Hierarchical forecasting of hospital admissions- ML approach (screen variables)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
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)
# cleaned up dataset downloaded from my github. Clean up of OG dataset done in 1st post
raw<- read_csv("https://raw.githubusercontent.com/notast/hierarchical-forecasting/main/stat_sg_CLEAN.csv")
The admissions were treated as a hierarchical time series. Every country has a hierarchical order to its public hospitals. In Singapore, there are 3 levels:
|– 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. Machine learning approach would be trial in the next few posts. In this post, different combinations of predictors were screened to determine the set of predictors for machine learning.
2 Data wrangling
The dataset starts from Jan 2016 and ends in Feb 2021. The training set was from Jan 16 to Apr 20 (3 years, 4months) and the testing set was from May 20 to Feb 21 (10 months). The forecast horizon was 10 months as the data ended in Feb 21 and the goal was to forecast admissions till the end of 2021. The splitting of training, testing and future data are covered later in this section.
2.1 Long format with aggregated values
When fpp3::reconcile was used for classical approach, each column represented the members of that particular level and aggregated values for each level were not required.
tribble( ~Level1_Hospital, ~Level2_Cluster, ~Admission, "CGH", "SHS", 100, "SKH", "SHS", 200, "TTSH", "NHG", 900) ## # A tibble: 3 x 3 ## Level1_Hospital Level2_Cluster Admission ## <chr> <chr> <dbl> ## 1 CGH SHS 100 ## 2 SKH SHS 200 ## 3 TTSH NHG 900
In the machine learning approach, all the hierarchical levels form a variable and the corresponding subordinate members form another variable. Hence, the aggregated values had to be calculated. The variable of all levels and the variable of the corresponding members were treated as categorical variables in this machine learning problem.
tribble(
~Level, ~Name, ~Admission,
"Level 1", "CGH", 100,
"Level 1", "SKH", 200,
"Level 1", "TTSH", 900,
"Level 2" ,"SHS", 300,
"Level 2", "NHG", 900,
"Level 3", "National", 1200)
## # A tibble: 6 x 3
## Level Name Admission
## <chr> <chr> <dbl>
## 1 Level 1 CGH 100
## 2 Level 1 SKH 200
## 3 Level 1 TTSH 900
## 4 Level 2 SHS 300
## 5 Level 2 NHG 900
## 6 Level 3 National 1200
df<-raw %>%
# add national
mutate(National_id= "National") %>%
# add id as suffix to all levels
rename_with(.fn= ~paste0(.x, "_id"), .cols = c(Hospital, Cluster )) %>%
pivot_longer(cols=ends_with("id"), names_to = "Level", values_to="Name")%>%
group_by(Level, Name, Date) %>% summarise(Admission= sum(Admission,na.rm=T), .groups="drop")
2.2 Extend into the future
The machine learning approach was supported with the modeltime meta-package which is like a time series equivalent to tidymodels. In modeltime when a machine learning approach is adopted with external regressors, the future period to be forecasted is appended to the dataset.
full<- df %>% group_by(Level, Name) %>% # .bind_data to append future_frame(Date, .length_out = 10, .bind_data = TRUE) %>% ungroup() full %>% tail(10) ## # A tibble: 10 x 4 ## Level Name Date Admission ## <chr> <chr> <date> <dbl> ## 1 National_id National 2021-03-01 NA ## 2 National_id National 2021-04-01 NA ## 3 National_id National 2021-05-01 NA ## 4 National_id National 2021-06-01 NA ## 5 National_id National 2021-07-01 NA ## 6 National_id National 2021-08-01 NA ## 7 National_id National 2021-09-01 NA ## 8 National_id National 2021-10-01 NA ## 9 National_id National 2021-11-01 NA ## 10 National_id National 2021-12-01 NA
2.3 External regressor
2.3.1 Lags and rolling lags
Lags and rolling lags were external regressors included in the machine learning approach as these features have seen success in the M5 competition. While lags and rolling windows could have been added with step_lags and step_slidify during the recipe phase, these values couldn’t be calculated for future dates. Thus, it was calculated in this dataset which included future dates.
