Model Free Method of Screening Training Data for Adversarial Datapoints Through Local Lipschitz Quotient Analysis

It is often challenging to pick suitable data features for learning problems. Sometimes certain regions of the data are harder to learn because they are not well characterized by the selected data features. The challenge is amplified when resources for sensing and computation are limited and time-critical, yet reliable decisions must be made. For example, a robotic system for preventing falls of elderly people needs a real-time fall predictor, with low false positive and false negative rates, using a simple wearable sensor to activate a fall prevention mechanism. Here we present a methodology for assessing the learnability of data based on the Lipschitz quotient. We develop a procedure for determining which regions of the dataset contain adversarial data points, input data that look similar but belong to different target classes. Regardless of the learning model, it will be hard to learn such data. We then present a method for determining which additional feature(s) are most effective in improving the predictability of each of these regions. This is a model-independent data analysis that can be executed before constructing a prediction model through machine learning or other techniques. We demonstrate this method on two synthetic datasets and a dataset of human falls, which uses inertial measurement unit signals. For the fall dataset, we identified two groups of adversarial data points and improved the predictability of each group over the baseline dataset, as assessed by Lipschitz, by using 2 different sets of features. This work offers a valuable tool for assessing data learnability that can be applied to not only fall prediction problems, but also other robotics applications that learn from data.