Cross-validation Inference, Relative Algorithmic Stability, and Machine Learning Application in Robotic Grasping

Abstract

This dissertation advances the theory of cross-validation, highlights the critical role of algorithmic stability in ensuring valid inference for cross-validation, and introduces a hybrid approach to grasp stability prediction. In Chapter 1, we address a fundamental problem relevant to both the statistical and machine learning communities. With the surge in the number of algorithms being developed, it is crucial to perform statistically sound evaluation and comparison of algorithms. We derive central limit theorems and consistent variance estimators for cross-validation under very mild stability conditions on the learning algorithm. Leveraging these results allows us to develop practical, asymptotically exact confidence intervals for evaluation of the test error, and also valid, powerful hypothesis tests for algorithm comparison. Notably, our results are applicable to any choice for the number of folds, thus including the popular setting of leave-one-out cross-validation. In Chapter 2, we demonstrate the importance of evaluating the stability of algorithms in a relative sense for cross-validation inference. We prove that the Lasso algorithm, considered individually in the setting of single algorithm evaluation, has sufficient stability to ensure statistical soundness of cross-validation for that task, while a difference of two Lasso algorithms, in the comparison setting, does not. In Chapter 3, we tackle the problem of grasp stability prediction in robotic grasping using a three-stage approach. We start with the estimation of key quantities critical to understanding grasp stability, known as the grasp parameters. Next, we predict the changes in contact forces caused by external disturbances. This, in turn, enables us to create an instance-by-instance slip prediction method. We develop a hybrid approach that combines physics and machine learning at each stage, effectively mitigating the limitations of both disciplines while leveraging their respective strengths. The experimental validation of this approach involved building an instrumented robot hand, designing experiments and collecting data.