Lag periods were set to be the same as the forecast horizon and the rolling lags were based temporal periods heuristically associated with a year e.g. 3,6,12 months.
full<- full %>% group_by(Level, Name) %>%
tk_augment_lags(Admission, .lags = 10) %>%
tk_augment_slidify(
Admission_lag10,
.f = ~ mean(., na.rm = TRUE),
.period = c(3,6,12),
.align = "center",
.partial = TRUE) %>% ungroup()
Impute
Lags and rolling lags resulted in missing values for earlier observations.
full %>% head(10) ## # A tibble: 10 x 8 ## Level Name Date Admission Admission_lag10 Admission_lag10_roll_3 ## <chr> <chr> <date> <dbl> <dbl> <dbl> ## 1 Cluster_id NHG 2016-01-01 8035 NA NaN ## 2 Cluster_id NHG 2016-02-01 7526 NA NaN ## 3 Cluster_id NHG 2016-03-01 8419 NA NaN ## 4 Cluster_id NHG 2016-04-01 7934 NA NaN ## 5 Cluster_id NHG 2016-05-01 8048 NA NaN ## 6 Cluster_id NHG 2016-06-01 8199 NA NaN ## 7 Cluster_id NHG 2016-07-01 8230 NA NaN ## 8 Cluster_id NHG 2016-08-01 8496 NA NaN ## 9 Cluster_id NHG 2016-09-01 7991 NA NaN ## 10 Cluster_id NHG 2016-10-01 8284 NA 8035 ## # ... with 2 more variables: Admission_lag10_roll_6 <dbl>, ## # Admission_lag10_roll_12 <dbl>
These observations were either to be discarded or imputed. As discarding might result in less than ideal number of observations for training , these values were imputed. Missing lags and rolling lags could have been imputed with step_ts_clean or step_ts_impute. However, these step_s do not operate on group data i.e. imputation at a global level and not for specific hospitals and clusters. Therefore, the imputation occurred earlier up here.
(full<-full %>% group_by(Level, Name) %>%
mutate(across(.cols= starts_with("Admission_"),
.fns = ~ ts_impute_vec(.x, period = 12))) %>%
ungroup() %>% rowid_to_column(var = "row_id"))
## # A tibble: 864 x 9
## 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 854 more rows, and 2 more variables: Admission_lag10_roll_6 <dbl>,
## # Admission_lag10_roll_12 <dbl>
The imputed values were visually inspected.
full %>% filter(Level=="Hospital_id") %>% group_by(Name) %>% plot_time_series(Date, Admission_lag10, .interactive=F, .smooth = F, .facet_ncol = 3, .title = "10 Month Lag of Admission")
SKH had lags which were below 0 which is impossible as negative admission is absurd. There were also lags above 0 in 2016 which was not impossible as the hospital opened only in Jul 18.
full %>%
filter(Name=="SKH") %>%
plot_time_series(Date, Admission_lag10, .interactive=F, .smooth = F,
.t= "10 Month Lag of SKH Admission")
Thus, the imputations were revised:
- The minimum values for lags and rolling lags were set to 0
- All lags and rolling lags for SKH before Jul 18 were set to 0
full<-full %>%
mutate(across(.cols=(starts_with("Admission_lag")),
.fns = ~ ifelse(.x<0, 0, .x))) %>%
mutate(across(.cols = (starts_with("Admission_lag")),
.fns = ~ifelse(Date<lubridate::ymd("2018-07-01")& Name=="SKH",
0, .x)))
2.3.2 Covid
Covid peak periods occurred between Jan 21 to Jul 21 and this period form another categorical variable.
full<- full %>%
mutate(Covid= ifelse(
between(Date, lubridate::ymd("2020-01-01"),lubridate::ymd("2020-07-01")),
"yes", "no"))
2.3.3 Time series features
Time series features and statistics have been used in machine learning approaches for forecasting. Likewise, the time series features of this hierarchical time series were used as predictors for our machine learning approach.
feat_all_url<-url("https://github.com/notast/hierarchical-forecasting/blob/main/3feat_all.RData?raw=true")
load(feat_all_url)
close(feat_all_url)
full<- left_join(full, feat_all, by=c("Level", "Name"))
Appending the future forecast periods and adding the external regressors, increased the dataset from 744 rows to 864 rows and from 4 columns to 47 columns.
