stressor

Data Generation

It is convenient when testing new functions or algorithms to be able to generate toy data sets. With these toy data sets, we can choose the distribution of the parameters, of the error term, and the underlying model of the toy data set.

In this section, we will show an example of generating linear data with an epsilon and intercept that we chose. We will generate 500 observations from a linear model with five independent variables and a y-intercept of zero. Observations are simulated from this model assuming that the residuals follow a normal distribution with a mean of zero and a standard deviation of one. With respect to the variables chosen, each variable is sampled from a normal distribution with mean zero and standard deviation of one. For this case, we chose to let the coefficients on each term be one, as we wanted each independent variable to be equally weighted. When we create the response variable, Y, it is the sum of each independent variable plus an epsilon term that is sampled from a standard normal distribution.

set.seed(43421)
lm_data <- data_gen_lm(500, weight_vec = rep(1, 5), y_int = 0, resp_sd = 1)
head(lm_data)
#>           Y         V1         V2         V3          V4          V5
#> 1 1.5101730  0.9493875 -0.2231050  0.7501904  0.31629917 -0.41787475
#> 2 2.0124439  1.4844310  1.0737816 -1.8404303  0.85267167 -0.96389423
#> 3 2.6647624 -0.3505283 -0.3922640  0.7192181  0.05188511  1.60003509
#> 4 3.9270489  2.2945235 -0.8998011  0.1046142  1.45699275  1.01588132
#> 5 2.6975509  0.8574341 -0.9723329 -0.9897257  2.80821651  0.00363803
#> 6 0.8071714  0.7676524 -1.2666080  0.5582797 -0.80401673  0.12742990

Machine Learning Model Workflow

In this section, we will demonstrate a typical workflow using the functions of this package to explore the machine learning models (mlm) that are accessible through the PyCaret module in python. First, we need to create a virtual environment for the PyCaret module to exist in. The first time you run this code it will take some time (~ 5 min), as it needs to install the necessary modules into the virtual environment. Note that this virtual environment will be about 1 GB of space on the user’s disk. PyCaret recommends that its library be used in a virtual environment. A virtual environment is a separate partition of python that can have a specific python version installed, as well as other python libraries. This enables the tools needed to be contained without disturbing the main version of python installed.

Once installed, the following message will be shown after you execute the code indicating that you are now using the virtual environment.

create_virtualenv()

See the troubleshoot section if other errors appear. The only time you will need to install a new environment is if you decide to delete a stressor environment and need to initiate a new one. You do not need to install a new environment for each R session, it is one and done. These environments are stored inside the python module on your computer.

To begin using, we need to create all the mlm. This may take a moment (< 3 min) the first time you run it, as the PyCaret module needs to be imported. Then depending on your data size it may take a moment (< 5 min for data <10,000) to fit the data. Note that console output will be shown and a progress bar will be displayed showing the progress of the fitting.

For reproducibility, we have set the seed again and have defined a new data set, and set the seed for the python side by passing the seed to the function. Here are the commands:

set.seed(43421)
lm_data <- data_gen_lm(1000)
# Split the data into a 80/20 split
indices <- split_data_prob(lm_data, .8)
train <- lm_data[indices, ]
test <- lm_data[!indices, ]
# Tune the models
mlm_lm <- mlm_regressor(Y ~ ., lm_data, sort_v = 'RMSE', seed = 43421)

Now, we can look at the initial training predictive accuracy measures such as RMSE. The mlm_lm is a list object where the first element is a list of all the models that were fitted. For example, if we were to pass these models back to PyCaret, they can be refitted or used again for predictions. The second element is a data frame for the initial values and the corresponding models. If you want to specify the models that are fitted, you can change the fit_models parameter – a character vector – specifying the models to be used. Also we can change how the models are sorted based upon the metrics listed which is given to the sort_v variable.

