Efficient Kernel-based Subsequence Search for User Identification from Walking Activity

This paper presents an efficient approach for subsequence search in data streams. The problem consists in identifying coherent repetitions of a given reference time-series, eventually multi-variate, within a longer data stream. Dynamic Time Warping (DTW) is the metric most widely used to implement pattern query, but its computational complexity is a well-known issue. In this paper we present an approach aimed at learning a kernel able to approximate DTW to be used for efficiently analyse streaming data collected from wearable sensors, reducing the burden of computation. Contrary to kernel, DTW allows for comparing time series with different length. Thus, to use a kernel, a feature embedding is used to represent a time-series as a fixed length vector. Each vector component is the DTW between the given time-series and a set of 'basis' series, usually randomly chosen. The vector size is the number of basis series used for the feature embedding. Searching for the portion of the data stream minimizing the DTW with the reference subsequence leads to a global optimization problem. The proposed approach has been validated on a benchmark dataset related to the identification of users depending on their walking activity. A comparison with a traditional DTW implementation is also provided.

Reachability-based safe learning for optimal control problem

In this work we seek for an approach to integrate safety in the learning process that relies on a partly known state-space model of the system and regards the unknown dynamics as an additive bounded disturbance. We introduce a framework for safely learning a control strategy for a given system with an additive disturbance. On the basis of the known part of the model, a safe set in which the system can learn safely, the algorithm can choose optimal actions for pursuing the target set as long as the safety-preserving condition is satisfied. After some learning episodes, the disturbance can be updated based on real-world data. To this end, Gaussian Process regression is conducted on the collected disturbance samples. Since the unstable nature of the law of the real world, for example, change of friction or conductivity with the temperature, we expect to have the more robust solution of optimal control problem. For evaluation of approach described above we choose an inverted pendulum as a benchmark model. The proposed algorithm manages to learn a policy that does not violate the pre-specified safety constraints. Observed performance is improved when it was incorporated exploration set up to make sure that an optimal policy is learned everywhere in the safe set. Finally, we outline some promising directions for future research beyond the scope of this paper.