glimpse(full) ## Rows: 864 ## Columns: 47 ## $ row_id <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14~ ## $ Level <chr> "Cluster_id", "Cluster_id", "Cluster_id", "Cl~ ## $ Name <chr> "NHG", "NHG", "NHG", "NHG", "NHG", "NHG", "NH~ ## $ Date <date> 2016-01-01, 2016-02-01, 2016-03-01, 2016-04-~ ## $ Admission <dbl> 8035, 7526, 8419, 7934, 8048, 8199, 8230, 849~ ## $ Admission_lag10 <dbl> 8184.009, 7801.307, 8282.589, 7925.547, 8167.~ ## $ Admission_lag10_roll_3 <dbl> 7839.890, 8184.588, 8071.753, 8187.940, 8168.~ ## $ Admission_lag10_roll_6 <dbl> 8049.493, 8091.948, 8236.410, 8140.612, 8162.~ ## $ Admission_lag10_roll_12 <dbl> 8057.390, 8068.275, 8064.694, 8049.987, 8035.~ ## $ Covid <chr> "no", "no", "no", "no", "no", "no", "no", "no~ ## $ F_trend_strength <dbl> 0.6829768, 0.6829768, 0.6829768, 0.6829768, 0~ ## $ F_seasonal_strength_year <dbl> 0.4330629, 0.4330629, 0.4330629, 0.4330629, 0~ ## $ F_seasonal_peak_year <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ~ ## $ F_seasonal_trough_year <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ~ ## $ F_spikiness <dbl> 10383595, 10383595, 10383595, 10383595, 10383~ ## $ F_linearity <dbl> -1526.063, -1526.063, -1526.063, -1526.063, -~ ## $ F_curvature <dbl> -2821.471, -2821.471, -2821.471, -2821.471, -~ ## $ F_stl_e_acf1 <dbl> 0.6609598, 0.6609598, 0.6609598, 0.6609598, 0~ ## $ F_stl_e_acf10 <dbl> 1.239149, 1.239149, 1.239149, 1.239149, 1.239~ ## $ F_acf1 <dbl> 0.6453483, 0.6453483, 0.6453483, 0.6453483, 0~ ## $ F_acf10 <dbl> 1.279804, 1.279804, 1.279804, 1.279804, 1.279~ ## $ F_diff1_acf1 <dbl> -0.4949473, -0.4949473, -0.4949473, -0.494947~ ## $ F_diff1_acf10 <dbl> 0.6419415, 0.6419415, 0.6419415, 0.6419415, 0~ ## $ F_diff2_acf1 <dbl> -0.7519704, -0.7519704, -0.7519704, -0.751970~ ## $ F_diff2_acf10 <dbl> 1.209413, 1.209413, 1.209413, 1.209413, 1.209~ ## $ F_season_acf1 <dbl> 0.1026575, 0.1026575, 0.1026575, 0.1026575, 0~ ## $ F_kpss_stat <dbl> 0.410627, 0.410627, 0.410627, 0.410627, 0.410~ ## $ F_kpss_pvalue <dbl> 0.07257455, 0.07257455, 0.07257455, 0.0725745~ ## $ F_pp_stat <dbl> -3.333663, -3.333663, -3.333663, -3.333663, -~ ## $ F_pp_pvalue <dbl> 0.02307222, 0.02307222, 0.02307222, 0.0230722~ ## $ F_ndiffs <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ~ ## $ F_bp_stat <dbl> 25.82141, 25.82141, 25.82141, 25.82141, 25.82~ ## $ F_bp_pvalue <dbl> 3.745109e-07, 3.745109e-07, 3.745109e-07, 3.7~ ## $ F_lb_stat <dbl> 27.09132, 27.09132, 27.09132, 27.09132, 27.09~ ## $ F_lb_pvalue <dbl> 1.940678e-07, 1.940678e-07, 1.940678e-07, 1.9~ ## $ F_var_tiled_var <dbl> 0.2356997, 0.2356997, 0.2356997, 0.2356997, 0~ ## $ F_var_tiled_mean <dbl> 0.696821, 0.696821, 0.696821, 0.696821, 0.696~ ## $ F_shift_level_max <dbl> 1404, 1404, 1404, 1404, 1404, 1404, 1404, 140~ ## $ F_shift_level_index <dbl> 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 5~ ## $ F_shift_var_max <dbl> 1057581, 1057581, 1057581, 1057581, 1057581, ~ ## $ F_shift_var_index <dbl> 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 4~ ## $ F_shift_kl_max <dbl> 2.08871, 2.08871, 2.08871, 2.08871, 2.08871, ~ ## $ F_shift_kl_index <dbl> 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 4~ ## $ F_spectral_entropy <dbl> 0.7173186, 0.7173186, 0.7173186, 0.7173186, 0~ ## $ F_n_crossing_points <int> 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 1~ ## $ F_longest_flat_spot <int> 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ~ ## $ F_stat_arch_lm <dbl> 0.5968071, 0.5968071, 0.5968071, 0.5968071, 0~
3 Splitting
The full dataset was split into
- Training (
to_train) and future prediction (to_predictfuture) dataset - The training dataset (
to_train) was further split into the analysis/training and assessment/testing sets.
