Evaluating adaptive smoothing models: some guidelines for implementation

An experimental comparison of exponential and adaptive smoothing forecasting models using actual operating data

Hypertensive disorders present significant morbidity and mortality during pregnancy. Although ambulatory blood pressure measurement remains the standard of care for normotensive women, self-monitoring at home is increasingly prevalent. The widespread use of smartphones worldwide has sparked interest in mobile applications that leverage the built-in hardware for blood pressure estimation, yet few trials have assessed their accuracy. This prospective, longitudinal and monocentric study evaluated the accuracy of the OptiBP algorithm against standard oscillometric blood pressure measurements in a sample of pregnant women. Patients scheduled for elective caesarean sections were enrolled during the preoperative anesthesia consultations. Paired blood pressure measurements using OptiBP and the reference method were obtained at multiple time-points in late pregnancy and the postpartum period. Agreement between methods was assessed using the AAMI/ESH/ISO 81060-2:2018 standard thresholds of 5 ± 8 mmHg for mean ± standard deviation of the error (criterion 1) and patient-specific standard deviation of the mean error (criterion 2) and represented graphically by Bland-Altman scatterplots. Forty-eight women were enrolled of which 32 completed the protocol, yielding 338 total valid measurement pairs. Mean and standard deviation of the error were -1.78 ± 7.94 and 1.19 ± 7.59, and the patient-specific standard deviation of the mean error was 4.68 and 4.52, for SBP and DBP, respectively. Compared with blood pressure measurements taken with an oscillometric device, OptiBP's blood pressure estimates meet the AAMI/ESH/ISO 81060-2:2018 criteria.

In this paper, we review the state of art of short-term traffic forecasting models, outlining their basic ideas, related works, advantages and disadvantages of each model. An improved adaptive exponential smoothing (IAES) model is also proposed to overcome the drawbacks of previous adaptive exponential smoothing model. Then comparing experiments are carried out under normal traffic condition and abnormal traffic condition to evaluate the performance of four main branches of forecasting models on direct travel time data obtained by license plate matching. The results of experiments show the forecasting performance of IASE is superior to other models in shorter forecasting horizon (one and two step forecasting).

Four methods are discussed for determining the smoothing parameters in an adaptive exponential smoothing model which is used to assess reliability of a complex system tested in stages. The adaptive model is defined as R_I = &#x003B1;_Ir_I + (1 - &#x003B1;_I)R_i-1, i = 2,...k, where R<sub.i-1</sub. is the assessed reliability at stage (i -1), ri is the ratio of the number of successes to the number of trials at stage i. Among the four procedures given here for determining the smoothing parameters &#x003B1;_I two empirical methods and an empirical Bayes procedure are considered in some detail including a numerical example in which these techniques are compared.

In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful basis vector for the set of data, and indicate which data use which basis vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the basis matrix, and the basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the basis matrix may not be smooth. We think that the basis vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, basis vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for basis vectors. However, the proposed method introduces the sparsity for coefficient vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient vectors and the smoothness for the basis vectors, can extract the smooth basis vectors and the original economical data are approximated as the weighted sum of the few bases vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.

Advances in micro robots in non-invasive medicine have enabled physicians to perform diagnostic and therapeutic procedures with higher resolution and lower risk than before. However, navigation and precise localisation of such micro robots inside human body still remains a challenge. This is mostly due to the 1) lack of precise communication channel models, 2) inhomogeneity of the propagation medium and 3) non-geometric boundaries of the tissues morphometric parameters. In this study, we derive novel intra-body path loss channel models for wave propagation in wireless capsule endoscopy, i.e., propagation through the gastrointestinal tract and the abdominal wall. We formulate an adaptive attenuation parameter as a function of permittivity, conductivity and the thickness of various layers between the transmitter and the receiver. The standard deviation of modelling error of the path loss using our adaptive channel model is smaller than 50% of that of existing channel models. We further analyse the sensitivity of the path loss model to the variations of thickness of different abdominal wall layers. We finally show that the thickness of the fat layer has the greatest influence on the total attenuation parameter of the path loss model and therefore, we modify our adaptive model accordingly.

