A Data-Transparent Probabilistic Model of Temporal Propositional Abstraction

TL;DR

This paper introduces a novel data-driven probabilistic model for temporal propositional reasoning that addresses data scarcity and transparency issues by reversing traditional domain knowledge assumptions, and demonstrates its theoretical properties and benefits.

Contribution

It proposes a new probabilistic model where data influences domain knowledge, unifying parameter learning and reasoning, and provides a rigorous theoretical foundation with proofs.

Findings

Model equivalent to a full-memory Markov chain

Handles data scarcity with natural limits

Enhances data transparency through generated distributions

Abstract

Standard probabilistic models face fundamental challenges such as data scarcity, a large hypothesis space, and poor data transparency. To address these challenges, we propose a novel probabilistic model of data-driven temporal propositional reasoning. Unlike conventional probabilistic models where data is a product of domain knowledge encoded in the probabilistic model, we explore the reverse direction where domain knowledge is a product of data encoded in the probabilistic model. This more data-driven perspective suggests no distinction between maximum likelihood parameter learning and temporal propositional reasoning. We show that our probabilistic model is equivalent to a highest-order, i.e., full-memory, Markov chain, and our model requires no distinction between hidden and observable variables. We discuss that limits provide a natural and mathematically rigorous way to handle data scarcity, including the zero-frequency problem. We also discuss that a probability distribution over data generated by our probabilistic model helps data transparency by revealing influential data used in predictions. The reproducibility of this theoretical work is fully demonstrated by the included proofs.