# Datasets to train and predict
to_train<- full %>% filter(!is.na(Admission))
to_predictfuture<- full %>% filter(is.na(Admission))
# Spiltting `to_train`
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.
4 Pre-processing recipes
When using modeltime for forecasting, the date column is treated differently for each approach.
- Classical: The date column is left untoched.
- Machine learning: Features are engineered from the date column e.g. using
as.numeric(date)or in this case withstep_timeseries_signature.
The date column is then
- either dropped. In the case of using
glmnet, the date format cannot be implicitly converted into numeric format for the needed matrix structure used inglmnet - or its role as a predictor is updated to something else.
4 combinations of predictors and pre-processing step_s were screened to determine the best combination of features for machine learning.
- Basic (
rec_basic)
- Lags (
Admission_lag10) - Rolling lags (
Admission_lag10_roll_???) - Covid peak period (
Covid) - Relevant features engineered from
step_timeseries_signature - Hierarchical levels (
Level) - Members in the corresponding level (
Name)
- Basic + Time series features and statistics (
rec_ft)
- Above
rec_basic - Time series features. (
F_???)
- Basic + PCA of the time series features and statistics (
rec_PC)
- Above
rec_basic - The first 5 principal components of the time series features. 5 components were shown to summarised 88% of the variance.
- Basic + kernel PCA of the time series and features and statistics (
rec_kPC)
- Above
rec_basic - The first 5 principal components of the time series features. Kernel PCA would be more suitable if there were a non-linear relationship between the time series features and the number of admissions.
Pre-processing order
Pre-processing tend to follow this order:
- Impute
- Handle Factor levels
- Individual transformations
- Discretize
- Lump minority observations
- Create dummy variables
- Create interactions
- Remove variables with near zero variance
- Normalize
- Create splines / Multivariate transformation (e.g. PCA, spatial)
fun_rec<- function(R){
LHS= "Admission ~"
RHS = paste(R, collapse = "+")
formula<- as.formula(paste0(LHS, RHS))
recipe(formula, data = training(splits)) %>%
update_role(c(row_id, Date), new_role = "id") %>%
step_timeseries_signature(Date) %>%
step_rm(matches("(.xts$)|(.iso$)|(hour)|(minute)|(second)|(am.pm)|(mweek)")) %>%
step_rm(starts_with("Date_wday")) %>% step_rm(starts_with("Date_mday")) %>% step_rm(Date_day) %>%
step_dummy(all_nominal(), one_hot = TRUE)}
col_lag<- to_train %>% select(starts_with("Admission_lag")) %>% colnames()
col_bare<- c("Level", "Name", "row_id", "Date", "Covid")
col_ft<- to_train %>% select(starts_with("F_")) %>% colnames()
rec_basic<-fun_rec(c(col_bare, col_lag))
rec_ft<-fun_rec(c(col_bare, col_lag, col_ft)) %>%
step_corr(!!col_ft) %>%
step_nzv(all_numeric_predictors())
rec_PC<- fun_rec(c(col_bare, col_lag, col_ft)) %>%
step_normalize(!!col_ft) %>%
step_pca(!!col_ft)
rec_kpca<- fun_rec(c(col_bare, col_lag, col_ft)) %>%
step_normalize(!!col_ft) %>%
step_kpca_rbf(!!col_ft)
5. Modelling
Random Forest was used as the model to screen the combinations of features as Random Forest tends to do relatively well without hyperparameter tuning. It has also been used in the M4 competition with success where time series features and statistics were predictors. (Random Forest was just part of the algorithm used in the paper).
mod<-rand_forest(trees= 1000) %>% # increase from 500->100
set_engine("ranger", verbose = TRUE) %>% # use ranger as faster, increased trees
set_mode("regression")
Workflow
The multiple combination of recipes was easily handed with workflowsets.
