Note
Click here to download the full example code
Interpretability¶
Silverkite generates easily interpretable forecasting models when using its default ML algorithms (e.g. Ridge). This is because after transforming the raw features to basis functions (transformed features), the model uses an additive structure. Silverkite can break down each forecast into various summable components e.g. long-term growth, seasonality, holidays, events, short-term growth (auto-regression), regressors impact etc.
The approach to generate these breakdowns consists of two steps:
Group the transformed variables into various meaningful groups.
Calculate the sum of the features multiplied by their regression coefficients within each group.
These breakdowns then can be used to answer questions such as:
Question 1: How is the forecast value is generated?
Question 2: What is driving the change of the forecast as new data comes in?
Forecast components can also help us analyze model behavior and sensitivity. This is because while it is not feasible to compare a large set of features across two model settings, it can be quite practical and informative to compare a few well-defined components.
26 27 28 29 30 31 32 33 34 35 36 37 38 39 | # required imports
import plotly
import warnings
import pandas as pd
from greykite.framework.benchmark.data_loader_ts import DataLoaderTS
from greykite.framework.templates.autogen.forecast_config import EvaluationPeriodParam
from greykite.framework.templates.autogen.forecast_config import ForecastConfig
from greykite.framework.templates.autogen.forecast_config import MetadataParam
from greykite.framework.templates.autogen.forecast_config import ModelComponentsParam
from greykite.framework.templates.forecaster import Forecaster
from greykite.framework.templates.model_templates import ModelTemplateEnum
from greykite.framework.utils.result_summary import summarize_grid_search_results
from greykite.common.viz.timeseries_plotting import plot_multivariate
warnings.filterwarnings("ignore")
|
Function to load and prepare data¶
This is the code to upload and prepare the daily bike-sharing data in Washington DC.
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 | def prepare_bikesharing_data():
"""Loads bike-sharing data and adds proper regressors."""
dl = DataLoaderTS()
agg_func = {"count": "sum", "tmin": "mean", "tmax": "mean", "pn": "mean"}
df = dl.load_bikesharing(agg_freq="daily", agg_func=agg_func)
# There are some zero values which cause issue for MAPE
# This adds a small number to all data to avoid that issue
value_col = "count"
df[value_col] += 10
# We drop last value as data might be incorrect as original data is hourly
df.drop(df.tail(1).index, inplace=True)
# We only use data from 2018 for demonstration purposes (run time is shorter)
df = df.loc[df["ts"] > "2018-01-01"]
df.reset_index(drop=True, inplace=True)
print(f"\n df.tail(): \n {df.tail()}")
# Creates useful regressors from existing raw regressors
df["bin_pn"] = (df["pn"] > 5).map(float)
df["bin_heavy_pn"] = (df["pn"] > 20).map(float)
df.columns = [
"ts",
value_col,
"regressor_tmin",
"regressor_tmax",
"regressor_pn",
"regressor_bin_pn",
"regressor_bin_heavy_pn"]
forecast_horizon = 7
train_df = df.copy()
test_df = df.tail(forecast_horizon).reset_index(drop=True)
# When using the pipeline (as done in the ``fit_forecast`` below),
# fitting and prediction are done in one step
# Therefore for demonstration purpose we remove the response values of last 7 days.
# This is needed because we are using regressors,
# and future regressor data must be augmented to ``df``.
# We mimic that by removal of the values of the response.
train_df.at[(len(train_df) - forecast_horizon):len(train_df), value_col] = None
print(f"train_df shape: \n {train_df.shape}")
print(f"test_df shape: \n {test_df.shape}")
print(f"train_df.tail(14): \n {train_df.tail(14)}")
print(f"test_df: \n {test_df}")
return {
"train_df": train_df,
"test_df": test_df}
|
Function to fit silverkite¶
This is the code for fitting a silverkite model to the data.
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 | def fit_forecast(
df,
time_col,
value_col):
"""Fits a daily model for this use case.
