Adaptive Sparse Representation of Continuous Input for Tsetlin Machines Based on Stochastic Searching on the Line

Abstract

This paper introduces a novel approach to representing continuous inputs in Tsetlin Machines (TMs). Instead of using one Tsetlin Automaton (TA) for every unique threshold found when Booleanizing continuous input, we employ two Stochastic Searching on the Line (SSL) automata to learn discriminative lower and upper bounds. The two resulting Boolean features are adapted to the rest of the clause by equipping each clause with its own team of SSLs, which update the bounds during the learning process. Two standard TAs finally decide whether to include the resulting features as part of the clause. In this way, only four automata altogether represent one continuous feature (instead of potentially hundreds of them). We evaluate the performance of the new scheme empirically using five datasets, along with a study of interpretability. On average, TMs with SSL feature representation use 4.3 times fewer literals than the TM with static threshold-based features. Furthermore, in terms of average memory usage and F1-Score, our approach outperforms simple Multi-Layered Artificial Neural Networks, Decision Trees, Support Vector Machines, K-Nearest Neighbor, Random Forest, Gradient Boosted Trees (XGBoost), and Explainable Boosting Machines (EBMs), as well as the standard and real-value weighted TMs. Our approach further outperforms Neural Additive Models on Fraud Detection and StructureBoost on CA-58 in terms of the Area Under Curve while performing competitively on COMPAS.