A New Model for Building Energy Modeling and Management Using Predictive Analytics: Partitioned Hierarchical Multitask Regression (PHMR)

Algorithm 2

Algorithm for constructing the PHMR model.

Input: A training set and a validation set on the indoor variable , outdoor variable

  and response variable .

Initialize:

    Fit a lasso model at the current node using to obtain the current empirical risk

Assume that there are outdoor variables,

    for to do

     Split the data of node into left and right child node, and , respectively;

     Fit two lasso models in both child nodes and obtain the coefficients of the regression

     models, and ;

     Calculate empirical risk reduction .

    end for

    if ( for all ) then

      Stop

    else

      Choose outdoor variable and associated splitting point leading to the

      largest empirical risk reduction ;

      Split the data of node into two new leaf nodes, and ,

      respectively;

      Apply Algorithm 1 on all leaf nodes to obtain hierML estimation;

      Re-calculate empirical risk for each leaf node on by using new estimates

       from hierML;

      Select the leaf node with largest .

    end if

Output: A set of leaf nodes and fitted regression models in each leaf node.