Non-linear lattice layer for partially monotonic neural network

A computer program product for training a lattice layer in a Deep Lattice Network (DLN) to infer a real-value output from an S-dimensional input having a monotonic-relationship with the real-value output, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to:

• generating a partially monotonic regression model to avoid unfair scoring by configure the DLN with a non-linear lattice layer having extended hypercubes, the program instructions further cause the computer to:
• prepare parameters θ of vertices, each of the parameters corresponding to each vertex of a subdivided unit hypercube defined by subdividing an S-dimensional unit hypercube by a predetermined number k with kS vertices;
• and
• define each parameter θ, of the parameters by:
• identifying a vertex, of the vertices in a specific order;
• identifying a first set of vertices, of the vertices, that appear before the identified vertex in the specific order and are dominated by the identified vertex with regards to each coordinate of the identified vertex;
• identifying a second set of vertices, of the vertices, that appear before the identified vertex in the specific order and are dominating the identified vertex with regards to each coordinate of the identified vertex;
• defining a lower bound as a maximum value among values of vertices in the first set of vertices;
• defining an upper bound as a minimum value among values of vertices in the second set of vertices;
• and
• defining the parameter of the identified vertex based on the lower bound and the upper bound so that the parameter represents a relative location of the identified vertex in an interval between the lower bound and the upper bound, wherein the hypercubes are extended by a number of vertices from 2S to kS, when k is less than S, to increase DLN granularity.

A system for training a lattice layer in a Deep Lattice Network (DLN) to infer a real-value output from an S-dimensional input having a monotonic-relationship with the real-value output, the system comprising:

• a memory;
• and
• one or more processors in communication with the memory configured to:
• generating a partially monotonic regression model to avoid unfair scoring by configuring the DLN with a non-linear lattice layer having extended hypercubes, which further causes the one or more processors to;
• prepare parameters θ0 of vertices, each of the parameters corresponding to each vertex of a subdivided unit hypercube defined by subdividing an S-dimensional unit hypercube by a predetermined number k with kS vertices;
• and
• define each parameter θ, of the parameters by:
• identifying a vertex, of the vertices, in a specific order;
• identifying a first set of vertices, of the vertices, that appear before the identified vertex in the specific order and are dominated by the identified vertex with regards to each coordinate of the identified vertex;
• identifying a second set of vertices, of the vertices, that appear before the identified vertex in the specific order and are dominating the identified vertex with regards to each coordinate of the identified vertex;
• defining a lower bound as a maximum value among values of vertices in the first set of vertices;
• defining an upper bound as a minimum value among values of vertices in the second set of vertices;
• and
• defining the parameter of the identified vertex based on the lower bound and the upper bound so that the parameter represents a relative location of the identified vertex in an interval between the lower bound and the upper bound, wherein the hypercubes are extended by a number of vertices from 2S to kS, when k is less than S, to increase DLN granularity.

A computer-implemented method for training a lattice layer in a Deep Lattice Network (DLN), the computer-implemented method comprising:

• generating a partially monotonic regression model to avoid unfair scoring by creating a non-linear lattice layer for the DLN, the non-linear lattice layer including an α-dimensional unit hypercube decomposed into (k−1)×(k−1)× . . . ×(k−1) sub-hypercubes by dividing an interval [0, 1] of each dimension into k−1 subintervals, wherein a dimension of the α-dimensional unit hypercube is changed from S to α, to increase DLN granularity;
• preparing parameters θ of vertices, each of the parameters corresponding to each vertex of the α-dimensional unit hypercube, the vertices being arbitrarily ordered, a parameter θ, of the parameters is defined to a value that satisfies:
• f(v)=(1−θv) 1+θv, u, where v is a vertex and u is an upper bound;
• and
• generating a monotone piecewise linear function ƒ(x) with k endpoints.

A computer program product for training a lattice layer in a Deep Lattice Network (DLN), the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to:

• generate a partially monotonic regression model to avoid unfair scoring to create a non-linear lattice layer for the DLN, the non-linear lattice layer including an α-dimensional unit hypercube decomposed into (k−1)×(k−1)× . . . ×(k−1) sub-hypercubes by dividing an interval [0, 1] of each dimension into k−1 subintervals, wherein dimension of the hypercube is changed from S to α, to increase DLN granularity;
• prepare parameters θ of vertices, each of the parameters corresponding to each vertex of the α-dimensional unit hypercube, a parameter θ is defined to a value that satisfies:
• f(v)=(1−θv) 1+θv u, where v is a vertex and u is an upper bound;
• and
• generate a monotone piecewise linear function ƒ(x) with k endpoints.