Tree Learning: Optimal Algorithms and Sample Complexity
This work provides foundational insights for data collection efficiency in machine learning, though it is incremental in refining theoretical bounds.
The paper tackles the problem of learning hierarchical tree representations from labeled data under arbitrary distributions, establishing optimal sample complexity bounds for PAC and online learning settings. The results include efficient near-linear time construction of tree classifiers.
We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical structure. The smallest number of such tuples required in order to be able to accurately label subsequent tuples is of interest for data collection in machine learning. We present optimal sample complexity bounds for this problem in several learning settings, including (agnostic) PAC learning and online learning. Our results are based on tight bounds of the Natarajan and Littlestone dimensions of the associated problem. The corresponding tree classifiers can be constructed efficiently in near-linear time.