(wfsets <- workflowsets::workflow_set(
preproc = list(basic = rec_basic, ft= rec_ft, PC= rec_PC, kPC=rec_kpca),
models = list(rf=mod),
cross = F))
## # A workflow set/tibble: 4 x 4
## wflow_id info option result
## <chr> <list> <list> <list>
## 1 basic_rf <tibble [1 x 4]> <wrkflw__ > <list [0]>
## 2 ft_rf <tibble [1 x 4]> <wrkflw__ > <list [0]>
## 3 PC_rf <tibble [1 x 4]> <wrkflw__ > <list [0]>
## 4 kPC_rf <tibble [1 x 4]> <wrkflw__ > <list [0]>
6. Evaluate
6.1 Evaluate against the training set
modeltime_fit_workflowset only described the models used. It did not not carry forward the wflow_id.
(wfset_table<-modeltime_fit_workflowset(wfsets, training(splits))) ## 2021-06-12 14:05:33: Calculating kernel PCA ## 2021-06-12 14:05:33: Trying to calculate reverse ## 2021-06-12 14:05:33: DONE ## # Modeltime Table ## # A tibble: 4 x 3 ## .model_id .model .model_desc ## <int> <list> <chr> ## 1 1 <workflow> RANGER ## 2 2 <workflow> RANGER ## 3 3 <workflow> RANGER ## 4 4 <workflow> RANGER
Before the models with various features were evaluated, the .model_descriptions were updated to reflect the recipes of the various features and models used. The models from modeltime_fit_workflowset were arranged in the alphabetical order of the wflow_id which made updating of .model_descriptions easier.
(wfset_table<-wfset_table %>% update_model_description(1, "rec_basic") %>% update_model_description(2, "rec_ft") %>% update_model_description(3, "rec_kPC") %>% update_model_description(4, "rec_PC")) ## # Modeltime Table ## # A tibble: 4 x 3 ## .model_id .model .model_desc ## <int> <list> <chr> ## 1 1 <workflow> rec_basic ## 2 2 <workflow> rec_ft ## 3 3 <workflow> rec_kPC ## 4 4 <workflow> rec_PC
Alternatively, one could refer to the recipe inside .model to infer the relevant feature combination
wfset_table$.model[[1]] ## == Workflow [trained] ========================================================== ## Preprocessor: Recipe ## Model: rand_forest() ## ## -- Preprocessor ---------------------------------------------------------------- ## 6 Recipe Steps ## ## * step_timeseries_signature() ## * step_rm() ## * step_rm() ## * step_rm() ## * step_rm() ## * step_dummy() ## ## -- Model ----------------------------------------------------------------------- ## Ranger result ## ## Call: ## ranger::ranger(x = maybe_data_frame(x), y = y, num.trees = ~1000, verbose = ~TRUE, num.threads = 1, seed = sample.int(10^5, 1)) ## ## Type: Regression ## Number of trees: 1000 ## Sample size: 624 ## Number of independent variables: 44 ## Mtry: 6 ## Target node size: 5 ## Variable importance mode: none ## Splitrule: variance ## OOB prediction error (MSE): 286072.1 ## R squared (OOB): 0.9949897
Renaming could have been skipped with this very new package as it specifically deals with workflowset for modeltime.
The models were calibrated on the training set.
(wfset_calibrate<-wfset_table %>% modeltime_calibrate(training(splits))) ## # Modeltime Table ## # A tibble: 4 x 5 ## .model_id .model .model_desc .type .calibration_data ## <int> <list> <chr> <chr> <list> ## 1 1 <workflow> rec_basic Test <tibble [624 x 4]> ## 2 2 <workflow> rec_ft Test <tibble [624 x 4]> ## 3 3 <workflow> rec_kPC Test <tibble [624 x 4]> ## 4 4 <workflow> rec_PC Test <tibble [624 x 4]>
What’s inside the calibrated table
The .calibration_data from modeltime_calibrate contains the .acutal number of admissions, the .prediction and the .residuals.
# just one example
wfset_calibrate$.calibration_data[[1]]
