## 1 Introduction  
A traffic state of congestion generally arises at the sites that have traffic volume exceeding the associated road capacity. The traffic congestion induces inefficiencies that cause excessive travel time, energy consumption and emission of greenhouse gases. In order to address this problem, departments of transportation (DOTs) and other authorities spend significant portions of their budgets on intelligent transportation system (ITS) applications to monitor traffic flows and manage congestion-related issues. Data collected from stationary detectors including loop detectors are most widely used for monitoring the traffic conditions. Although the ITS applications ideally need complete and continuous streams of traffic data in order to function properly, in reality, significant portions of the collected data from the loop detectors are often missing, causing flaws potentially resulting in under or overshooting errors with existing prediction models for ITS applications [1; 2; 3; 4]. For example, [PERSON] et al. [5] report that roughly 10% of daily traffic volume data is missing in Beijing, China, mainly due to malfunctions of detectors. [PERSON] and [PERSON] [6] point out that about 25% to 30% of the traffic detectors managed by the Virginia Department of Transportation are offline at any given time. There are different categories of imputation methods. They are historical (neighboring), spline/regression, matrix-based, and non-parametric methods. The historical method recovers the missing portion of traffic data based on the data collected at the same location from neighboring days or an average of adjacent locations [7; 8]. According to [PERSON] et al. [5], the historical imputation method cannot guarantee that the data include all the traffic flow patterns that vary from day to day, even if a large amount of the data has been collected. The spline/regression approach estimates the missing data by applying mathematical interpolations utilizing the neighboring spatiotemporal data on the same day [9; 10]. According to [PERSON] [11], the historical and spline/regression approaches are structurally simple and hence less demanding on computational resources while providing opportunities for intuitive interpretations of data. A matrix-based imputation method models traffic data by a matrix which can contain more information, including traffic patterns, than vectors and has been initially introduced by [PERSON] et al. [5; 12]. They proposed the Bayesian principal component analysis and probabilistic principal component analysis (PPCA) for imputing incomplete traffic-flow volume data. These imputation methods have outperformed other conventional methods in terms of effectiveness and accuracy, and show superior imputation performances when the missing patterns are randomly distributed. However, [PERSON] et al. [13] mention that the existing methods do not work well when the proportion of the missing data gets larger including some extreme cases of dealing with multiple days' worth of missing data. Another approach for missing value imputation is non-parametric modeling. The general structure of the non-parametric model is not predefined and therefore obtained from historical data. \"Non-parametric\" implies that the number of parameters and their typology is unknown prior to the application. The main advantage of this model is that they can handle complex and non-linear structures. There are many variations of the non-parametric model including, artificial neural networks (ANN), decision trees, k-nearest neighbor (KNN) and support vector regression (SVR). Most machine learning (ML) methods can be considered as non-parametric models. Several researchers have identified non-parametric modeling as a flexible approach for imputations of missing traffic data [14]. The spatial and temporal correlation-aspects based on the actual relationship have been employed with matrix-based or non-parametric imputation methods to solve the large-data missing problems [3; 13; 14; 15; 16].