The daily model is a generic silverkite model with regressors."""
meta_data_params = MetadataParam(
time_col=time_col,
value_col=value_col,
freq="D",
)
# Autoregression to be used in the function
autoregression = {
"autoreg_dict": {
"lag_dict": {"orders": [1, 2, 3]},
"agg_lag_dict": {
"orders_list": [[7, 7*2, 7*3]],
"interval_list": [(1, 7), (8, 7*2)]},
"series_na_fill_func": lambda s: s.bfill().ffill()},
"fast_simulation": True
}
# Changepoints configuration
# The config includes changepoints both in trend and seasonality
changepoints = {
"changepoints_dict": {
"method": "auto",
"yearly_seasonality_order": 15,
"resample_freq": "2D",
"actual_changepoint_min_distance": "100D",
"potential_changepoint_distance": "50D",
"no_changepoint_distance_from_end": "50D"},
"seasonality_changepoints_dict": {
"method": "auto",
"yearly_seasonality_order": 15,
"resample_freq": "2D",
"actual_changepoint_min_distance": "100D",
"potential_changepoint_distance": "50D",
"no_changepoint_distance_from_end": "50D"}
}
regressor_cols = [
"regressor_tmin",
"regressor_bin_pn",
"regressor_bin_heavy_pn",
]
# Model parameters
model_components = ModelComponentsParam(
growth=dict(growth_term="linear"),
seasonality=dict(
yearly_seasonality=[15],
quarterly_seasonality=[False],
monthly_seasonality=[False],
weekly_seasonality=[7],
daily_seasonality=[False]
),
custom=dict(
fit_algorithm_dict=dict(fit_algorithm="ridge"),
extra_pred_cols=None,
normalize_method="statistical"
),
regressors=dict(regressor_cols=regressor_cols),
autoregression=autoregression,
uncertainty=dict(uncertainty_dict=None),
events=dict(holiday_lookup_countries=["US"]),
changepoints=changepoints
)
# Evaluation is done on same ``forecast_horizon`` as desired for output
evaluation_period_param = EvaluationPeriodParam(
test_horizon=None,
cv_horizon=forecast_horizon,
cv_min_train_periods=365*2,
cv_expanding_window=True,
cv_use_most_recent_splits=False,
cv_periods_between_splits=None,
cv_periods_between_train_test=0,
cv_max_splits=5,
)
# Runs the forecast model using "SILVERKITE" template
forecaster = Forecaster()
result = forecaster.run_forecast_config(
df=df,
config=ForecastConfig(
model_template=ModelTemplateEnum.SILVERKITE.name,
coverage=0.95,
forecast_horizon=forecast_horizon,
metadata_param=meta_data_params,
evaluation_period_param=evaluation_period_param,
model_components_param=model_components
)
)
# Gets cross-validation results
grid_search = result.grid_search
cv_results = summarize_grid_search_results(
grid_search=grid_search,
decimals=2,
cv_report_metrics=None)
cv_results = cv_results.transpose()
cv_results = pd.DataFrame(cv_results)
cv_results.columns = ["err_value"]
cv_results["err_name"] = cv_results.index
cv_results = cv_results.reset_index(drop=True)
cv_results = cv_results[["err_name", "err_value"]]
print(f"\n cv_results: \n {cv_results}")
return result
|
Loads and prepares data¶
The data is loaded and some information about the input data is printed. We use the number of daily rented bikes in Washington DC over time. The data is augmented with weather data (precipitation, min/max daily temperature).