mlm_lm$pred_accuracy

#>                                    Model    MAE    MSE   RMSE      R2  RMSLE
#> lr                     Linear Regression 0.8345 1.0955 1.0429  0.8261 0.3664
#> ridge                   Ridge Regression 0.8344 1.0955 1.0429  0.8261 0.3664
#> lar               Least Angle Regression 0.8345 1.0955 1.0429  0.8261 0.3664
#> br                        Bayesian Ridge 0.8344 1.0955 1.0429  0.8261 0.3664
#> huber                    Huber Regressor 0.8356 1.0976 1.0440  0.8259 0.3671
#> gbr          Gradient Boosting Regressor 1.0308 1.6365 1.2731  0.7425 0.4293
#> et                 Extra Trees Regressor 0.9922 1.6474 1.2785  0.7406 0.4308
#> knn                K Neighbors Regressor 1.0231 1.6798 1.2936  0.7336 0.4390
#> lightgbm Light Gradient Boosting Machine 1.0432 1.7054 1.3013  0.7303 0.4331
#> rf               Random Forest Regressor 1.0448 1.7751 1.3253  0.7221 0.4406
#> ada                   AdaBoost Regressor 1.1535 2.1419 1.4542  0.6656 0.4869
#> par         Passive Aggressive Regressor 1.2356 2.4503 1.5240  0.6015 0.4654
#> en                           Elastic Net 1.4439 3.3031 1.8107  0.4877 0.6173
#> dt               Decision Tree Regressor 1.5140 3.6288 1.8966  0.4181 0.5561
#> omp          Orthogonal Matching Pursuit 1.8988 5.6044 2.3593  0.1243 0.6988
#> lasso                   Lasso Regression 1.9174 5.7881 2.3973  0.1022 0.9362
#> llar        Lasso Least Angle Regression 1.9174 5.7881 2.3973  0.1022 0.9362
#> dummy                    Dummy Regressor 2.0239 6.5123 2.5450 -0.0132 1.0254
#>            MAPE TT (Sec)
#> lr       1.5432    0.009
#> ridge    1.5407    0.009
#> lar      1.5432    0.008
#> br       1.5405    0.009
#> huber    1.5460    0.010
#> gbr      1.8618    0.115
#> et       1.6469    0.133
#> knn      1.7811    0.009
#> lightgbm 2.0825    0.037
#> rf       1.6010    0.251
#> ada      1.5053    0.069
#> par      2.2490    0.009
#> en       1.0218    0.009
#> dt       2.2846    0.011
#> omp      2.1174    0.009
#> lasso    1.0678    0.009
#> llar     1.0678    0.008
#> dummy    1.0414    0.007

We pulled out a test validation set and we can currently check the accuracy measures of those predicted values, such as RMSE.

pred_lm <- predict(mlm_lm, test)
score(test$Y, pred_lm)

#>               rmse       mae       mse            r2     rmsle     mape
#> lr       0.9811816 0.7855389 0.9627174  0.8489721348 0.1575507 1.787733
#> ridge    0.9814217 0.7857800 0.9631885  0.8488982396 0.1576890 1.785325
#> lar      0.9811817 0.7855389 0.9627175  0.8489721181 0.1575508 1.787733
#> br       0.9814372 0.7857951 0.9632189  0.8488934604 0.1576978 1.785174
#> huber    0.9810649 0.7866087 0.9624883  0.8490080733 0.1576332 1.784634
#> gbr      1.1519822 0.8913621 1.3270630  0.7918148288 0.1819330 1.779195
#> et       1.2112827 0.9544208 1.4672058  0.7698296888 0.2063202 1.538019
#> knn      1.2961473 1.0304869 1.6799978  0.7364476099 0.2127031 1.447863
#> lightgbm 1.1740861 0.9132695 1.3784782  0.7837489759 0.1870156 1.385519
#> rf       1.2685104 0.9956673 1.6091187  0.7475668762 0.2078816 1.752251
#> ada      1.4734451 1.1557082 2.1710406  0.6594144709 0.2363207 1.464789
#> par      2.2243526 1.8216665 4.9477444  0.2238145292 0.2836395 3.536359
#> en       1.7919837 1.4126925 3.2112056  0.4962368798 0.2888262 1.161516
#> dt       1.9384331 1.4986607 3.7575229  0.4105324586 0.3019004 1.988530
#> omp      2.2605309 1.7922139 5.1100000  0.1983604118 0.3411484 1.932450
#> lasso    2.3843600 1.8606841 5.6851724  0.1081293000 0.3579984 1.037209
#> llar     2.3843599 1.8606841 5.6851724  0.1081293122 0.3579984 1.037209
#> dummy    2.5257071 1.9860032 6.3791965 -0.0007468551 0.3739615 1.065824

