Improving Stability in Decision Tree Models

Owing to their inherently interpretable structure, decision trees are commonly used in applications where interpretability is essential. Recent work has focused on improving various aspects of decision trees, including their predictive power and robustness; however, their instability, albeit well-documented, has been addressed to a lesser extent. In this paper, we take a step towards the stabilization of decision tree models through the lens of real-world health care applications due to the relevance of stability and interpretability in this space. We introduce a new distance metric for decision trees and use it to determine a tree's level of stability. We propose a novel methodology to train stable decision trees and investigate the existence of trade-offs that are inherent to decision tree models - including between stability, predictive power, and interpretability. We demonstrate the value of the proposed methodology through an extensive quantitative and qualitative analysis of six case studies from real-world health care applications, and we show that, on average, with a small 4.6% decrease in predictive power, we gain a significant 38% improvement in the model's stability

On The Stability of Interpretable Models

Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or a linear model, are widely recognized as human-interpretable. However, such models are generated as part of a larger analytical process. Bias in data collection and preparation, or in model's construction may severely affect the accountability of the design process. We conduct an experimental study of the stability of interpretable models with respect to feature selection, instance selection, and model selection. Our conclusions should raise awareness and attention of the scientific community on the need of a stability impact assessment of interpretable models

Technical note: Bias and the quantification of stability

Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is the stability of the algorithm; in other words, the repeatability of the results. If we obtain two sets of data from the same phenomenon, with the same underlying probability distribution, then we would like our learning algorithm to induce approximately the same concepts from both sets of data. This paper introduces a method for quantifying stability, based on a measure of the agreement between concepts. We also discuss the relationships among stability, predictive accuracy, and bias

Classification hardness for supervised learners on 20 years of intrusion detection data

This article consolidates analysis of established (NSL-KDD) and new intrusion detection datasets (ISCXIDS2012, CICIDS2017, CICIDS2018) through the use of supervised machine learning (ML) algorithms. The uniformity in analysis procedure opens up the option to compare the obtained results. It also provides a stronger foundation for the conclusions about the efficacy of supervised learners on the main classification task in network security. This research is motivated in part to address the lack of adoption of these modern datasets. Starting with a broad scope that includes classification by algorithms from different families on both established and new datasets has been done to expand the existing foundation and reveal the most opportune avenues for further inquiry. After obtaining baseline results, the classification task was increased in difficulty, by reducing the available data to learn from, both horizontally and vertically. The data reduction has been included as a stress-test to verify if the very high baseline results hold up under increasingly harsh constraints. Ultimately, this work contains the most comprehensive set of results on the topic of intrusion detection through supervised machine learning. Researchers working on algorithmic improvements can compare their results to this collection, knowing that all results reported here were gathered through a uniform framework. This work's main contributions are the outstanding classification results on the current state of the art datasets for intrusion detection and the conclusion that these methods show remarkable resilience in classification performance even when aggressively reducing the amount of data to learn from

Verifiable Reinforcement Learning via Policy Extraction

While deep reinforcement learning has successfully solved many challenging control tasks, its real-world applicability has been limited by the inability to ensure the safety of learned policies. We propose an approach to verifiable reinforcement learning by training decision tree policies, which can represent complex policies (since they are nonparametric), yet can be efficiently verified using existing techniques (since they are highly structured). The challenge is that decision tree policies are difficult to train. We propose VIPER, an algorithm that combines ideas from model compression and imitation learning to learn decision tree policies guided by a DNN policy (called the oracle) and its Q-function, and show that it substantially outperforms two baselines. We use VIPER to (i) learn a provably robust decision tree policy for a variant of Atari Pong with a symbolic state space, (ii) learn a decision tree policy for a toy game based on Pong that provably never loses, and (iii) learn a provably stable decision tree policy for cart-pole. In each case, the decision tree policy achieves performance equal to that of the original DNN policy

Stochastic Coalitional Better-response Dynamics and Strong Nash Equilibrium

We consider coalition formation among players in an n-player finite strategic game over infinite horizon. At each time a randomly formed coalition makes a joint deviation from a current action profile such that at new action profile all players from the coalition are strictly benefited. Such deviations define a coalitional better-response (CBR) dynamics that is in general stochastic. The CBR dynamics either converges to a strong Nash equilibrium or stucks in a closed cycle. We also assume that at each time a selected coalition makes mistake in deviation with small probability that add mutations (perturbations) into CBR dynamics. We prove that all strong Nash equilibria and closed cycles are stochastically stable, i.e., they are selected by perturbed CBR dynamics as mutations vanish. Similar statement holds for strict strong Nash equilibrium. We apply CBR dynamics to the network formation games and we prove that all strongly stable networks and closed cycles are stochastically stable