources. Water, 11(5), 910. https://doi.org/10.3390/w11050910