Time-of-Week + X Models

[stephen-frank]

New feature: create two new model architectures that implement time-of-week + X models, where X are arbitrary exogenous variables.

• delta: ToW+X model using quantile regression and based on the data structure of LBNL's time-of-week + temperature model (see also this earlier article)
  • Implementation example: nmecr
• echo: As delta, but instead of individual quantile regression models for each time slice, use a single ML model (neural network?) that leverages all the data with time slices as indicator variables

The delta and echo models will have the following features:

• Accept as inputs three types of data...
  • Timestamp, which is used to create the time-of-week bins (delta) or indicator variables (echo)
  • One or more continuous exogenous variables (the X in ToW+X) structured as piecewise linear curves per the original data transformation methodology used for the temperature variable
  • One or more arbitrary binary time-slicing variables used to differentiate distinct modes of building operation:
    • delta: further bin the data when fitting individual quantile regression models
    • echo: as further indicator variables fed to the ML model
• Configurable hyperparameters
  • Number of bins for time-of-week data (default = 168, i.e. 1 bin per hour; warn if greater than 672, i.e. 1 bin per 15 min)
  • Number of breakpoints, aka "knots", for each X variable (default = 6)
  • Min and max values for establishing breakpoints for each X variable (default = computed from training data set)
  • Coverage factor requirements and warning thresholds (especially necessary with multiple time-slicing variables!)
• Multi-quantile, multi-time-horizon predictions
  • delta: Via independent quantile regression models (one set per time horizon)?
  • echo: Via matrix output from a single ML model? Or ensemble?

The intent of this issue is to summarize the overall effort. Please create smaller issues for specific tasks related to this feature request.

TO DO: Create and attach a graphic showing the anticipated model structure for delta and echo