Integrating symbolic and statistical methods for testing intelligent systems: Applications to machine learning and computer vision

Embedded intelligent systems ranging from tiny implantable biomedical devices to large swarms of autonomous unmanned aerial systems are becoming pervasive in our daily lives. While we depend on the flawless functioning of such intelligent systems, and often take their behavioral correctness and safety for granted, it is notoriously difficult to generate test cases that expose subtle errors in the implementations of machine learning algorithms. Hence, the validation of intelligent systems is usually achieved by studying their behavior on representative data sets, using methods such as cross-validation and bootstrapping. In this paper, we present a new testing methodology for studying the correctness of intelligent systems. Our approach uses symbolic decision procedures coupled with statistical hypothesis testing to validate machine learning algorithms. We show how we have employed our technique to successfully identify subtle bugs (such as bit flips) in implementations of the k-means algorithm. Such errors are not readily detected by standard validation methods such as randomized testing. We also use our algorithm to analyze the robustness of a human detection algorithm built using the OpenCV open-source computer vision library. We show that the human detection implementation can fail to detect humans in perturbed video frames even when the perturbations are so small that the corresponding frames look identical to the naked eye.