221 | data = prepare_bikesharing_data()
|
Out:
df.tail():
ts count tmin tmax pn
602 2019-08-27 12216 17.2 26.7 0.0
603 2019-08-28 11401 18.3 27.8 0.0
604 2019-08-29 12685 16.7 28.9 0.0
605 2019-08-30 12097 14.4 32.8 0.0
606 2019-08-31 11281 17.8 31.1 0.0
train_df shape:
(607, 7)
test_df shape:
(7, 7)
train_df.tail(14):
ts count regressor_tmin regressor_tmax regressor_pn regressor_bin_pn regressor_bin_heavy_pn
593 2019-08-18 9655.0 22.2 35.6 0.3 0.0 0.0
594 2019-08-19 10579.0 21.1 37.2 0.0 0.0 0.0
595 2019-08-20 8898.0 22.2 36.1 0.0 0.0 0.0
596 2019-08-21 11648.0 21.7 35.0 1.8 0.0 0.0
597 2019-08-22 11724.0 21.7 35.0 30.7 1.0 1.0
598 2019-08-23 8158.0 17.8 23.3 1.8 0.0 0.0
599 2019-08-24 12475.0 16.7 26.1 0.0 0.0 0.0
600 2019-08-25 NaN 15.6 26.7 0.0 0.0 0.0
601 2019-08-26 NaN 17.2 25.0 0.0 0.0 0.0
602 2019-08-27 NaN 17.2 26.7 0.0 0.0 0.0
603 2019-08-28 NaN 18.3 27.8 0.0 0.0 0.0
604 2019-08-29 NaN 16.7 28.9 0.0 0.0 0.0
605 2019-08-30 NaN 14.4 32.8 0.0 0.0 0.0
606 2019-08-31 NaN 17.8 31.1 0.0 0.0 0.0
test_df:
ts count regressor_tmin regressor_tmax regressor_pn regressor_bin_pn regressor_bin_heavy_pn
0 2019-08-25 11634 15.6 26.7 0.0 0.0 0.0
1 2019-08-26 11747 17.2 25.0 0.0 0.0 0.0
2 2019-08-27 12216 17.2 26.7 0.0 0.0 0.0
3 2019-08-28 11401 18.3 27.8 0.0 0.0 0.0
4 2019-08-29 12685 16.7 28.9 0.0 0.0 0.0
5 2019-08-30 12097 14.4 32.8 0.0 0.0 0.0
6 2019-08-31 11281 17.8 31.1 0.0 0.0 0.0
Fits model to daily data¶
In this step we fit a silverkite model to the data which uses weather regressors, holidays, auto-regression etc.
228 229 230 231 232 233 234 235 236 237 238 239 240 |
Out:
Fitting 1 folds for each of 1 candidates, totalling 1 fits
cv_results:
err_name err_value
0 rank_test_MAPE 1
1 mean_test_MAPE 10.28
2 split_test_MAPE (10.28,)
3 mean_train_MAPE 21.66
4 params []
5 param_estimator__yearly_seasonality 15
6 param_estimator__weekly_seasonality 7
7 param_estimator__uncertainty_dict None
8 param_estimator__training_fraction None
9 param_estimator__train_test_thresh None
10 param_estimator__time_properties {'period': 86400, 'simple_freq': SimpleTimeFre...
11 param_estimator__simulation_num 10
12 param_estimator__seasonality_changepoints_dict {'method': 'auto', 'yearly_seasonality_order':...
13 param_estimator__regressor_cols [regressor_tmin, regressor_bin_pn, regressor_b...
14 param_estimator__regression_weight_col None
15 param_estimator__quarterly_seasonality False
16 param_estimator__origin_for_time_vars None
17 param_estimator__normalize_method statistical
18 param_estimator__monthly_seasonality False
19 param_estimator__min_admissible_value None
20 param_estimator__max_weekly_seas_interaction_o... 2
21 param_estimator__max_daily_seas_interaction_order 5
22 param_estimator__max_admissible_value None
23 param_estimator__lagged_regressor_dict None
24 param_estimator__holidays_to_model_separately auto
25 param_estimator__holiday_pre_post_num_dict None
26 param_estimator__holiday_pre_num_days 2
27 param_estimator__holiday_post_num_days 2
28 param_estimator__holiday_lookup_countries [US]
29 param_estimator__growth_term linear
30 param_estimator__fit_algorithm_dict {'fit_algorithm': 'ridge'}
31 param_estimator__feature_sets_enabled auto
32 param_estimator__fast_simulation True
33 param_estimator__extra_pred_cols None
34 param_estimator__explicit_pred_cols None
35 param_estimator__drop_pred_cols None
36 param_estimator__daily_seasonality False
37 param_estimator__daily_event_df_dict None
38 param_estimator__changepoints_dict {'method': 'auto', 'yearly_seasonality_order':...