In comparison, we can fit this data using the lm() function and check the initial predictive accuracy with simple test data.

test_index <- split_data_prob(lm_data, .2)
test <- lm_data[test_index, ]
train <- lm_data[!test_index, ]
lm_test <- lm(Y ~ ., train)
lm_pred <- predict(lm_test, newdata = test)
lm_score <- score(test$Y, lm_pred)
lm_score
#>      RMSE       MAE       MSE        R2     RMSLE      MAPE 
#> 0.9716537 0.7793268 0.9441110 0.8095243 0.1563934 1.0339178

As we look at this initial result, we see that there are some comparable models to the RMSE generated from lm() (which is 0.97 compared to 0.98 fitted by Huber Regressor). We see that the mlm outperforms the models that were fitted by lm(). However, it is not clear from this output alone whether the better performance observed from the lm model is statistically significant. A better practice would be performing a cross-validation.

In this code we are fitting the mlm_lm and lm_test to the lm_data using a 10 fold cross-validation.

First the ML models:

mlm_cv <- cv(mlm_lm, lm_data, n_folds = 10)

Then the lm_test:

lm_cv <- cv(lm_test, lm_data, n_folds = 10)

Now to compare the corresponding RMSE.

score(lm_data$Y, mlm_cv)
#>              RMSE      MAE      MSE         R2     RMSLE     MAPE
#> lr       2.364924 1.870219 5.592865 -0.9244870 0.2981139 2.776382
#> ridge    2.363766 1.869422 5.587389 -0.9226029 0.2979252 2.773871
#> lar      2.364924 1.870219 5.592865 -0.9244870 0.2981139 2.776382
#> br       2.363785 1.869435 5.587481 -0.9226344 0.2979288 2.773913
#> huber    2.353164 1.861261 5.537381 -0.9053951 0.2965040 2.761076
#> gbr      2.311607 1.828339 5.343527 -0.8386907 0.2905366 2.638235
#> et       2.269689 1.806269 5.151489 -0.7726111 0.2854914 2.508345
#> knn      2.335107 1.855689 5.452724 -0.8762651 0.2938159 2.636042
#> lightgbm 2.372964 1.869536 5.630957 -0.9375943 0.2985878 2.837477
#> rf       2.281818 1.817093 5.206693 -0.7916066 0.2870201 2.552018
#> ada      2.186354 1.754228 4.780145 -0.6448326 0.2771474 2.193652
#> par      2.576865 2.055230 6.640235 -1.2848838 0.2992653 3.583453
#> en       2.124765 1.711973 4.514628 -0.5534691 0.2731174 1.411179
#> dt       2.716927 2.166145 7.381690 -1.5400162 0.3503943 3.437621
#> omp      2.421582 1.945890 5.864059 -1.0178041 0.3030696 1.884166
#> lasso    2.355189 1.899553 5.546917 -0.9086763 0.3000909 1.058293
#> llar     2.355189 1.899553 5.546917 -0.9086763 0.3000909 1.058293
#> dummy    2.414994 1.947364 5.832195 -1.0068397 0.3066178 1.023737
score(lm_data$Y, lm_cv)
#>      RMSE       MAE       MSE        R2     RMSLE      MAPE 
#> 1.0640627 0.8360287 1.1322295 0.8052017 0.1406658 1.5685498

We can see that the top five ML models are close in value to the linear model.

Real Data Example

We want to show how our functions apply to a real data example. We can simulate data, but it is never quite like observed data. The purpose of this data set is to show the use of the functions in this package – specifically cross-validation. This is crucial to show how these work in comparison to existing functions.

We will be using the Boston Housing Data from the mlbench package. There are two versions of this data, the second version includes a corrected medv value, standardizing the median income to USD 1000’s. As some of the original data was missing. This data version also has had the town, tract, longitude and latitude added. For this analysis, we are ignoring spatial autocorrelation and therefore will be removing these variables from the analysis.

