Learning programs from noisy data

We present a new approach for learning programs from noisy datasets. Our approach is based on two new concepts: a regularized program generator which produces a candidate program based on a small sample of the entire dataset while avoiding overfitting, and a dataset sampler which carefully samples the dataset by leveraging the candidate program's score on that dataset. The two components are connected in a continuous feedback-directed loop. We show how to apply this approach to two settings: one where the dataset has a bound on the noise, and another without a noise bound. The second setting leads to a new way of performing approximate empirical risk minimization on hypotheses classes formed by a discrete search space. We then present two new kinds of program synthesizers which target the two noise settings. First, we introduce a novel regularized bitstream synthesizer that successfully generates programs even in the presence of incorrect examples. We show that the synthesizer can detect errors in the examples while combating overfitting -- a major problem in existing synthesis techniques. We also show how the approach can be used in a setting where the dataset grows dynamically via new examples (e.g., provided by a human). Second, we present a novel technique for constructing statistical code completion systems. These are systems trained on massive datasets of open source programs, also known as ``Big Code''. The key idea is to introduce a domain specific language (DSL) over trees and to learn functions in that DSL directly from the dataset. These learned functions then condition the predictions made by the system. This is a flexible and powerful technique which generalizes several existing works as we no longer need to decide a priori on what the prediction should be conditioned (another benefit is that the learned functions are a natural mechanism for explaining the prediction). As a result, our code completion system surpasses the prediction capabilities of existing, hard-wired systems.