Hierarchical forecasting of hospital admissions- ML approach (modeltime package)
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1 Intro
The aim of this series of blog is to predict monthly admissions to Singapore public acute adult hospitals. EDA for the dataset was explored in past posts ( part 1 ; part 2 ).
library(tidyverse)
library(tidymodels)
library(timetk)
library(modeltime)
library(modeltime.ensemble)
# dataset and dataset for future forecast dats and pre-processing recipes were done in the past post. The output was uploaded onto my github.
url_datasets<-url("https://github.com/notast/hierarchical-forecasting/blob/main/4Dataset_ML.rds?raw=true")
load(url_datasets)
close(url_datasets)
head(to_train,10)
## # A tibble: 10 x 47
## row_id Level Name Date Admission Admission_lag10 Admission_lag10_r~
## <int> <chr> <chr> <date> <dbl> <dbl> <dbl>
## 1 1 Cluster~ NHG 2016-01-01 8035 8184. 7840.
## 2 2 Cluster~ NHG 2016-02-01 7526 7801. 8185.
## 3 3 Cluster~ NHG 2016-03-01 8419 8283. 8072.
## 4 4 Cluster~ NHG 2016-04-01 7934 7926. 8188.
## 5 5 Cluster~ NHG 2016-05-01 8048 8168. 8169.
## 6 6 Cluster~ NHG 2016-06-01 8199 8229. 8097.
## 7 7 Cluster~ NHG 2016-07-01 8230 7608. 7982.
## 8 8 Cluster~ NHG 2016-08-01 8496 7969. 7844.
## 9 9 Cluster~ NHG 2016-09-01 7991 7792. 8009.
## 10 10 Cluster~ NHG 2016-10-01 8284 8041. 8035
## # ... with 40 more variables: Admission_lag10_roll_6 <dbl>,
## # Admission_lag10_roll_12 <dbl>, Covid <chr>, F_trend_strength <dbl>,
## # F_seasonal_strength_year <dbl>, F_seasonal_peak_year <dbl>,
## # F_seasonal_trough_year <dbl>, F_spikiness <dbl>, F_linearity <dbl>,
## # F_curvature <dbl>, F_stl_e_acf1 <dbl>, F_stl_e_acf10 <dbl>, F_acf1 <dbl>,
## # F_acf10 <dbl>, F_diff1_acf1 <dbl>, F_diff1_acf10 <dbl>, F_diff2_acf1 <dbl>,
## # F_diff2_acf10 <dbl>, F_season_acf1 <dbl>, F_kpss_stat <dbl>,
## # F_kpss_pvalue <dbl>, F_pp_stat <dbl>, F_pp_pvalue <dbl>, F_ndiffs <int>,
## # F_bp_stat <dbl>, F_bp_pvalue <dbl>, F_lb_stat <dbl>, F_lb_pvalue <dbl>,
## # F_var_tiled_var <dbl>, F_var_tiled_mean <dbl>, F_shift_level_max <dbl>,
## # F_shift_level_index <dbl>, F_shift_var_max <dbl>, F_shift_var_index <dbl>,
## # F_shift_kl_max <dbl>, F_shift_kl_index <dbl>, F_spectral_entropy <dbl>,
## # F_n_crossing_points <int>, F_longest_flat_spot <int>, F_stat_arch_lm <dbl>
The admissions were treated as a hierarchical time series as every country has a hierarchical order to its public hospitals including Singapore. The levels are
|– Cluster level (Clusters are a network of hospitals based on geographical regions. There are 3 health clusters in Singapore.)
|– Hospital level (There are 8 public acute adult hospitals.)
Admissions were forecasted at each level. Previously, classical approach using traditional techniques e.g. bottoms up and newer techniques e.g. reconciliation were employed. In this blog, machine learning approaches were experimented.
2 Cross validation
The dataset starts from Jan 2016 and ends in Feb 2021 (to_train). This dataset was split into training and testing set. The training set was from Jan 16 to Apr 20 (3 years, 4months) and the test set was from May 20 to Feb 21 (10 months). Cross validation was applied to the training set as the forecasting was a machine learning problem.