Money currency availability in Bank Indonesia can be examined by inflow and outflow of money currency. The objective of this research is to forecast the inflow and outflow of money currency in each Representative Office (RO) of BI in East Java by using a hybrid exponential smoothing based on state space approach and calendar variation model. Hybrid model is expected to generate more accurate forecast. There are two studies that will be discussed in this research. The first studies about hybrid model using simulation data that contain pattern of trends, seasonal and calendar variation. The second studies about the application of a hybrid model for forecasting the inflow and outflow of money currency in each RO of BI in East Java. The first of results indicate that exponential smoothing model can not capture the pattern calendar variation. It results RMSE values 10 times standard deviation of error. The second of results indicate that hybrid model can capture the pattern of trends, seasonal and calendar variation. It results RMSE values approaching the standard deviation of error. In the applied study, the hybrid model give more accurate forecast for five variables : the inflow of money currency in Surabaya, Malang, Jember and outflow of money currency in Surabaya and Kediri. Otherwise, the time series regression model yields better for three variables : outflow of money currency in Malang, Jember and inflow of money currency in Kediri.

The traditional global template matching is time consuming, has low accuracy, and cannot be adapted to rotation and scale change. The template matching technique proposed in this study improves the time, accuracy and robustness for printed circuit boards (PCB). In order to shorten the image positioning time, the image preprocessing is implemented on PCB image and the image blocks are labeled to obtain the tagged image, and the feature vector is extracted and the marking point region image is selected. The feature vector with rotation change and scale change robustness is extracted from the tagged image after labeling in the PCB image by using artificial neural network, combined with image moments for training. The marking point region image in the PCB image is selected. The scale value of the marking point region image is estimated by parametric template vector matching. The deflection angle of marking point region image is calculated by Hough transform. The obtained scale value and deflection angle value are used for fast template matching to determine the marking point positioning. The three-dimensional (3D) parabolic curve fitting is implemented in marking point positioning and adjacent pixel position to reach the sub-pixel level accuracy. The experiment showed that the proposed template matching technique for the PCB image with or without noise or angle rotation, the average position accuracy error of each translated image is lower than 7 \(\upmu \)m, and the error standard deviation is lower than 5 \(\upmu \)m. The rotation angle error average and standard deviation of angular error of Hough transform are lower than 0.2\(^{\circ }\), more accurate than orientation code (OC) method. The scale value estimation, relative error average and error standard deviation are lower than 0.004 and 0.006 for the image with or without noise. The average complete positioning time of PCB image at resolution of \(2500\times 2500\) is only 0.55 s, which is better than the 3.97 s of traditional global template matching. The results prove that the template matching technique of this study not only has sub-pixel level high accuracy and short computing time, but also has the robustness of rotation change and scale change interference. It can implement rapid, efficient and accurate positioning.

TEStool: A visual interactive environment for modeling autocorrelated time series

In an event-related functional MRI data analysis, an accurate and robust extraction of the hemodynamic response function (HRF) and its associated statistics (e.g., magnitude, width, and time to peak) is critical to infer quantitative information about the relative timing of the neuronal events in different brain regions. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) to accurately estimate HRFs pertaining to each stimulus sequence across all voxels. MASM explicitly accounts for both spatial and temporal smoothness information, while incorporating such information to adaptively estimate HRFs in the frequency domain. One simulation study and a real data set are used to demonstrate the methodology and examine its finite sample performance in HRF estimation, which confirms that MASM significantly outperforms the existing methods including the smooth finite impulse response model, the inverse logit model and the canonical HRF.

Forecasting time series data is an integral component for management, planning and decision making. Following the Big Data trend, large amounts of time series data are available from many heterogeneous data sources in more and more applications domains. The highly dynamic and often fluctuating character of these domains in combination with the logistic problems of collecting such data from a variety of sources, imposes new challenges to forecasting. Traditional approaches heavily rely on extensive and complete historical data to build time series models and are thus no longer applicable if time series are short or, even more important, intermittent. In addition, large numbers of time series have to be forecasted on different aggregation levels with preferably low latency, while forecast accuracy should remain high. This is almost impossible, when keeping the traditional focus on creating one forecast model for each individual time series. In this paper we tackle these challenges by presenting a novel forecasting approach called cross-sectional forecasting. This method is especially designed for Big Data sets with a multitude of time series. Our approach breaks with existing concepts by creating only one model for a whole set of time series and requiring only a fraction of the available data to provide accurate forecasts. By utilizing available data from all time series of a data set, missing values can be compensated and accurate forecasting results can be calculated quickly on arbitrary aggregation levels.

