Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications, understanding how a decision is made is often as crucial as the decision itself. Traditional interpretable models, such as decision trees and logistic regression, provide transparency but may struggle with datasets containing intricate feature interactions. However, complexity in decision-making stem from interactions that are only relevant within certain subsets of data. Within these subsets, feature interactions may be simplified, forming simple structures where simple interpretable models can perform effectively. We propose a bottom-up simple structure-identifying algorithm that partitions data into interpretable subgroups known as simple structure, where feature interactions are minimized, allowing simple models to be trained within each subgroup. We demonstrate the robustness of the algorithm on synthetic data and show that the decision boundaries derived from simple structures are more interpretable and aligned with the intuition of the domain than those learned from a global model. By improving both explainability and predictive accuracy, our approach provides a principled framework for decision support in applications where model transparency is essential.

Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data. Be(cid:173) low we consider PoE models in which each expert is a Gaussian. Although the product of Gaussians is also a Gaussian, if each Gaus(cid:173) sian has a simple structure the product can have a richer structure. We examine (1) Products of Gaussian pancakes which give rise to probabilistic Minor Components Analysis, (2) products of I-factor PPCA models and (3) a products of experts construction for an AR(l) process. Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data.

Modern pattern recognition tasks use complex algorithms that take advantage of large datasets to make more accurate predictions than traditional algorithms such as decision trees or k-nearest-neighbor better suited to describe simple structures. While increased accuracy is often crucial, less complexity also has value. This paper proposes a training data selection algorithm that identifies multiple subsets with simple structures. A learning algorithm trained on such a subset can classify an instance belonging to the subset with better accuracy than the traditional learning algorithms. In other words, while existing pattern recognition algorithms attempt to learn a global mapping function to represent the entire dataset, we argue that an ensemble of simple local patterns may better describe the data. Hence the sub-setting algorithm identifies multiple subsets with simple local patterns by identifying similar instances in the neighborhood of an instance. This motivation has similarities to that of gradient boosted trees but focuses on the explainability of the model that is missing for boosted trees. The proposed algorithm thus balances accuracy and explainable machine learning by identifying a limited number of subsets with simple structures. We applied the proposed algorithm to the international stroke dataset to predict the probability of survival. Our bottom-up sub-setting algorithm performed on an average 15% better than the top-down decision tree learned on the entire dataset. The different decision trees learned on the identified subsets use some of the previously unused features by the whole dataset decision tree, and each subset represents a distinct population of data.