# train/test
splits<- to_train %>%
time_series_split(Date, assess= "10 months", cumulative = T)
## Data is not ordered by the 'date_var'. Resamples will be arranged by `Date`.
## Overlapping Timestamps Detected. Processing overlapping time series together using sliding windows.
# training set
splits_train<- training(splits)
# vfold from training set
set.seed(69)
folds<-vfold_cv(splits_train, strata = Admission, v=5)
Metrics
metrics_custom= metric_set(rmse, mae)
3. Pre-processing
The base recipe, rec_PC, was crafted in the previous post where different combination of predictors and features engineered for machine learning were screened
The predictors are:
- Lags (
Admission_lag10) - Rolling lags (
Admission_lag_roll_???) - Covid peak period (
Covid) - The PCA of time series features and statistics (
F_???) - The hierarchical level (
Level) and its members (Name)
rec_PC %>% summary() %>% filter(role=="predictor") %>% pull(variable) ## [1] "Level" "Name" ## [3] "Covid" "Admission_lag10" ## [5] "Admission_lag10_roll_3" "Admission_lag10_roll_6" ## [7] "Admission_lag10_roll_12" "F_trend_strength" ## [9] "F_seasonal_strength_year" "F_seasonal_peak_year" ## [11] "F_seasonal_trough_year" "F_spikiness" ## [13] "F_linearity" "F_curvature" ## [15] "F_stl_e_acf1" "F_stl_e_acf10" ## [17] "F_acf1" "F_acf10" ## [19] "F_diff1_acf1" "F_diff1_acf10" ## [21] "F_diff2_acf1" "F_diff2_acf10" ## [23] "F_season_acf1" "F_kpss_stat" ## [25] "F_kpss_pvalue" "F_pp_stat" ## [27] "F_pp_pvalue" "F_ndiffs" ## [29] "F_bp_stat" "F_bp_pvalue" ## [31] "F_lb_stat" "F_lb_pvalue" ## [33] "F_var_tiled_var" "F_var_tiled_mean" ## [35] "F_shift_level_max" "F_shift_level_index" ## [37] "F_shift_var_max" "F_shift_var_index" ## [39] "F_shift_kl_max" "F_shift_kl_index" ## [41] "F_spectral_entropy" "F_n_crossing_points" ## [43] "F_longest_flat_spot" "F_stat_arch_lm"
The pre-processing steps are:
tidy(rec_PC) ## # A tibble: 8 x 6 ## number operation type trained skip id ## <int> <chr> <chr> <lgl> <lgl> <chr> ## 1 1 step timeseries_signature FALSE FALSE timeseries_signature_ExurK ## 2 2 step rm FALSE FALSE rm_OHKgv ## 3 3 step rm FALSE FALSE rm_GnkOP ## 4 4 step rm FALSE FALSE rm_CeaGH ## 5 5 step rm FALSE FALSE rm_BZcN8 ## 6 6 step dummy FALSE FALSE dummy_xLyW5 ## 7 7 step normalize FALSE FALSE normalize_pAZbw ## 8 8 step pca FALSE FALSE pca_aRkvg
The following machine learning models were trial thus the base recipes had to be revised to compliment some of the models.
- Elastic net regression
GLM(Linear model) - Multivariate adaptive regression spline
MARS(Non-linear model) - Random forest
RF(Tree model) - Extreme gradient boost
XGB(Tree-model) - Boosted PROPHET
PB(Classical approach + Tree-model )6. LightGBM (Tree-model, Light GBM has seen success with hierarchical time series in the M5 competition but fatal errors were encountered when running it inR)
3.1 Base recipe
The base recipe was extended to remove non-zero variance.
rec_PC<- rec_PC %>% step_nzv(all_numeric_predictors()) rec_PC %>% tidy() ## # A tibble: 9 x 6 ## number operation type trained skip id ## <int> <chr> <chr> <lgl> <lgl> <chr> ## 1 1 step timeseries_signature FALSE FALSE timeseries_signature_ExurK ## 2 2 step rm FALSE FALSE rm_OHKgv ## 3 3 step rm FALSE FALSE rm_GnkOP ## 4 4 step rm FALSE FALSE rm_CeaGH ## 5 5 step rm FALSE FALSE rm_BZcN8 ## 6 6 step dummy FALSE FALSE dummy_xLyW5 ## 7 7 step normalize FALSE FALSE normalize_pAZbw ## 8 8 step pca FALSE FALSE pca_aRkvg ## 9 9 step nzv FALSE FALSE nzv_bU0rc
3.2 Spline recipe
To assist the linear model GLM to capture the wiggles of the time series, splines were included.
to_train %>% filter(Name=="SHS") %>% ggplot(aes(Date, Admission)) + geom_line() + labs(title = "Admissions for SHS Cluster")
However glmnet does not tolerate non-numeric variables thus Date cannot be used as the variable for creating the splines. step_timeseries_signature derives various features from Date including a numeric equivalent, Date_index.num.
to_train %>% filter(Name=="SHS") %>% recipe(~.) %>% step_timeseries_signature(Date) %>% prep() %>% juice() %>% ggplot(aes(Date_index.num, Admission)) + geom_line() + labs(title = "Admissions for SHS Cluster")
B-splines were created as there are more flexible than natural splines; hopefully, capturing the wiggles of the time series. The degrees of freedom was tuned.