39 param_estimator__autoreg_dict {'lag_dict': {'orders': [1, 2, 3]}, 'agg_lag_d...
40 param_estimator__auto_seasonality False
41 param_estimator__auto_holiday False
42 param_estimator__auto_growth False
43 split_train_MAPE (21.66,)
44 mean_fit_time 4.79
45 std_fit_time 0
46 mean_score_time 10.1
47 std_score_time 0
48 split0_test_MAPE 10.28
49 std_test_MAPE 0
50 split0_train_MAPE 21.66
51 std_train_MAPE 0
Model Summary:
================================ Model Summary =================================
Number of observations: 600, Number of features: 134
Method: Ridge regression
Number of nonzero features: 133
Regularization parameter: 174.3
Residuals:
Min 1Q Median 3Q Max
-7534.0 -895.1 89.89 997.0 7621.0
Pred_col Estimate Std. Err Pr(>)_boot sig. code 95%CI
Intercept 9633.0 73.94 <2e-16 *** (9504.0, 9787.0)
events_Christmas Day -145.0 77.24 <2e-16 *** (-185.9, 7.917e-28)
events_C...as Day-1 -135.8 71.9 <2e-16 *** (-174.6, 8.152e-28)
events_C...as Day-2 -51.78 29.98 0.004 ** (-81.94, 8.064e-28)
events_C...as Day+1 -72.6 40.1 <2e-16 *** (-104.4, 8.861e-28)
events_C...as Day+2 -23.42 17.43 0.120 (-51.7, 8.766e-28)
events_I...ence Day 45.72 22.53 0.018 * (-9.712e-28, 79.14)
events_I...ce Day-1 -27.68 20.22 0.142 (-64.06, 9.238)
events_I...ce Day-2 -14.51 28.19 0.572 (-64.88, 38.62)
events_I...ce Day+1 -15.82 15.06 0.236 (-45.41, 13.12)
events_I...ce Day+2 -65.05 47.52 0.132 (-139.9, 12.1)
events_Labor Day -61.41 32.19 0.006 ** (-88.66, 6.223e-28)
events_Labor Day-1 92.37 47.65 <2e-16 *** (-6.695e-28, 122.2)
events_Labor Day-2 -59.2 32.58 0.010 * (-92.38, 5.980e-28)
events_Labor Day+1 -51.36 29.33 0.024 * (-83.99, 5.986e-28)
events_Labor Day+2 -3.448 11.31 0.486 (-30.33, 19.85)
events_Memorial Day -42.14 21.76 0.026 * (-74.79, 1.215e-27)
events_M...al Day-1 125.1 72.99 0.024 * (-1.820e-27, 223.7)
events_M...al Day-2 -29.22 21.61 0.144 (-66.9, 13.46)
events_M...al Day+1 -57.53 51.18 0.302 (-130.4, 33.14)
events_M...al Day+2 -35.5 19.77 0.044 * (-65.59, 1.754e-27)
events_New Years Day -46.89 26.3 0.012 * (-78.04, 8.683e-28)
events_N...rs Day-1 -42.7 25.41 0.026 * (-73.79, 8.004e-28)
events_N...rs Day-2 7.73 11.58 0.358 (-17.03, 30.31)
events_N...rs Day+1 -23.69 32.25 0.476 (-82.48, 32.99)
events_N...rs Day+2 33.59 33.2 0.324 (-29.95, 91.51)
events_Other -129.2 49.37 0.008 ** (-210.3, -16.32)
events_Other-1 29.81 51.27 0.574 (-75.87, 118.6)
events_Other-2 -107.1 44.54 0.022 * (-180.5, -8.931)
events_Other+1 32.0 46.15 0.482 (-51.08, 116.1)
events_Other+2 -45.72 67.19 0.494 (-162.4, 88.56)
events_Thanksgiving -184.4 95.57 <2e-16 *** (-225.9, 6.168e-28)
events_T...giving-1 -46.46 26.53 0.016 * (-73.42, 6.497e-28)
events_T...giving-2 1.876 8.613 0.506 (-20.18, 17.97)
events_T...giving+1 -128.7 65.43 <2e-16 *** (-172.3, 6.463e-28)