## # A tibble: 624 x 4
## Date .actual .prediction .residuals
## <date> <dbl> <dbl> <dbl>
## 1 2016-01-01 8035 8145. -110.
## 2 2016-01-01 7861 8152. -291.
## 3 2016-01-01 10659 10554. 105.
## 4 2016-01-01 75 245. -170.
## 5 2016-01-01 3977 3967. 10.5
## 6 2016-01-01 3214 3366. -152.
## 7 2016-01-01 2944 3142. -198.
## 8 2016-01-01 4842 4863. -21.4
## 9 2016-01-01 6682 6606. 75.9
## 10 2016-01-01 0 202. -202.
## # ... with 614 more rows
modeltime_accuracy(object=wfset_calibrate,
metric_set = metric_set(rmse,mae)) %>%
arrange(rmse, sort=T)
## # A tibble: 4 x 5
## .model_id .model_desc .type rmse mae
## <int> <chr> <chr> <dbl> <dbl>
## 1 4 rec_PC Test 264. 151.
## 2 3 rec_kPC Test 266. 151.
## 3 1 rec_basic Test 277. 161.
## 4 2 rec_ft Test 314. 182.
6.1 Evaluate with cross validation
To increase the robustness of the accuracy, cross validation was executed. The cross validation scores were different than without cross validation.
set.seed(69)
folds <- vfold_cv(training(splits), strata = Admission)
set.seed(69)
(wfsets_done<- wfsets %>%
workflow_map("fit_resamples", resamples = folds))
## 2021-06-12 14:06:06: Calculating kernel PCA
## 2021-06-12 14:06:07: Trying to calculate reverse
## 2021-06-12 14:06:07: DONE
## 2021-06-12 14:06:08: Calculating kernel PCA
## 2021-06-12 14:06:08: Trying to calculate reverse
## 2021-06-12 14:06:08: DONE
## 2021-06-12 14:06:10: Calculating kernel PCA
## 2021-06-12 14:06:10: Trying to calculate reverse
## 2021-06-12 14:06:10: DONE
## 2021-06-12 14:06:11: Calculating kernel PCA
## 2021-06-12 14:06:11: Trying to calculate reverse
## 2021-06-12 14:06:11: DONE
## 2021-06-12 14:06:12: Calculating kernel PCA
## 2021-06-12 14:06:13: Trying to calculate reverse
## 2021-06-12 14:06:13: DONE
## 2021-06-12 14:06:14: Calculating kernel PCA
## 2021-06-12 14:06:14: Trying to calculate reverse
## 2021-06-12 14:06:14: DONE
## 2021-06-12 14:06:15: Calculating kernel PCA
## 2021-06-12 14:06:16: Trying to calculate reverse
## 2021-06-12 14:06:16: DONE
## 2021-06-12 14:06:17: Calculating kernel PCA
## 2021-06-12 14:06:17: Trying to calculate reverse
## 2021-06-12 14:06:17: DONE
## 2021-06-12 14:06:18: Calculating kernel PCA
## 2021-06-12 14:06:18: Trying to calculate reverse
## 2021-06-12 14:06:19: DONE
## 2021-06-12 14:06:20: Calculating kernel PCA
## 2021-06-12 14:06:20: Trying to calculate reverse
## 2021-06-12 14:06:20: DONE
## # A workflow set/tibble: 4 x 4
## wflow_id info option result
## <chr> <list> <list> <list>
## 1 basic_rf <tibble [1 x 4]> <wrkflw__ > <rsmp[+]>
## 2 ft_rf <tibble [1 x 4]> <wrkflw__ > <rsmp[+]>
## 3 PC_rf <tibble [1 x 4]> <wrkflw__ > <rsmp[+]>
## 4 kPC_rf <tibble [1 x 4]> <wrkflw__ > <rsmp[+]>
collect_metrics(wfsets_done, summarize = T ) %>% # summarised all folds
filter(.metric=="rmse") %>%
select(wflow_id, avg_rmse=mean) %>% arrange(avg_rmse,sort=T)
## # A tibble: 4 x 2
## wflow_id avg_rmse
## <chr> <dbl>
## 1 PC_rf 514.
## 2 kPC_rf 516.
## 3 basic_rf 526.
## 4 ft_rf 543.
8 Conclusion
The cross validation scores were different than without cross validation.The bottom 2 performing feature combinations were consistent (rec_basic & rec_ft). However, when the time series features were condensed into principal components the accuracy improved. The relationship between the time series features and the number of admissions was linear-ish as the performance between kernel PCA and PCA were close for evaluations with and without cross validation. For the marginal difference in rmse and shorter computational time, PCA was selected. The feature combination for machine learning forecasting in the next few posts would be
- Lags
- Rolling lags
- Covid peak period
- Relevant features engineered from
step_timeseries_signature - The first 5 principal components (PCA) of the time series features
- Hierarchical levels and their members
# save the dataset for machine learning and the dataset for future prediction; save the recipe save(to_train, to_predictfuture, rec_PC, file= "4Dataset4ML.rds")
R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.