All numeric predictors with zero variance were removed and then all numeric predictors were normalized to prepare it for elastic net regression.
rec_spline<- rec_PC %>%
step_bs(Date_index.num, deg_free = tune("bs_df")) %>%
step_zv(all_numeric_predictors())%>%
step_normalize(all_numeric_predictors())
rec_spline %>% tidy() %>% pull(type)
## [1] "timeseries_signature" "rm" "rm"
## [4] "rm" "rm" "dummy"
## [7] "normalize" "pca" "nzv"
## [10] "bs" "zv" "normalize"
3.3 Prophet boost recipe
When using modeltime for forecasting, the date column is treated differently for classical and machine learning approach.
Previously, the date column was not treated as a predictor as a machine learning approach was adopted. However, Prophet Boost requires the date to be a predictor for the Prophet part of the model as prophet is a classical approach.
rec_Date<- rec_PC %>% update_role(Date, new_role = "predictor")
4 Modelling
Modelling steps are easy with tidymodels.
- Set up the model
- Add the recipe and model into a workflow
- Tune the workflow which in turn tunes parameters of the recipe and/or the model inside the workflow
- Finalize the workflow with the best tuned parameters
- Fit the finalized workflow with its best tuned recipe and best tuned model onto the whole training data.
4.1 GLM
While it is possible to increase the speed of glmnet modelling with blueprint = hardhat::default_recipe_blueprint(composition = "dgCMatrix"), this sparse matrix is not tolerated further downstream when modeltime functions are used for forecasting.
glm_m<- linear_reg(penalty = tune(), mixture = tune()) %>%
set_engine("glmnet") %>% set_mode("regression")
glm_wf<- workflow() %>%
add_recipe(rec_spline) %>%
add_model(glm_m)
The current degree of freedom is:
parameters(glm_wf)$object[[3]] ## Piecewise Polynomial Degree (quantitative) ## Range: [1, 15]
Splines have been recommended to use a different range of degrees of freedom.
param_spline<-glm_wf %>% parameters() %>% update(bs_df=spline_degree())
param_spline$object[[3]]
## Piecewise Polynomial Degree (quantitative)
## Range: [1, 10]
set.seed(69)
glm_t<- tune_grid(
object= glm_wf,
resamples= folds,
param_info= param_spline,
grid= 20,
metrics= metrics_custom)
fun_fwf<- function(wf, t_wf){
finalize_workflow(
x= wf,
parameters= select_best(t_wf, "rmse")) %>%
fit(splits_train)
}
glm_f<-fun_fwf(glm_wf, glm_t)
4.2 MARS
mars_m<- mars(num_terms = tune(),prod_degree = tune()) %>%
set_engine("earth") %>% set_mode("regression")
mars_wf<- workflow() %>% add_recipe(rec_PC) %>% add_model(mars_m)
set.seed(69)
mars_t<- tune_grid(
object= mars_wf,
resamples= folds, para_info_NULL, grid=10, metrics=metrics_custom)
mars_f<- fun_fwf(mars_wf, mars_t)
4.3 RF
rf_m<- rand_forest(min_n = tune(), trees = tune()) %>%
set_engine("ranger") %>% set_mode("regression")
rf_wf<- workflow() %>% add_recipe(rec_PC) %>% add_model(rf_m)
set.seed(69)
rf_t<- tune_grid(
object=rf_wf,
resamples = folds,
grid=10,
param_info = NULL, metrics = metrics_custom)
rf_f<-fun_fwf(rf_wf, rf_t)
4.4 XGB
xgb_m<- boost_tree(sample_size = tune(),
min_n = tune(),
tree_depth = tune(),
loss_reduction = tune(),
trees=tune()) %>%
set_engine("xgboost") %>% set_mode("regression")
xgb_wf<- workflow() %>% add_recipe(rec_PC ) %>% add_model(xgb_m)
all_cores <- parallel::detectCores(logical = FALSE)
library(doParallel)
cl <- makePSOCKcluster(all_cores)
registerDoParallel(cl)
set.seed(69)
xgb_t<-tune_bayes(
object= xgb_wf,
resamples = folds,
iter = 20,
param_info = NULL, initial = 9,
metrics = metrics_custom,
control = control_bayes(no_improve = 20))
xgb_f<-fun_fwf(xgb_wf, xgb_t)
4.5 Prophet boost
pb_m<- prophet_boost(
seasonality_daily = FALSE, seasonality_weekly = FALSE, seasonality_yearly = FALSE,
min_n = tune(),
tree_depth = tune(),
loss_reduction = tune(),
trees=tune()) %>%
set_engine("prophet_xgboost")
pb_wf<- workflow() %>% add_recipe(rec_Date) %>% add_model(pb_m)
set.seed(69)
pb_t<- tune_bayes(
object= pb_wf,
resamples = folds,
iter = 20,
param_info = NULL, initial = 9, # Generate five at semi-random to start
metrics = metrics_custom,
control = control_bayes(no_improve = 20))
pb_f<- fun_fwf(pb_wf, pb_t)
5. Evaluation
After machine learning was completed with tidymodels, the evaluation and forecasting was completed with modeltime.