events_T...giving+2 -53.12 31.73 0.036 * (-90.99, 1.163e-27)
events_Veterans Day -28.32 19.92 0.102 (-61.6, 0.9676)
events_V...ns Day-1 -36.49 24.0 0.072 . (-74.64, 6.280e-28)
events_V...ns Day-2 -77.61 41.2 <2e-16 *** (-104.4, 6.548e-28)
events_V...ns Day+1 32.43 19.94 0.080 . (-4.655, 58.78)
events_V...ns Day+2 4.144 15.34 0.542 (-32.25, 34.99)
str_dow_2-Tue 20.87 29.08 0.470 (-36.43, 79.57)
str_dow_3-Wed 19.99 23.17 0.406 (-25.45, 61.91)
str_dow_4-Thu 28.17 26.45 0.300 (-26.37, 79.17)
str_dow_5-Fri 40.95 32.01 0.210 (-20.11, 102.0)
str_dow_6-Sat -8.635 38.43 0.840 (-77.99, 67.03)
str_dow_7-Sun -105.5 28.85 0.002 ** (-163.1, -54.52)
regressor_tmin 598.5 62.21 <2e-16 *** (456.7, 701.9)
regressor_bin_pn -835.9 61.1 <2e-16 *** (-941.6, -699.5)
regresso...heavy_pn -364.5 80.62 <2e-16 *** (-530.8, -217.2)
ct1 -8.196 30.9 0.810 (-67.44, 49.18)
is_weekend:ct1 -13.61 24.44 0.586 (-60.22, 32.66)
str_dow_2-Tue:ct1 21.7 23.97 0.368 (-27.01, 67.37)
str_dow_3-Wed:ct1 14.95 20.4 0.474 (-26.38, 51.67)
str_dow_4-Thu:ct1 4.774 22.7 0.830 (-36.84, 53.22)
str_dow_5-Fri:ct1 8.282 26.9 0.738 (-47.55, 57.74)
str_dow_6-Sat:ct1 17.64 32.06 0.614 (-42.43, 78.95)
str_dow_7-Sun:ct1 -36.09 28.37 0.200 (-89.29, 22.5)
cp0_2018_07_21_00 -155.5 25.68 <2e-16 *** (-194.9, -97.24)
is_weeke...07_21_00 -26.61 28.84 0.338 (-76.35, 32.09)
str_dow_...07_21_00 -38.97 35.66 0.270 (-110.4, 31.26)
str_dow_...07_21_00 -33.33 22.34 0.148 (-72.5, 10.25)
str_dow_...07_21_00 -14.47 30.92 0.658 (-77.68, 45.39)
str_dow_...07_21_00 -88.07 42.61 0.042 * (-170.8, -7.553)
str_dow_...07_21_00 15.77 44.21 0.724 (-73.23, 102.0)
str_dow_...07_21_00 -52.68 43.61 0.238 (-129.4, 41.76)
ct1:sin1_tow_weekly 20.52 22.18 0.364 (-21.43, 62.33)
ct1:cos1_tow_weekly -35.92 23.38 0.134 (-82.59, 6.589)
ct1:sin2_tow_weekly 30.35 21.04 0.128 (-11.45, 70.39)
ct1:cos2_tow_weekly -30.92 24.69 0.222 (-77.93, 18.5)
cp0_2018...w_weekly -2.809 26.49 0.878 (-55.41, 45.86)
cp0_2018...w_weekly -25.97 32.89 0.432 (-92.45, 40.25)
cp0_2018...w_weekly -12.22 33.21 0.690 (-82.95, 46.34)
cp0_2018...w_weekly -61.22 31.85 0.042 * (-121.2, -4.486)
sin1_tow_weekly 59.81 27.95 0.038 * (1.393, 115.4)
cos1_tow_weekly -56.32 30.1 0.050 . (-113.0, -4.038)
sin2_tow_weekly 59.61 30.24 0.046 * (3.018, 120.4)
cos2_tow_weekly 27.39 32.29 0.378 (-31.46, 90.84)
sin3_tow_weekly 9.787 30.41 0.746 (-46.12, 71.02)
cos3_tow_weekly 35.32 28.01 0.226 (-14.59, 93.59)
sin4_tow_weekly -9.787 30.41 0.746 (-71.02, 46.12)
cos4_tow_weekly 35.32 28.01 0.226 (-14.59, 93.59)
sin5_tow_weekly -59.61 30.24 0.046 * (-120.4, -3.018)
cos5_tow_weekly 27.39 32.29 0.378 (-31.46, 90.84)
sin6_tow_weekly -59.81 27.95 0.038 * (-115.4, -1.393)
cos6_tow_weekly -56.32 30.1 0.050 . (-113.0, -4.038)
sin7_tow_weekly 63.92 26.24 0.012 * (10.52, 112.1)
cos7_tow_weekly 0. 0. 1.000 (0., 0.)
