Mode hunting through active information

Abstract

We propose a new method to find modes based on active information. We develop an algorithm called active information mode hunting (AIMH) that, when applied to the whole space, will say whether there are any modes present and where they are. We show AIMH is consistent and, given that information increases where probability decreases, it helps to overcome issues with the curse of dimensionality. The AIMH also reduces the dimensionality with no resource to principal components. We illustrate the method in three ways: with a theoretical example (showing how it performs better than other mode hunting strategies), a real dataset business application, and a simulation.

Generalized active information: extensions to unbounded domains

“…Active information has recently been expanded as a multidimensional mode hunting tool [11]. Briefly speaking, in a finite space every deviation from equiprobability constitutes a local mode.…”

Hypothesis testing with active information

“…Actinfo is at the core of the algorithm called AIMH (active information mode hunting). This algorithm is more efficient to find modes in large dimensions than its competitors, as illustrated in [5] (for other models of bump hunting see e.g., [1,6,7]). However, other applications are possible; for instance, actinfo is able to compare two different learning strategies.…”

Correcting prevalence estimation for biased sampling with testing errors

“…as N → ∞, where p( 1) is defined as in (35), Z 4 ∼  (0, V 5 + V 6 ), Z 5 ∼  (0, V 7 + V 8 ) are normally distributed random variables, and V 5 , V 6 , V 7 , and V 8 are defined in the Appendix.…”