Many real-life dynamical systems change abruptly followed by almost stationary periods. In this paper, we consider streams of data with such abrupt behavior and investigate the problem of tracking their statistical properties in an online manner. We devise a tracking procedure where an estimator that is suitable for a stationary environment is combined together with an event detection method such that the estimator rapidly can jump to a more suitable value if an event is detected. Combining an estimation procedure with detection procedure is commonly known idea in the literature. However, our contribution lies in building the detection procedure based on the difference between the stationary estimator and a Stochastic Learning Weak Estimator (SLWE). The SLWE estimator is known to be the state-of-the art approach to tracking properties of non-stationary environments and thus should be a better choice to detect changes in abruptly changing environments than the far more common sliding window based approaches. To the best of our knowledge, the event detection procedure suggested by (2012) is the only procedure in the literature taking advantage of the powerful tracking properties of the SLWE estimator. The procedure in is however quite complex and not well founded theoretically compared to the procedures in this paper. In this paper, we focus on estimation procedure for the binomial and multinomial distributions, but our approach can be easily generalized to cover other distributions as well. Extensive simulation results based on both synthetic and real-life data related to news classification demonstrate that our estimation procedure is easy to tune and performs well.
An ophthalmic lens for providing correction of distortion of the vertical position of an image in a lens prescribed for the condition of anisometropia comprises upper and lower portions having different optical centers. The lens surfaces of the upper and lower portions merge in a transverse band providing a smooth transition between the upper and lower lens surfaces over a vertical distance for example of 2 - 8 mm. The transverse band removes the conventional sharply visible boundary between the upper and lower lens surfaces and by introducing aberration into the lens at this point deters effective use of the lens over an angle of vision corresponding substantially to the angle of a cone of light entering the pupil of the eye and so prevents double vision occurring at the boundary of the lens surfaces. Methods of production of the lens are also disclosed. Classifying streaming data requires the development of methods which are computationally efficient and able to cope with changes in the underlying distribution of the stream, a phenomenon known in the literature as concept drift. We propose a new method for detecting concept drift which uses an exponentially weighted moving average (EWMA) chart to monitor the misclassification rate of an streaming classifier. Our approach is modular and can hence be run in parallel with any underlying classifier to provide an additional layer of concept drift detection. Moreover our method is computationally efficient with overhead O(1) and works in a fully online manner with no need to store data points in memory. Unlike many existing approaches to concept drift detection, our method allows the rate of false positive detections to be controlled and kept constant over time. In this paper we study the problem of constructing histograms from high-speed time-changing data streams. Learning in this context requires the ability to process examples once at the rate they arrive, maintaining a histogram consistent with the most recent data, and forgetting out-date data whenever a change in the distribution is detected. To construct histogram from high-speed data streams we use the two layer structure used in the Partition Incremental Discretization (PiD) algorithm. Our contribution is a new method to detect whenever a change in the distribution generating examples occurs. The base idea consists of monitoring distributions from two different time windows: the reference time window, that reflects the distribution observed in the past; and the current time window reflecting the distribution observed in the most recent data. We compare both distributions and signal a change whenever they are greater than a threshold value, using three different methods: the Entropy Absolute Difference, the Kullback-Leibler divergence and the Cosine Distance. The experimental results suggest that Kullback-Leibler divergence exhibit high probability in change detection, faster detection rates, with few false positives alarms. An established method to detect concept drift in data streams is to perform statistical hypothesis testing on the multivariate data in the stream. The statistical theory offers rank-based statistics for this task. However, these statistics depend on a fixed set of characteristics of the underlying distribution. Thus, they work well whenever the change in the underlying distribution affects the properties measured by the statistic, but they perform not very well, if the drift influences the characteristics caught by the test statistic only to a small degree. To address this problem, we show how uniform convergence bounds in learning theory can be adjusted for adaptive concept drift detection. In particular, we present three novel drift detection tests, whose test statistics are dynamically adapted to match the actual data at hand. The first one is based on a rank statistic on density estimates for a binary representation of the data, the second compares average margins of a linear classifier induced by the 1-norm support vector machine (SVM), and the last one is based on the average zero-one, sigmoid or stepwise linear error rate of an SVM classifier. We compare these new approaches with the maximum mean discrepancy method, the StreamKrimp system, and the multivariate Wald–Wolfowitz test. The results indicate that the new methods are able to detect concept drift reliably and that they perform favorably in a precision-recall analysis. Copyright © 2009 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 2: 311-327, 2009