A time series forecasting model—which is typically built on a single time series—is known as a local time series model (tsLM). In contrast, a forecasting model trained on multiple time series is referred to as a global time series model (tsGM). tsGMs can enhance forecasting accuracy and improve generalisation by learning cross-series information. As such, developing tsGMs has become a prominent research focus within the time series forecasting community. However, the benefits of tsGMs may not always be realised if the given set of time series is heterogeneous. While increasing model complexity can help tsGMs adapt to such a set of data, it can also increase the risk of overfitting and forecasting error. Additionally, the definition of homogeneity remains ambiguous in the literature. To address these challenges, this paper explores how to define data heterogeneity and proposes a two-stage modelling framework: At stage one, a tsGM is learnt to identify homogeneous patterns; and at stage two, tsLMs (e.g., ARIMA) or sub-tsGMs tailored to different groups are learnt to capture the heterogeneity. Numerical experiments on four open datasets demonstrate that the proposed approach significantly outperforms six state-of-the-art models. These results highlight its effectiveness in unlocking the full potential of global forecasting models for heterogeneous datasets.

Time series are an important type of data with applications in virtually every aspect of the real world. Often a large number of time series have to be monitored and analyzed in parallel. Sets of time series may show intrinsic hierarchical relationships and varying degrees of importance among the individual time series. Effective techniques for visually analyzing large sets of time series should encode the relative importance and hierarchical ordering of the time series data by size and position, and should also provide a high degree of regularity in order to support comparability by the analyst. In this paper, we present a framework for visualizing large sets of time series. Based on the notion of inter time series importance relationships, we define a set of objective functions that space-filling layout schemes for time series data should obey. We develop an efficient algorithm addressing the identified problems by generating layouts that reflect hierarchy and importance based relationships in a regular layout with favorable aspect ratios. We apply our technique to a number of real world data sets including sales and stock data, and we compare our technique with an aspect ratio aware variant of the well known TreeMap algorithm. The examples show the advantages and practical usefulness of our layout algorithm.

This work addresses the problem of energy consumption time series forecasting. In our approach, a set of time series containing energy consumption data is used to train a single, parameterised prediction model that can be used to predict future values for all the input time series. As a result, the proposed method is able to learn the common behaviour of all time series in the set (i.e., a fingerprint) and use this knowledge to perform the prediction task, and to explain this common behaviour as an algebraic formula. To that end, we use symbolic regression methods trained with both single- and multi-objective algorithms. Experimental results validate this approach to learn and model shared properties of different time series, which can then be used to obtain a generalised regression model encapsulating the global behaviour of different energy consumption time series.

Time series indexing plays an important role in querying and pattern mining of big data. This paper proposes a novel structure for tightly covering a given set of time series under the dynamic time warping similarity measurement. The structure, referred to as dynamic covering with cross-range constraints (DCRC), enables more efficient and scalable indexing to be developed than current hypercube-based partitioning approaches. In particular, a lower bound of the DTW distance from a given query time series to a DCRC-based cover set is introduced. By virtue of its tightness, which is proven theoretically, the lower bound can be used for pruning when querying on an indexing tree. If the DCRC-based lower bound (LB_DCRC) of an upper node in an index tree is larger than a given threshold, all child nodes can be pruned yielding a significant reduction in computational time. A hierarchical DCRC (HDCRC) structure is proposed to generate the DCRC-tree-based indexing and used to develop time series indexing and insertion algorithms. Experimental results for a selection of benchmark time series datasets are presented to illustrate the tightness of LB_DCRC, as well as the pruning efficiency on the DCRC-tree, especially when the time series have large deformations.