Active Classification with Comparison Queries

We study an extension of active learning in which the learning algorithm may ask the annotator to compare the distances of two examples from the boundary of their label-class. For example, in a recommendation system application (say for restaurants), the annotator may be asked whether she liked or disliked a specific restaurant (a label query); or which one of two restaurants did she like more (a comparison query). We focus on the class of half spaces, and show that under natural assumptions, such as large margin or bounded bit-description of the input examples, it is possible to reveal all the labels of a sample of size n using approximately O(log n) queries. This implies an exponential improvement over classical active learning, where only label queries are allowed. We complement these results by showing that if any of these assumptions is removed then, in the worst case, Ω(n) queries are required. Our results follow from a new general framework of active learning with additional queries. We identify a combinatorial dimension, called the inference dimension, that captures the query complexity when each additional query is determined by O(1) examples (such as comparison queries, each of which is determined by the two compared examples). Our results for half spaces follow by bounding the inference dimension in the cases discussed above.

Authors

• Daniel M. Kane
• Shachar Lovett
• Shay Moran
• Jiapeng Zhang

Keywords

• Complexity theory
• Computer science
• Inference algorithms
• Standards
• Labeling
• Context modeling
• Comparison Query
• Learning Algorithms
• Active Learning
• Large Margin
• Half Space
• Class Of Spaces
• Additional Queries
• Lower Bound
• Upper Bound
• Functional Class
• Input Samples
• Total Run Time
• Concept Of Learning
• Interactive Learning
• Closest Point
• Threshold Function
• Real-valued Function
• Update Step
• Standard Argument
• Neural Net
• Point Labels
• Weak Learners
• Confidence Region
• Unlabeled Examples
• List Of Examples
• Concept Of Class
• Passive Learning
• Functional Form