Manuel F. Fernández

Manuel Fernandez-Carmona, Sariah Mghames, Nicola Bellotto

Abstract. Detecting anomalies in patterns of sensor data is important in many practical applications, including domestic activity monitoring for Active Assisted Living (AAL). How to represent and analyse these patterns, however, remains a challenging task, especially when data is relatively scarce and an explicit model is required to be fine-tuned for specific scenarios. This paper, therefore, presents a new approach for temporal modelling of long-term human activities with smart-home sensors, which is used to detect anomalous situations in a robot-assisted environment. The model is based on wavelet transforms and used to forecast smart sensor data, providing a temporal prior to detect unexpected events in human environments. To this end, a new extension of Hybrid Markov Logic Networks has been developed that merges different anomaly indicators, including activities detected by binary sensors, expert logic rules, and wavelet-based temporal models. The latter in particular allows the inference system to discover deviations from long-term activity patterns, which cannot be detected by simpler frequency-based models. Two new publicly available datasets were collected using several smart-sensors to evaluate the approach in office and domestic scenarios. The experimental results demonstrate the effectiveness of the proposed solutions and their successful deployment in complex human environments, showing their potential for future smart-home and robot integrated services.

Manuel Fernandez, David P. Woodruff, Taisuke Yasuda

We present tight lower bounds on the number of kernel evaluations required to approximately solve kernel ridge regression (KRR) and kernel $k$-means clustering (KKMC) on $n$ input points. For KRR, our bound for relative error approximation to the minimizer of the objective function is $Ω(nd_{\mathrm{eff}}^λ/\varepsilon)$ where $d_{\mathrm{eff}}^λ$ is the effective statistical dimension, which is tight up to a $\log(d_{\mathrm{eff}}^λ/\varepsilon)$ factor. For KKMC, our bound for finding a $k$-clustering achieving a relative error approximation of the objective function is $Ω(nk/\varepsilon)$, which is tight up to a $\log(k/\varepsilon)$ factor. Our KRR result resolves a variant of an open question of El Alaoui and Mahoney, asking whether the effective statistical dimension is a lower bound on the sampling complexity or not. Furthermore, for the important practical case when the input is a mixture of Gaussians, we provide a KKMC algorithm which bypasses the above lower bound.