Systems and methods for generating a single-index model tree

An apparatus for generating a single-index model (SIM) tree, the apparatus comprising:

• input-output circuitry configured to receive a data set and a maximum tree depth;
• and
• a modeling engine configured to:
• screen a set of variables from the data set to thereby form split variables,
• in response to a determination that maximum tree depth has not been reached:
• (i) generate a SIM estimation for one or more nodes of a tree level,
• (ii) for each particular node of the one or more nodes, select a split point and split variable based on the fast-SIM estimation for the particular node,
• (iii) based on the selected split points and split variables for the nodes at the tree level, generate a set of nodes for a next tree level, wherein each node for the next tree level includes a subset of data included in a node at the tree level, and
• (iv) determine whether the next tree level is equal to the maximum tree level, and
• in response to a determination that the next tree level is equal to the maximum tree level:
• (i) fit a SIM for each node at each leaf node of the SIM tree based on a subset of the data set represented by the leaf node.

A computer program product for generating a single-index model (SIM) tree, the computer program product comprising at least one non-transitory computer-readable storage medium storing software instructions that, when executed, cause an apparatus to:

• receive a data set, a maximum tree depth, a smoothness strength, a sparsity strength, and a sample threshold;
• determine a set of variables from the data set to form a set of split variables;
• while a tree level is not equal to a maximum tree depth:
• generate a SIM estimation for each node of a current tree level based on a set of data corresponding to each one or more nodes, the smoothness strength, and the sparsity strength,
• determine, based on the SIM estimation, a split point and split variable for each node of the current tree level based on the sample threshold and a minimum loss,
• generate, based on the split point and split variable, a set of nodes for a next tree level, each node of the set of nodes including a subset of data included in a parent node, and
• determine whether the next tree level is at the maximum tree depth;
• and
• in response to a determination that the next tree level is at the maximum tree depth, fit a SIM for each node at the maximum tree depth based on a subset of data of each node at the maximum tree depth.