Trusted Machine Learning: Model Repair and Data Repair for Probabilistic Models

When machine learning algorithms are used in life-critical or mission-critical applications (e.g., self driving cars, cyber security, surgical robotics), it is important to ensure that they provide some high-level correctness guarantees. We introduce a paradigm called Trusted Machine Learning (TML) with the goal of making learning techniques more trustworthy. We outline methods that show how symbolic analysis (specifi- cally parametric model checking) can be used to learn the dynamical model of a system where the learned model satis- fies correctness requirements specified in the form of temporal logic properties (e.g., safety, liveness). When a learned model does not satisfy the desired guarantees, we try two approaches: (1) Model Repair, wherein we modify a learned model directly, and (2) Data Repair, wherein we modify the data so that re-learning from the modified data will result in a trusted model. Model Repair tries to make the minimal changes to the trained model while satisfying the properties, whereas Data Repair tries to make the minimal changes to the dataset used to train the model for ensuring satisfaction of the properties. We show how the Model Repair and Data Repair problems can be solved for the case of probabilistic models, specifically Discrete-Time Markov Chains (DTMC) or Markov Decision Processes (MDP), when the desired properties are expressed in Probabilistic Computation Tree Logic (PCTL). Specifically, we outline how the parameter learning problem in the probabilistic Markov models under temporal logic constraints can be equivalently expressed as a non-linear optimization with non-linear rational constraints, by performing symbolic transformations using a parametric model checker. We illustrate the approach on two case studies: a controller for automobile lane changing, and query router for a wireless sensor network.