Real-world optimization problems often have expensive objective functions in terms of cost and time. It is desirable to find near-optimal solutions with very few function evaluations. Surrogate... Show moreReal-world optimization problems often have expensive objective functions in terms of cost and time. It is desirable to find near-optimal solutions with very few function evaluations. Surrogate-assisted optimizers tend to reduce the required number of function evaluations by replacing the real function with an efficient mathematical model built on few evaluated points. Problems with a high condition number are a challenge for many surrogate-assisted optimizers including SACOBRA. To address such problems we propose a new online whitening operating in the black-box optimization paradigm. We show on a set of high-conditioning functions that online whitening tackles SACOBRA's early stagnation issue and reduces the optimization error by a factor between 10 to 1e12 as compared to the plain SACOBRA, though it imposes many extra function evaluations. Covariance matrix adaptation evolution strategy (CMA-ES) has for very high numbers of function evaluations even lower errors, whereas SACOBRA performs better in the expensive setting (less than 1e03 function evaluations). If we count all parallelizable function evaluations (population evaluation in CMA-ES, online whitening in our approach) as one iteration, then both algorithms have comparable strength even on the long run. This holds for problems with dimension D <= 20. Show less
Thill, M.; Däubener, S.; Konen, W.; Bäck, T.H.W. 2019
Real-world anomaly detection for time series is still a challenging task. This is especially true for periodic or quasi-periodic time series since automated approaches have to learn long-term... Show moreReal-world anomaly detection for time series is still a challenging task. This is especially true for periodic or quasi-periodic time series since automated approaches have to learn long-term correlations before they are able to detect anomalies. Electrocardiography (ECG) time series, a prominent real-world example of quasi-periodic signals, are investigated in this work. Anomaly detection algorithms often have the additional goal to identify anomalies in an unsupervised manner. In this paper we present an unsupervised time series anomaly detection algorithm. It learns with recurrent Long Short-Term Memory (LSTM) networks to predict the normal time series behavior. The prediction error on several prediction horizons is used to build a statistical model of normal behavior. We propose new methods that are essential for a successful model-building process and for a high signal-to-noise-ratio. We apply our method to the well-known MIT-BIH ECG data set and present first results. We obtain a good recall of anomalies while having a very low false alarm rate (FPR) in a fully unsupervised procedure. We compare also with other anomaly detectors (NuPic, ADVec) from the state-of-the-art. Show less