This next code chunk opens the cleaned Boston data set attached to this package and fits the initial machine learning models. It then displays the initial values from the first fit.

data(boston)
mlm_boston <- mlm_regressor(cmedv ~ ., boston)
mlm_boston$pred_accuracy

#>                                    Model    MAE     MSE   RMSE      R2  RMSLE
#> gbr          Gradient Boosting Regressor 2.1218  9.7524 3.0077  0.8615 0.1393
#> et                 Extra Trees Regressor 2.1753 11.2063 3.1583  0.8453 0.1414
#> rf               Random Forest Regressor 2.2152 11.2131 3.2292  0.8441 0.1467
#> lightgbm Light Gradient Boosting Machine 2.4390 13.9694 3.6343  0.8122 0.1570
#> ada                   AdaBoost Regressor 2.7002 15.1353 3.7275  0.7950 0.1755
#> dt               Decision Tree Regressor 3.0190 20.6916 4.4073  0.7180 0.2007
#> lr                     Linear Regression 3.3687 24.0099 4.7956  0.6858 0.2453
#> ridge                   Ridge Regression 3.3493 24.0915 4.7963  0.6849 0.2513
#> lar               Least Angle Regression 3.4298 24.4397 4.8504  0.6785 0.2473
#> br                        Bayesian Ridge 3.3931 24.7832 4.8727  0.6777 0.2589
#> huber                    Huber Regressor 3.3622 27.7117 5.0719  0.6496 0.2931
#> en                           Elastic Net 3.5681 27.9055 5.1803  0.6461 0.2562
#> lasso                   Lasso Regression 3.6315 29.0143 5.2788  0.6328 0.2506
#> llar        Lasso Least Angle Regression 3.6315 29.0141 5.2788  0.6328 0.2506
#> knn                K Neighbors Regressor 3.9844 33.5862 5.7336  0.5557 0.2237
#> omp          Orthogonal Matching Pursuit 5.5777 62.2987 7.7159  0.2226 0.3140
#> dummy                    Dummy Regressor 6.4549 78.6894 8.7760 -0.0148 0.3798
#> par         Passive Aggressive Regressor 7.1163 83.3044 8.9282 -0.1049 0.4482
#>            MAPE TT (Sec)
#> gbr      0.1106    0.122
#> et       0.1115    0.151
#> rf       0.1148    0.263
#> lightgbm 0.1197    0.056
#> ada      0.1439    0.091
#> dt       0.1550    0.035
#> lr       0.1706    0.035
#> ridge    0.1708    0.035
#> lar      0.1737    0.035
#> br       0.1730    0.035
#> huber    0.1731    0.051
#> en       0.1724    0.035
#> lasso    0.1735    0.034
#> llar     0.1735    0.036
#> knn      0.1832    0.033
#> omp      0.2728    0.032
#> dummy    0.3508    0.032
#> par      0.3716    0.034

Observe the initial values for the Boston data set. Now compare these to the cross-validated values.

mlm_boston_cv <- cv(mlm_boston, boston, n_folds = 10)
mlm_boston_score <- score(boston$cmedv, mlm_boston_cv)
mlm_boston_score

#>              RMSE      MAE       MSE           R2      RMSLE      MAPE
#> gbr      2.880214 2.096367  8.295632  0.901413505 0.03826106 0.1097795
#> et       3.095790 2.038773  9.583918  0.886103331 0.04008861 0.1035976
#> rf       3.091200 2.145828  9.555518  0.886440846 0.04044387 0.1106439
#> lightgbm 3.223722 2.129938 10.392383  0.876495421 0.04176346 0.1082107
#> ada      3.582974 2.773172 12.837703  0.847434883 0.04837222 0.1497296
#> dt       4.485803 2.837352 20.122431  0.760862124 0.05795620 0.1437426
#> lr       4.908502 3.451202 24.093388  0.713670689 0.06492690 0.1745373
#> ridge    4.931873 3.439230 24.323376  0.710937485 0.06533195 0.1745591
#> lar      4.909012 3.469367 24.098402  0.713611106 0.06523700 0.1759787
#> br       5.006509 3.486602 25.065131  0.702122364 0.06636305 0.1770225
#> huber    5.584459 3.587230 31.186187  0.629378842 0.07572677 0.1812409
#> en       5.328285 3.710624 28.390621  0.662601752 0.06863061 0.1788665
#> lasso    5.386974 3.754152 29.019492  0.655128160 0.06925798 0.1803929
#> llar     5.386960 3.754145 29.019338  0.655129997 0.06925790 0.1803927
#> knn      5.836711 4.009170 34.067194  0.595140547 0.07285509 0.1819197
#> omp      8.116394 5.873471 65.875855  0.217121821 0.10323051 0.2868320
#> dummy    9.183814 6.643323 84.342437 -0.002337712 0.11942902 0.3630920
#> par      8.937533 6.676229 79.879500  0.050700482 0.12318012 0.3213036

Clustered cross-validation is subsetting the parameter space into groups that share similar attributes with one another. Therefore, if we train on those groups the other group should fit similarly across the test group.

