Explainable artificial intelligence from modal interval analysis solutions
A method for extracting an explanation from a solution of a global optimization problem derived via an interval analysis is provided. In the context of a global optimization problem characterized by a model, a set of model parameters, and an objective function delimiting relationships between and among the set of model parameters, each model parameter in the set of model parameters corresponding to a unique solution interval of a set of solution intervals, a ranked order of significance for a solution interval in the set of solution intervals as a function of first and second endpoints of the solution interval is derived. Thereafter, an explanation to the solution of the global optimization problem is provided, the explanation embodied in a list or an index that effectively sorts model parameters in the set of model parameters as a function of the ranked order of significance derived for a model parameter's corresponding solution interval.
1 . A method for generating an explanation from a solution of a global optimization problem for an artificial neural network model (ANN), the method including:
determining the solution to the global optimization problem for the ANN by:
initializing each ANN parameter of a set of model parameters with an interval having a lower bound and an upper bound, the initialized model parameters defining an axis-aligned parallelotope that defines a search region;
iteratively bisecting the search region into subdomains;
for each subdomain, evaluating an objective function using modal interval arithmetic to compute an interval enclosure;
eliminating subdomains proven not to contain a global minimum based on the interval enclosure;
continuing the iterative bisecting until obtaining the solution comprising a set of solution intervals, each solution interval delimited by a first endpoint and a second endpoint;
deriving a ranked order of significance for a solution interval in the set of solution intervals as a function of the first and second endpoints of said solution interval, wherein deriving includes:
retrieving from a respective first endpoint and a respective second endpoint of each respective solution interval;
computing a distance value between the respective first endpoint and the respective second endpoint by calculating an absolute value of a difference between the respective first endpoint and the respective second endpoint; and
assigning a significance metric for the respective solution interval based on the distance value;
sorting model parameters in the set of model parameters as a function of the assigned significance metrics;
generating an output comprising a list or an index that maps each ANN parameter to its ranked order of significance; and
providing the output as an explanation for the solution of the global optimization problem.
2 . The method of claim 1 wherein said deriving the ranked order of significance comprises obtaining a logarithmic value of a distance between said first and second endpoints of said solution interval.
3 . The method of claim 1 wherein the global optimization problem is a supervised machine learning problem.
4 . The method of claim 1 wherein the model parameters correspond to all of the model parameters in the set of model parameters.
5 . The method of claim 1 wherein the model parameters correspond to a select set of model parameters in the set of model parameters.
6 . The method of claim 5 wherein the select set of model parameters are input features of the model.
7 . The method of claim 5 wherein the select set of model parameters are output features of the model.
8 . The method of claim 1 wherein the explanation is provided as input to a use-case scenario, the use-case scenario predicated on the explanation.
9 . The method of claim 8 wherein the use-case scenario is a discovery of significant model parameters, and the explanation is used to identify which model parameters are most significant in solving the global optimization problem.
10 . The method of claim 8 wherein the use-case scenario is a normalization of model data using insignificant model parameters, and the explanation is used to identify which model parameters are insignificant, select insignificant model parameters used to normalize model data between scientific experiments performed by different research groups and/or with different data collection processes and methods.
11 . The method of claim 8 wherein the use-case scenario is a validation or falsification of a scientific hypotheses, and the explanation is used to confirm or deny that select model parameters have a high or low significance in relation to the scientific hypothesis.
12 . The method of claim 8 wherein the use-case scenario is a model adjustment or refinement, select model parameters of low significance deleted from the model in furtherance of reducing the complexity of the model and improving overall speed and performance of the model.