Formal Verification of Input-Output Mappings of Tree Ensembles

Recent advances in machine learning and artificial intelligence are now being considered in safety-critical autonomous systems where software defects may cause severe harm to humans and the environment. Design organizations in these domains are currently unable to provide convincing arguments that their systems are safe to operate when machine learning algorithms are used to implement their software. In this paper, we present an efficient method to extract equivalence classes from decision trees and tree ensembles, and to formally verify that their input-output mappings comply with requirements. The idea is that, given that safety requirements can be traced to desirable properties on system input-output patterns, we can use positive verification outcomes in safety arguments. This paper presents the implementation of the method in the tool VoTE (Verifier of Tree Ensembles), and evaluates its scalability on two case studies presented in current literature. We demonstrate that our method is practical for tree ensembles trained on low-dimensional data with up to 25 decision trees and tree depths of up to 20. Our work also studies the limitations of the method with high-dimensional data and preliminarily investigates the trade-off between large number of trees and time taken for verification

Postponing Branching Decisions

Solution techniques for Constraint Satisfaction and Optimisation Problems often make use of backtrack search methods, exploiting variable and value ordering heuristics. In this paper, we propose and analyse a very simple method to apply in case the value ordering heuristic produces ties: postponing the branching decision. To this end, we group together values in a tie, branch on this sub-domain, and defer the decision among them to lower levels of the search tree. We show theoretically and experimentally that this simple modification can dramatically improve the efficiency of the search strategy. Although in practise similar methods may have been applied already, to our knowledge, no empirical or theoretical study has been proposed in the literature to identify when and to what extent this strategy should be used.Comment: 11 pages, 3 figure

Combination Strategies for Semantic Role Labeling

This paper introduces and analyzes a battery of inference models for the problem of semantic role labeling: one based on constraint satisfaction, and several strategies that model the inference as a meta-learning problem using discriminative classifiers. These classifiers are developed with a rich set of novel features that encode proposition and sentence-level information. To our knowledge, this is the first work that: (a) performs a thorough analysis of learning-based inference models for semantic role labeling, and (b) compares several inference strategies in this context. We evaluate the proposed inference strategies in the framework of the CoNLL-2005 shared task using only automatically-generated syntactic information. The extensive experimental evaluation and analysis indicates that all the proposed inference strategies are successful -they all outperform the current best results reported in the CoNLL-2005 evaluation exercise- but each of the proposed approaches has its advantages and disadvantages. Several important traits of a state-of-the-art SRL combination strategy emerge from this analysis: (i) individual models should be combined at the granularity of candidate arguments rather than at the granularity of complete solutions; (ii) the best combination strategy uses an inference model based in learning; and (iii) the learning-based inference benefits from max-margin classifiers and global feedback