sin1_ct1_yearly 14.61 46.95 0.748 (-84.11, 94.62)
cos1_ct1_yearly -523.4 38.97 <2e-16 *** (-586.6, -439.0)
sin2_ct1_yearly -203.5 45.51 <2e-16 *** (-294.1, -108.1)
cos2_ct1_yearly -83.95 56.28 0.162 (-180.6, 34.07)
sin3_ct1_yearly -69.93 54.06 0.182 (-170.1, 41.85)
cos3_ct1_yearly -40.88 49.84 0.418 (-133.4, 63.62)
sin4_ct1_yearly 34.08 50.49 0.492 (-72.56, 129.7)
cos4_ct1_yearly 36.63 55.76 0.550 (-52.64, 152.3)
sin5_ct1_yearly -57.09 53.62 0.292 (-155.4, 50.06)
cos5_ct1_yearly -59.11 57.11 0.316 (-171.0, 54.01)
sin6_ct1_yearly -17.35 52.76 0.744 (-118.0, 77.28)
cos6_ct1_yearly -198.7 58.58 <2e-16 *** (-295.9, -66.54)
sin7_ct1_yearly -23.14 54.46 0.672 (-132.0, 80.12)
cos7_ct1_yearly 60.45 61.08 0.326 (-51.5, 183.9)
sin8_ct1_yearly 16.92 63.72 0.806 (-101.6, 130.8)
cos8_ct1_yearly 29.37 57.44 0.620 (-77.54, 143.5)
sin9_ct1_yearly -21.39 60.04 0.718 (-141.6, 88.29)
cos9_ct1_yearly -32.55 54.76 0.544 (-129.3, 83.25)
sin10_ct1_yearly 95.53 59.54 0.098 . (-24.03, 209.3)
cos10_ct1_yearly -24.85 55.15 0.662 (-126.2, 79.35)
sin11_ct1_yearly -14.08 56.79 0.844 (-129.9, 92.91)
cos11_ct1_yearly -9.692 60.93 0.904 (-129.0, 101.1)
sin12_ct1_yearly -42.91 54.95 0.420 (-158.5, 56.08)
cos12_ct1_yearly 119.3 59.78 0.038 * (7.019, 231.5)
sin13_ct1_yearly -78.89 56.16 0.150 (-188.1, 32.5)
cos13_ct1_yearly -50.95 59.49 0.386 (-167.6, 62.37)
sin14_ct1_yearly -54.58 54.88 0.302 (-171.6, 50.61)
cos14_ct1_yearly -22.74 59.79 0.700 (-143.8, 90.64)
sin15_ct1_yearly -165.8 57.89 <2e-16 *** (-276.7, -48.78)
cos15_ct1_yearly -36.63 60.13 0.568 (-150.3, 82.42)
sin1_con...07_21_00 38.06 46.58 0.378 (-64.74, 122.8)
cos1_con...07_21_00 -136.9 53.88 0.010 * (-252.7, -35.97)
sin2_con...07_21_00 32.56 45.06 0.472 (-59.63, 113.8)
cos2_con...07_21_00 -172.8 61.73 0.004 ** (-288.6, -43.99)
sin3_con...07_21_00 -27.26 56.41 0.628 (-143.6, 76.76)
cos3_con...07_21_00 -3.896 48.86 0.936 (-91.08, 97.2)
sin4_con...07_21_00 -18.09 43.46 0.702 (-108.8, 62.85)
cos4_con...07_21_00 43.25 53.98 0.422 (-67.3, 151.9)
sin5_con...07_21_00 45.09 59.12 0.434 (-66.86, 166.5)
cos5_con...07_21_00 67.98 48.38 0.156 (-24.62, 156.7)
y_lag1 606.3 81.57 <2e-16 *** (419.2, 733.3)
y_lag2 89.37 66.61 0.146 (-32.68, 229.8)
y_lag3 158.1 70.68 0.030 * (26.69, 305.2)
y_avglag_7_14_21 331.3 57.69 <2e-16 *** (209.5, 424.2)
y_avglag_1_to_7 235.6 43.37 <2e-16 *** (173.6, 331.3)
y_avglag_8_to_14 334.5 57.35 <2e-16 *** (218.0, 445.0)
Signif. Code: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Multiple R-squared: 0.7796, Adjusted R-squared: 0.7502
F-statistic: 22.675 on 70 and 528 DF, p-value: 1.110e-16
Model AIC: 12944.0, model BIC: 13259.0
WARNING: the F-ratio and its p-value on regularized methods might be misleading, they are provided only for reference purposes.
