Browsing by Subject "Outliers"
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Item Forecast combination for outlier protection and forecast combination under heavy tailed errors(2014-11) Cheng, GangForecast combination has been proven to be a very important technique to obtain accurate predictions. Numerous forecast combination schemes with distinct properties have been proposed. However, to our knowledge, little has been discussed in the literature on combining forecasts with minimizing the occurrence of forecast outliers in mind. An unnoticed phenomenon is that robust combining, which often improves predictive accuracy (under square or absolute error loss) when innovation errors have a tail heavier than a normal distribution, may have a higher frequency of prediction outliers. Given the importance of reducing outlier forecasts, it is desirable to seek new loss functions to achieve both the usual accuracy and outlier-protection simultaneously.In the second part of this dissertation, we propose a synthetic loss function and apply it on a general adaptive theoretical and numeric results support the advantages of the new method in terms of providing combined forecasts with relatively fewer large forecast errors and comparable overall performances. For various reasons, in many applications, forecast errors exhibit heavy tail behaviors. Unfortunately, to our knowledge, little has been done to deal with forecast combination for such situations. The familiar forecast combination methods such as simple average, least squares regression, or those based on variance-covariance of the forecasts, may perform very poorly in such situations. In the third part of this dissertation, we propose two forecast combination methods to address the problem. One is specially proposed for the situations that the forecast errors are strongly believed to have heavy tails that can be modeled by a scaled Student's t-distribution; the other is designed for relatively more general situations when there is a lack of strong or consistent evidence on the tail behaviors of the forecast errors due to shortage of data and/or evolving data generating process. adaptive risk bounds of both methods are developed. Simulations and a real example show the excellent performance of the new methods.Item Scalable Techniques for Trajectory Outlier Detection(2019-06) Gohar, UsmanThe recent improvements in tracking devices and positioning satellites have led to an increased availability of spatial data describing the movement of objects such as vehicles, animals, etc. Such data is obtained by recording the positions of the objects at regular intervals and then arranging the collected positions of each object into a time-ordered sequence called trajectory. The high availability of trajectory data has permitted the execution of data analysis operations such as trajectory outlier detection, which consists in the identification of those trajectories that behave much differently from the rest of the trajectories in a database. There are several time-critical applications such as traffic management systems, security surveillance systems and real-time stock monitoring, etc. which can be solved through trajectory outlier detection. However, the time-critical nature of such applications imposes tight constraints on the execution time of trajectory outlier detection algorithms. To deal with these constraints, we propose three strategies to accelerate the performance of the existing trajectory outlier detection algorithm ODMTS. First, we consider using spatial data structures such as k-d trees and R-trees to improve the running time performance of the ODMTS algorithm for trajectory outlier detection. Our results showed that by using R-trees we can improve the execution time of ODMTS by a factor of 10X. Our second strategy consists in harnessing the power of multiple CPUs to parallelize the ODMTS algorithm. This strategy yielded an execution time improvement that scales linearly with the number of cores, which in our case achieved 32X. The third strategy consists in a new partitioning-based streaming algorithm, called PDMTS, for trajectory outlier detection that leverages data streams in order to find trajectory outliers. Our experiments on real-life datasets showed that our proposed algorithm detected almost 45% outliers more than ODMTS, but is almost 18% slower than compared to ODMTS due to the partitioning step.