Now, compare to the clustered cross-validation:

mlm_boston_clust_cv <- cv(mlm_boston, boston, n_folds = 10, k_mult = 5)
mlm_boston_clust_score <- score(boston$cmedv, mlm_boston_clust_cv)
mlm_boston_clust_score

#>               RMSE       MAE       MSE         R2      RMSLE      MAPE
#> gbr       3.752646  2.722356  14.08235  0.8326433 0.04915424 0.1408009
#> et        3.665735  2.566496  13.43761  0.8403055 0.04730942 0.1309730
#> rf        4.154256  2.798413  17.25785  0.7949053 0.05368193 0.1450138
#> lightgbm  4.023057  2.752783  16.18499  0.8076553 0.05210606 0.1408062
#> ada       4.433633  3.332406  19.65710  0.7663922 0.05852669 0.1778279
#> dt        5.394398  3.608300  29.09953  0.6541770 0.06953791 0.1882557
#> lr        5.879360  4.278917  34.56687  0.5892023 0.07986385 0.2287874
#> ridge     5.741469  4.099545  32.96447  0.6082455 0.07815901 0.2207254
#> lar       6.092678  4.370884  37.12072  0.5588520 0.08399236 0.2395658
#> br        5.808605  4.075319  33.73989  0.5990303 0.07884975 0.2192994
#> huber     6.444105  4.469043  41.52649  0.5064932 0.08726243 0.2302259
#> en        5.900504  4.247760  34.81595  0.5862423 0.07639839 0.2110481
#> lasso     6.105984  4.411099  37.28304  0.5569229 0.07907545 0.2195190
#> llar      6.106000  4.411162  37.28323  0.5569207 0.07907643 0.2195278
#> knn       8.027975  5.668933  64.44838  0.2340862 0.10082338 0.2561170
#> omp       8.542734  6.256828  72.97830  0.1327154 0.10913893 0.3073734
#> dummy     9.640141  7.050797  92.93233 -0.1044212 0.12579351 0.3862600
#> par      21.356794 14.663207 456.11264 -4.4205085 0.18068971 0.8859428

What we notice about this result is when we ignore spatial autocorrelation and we compare the 10 fold cross-validation with the clustered cross-validation, we see a general improvement in the values. This suggests that maybe there is some other underlying factors, i.e. spatial relationships.

The power to be able to explore is a compliment to the purpose of R. With stressor, you are able to fit multiple machine learning models with a few lines of code and perform 10 fold cross-validation and clustered cross-validation. With a simple command, you can return the values from the predictions.

Troubleshooting

When initiating the virtual environment, you may receive some errors or warnings. reticulate has done a nice job with the error handling of initiating the virtual environments. reticulate is a package in R that handles the connection between R and python.

For MacOS and Linux, please note that the create_virtualenv() function will not work unless you have cmake. lightgbm requires this compiler and they have detailed instructions of how to install it, see here.

If your system is not recognizing the python path that you have, you will need to add it to your system variables, or specify initially the python path that create_virtualenv() needs to use. If you are still having trouble getting the virtual environment to start you can use reticulate’s function reticulate::use_virtualenv(). It also helps sometimes to unset the RETICULATE_PYTHON variable. Also note that if the environment has python objects in it the user will have to clear them to restart the reticulate python version.

If you receive a warning that says

“Warning Message: Previous request to use_python() … will be ignored. It is superseded by request to use_python()”

If the second use_python command has the matching virtual environment you can ignore this warning and continue with your analysis.

If you receive an error stating

ERROR: The requested version of Python … cannot be used, as another version of Python … has already been initialized. Please restart the R session if you need to attach reticulate to a different version of Python.

If this error appears, restart your R session and make sure to clear all python objects. Then run the create_virtualenv() function again. There should be no problems attaching it after that, as long as your environment does not contain any Python objects.