WARNING: the following columns have estimated coefficients equal to zero, while ridge is not supposed to have zero estimates. This is probably because these columns are degenerate in the design matrix. Make sure these columns do not have constant values.
['cos7_tow_weekly']
WARNING: the following columns are degenerate, do you really want to include them in your model? This may cause some of them to show unrealistic significance. Consider using the `drop_degenerate` transformer.
['Intercept', 'cos7_tow_weekly']
Grouping of variables¶
Regex expressions are used to group variables in the breakdown plot. Each group is given in one key of this dictionary. The grouping is done using variable names and for each group multiple regex are given. For each group, variables that satisfy EITHER regex are chosen. Note that this grouping assumes that regressor variables start with “regressor_”. Also note that the order of this grouping matters (Python treats the dictionary as ordered in 3.6+). That means the variables chosen using regex in top groups will not be picked up again. If some variables do not satisfy any of the groupings, they will be grouped into “OTHER”. The following breakdown dictionary should work for many use cases. However, the users can customize it as needed.
257 258 259 260 261 262 263 | grouping_regex_patterns_dict = {
"regressors": "regressor_.*", # regressor effects
"AR": ".*lag", # autoregression component
"events": ".*events_.*", # events and holidays
"seasonality": ".*quarter.*|.*month.*|.*C\(dow.*|.*C\(dow_hr.*|sin.*|cos.*|.*doq.*|.*dom.*|.*str_dow.*|.*is_weekend.*|.*tow_weekly.*", # seasonality
"trend": "ct1|ct2|ct_sqrt|ct3|ct_root3|.*changepoint.*", # long term trend (includes changepoints)
}
|
Creates forecast breakdown¶
This is generated for observed data plus the prediction data (available in df).
Each component is centered around zero and the sum of all components is equal to forecast.
271 272 273 274 275 276 277 | breakdown_result = trained_estimator.forecast_breakdown(
grouping_regex_patterns_dict=grouping_regex_patterns_dict,
center_components=True,
plt_title="forecast breakdowns")
forecast_breakdown_df = breakdown_result["breakdown_df_with_index_col"]
forecast_components_fig = breakdown_result["breakdown_fig"]
plotly.io.show(forecast_components_fig)
|
Standardization of the components¶
Next we provide a more “standardized” view of the breakdown. This is achieved by dividing all components by observed absolute value of the metric. By doing so, intercept should be mapped to 1 and the y-axis changes can be viewed relative to the average magnitude of the series. The sum of all components at each time point will be equal to “forecast / obs_abs_mean”.
