Tsetlin Machines (TMs) have emerged as a compelling alternative to conventional deep learning methods, offering notable advantages such as smaller memory footprint, faster inference, fault-tolerant properties, and interpretability. Although various adaptations of TMs have expanded their applicability across diverse domains, a fundamental gap remains in understanding how TMs quantify uncertainty in their predictions. In response, this paper introduces the Probabilistic Tsetlin Machine (PTM) framework, aimed at providing a robust, reliable, and interpretable approach for uncertainty quantification. Unlike the original TM, the PTM learns the probability of staying on each state of each Tsetlin Automaton (TA) across all clauses. These probabilities are updated using the feedback tables that are part of the TM framework: Type I and Type II feedback. During inference, TAs decide their actions by sampling states based on learned probability distributions, akin to Bayesian neural networks when generating weight values. In our experimental analysis, we first illustrate the spread of the probabilities across TA states for the noisy-XOR dataset. Then we evaluate the PTM alongside benchmark models using both simulated and real-world datasets. The experiments on the simulated dataset reveal the PTM's effectiveness in uncertainty quantification, particularly in delineating decision boundaries and identifying regions of high uncertainty. Moreover, when applied to multiclass classification tasks using the Iris dataset, the PTM demonstrates competitive performance in terms of predictive entropy and expected calibration error, showcasing its potential as a reliable tool for uncertainty estimation. Our findings underscore the importance of selecting appropriate models for accurate uncertainty quantification in predictive tasks, with the PTM offering a particularly interpretable and effective solution.

翻译：Tsetlin机（TM）已成为传统深度学习方法的引人注目的替代方案，具有内存占用小、推理速度快、容错性强和可解释性等显著优势。尽管TM的各种变体已扩展了其在多个领域的适用性，但在理解TM如何量化其预测的不确定性方面仍存在根本性差距。为此，本文提出了概率Tsetlin机（PTM）框架，旨在为不确定性量化提供一种稳健、可靠且可解释的方法。与原始TM不同，PTM学习所有子句中每个Tsetlin自动机（TA）停留在每个状态的概率。这些概率使用TM框架中的反馈表（I型和II型反馈）进行更新。在推理过程中，TA通过基于学习到的概率分布对状态进行抽样来决定其动作，类似于贝叶斯神经网络生成权重值的方式。在我们的实验分析中，我们首先展示了噪声XOR数据集上TA状态概率的分布情况。随后，我们使用模拟和真实数据集将PTM与基准模型进行了比较评估。模拟数据集的实验揭示了PTM在不确定性量化方面的有效性，特别是在划定决策边界和识别高不确定性区域方面。此外，当应用于使用Iris数据集的多类别分类任务时，PTM在预测熵和预期校准误差方面表现出具有竞争力的性能，展示了其作为不确定性估计可靠工具的潜力。我们的研究结果强调了为预测任务选择合适模型以实现准确不确定性量化的重要性，而PTM提供了一种尤其可解释且有效的解决方案。