Recent developments in sensors, global positioning system devices and smart phones have increased the availability of spatiotemporal data streams. Developing models for mining such streams is challenged by the huge amount of data that cannot be stored in the memory, the high arrival speed and the dynamic changes in the data distribution. Density estimation is an important technique in stream mining for a wide variety of applications. In this paper, we present a method called KDE-Track to estimate the density of spatiotemporal data streams. KDE-Track can efficiently estimate the density function with linear time complexity using interpolation on a kernel model, which is incrementally updated upon the arrival of new samples from the stream.

Recent developments in sensors, global positioning system devices, and smart phones have increased the availability of spatiotemporal data streams. Developing models for mining such streams is challenged by the huge amount of data that cannot be stored in the memory, the high arrival speed, and the dynamic changes in the data distribution. Density estimation is an important technique in stream mining for a wide variety of applications. The construction of kernel density estimators is well studied and documented. However, existing techniques are either expensive or inaccurate and unable to capture the changes in the data distribution. In this paper, we present a method called KDE-Track to estimate the density of spatiotemporal data streams. KDE-Track can efficiently estimate the density function with linear time complexity using interpolation on a kernel model, which is incrementally updated upon the arrival of new samples from the stream. We also propose an accurate and efficient method for selecting the bandwidth value for the kernel density estimator, which increases its accuracy significantly. Both theoretical analysis and experimental validation show that KDE-Track outperforms a set of baseline methods on the estimation accuracy and computing time of complex density structures in data streams.

Detecting changes in multidimensional data streams is an important and challenging task. In unsupervised change detection, changes are usually detected by comparing the distribution in a current (test) window with a reference window. It is thus essential to design divergence metrics and density estimators for comparing the data distributions, which are mostly done for univariate data. Detecting changes in multidimensional data streams brings difficulties to the density estimation and comparisons. In this paper, we propose a framework for detecting changes in multidimensional data streams based on principal component analysis, which is used for projecting data into a lower dimensional space, thus facilitating density estimation and change-score calculations.

Parameter estimation is a challenging computational problem in the reverse engineering of biological systems. Because advances in biotechnology have facilitated wide availability of time-series gene expression data, systematic parameter estimation of gene circuit models from such time-series mRNA data has become an important method for quantitatively dissecting the regulation of gene expression. By focusing on the modeling of gene circuits, we examine here the performance of three types of state-of-the-art parameter estimation methods: population-based methods, online methods and model-decomposition-based methods. Our results show that certain population-based methods are able to generate high-quality parameter solutions. The performance of these methods, however, is heavily dependent on the size of the parameter search space, and their computational requirements substantially increase as the size of the search space increases. In comparison, online methods and model decomposition-based methods are computationally faster alternatives and are less dependent on the size of the search space. Among other things, our results show that a hybrid approach that augments computationally fast methods with local search as a subsequent refinement procedure can substantially increase the quality of their parameter estimates to the level on par with the best solution obtained from the population-based methods while maintaining high computational speed. These suggest that such hybrid methods can be a promising alternative to the more commonly used population-based methods for parameter estimation of gene circuit models when limited prior knowledge about the underlying regulatory mechanisms makes the size of the parameter search space vastly large.

Streaming data are dynamic in nature with frequent changes. To detect such changes, most methods measure the difference between the data distributions in a current time window and a reference window. Divergence metrics and density estimation are required to measure the difference between the data distributions. Our study shows that the Kullback-Leibler (KL) divergence, the most popular metric for comparing distributions, fails to detect certain changes due to its asymmetric property and its dependence on the variance of the data. We thus consider two metrics for detecting changes in univariate data streams: a symmetric KL-divergence and a divergence metric measuring the intersection area of two distributions. The experimental results show that these two metrics lead to more accurate results in change detection than baseline methods such as Change Finder and using conventional KL-divergence.

MOTIVATION: Systematic and scalable parameter estimation is a key to construct complex gene regulatory models and to ultimately facilitate an integrative systems biology approach to quantitatively understand the molecular mechanisms underpinning gene regulation. RESULTS: Here, we report a novel framework for efficient and scalable parameter estimation that focuses specifically on modeling of gene circuits. Exploiting the structure commonly found in gene circuit models, this framework decomposes a system of coupled rate equations into individual ones and efficiently integrates them separately to reconstruct the mean time evolution of the gene products. The accuracy of the parameter estimates is refined by iteratively increasing the accuracy of numerical integration using the model structure. As a case study, we applied our framework to four gene circuit models with complex dynamics based on three synthetic datasets and one time series microarray data set. We compared our framework to three state-of-the-art parameter estimation methods and found that our approach consistently generated higher quality parameter solutions efficiently. Although many general-purpose parameter estimation methods have been applied for modeling of gene circuits, our results suggest that the use of more tailored approaches to use domain-specific information may be a key to reverse engineering of complex biological systems. AVAILABILITY: http://sfb.kaust.edu.sa/Pages/Software.aspx. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In this paper, we propose a new method to estimate the dynamic density over data streams, named KDE-Track as it is based on a conventional and widely used Kernel Density Estimation (KDE) method. KDE-Track can efficiently estimate the density with linear complexity by using interpolation on a kernel model, which is incrementally updated upon the arrival of streaming data. Both theoretical analysis and experimental validation show that KDE-Track outperforms traditional KDE and a baseline method Cluster-Kernels on estimation accuracy of the complex density structures in data streams, computing time and memory usage. KDE-Track is also demonstrated on timely catching the dynamic density of synthetic and real-world data. In addition, KDE-Track is used to accurately detect outliers in sensor data and compared with two existing methods developed for detecting outliers and cleaning sensor data.

MOTIVATION: Estimation of misclassification error has received increasing attention in clinical diagnosis and bioinformatics studies, especially in small sample studies with microarray data. Current error estimation methods are not satisfactory because they either have large variability (such as leave-one-out cross-validation) or large bias (such as resubstitution and leave-one-out bootstrap). While small sample size remains one of the key features of costly clinical investigations or of microarray studies that have limited resources in funding, time and tissue materials, accurate and easy-to-implement error estimation methods for small samples are desirable and will be beneficial. RESULTS: A bootstrap cross-validation method is studied. It achieves accurate error estimation through a simple procedure with bootstrap resampling and only costs computer CPU time. Simulation studies and applications to microarray data demonstrate that it performs consistently better than its competitors. This method possesses several attractive properties: (1) it is implemented through a simple procedure; (2) it performs well for small samples with sample size, as small as 16; (3) it is not restricted to any particular classification rules and thus applies to many parametric or non-parametric methods.