288 289 290 291 292 293 294 295 296 297 298 299 300 301 | column_grouping_result = breakdown_result["column_grouping_result"]
component_cols = list(grouping_regex_patterns_dict.keys())
forecast_breakdown_stdzd_df = forecast_breakdown_df.copy()
obs_abs_mean = abs(df[value_col]).mean()
for col in component_cols + ["Intercept", "OTHER"]:
if col in forecast_breakdown_stdzd_df.columns:
forecast_breakdown_stdzd_df[col] /= obs_abs_mean
forecast_breakdown_stdzd_fig = plot_multivariate(
df=forecast_breakdown_stdzd_df,
x_col=time_col,
title="forecast breakdowns divided by mean of abs value of response",
ylabel="component")
forecast_breakdown_stdzd_fig.update_layout(yaxis_range=[-1.1, 1.1])
plotly.io.show(forecast_breakdown_stdzd_fig)
|
Breaking down the predictions¶
Next we perform a prediction and generate a breakdown plot for that prediction.
307 308 309 310 311 312 313 314 315 316 317 318 319 | test_df = data["test_df"].reset_index()
test_df[value_col] = None
print(f"\n test_df: \n {test_df}")
pred_df = trained_estimator.predict(test_df)
forecast_x_mat = trained_estimator.forecast_x_mat
# Generate the breakdown plot
breakdown_result = trained_estimator.forecast_breakdown(
grouping_regex_patterns_dict=grouping_regex_patterns_dict,
forecast_x_mat=forecast_x_mat,
time_values=pred_df[time_col])
breakdown_fig = breakdown_result["breakdown_fig"]
plotly.io.show(breakdown_fig)
|
Out:
test_df:
index ts count regressor_tmin regressor_tmax regressor_pn regressor_bin_pn regressor_bin_heavy_pn
0 0 2019-08-25 None 15.6 26.7 0.0 0.0 0.0
1 1 2019-08-26 None 17.2 25.0 0.0 0.0 0.0
2 2 2019-08-27 None 17.2 26.7 0.0 0.0 0.0
3 3 2019-08-28 None 18.3 27.8 0.0 0.0 0.0
4 4 2019-08-29 None 16.7 28.9 0.0 0.0 0.0
5 5 2019-08-30 None 14.4 32.8 0.0 0.0 0.0
6 6 2019-08-31 None 17.8 31.1 0.0 0.0 0.0
Demonstrating a scenario-based breakdown¶
We artificially inject a “bad weather” day into test data on the second day of prediction. This is done to observe if the breakdown plot captures a decrease in the collective regressors’ effect. The impact of the change in the regressor values can be clearly seen in the updated breakdown.
329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 | # Altering the test data.
# We alter the normal weather conditions on the second day to heavy precipitation and low temperature.
test_df["regressor_bin_pn"] = [0, 1, 0, 0, 0, 0, 0]
test_df["regressor_bin_heavy_pn"] = [0, 1, 0, 0, 0, 0, 0]
test_df["regressor_tmin"] = [15, 0, 15, 15, 15, 15, 15]
print(f"altered test_df: \n {test_df}")
# Gets predictions and the design matrix used during predictions.
pred_df = trained_estimator.predict(test_df.reset_index())
forecast_x_mat = trained_estimator.forecast_x_mat
# Generates the breakdown plot.
breakdown_result = trained_estimator.forecast_breakdown(
grouping_regex_patterns_dict=grouping_regex_patterns_dict,
forecast_x_mat=forecast_x_mat,
time_values=pred_df[time_col])
breakdown_fig = breakdown_result["breakdown_fig"]
plotly.io.show(breakdown_fig)
|
Out:
altered test_df:
index ts count regressor_tmin regressor_tmax regressor_pn regressor_bin_pn regressor_bin_heavy_pn
0 0 2019-08-25 None 15 26.7 0.0 0 0
1 1 2019-08-26 None 0 25.0 0.0 1 1
2 2 2019-08-27 None 15 26.7 0.0 0 0
3 3 2019-08-28 None 15 27.8 0.0 0 0
4 4 2019-08-29 None 15 28.9 0.0 0 0
5 5 2019-08-30 None 15 32.8 0.0 0 0
6 6 2019-08-31 None 15 31.1 0.0 0 0
Total running time of the script: ( 0 minutes 33.933 seconds)