Geometrical Approaches to Active Learning

Learning from examples is a key property of autonomous agents. In our contribution, we want to focus on a particular class of strategies which are often referred to as “optimal experimental design“ or “active learning“. Learning machines, which employ these strategies, request examples which are maximal “informative“ for learning a predictor rather than “passively“ scanning their environment. There is a large body of empirical evidence, that active learning is more efficient in terms of the required number of examples. Hence, active learning should be preferred whenever training examples are costly to obtain. In our contribution, we will report new results for active learning methods which we are currently investigating and which are based on the geometrical concept of a version space. We will derive universal hard bounds for the prediction performance using tools from differential geometry, and we will also provide practical algorithms based on kernel methods and Monte-Carlo techniques. The new techniques are applied in psychoacoustical experiments for sound design.