[Fix] [forecasting] low accuracy when backtesting because correlation of ODE parameters are not considered

[lisphilar]

Summary

In forecasting, accuracy is quite low (i.e. predicted number of cases is far from actual values) when backtesting with Italy data and today=24Apr2021 because of correlation of ODE parameters are not considered. As failed in #778, ODE parameter values have correlation. This is related to #778 and #783.

Codes

import covsirphy as cs
# Dataset preparation
data_loader = cs.DataLoader("input")
jhu_data = data_loader.jhu()
oxcgr_data = data_loader.oxcgrt()
# Scenario analysis
snl = cs.Scenario(country="Italy")
snl.register(jhu_data, extras=[oxcgrt_data]))
snl.timepoints(today="24Apr2021")
snl.trend()
snl.estimate(cs.SIRF)
snl.fit(name="Forecast")
snl.predict(name="Forecast")
snl.adjust_end()
snl.history("Confirmed")
snl.history("Infected")
snl.history("Recovered")
snl.history("Fatal")

Outputs

Environment

• CovsirPhy version: 2.20.1-alpha
• Python version: 3.9.5
• Installation: poetry
• System: WSL (Ubuntu)

[lisphilar]

In sklearn, Decision Tree Regressor accepts multioutput (y=ODE parameter values), considering correlation of y values. We can remove MultioutputRegressor in decision tree regression. https://scikit-learn.org/stable/modules/tree.html#multi-output-problems

[lisphilar]

With #787, accuracy was improved especially for Confirmed/Recovered, which leads major improvement in Infected.

[lisphilar]

Because not completed in Confirmed/Fatal (-> Infected), we need to continue efforts in new issues.