The finalized and fitted workflows were housed in a modeltime_table.
(e_table<-modeltime_table(glm_f, mars_f, rf_f, xgb_f, pb_f)) ## # Modeltime Table ## # A tibble: 5 x 3 ## .model_id .model .model_desc ## <int> <list> <chr> ## 1 1 <workflow> GLMNET ## 2 2 <workflow> EARTH ## 3 3 <workflow> RANGER ## 4 4 <workflow> XGBOOST ## 5 5 <workflow> PROPHET W/ XGBOOST ERRORS
The workflows in the modeltime_table were calibrated on the testing set.
(e_cal <- e_table %>% modeltime_calibrate(testing(splits))) ## Warning in bs(x = c(1588291200, 1590969600, 1593561600, 1596240000, ## 1598918400, : some 'x' values beyond boundary knots may cause ill-conditioned ## bases ## Warning in bs(x = c(1588291200, 1590969600, 1593561600, 1596240000, ## 1598918400, : some 'x' values beyond boundary knots may cause ill-conditioned ## bases ## Warning in bs(x = c(1588291200, 1590969600, 1593561600, 1596240000, ## 1598918400, : some 'x' values beyond boundary knots may cause ill-conditioned ## bases ## # Modeltime Table ## # A tibble: 5 x 5 ## .model_id .model .model_desc .type .calibration_data ## <int> <list> <chr> <chr> <list> ## 1 1 <workflow> GLMNET Test <tibble [120 x 4]> ## 2 2 <workflow> EARTH Test <tibble [120 x 4]> ## 3 3 <workflow> RANGER Test <tibble [120 x 4]> ## 4 4 <workflow> XGBOOST Test <tibble [120 x 4]> ## 5 5 <workflow> PROPHET W/ XGBOOST ERRORS Test <tibble [120 x 4]>
The tree models performed well on the testing set. XGB performer poorer than prophet boost likely due to XGB’s reduced ability to capture trends which is better captured by the Prophet part of Prophet Boost. Earlier EDA revealed that more hospitals have higher trend strength than seasonal strength (yearly).
e_cal %>% modeltime_accuracy(metric_set = metrics_custom) %>% arrange(rmse, sort=T) ## # A tibble: 5 x 5 ## .model_id .model_desc .type rmse mae ## <int> <chr> <chr> <dbl> <dbl> ## 1 3 RANGER Test 549. 410. ## 2 5 PROPHET W/ XGBOOST ERRORS Test 1137. 799. ## 3 4 XGBOOST Test 1231. 888. ## 4 2 EARTH Test 3796. 3312. ## 5 1 GLMNET Test 9847. 8281.
Conclusion
The top 2 models, Random forest and Prophet Boost, were selected for retuning to improve performance. Retuning would be covered in the next post.
#The folllowing were exported to save code and computational time for future posts #1. Datasets and the cross validation splits AND folds save(to_train, to_predictfuture, splits, splits_train, folds, file="5Data_CV.RData") #2. tuned grids and workflows (for retunining) save(rf_t, rf_wf, pb_t, pb_wf, file="5Retunning_objects.RData") #3. finalized and fitted wf (to add to modeltime table and compare retunned and OG wf) save(glm_f, mars_f, rf_f, xgb_f, pb_f, file="5FFWf.RData")
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