Unveiling Latent Causal Rules: A Temporal Point Process Approach for Abnormal Event Explanation

TL;DR

This paper proposes an automated method for uncovering "if-then"logic rules to explain observational events, and introduces temporal point processes to model the events of interest, and discovers the set of latent rules to explain the occurrence of events.

Abstract

In high-stakes systems such as healthcare, it is critical to understand the causal reasons behind unusual events, such as sudden changes in patient's health. Unveiling the causal reasons helps with quick diagnoses and precise treatment planning. In this paper, we propose an automated method for uncovering "if-then" logic rules to explain observational events. We introduce temporal point processes to model the events of interest, and discover the set of latent rules to explain the occurrence of events. To achieve this, we employ an Expectation-Maximization (EM) algorithm. In the E-step, we calculate the likelihood of each event being explained by each discovered rule. In the M-step, we update both the rule set and model parameters to enhance the likelihood function's lower bound. Notably, we optimize the rule set in a differential manner. Our approach demonstrates accurate performance in both discovering rules and identifying root causes. We showcase its promising results using synthetic and real healthcare datasets.

Figures (12)

• Figure 1: Illustration of the feature construction. For a logic rule $f$ such as: $Y \gets X_1\bigwedge X_2\bigwedge X_3$, whenever the body condition becomes true, the rule gets fired. As a result, the feature $\phi_f$ becomes 1, and the intensity function of the head predicate is boosted.
• Figure 2: Illustration of how to encode the rule content into a binary matrix $A$. In the top diagrams, the content for a total of $H$ rules is depicted. In the bottom diagram, the corresponding encoded binary matrix $A$ is demonstrated. The colorful areas in the matrix indicate a value of 1, while the grey areas indicate a value of 0. Each row in the matrix represents a rule, and each column corresponds to a predicate. $\xi_1$ and $\xi_2$ are dummy predicates, and $K$=3 in this example.
• Figure 3: Our proposed model's performance is evaluated across all five scenarios for group 2, with two ground truth rules. We evaluate our model's performance in terms of rule discovery, rule weight learning, and rule prior distribution learning. The color "blue" indicates ground truth rules, weights, and prior distributions, whereas the colors "red" and "yellow" indicate the learning results.
• Figure 4: Jaccard similarity score and MAE of rule weights and rule prior probabilities for all 4 groups. The X-axis indicates predicate library size and the Y-axis indicates the value of Jaccard similarity and MAE.
• Figure 5: One example of inaccurately uncovered rule for Group-3 (3 ground truth rules) Case-4 (23 to-be-searched predicates). Ground truth rule: $Y \leftarrow x_4 \land x_5 \land ( x_4\,\text{Before}\, x_5)$. Learned rule: $Y \leftarrow x_1 \land x_4 \land x_5 \land(\ x_4 \,\text{Before} \ x_5)$. We see that only one more predicate was wrongly excluded.