Mathematics & Statistics

Lam Ho received the 'Best Paper Award' at the 17th International Conference on Intelligent Software Methodologies, Tools and Techniques (SoMeT 2018) which was held in Spain September, 2018.

The title of the paper is "OASIS: An Active Framework for Set Inversion"

An explanation of the contents of the paper follows:

Set inversion is the problem of determining the pre-image of a set by a function. Despite the simplicity of its formulation, this problem is challenging due to the fact that the pre-image can have a complicated geometric structure. SIVIA (Set Inverter Via Interval Analysis), the current state-of-the-art algorithm for set inversion, relies heavily on partitioning the space of interest into several small intervals. As a result, the computational cost increases exponentially in terms of the dimension, rendering the method impractical for studies of moderate- and high-dimensional functions.

In this paper, we reformulate the set inversion problem as a classification task in which the first class includes points that lie inside the pre-image and the second class includes points that lie outside. So, set inversion becomes the problem of detecting the boundary of these two classes. We propose an active learning algorithm, called OASIS, which aggressively searches for this boundary.  Our simulations show that the proposed method achieves high accuracy, even for moderate- and high-dimensional problems which SIVIA cannot handle.

Congratulations to Dr. Ho!