Time Series Data Cleaning: A Survey <s> A. MAXIMUM LIKELIHOOD <s> A unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise, encompassing both the time series and the array problems, is presented. An exact expression for the ML criterion is derived in terms of the linear prediction polynomial of the signal, and an iterative algorithm for the maximization of this criterion is presented. The algorithm is equally applicable in the case of signal coherence in the array problem. Simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques. The algorithm is similar to those independently derived by Kumaresan et al. In addition to its practical value, the present formulation is used to interpret previous methods such as Prony's, Pisarenko's, and modifications thereof. <s> BIB001 </s> Time Series Data Cleaning: A Survey <s> A. MAXIMUM LIKELIHOOD <s> Various computational procedures or constraint-based methods for data repairing have been proposed over the last decades to identify errors and, when possible, correct them. However, these approaches have several limitations including the scalability and quality of the values to be used in replacement of the errors. In this paper, we propose a new data repairing approach that is based on maximizing the likelihood of replacement data given the data distribution, which can be modeled using statistical machine learning techniques. This is a novel approach combining machine learning and likelihood methods for cleaning dirty databases by value modification. We develop a quality measure of the repairing updates based on the likelihood benefit and the amount of changes applied to the database. We propose SCARE (SCalable Automatic REpairing), a systematic scalable framework that follows our approach. SCARE relies on a robust mechanism for horizontal data partitioning and a combination of machine learning techniques to predict the set of possible updates. Due to data partitioning, several updates can be predicted for a single record based on local views on each data partition. Therefore, we propose a mechanism to combine the local predictions and obtain accurate final predictions. Finally, we experimentally demonstrate the effectiveness, efficiency, and scalability of our approach on real-world datasets in comparison to recent data cleaning approaches. <s> BIB002 </s> Time Series Data Cleaning: A Survey <s> A. MAXIMUM LIKELIHOOD <s> This article addresses the challenge of truth discovery from noisy social sensing data. The work is motivated by the emergence of social sensing as a data collection paradigm of growing interest, where humans perform sensory data collection tasks. Unlike the case with well-calibrated and well-tested infrastructure sensors, humans are less reliable, and the likelihood that participants' measurements are correct is often unknown a priori. Given a set of human participants of unknown trustworthiness together with their sensory measurements, we pose the question of whether one can use this information alone to determine, in an analytically founded manner, the probability that a given measurement is true. In our previous conference paper, we offered the first maximum likelihood solution to the aforesaid truth discovery problem for corroborating observations only. In contrast, this article extends the conference paper and provides the first maximum likelihood solution to handle the cases where measurements from different participants may be conflicting. The article focuses on binary measurements. The approach is shown to outperform our previous work used for corroborating observations, the state-of-the-art fact-finding baselines, as well as simple heuristics such as majority voting. <s> BIB003 </s> Time Series Data Cleaning: A Survey <s> A. MAXIMUM LIKELIHOOD <s> We study the problem of finding the worst-case bound for the size of the result $Q(\mathbb{ D})$ of a fixed conjunctive query $Q$ applied to a database $\mathbb{ D}$ satisfying given functional dependencies. We provide a precise characterization of this bound in terms of entropy vectors, and in terms of finite groups. In particular, we show that an upper bound provided by Gottlob, Lee, Valiant and Valiant is tight, answering a question from their paper. Our result generalizes the bound due to Atserias, Grohe and Marx, who consider the case without functional dependencies. Our result shows that the problem of computing the worst-case size bound, in the general case, is closely related to difficult problems from information theory. <s> BIB004 </s> Time Series Data Cleaning: A Survey <s> A. MAXIMUM LIKELIHOOD <s> Errors are prevalent in data sequences, such as GPS trajectories or sensor readings. Existing methods on cleaning sequential data employ a constraint on value changing speeds and perform constraint-based repairing. While such speed constraints are effective in identifying large spike errors, the small errors that do not significantly deviate from the truth and indeed satisfy the speed constraints can hardly be identified and repaired. To handle such small errors, in this paper, we propose a statistical based cleaning method. Rather than declaring a broad constraint of max/min speeds, we model the probability distribution of speed changes. The repairing problem is thus to maximize the likelihood of the sequence w.r.t. the probability of speed changes. We formalize the likelihood-based cleaning problem, show its NP-hardness, devise exact algorithms, and propose several approximate/heuristic methods to trade off effectiveness for efficiency. Experiments on real data sets (in various applications) demonstrate the superiority of our proposal. <s> BIB005
The intuitive idea of the maximum likelihood principle is a random test, if there are several possible outcomes x 1 , x 2 . . . x t , if the result x i occurs in one test, it is generally considered that the test conditions are favorable for x i , or think that x i has the highest probability of occurrence. Notation: For a given time series data x(t), which consistents with a probability distribution d, and assume that its probability aggregation function (discrete distribution) is F d ; consider a distribution parameter θ , sampling x 1 , x 2 . . . x n from this distribution, then use F d to calculate its probability BIB001 as shown in equation BIB001 . Gogacz and S. Toruńczyk BIB004 use the maximum likelihood technique to clean Radio Frequency Identification (RFID) data. Wang et al. BIB003 propose the first maximum likelihood solution to address the challenge of truth discovery from noisy social sensing data. Yakout et al. BIB002 argue a new data repairing approach that is based on maximizing the likelihood of replacement data in the given data distribution, which can be modeled using statistical machine learning techniques, but this technology is used to repair the data of the database. For the repairing of time series data errors, Zhang et al. BIB005 propose a better solution based on maximum likelihood, which solves the problem from the perspective of probability. According to the probability distribution of the speed change of adjacent data points in the time series, the time series cleaning problem can be converted to find a cleaned time series, which is based on the probability of speed change that has the greatest likelihood.