Scalable Bayesian Rule Lists (1602.08610v2)

Abstract: We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are built from pre-mined association rules. They have a logical structure that is a sequence of IF-THEN rules, identical to a decision list or one-sided decision tree. Instead of using greedy splitting and pruning like decision tree algorithms, we fully optimize over rule lists, striking a practical balance between accuracy, interpretability, and computational speed. The algorithm presented here uses a mixture of theoretical bounds (tight enough to have practical implications as a screening or bounding procedure), computational reuse, and highly tuned language libraries to achieve computational efficiency. Currently, for many practical problems, this method achieves better accuracy and sparsity than decision trees; further, in many cases, the computational time is practical and often less than that of decision trees. The result is a probabilistic classifier (which estimates P(y = 1|x) for each x) that optimizes the posterior of a Bayesian hierarchical model over rule lists.

• The paper introduces a Bayesian rule list model that globally optimizes the posterior, avoiding greedy heuristics to boost accuracy and interpretability.
• It employs statistical approximations and pre-mined frequent patterns to reduce the search space and reuse computations for significant speed improvements.
• Experimental results show that the model achieves comparable or superior accuracy and sparsity on datasets like UCI Mushroom and Adult compared to decision tree algorithms.

An Analysis of Scalable Bayesian Rule Lists

The paper "Scalable Bayesian Rule Lists" by Yang, Rudin, and Seltzer presents an algorithm designed to construct probabilistic rule lists that effectively compete with decision tree algorithms in terms of accuracy, interpretability, and computational efficiency. This work represents a significant advancement in the development of associative classifiers, which utilize pre-mined association rules arranged in IF-THEN sequences to form decision lists or one-sided decision trees. The methodology described in this paper aims to address inherent limitations in decision tree algorithms, such as their reliance on greedy splitting and pruning, which can lead to suboptimal and uninterpretable models.

Core Contributions

The primary contributions of this paper are:

1. Optimized Objective Function: The algorithm optimizes the posterior distribution for the Bayesian Rule List (BRL) model, enhancing the accuracy and interpretability of the rule lists without relying on greedy heuristics.
2. Statistical Approximation: A reduction in the search space is achieved by assuming bounded observations at each leaf, allowing the pre-mining of frequent patterns from the dataset. This approach transforms the rule list optimization into a manageably smaller problem.
3. Computational Efficiency: Utilization of high-performance language libraries and computational reuse provides significant speed improvements. Specifically, the paper highlights the ability to reuse calculations above changes in the rule lists during iterations, which synergistically accelerates computational processes.
4. Theoretical Bounds: The paper introduces two important theorems providing practical bounds. First, it establishes an upper bound on the number of rules in a maximum a posteriori rule list. Second, it uses prefix analysis to eliminate regions of the search space that cannot contain optimal solutions, streamlining the optimization process.

Experimental Results

The experimental evaluation conducted on several datasets, including the UCI Mushroom and Adult datasets, demonstrates that the Scalable Bayesian Rule List (SBRL) consistently achieves comparable or superior accuracy and sparsity compared to traditional decision tree algorithms such as CART and C4.5. The ruling mechanism facilitates interpretability by generating compact rule lists that remain easily understandable.

Scalability: The SBRL shows promising results in scalability benchmarks, handling datasets with high dimensionality, as evidenced in tests involving large-scale datasets like the USCensus1990. The algorithm achieves two orders of magnitude faster computation than previous probabilistic rule list implementations, showcasing its efficiency in processing large datasets.

Implications and Future Directions

The approach outlined in this paper opens multiple avenues for advancing interpretable machine learning models. By replacing greedy decision tree constructions with a globally optimized rule list structure, users of machine learning tools can obtain models that are both intelligible and robust. The ability to handle higher-dimensional datasets suggests potential applications in diverse fields such as healthcare, finance, and text processing.

Future developments could include enhancing rule list generation with mixed logical-linear models or applying similar global optimization strategies to other probabilistic classifiers. Moreover, the integration of advanced parallel computing techniques could further accelerate computational efficiency, expanding the applicability of SBRL to even larger datasets.

In conclusion, the Scalable Bayesian Rule Lists paper outlines a methodologically rigorous and computationally efficient path to constructing interpretable classifiers. This work reinforces the paradigm that interpretability does not necessitate compromising on performance, addressing a critical need within the machine learning community to balance complexity with clarity.