Gaussian Process Classification Bandits

Classification bandits are multi-armed bandit problems whose task is to classify a given set of arms into either positive or negative class depending on whether the rate of the arms with the expected reward of at least h is not less than w for given thresholds h and w. We study a special classification bandit problem in which arms correspond to points x in d-dimensional real space with expected rewards f(x) which are generated according to a Gaussian process prior. We develop a framework algorithm for the problem using various arm selection policies and propose policies called FCB and FTSV. We show a smaller sample complexity upper bound for FCB than that for the existing algorithm of the level set estimation, in which whether f(x) is at least h or not must be decided for every arm's x. Arm selection policies depending on an estimated rate of arms with rewards of at least h are also proposed and shown to improve empirical sample complexity. According to our experimental results, the rate-estimation versions of FCB and FTSV, together with that of the popular active learning policy that selects the point with the maximum variance, outperform other policies for synthetic functions, and the version of FTSV is also the best performer for our real-world dataset.

Propagation Graph Estimation by Pairwise Alignment of Time Series Observation Sequences

Various things propagate through the medium of individuals. Some biological cells fire right after the firing of their neighbor cells, and such firing propagates from cells to cells. In this paper, we study the problem of estimating the firing propagation order of cells from the $\{0,1 \}$-state sequences of all the cells, where '1' at the $i$-th position means the firing state of the cell at time step $i$. We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently. The propagation order estimated by our proposed method is demonstrated to be correct for our synthetic datasets, and also to be consistent with visually recognizable firing order for the dataset of soil-dwelling amoeba's chemical signal emitting state sequences.