Universal Bias Corrections

Holdout set accuracy for Universal Bias Corrections, 2021-04-26

Evaluation Results

Last iteration of these models: 2021-02-02

Change Summary

• Each component model (RF, LGB, SVM) is now post-processed with a bias adjustment:
  • After the model is fit to the training data, two linear models (AGB ~ prediction and AGB ~ poly(prediction, 2)) are fit on model predictions against the training data
  • Predictions are then adjusted using whichever linear model had the lowest RMSE against the training sample
  • Bias models are recalculated for each training sample – so the holdout set is using a single adjuster for each component model, the bootstrap 1,000 different adjusters for each model, the validation stage 100
  • RMSE-weighted and linear model ensembles are fit using the bias-corrected predictions
• RMSE-weighted and linear model ensembles are also post-processed with a bias adjustment

	RF (ranger)	GBM (LightGBM)	SVM (kernlab)	Ensemble (model weighted)	Ensemble (RMSE weighted)
RMSE	35.515	35.480	36.671	35.463	35.043
MBE	3.165	3.789	3.552	3.186	3.283
R2	0.791	0.792	0.780	0.791	0.797

AGB Distribution

summary(bind_rows(training, testing)$agb_mgha)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   7.096  86.038  91.674 149.404 425.363 

Validation Results

RMSE	Min	Median	Max
Rf	34.918	40.585	46.213
Lgb	34.102	40.424	46.415
Svm	36.847	41.906	47.528
Ensemble	34.886	40.586	46.312

“Ensemble” here refers to the RMSE-weighted ensemble; the linear model ensemble is trained using the predictions from the validation stage (so doesn’t have any “test” data until we do the final evaluation).

R2	Min	Median	Max
rf	0.689	0.744	0.794
lgb	0.682	0.744	0.792
svm	0.637	0.727	0.780
ensemble	0.689	0.743	0.796

Metadata

Ensembles

• RMSE-weighted model weights:

      lgb        rf       svm 
0.3386723 0.3351334 0.3261943 

• Linear model weights:

Call:
lm(formula = agb_mgha ~ rf_pred * lgb_pred * svm_pred, data = pred_values)

Residuals:
    Min      1Q  Median      3Q     Max 
-135.84  -21.00   -0.54   15.65  220.05 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)               -2.030e+00  5.557e-01  -3.654 0.000259 ***
rf_pred                    2.987e-01  8.609e-02   3.470 0.000521 ***
lgb_pred                   7.340e-01  7.983e-02   9.195  < 2e-16 ***
svm_pred                   1.968e-01  4.337e-02   4.537 5.73e-06 ***
rf_pred:lgb_pred          -1.261e-03  3.022e-04  -4.174 3.00e-05 ***
rf_pred:svm_pred           2.327e-03  5.495e-04   4.234 2.30e-05 ***
lgb_pred:svm_pred         -3.083e-03  4.915e-04  -6.272 3.63e-10 ***
rf_pred:lgb_pred:svm_pred  3.270e-06  1.085e-06   3.015 0.002572 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 39.79 on 22992 degrees of freedom
Multiple R-squared:  0.7478,    Adjusted R-squared:  0.7478 
F-statistic:  9741 on 7 and 22992 DF,  p-value: < 2.2e-16

Coverages

• 17 coverages:
  • FEMA_FranklinStLawrence2016, FEMA_FultonSaratogaHerkimerFran, FEMA_GreatLakes2014, FEMA_OniedaSubbasin2016, NYSGPO_AlleganySteuben2016, NYSGPO_CayugaOswego_2018, NYSGPO_ColumbiaRensselaer2016, NYSGPO_ErieGeneseeLivingston201, NYSGPO_MadisonOtsego_2015, NYSGPO_Southwest_spring_2017, NYSGPO_SouthwestB_fall_2017, NYSGPO_WarrenWashingtonEssex_20, USGS_3County2014, USGS_ClintonEssexFranklin2014, USGS_LongIsland2014, USGS_NorthEast2011, USGS_Schoharie2014

\(n\) and \(p\)

• 1108 observations
  • 767 training
  • 341 testing
• 73 predictors
  • n, zmean, zmean_c, max, quad_mean, quad_mean_c, cv, cv_c, z_kurt, z_skew, L2, L3, L4, L_cv, L_skew, L_kurt, h10, h20, h30, h40, h50, h60, h70, h80, h90, h95, h99, hvol, cancov, rpc1, d10, d20, d30, d40, d50, d60, d70, d80, d90, precip, tmin, tmax, twi, slope, aspect, elev, tax_code_105, tax_code_210, tax_code_240, tax_code_260, tax_code_270, tax_code_280, tax_code_312, tax_code_314, tax_code_322, tax_code_323, tax_code_910, tax_code_911, tax_code_912, tax_code_931, tax_code_932, tax_code_1000, tax_category_100, tax_category_200, tax_category_300, tax_category_900, tax_code_112, tax_code_120, tax_code_241, tax_code_321, tax_code_930, tax_code_941, tax_code_2000

Component Models

• Tuning used 5-fold CV
• Final hyperparameters:

Random forest:

$num.trees
[1] 1000

$mtry
[1] 18

$min.node.size
[1] 7

$sample.fraction
[1] 0.2

$splitrule
[1] "variance"

$replace
[1] TRUE

$formula
agb_mgha ~ .

LGB:

$learning_rate
[1] 0.05

$nrounds
[1] 100

$num_leaves
[1] 5

$max_depth
[1] 2

$extra_trees
[1] TRUE

$min_data_in_leaf
[1] 10

$bagging_fraction
[1] 0.3

$bagging_freq
[1] 1

$feature_fraction
[1] 0.4

$min_data_in_bin
[1] 8

$lambda_l1
[1] 5

$lambda_l2
[1] 1

$force_col_wise
[1] TRUE

SVM:

$x
agb_mgha ~ .

$kernel
[1] "laplacedot"

$type
[1] "eps-svr"

$kpar
$kpar$sigma
[1] 0.0078125


$C
[1] 12

$epsilon
[1] 1.525879e-05

Bias correction models:

Random forest:

[1] ""

LGB:

[1] ""

SVM:

[1] ""

Linear model:

[1] ""

RMSE-weighted:

[1] ""