Real time prediction of irregular periodic time series data

Abstract

By means of a novel time-dependent cumulated variation penalty function, a new class of real-time prediction methods is developed to improve the prediction accuracy of time series exhibiting irregular periodic patterns: in particular, the breathing motion data of the patients during robotic radiation therapy. It is illustrated that for both simulated and empirical data involving changes in mean, trend, and amplitude, the proposed methods outperform existing forecasting methods based on support vector machines and artificial neural network in terms of prediction accuracy. Moreover, the proposed methods are designed so that real-time updates can be done efficiently with O(1) computational complexity upon the arrival of a new signal without scanning the old data repeatedly.

Inferring serial correlation with dynamic backgrounds

“…There are two closely related recent works: Xu [2008] used polynomials to approximate the dynamic background, and Zhang et al [2020] developed an online forecasting algorithm based on least square estimation with 2 variable fusion constraint. These works do not explicitly consider highly unstructured backgrounds.…”

“…Experiment 3. We compare our method with the method in Zhang et al [2020]. In the following, we refer to their method as the " 2 variant," since it is obtained by solving the convex program with same objective function as (2) except for a different constraint:…”

“…Again, δ ≥ 0 is the tuning parameter. We should mention Zhang et al [2020] did not have a systematic way to tune δ and here we enhance their method by adding our statistical test based hyperparameter tuning as well.…”

“…w D T j a K P M 2 x C 8 5 Z N X Q a N c 8 i 5 L 5 b u r Y s V d x J E j p + S M X B C P X J M K u S U 1 U i e c P J J n 8 k r e n C f n x X l 3 P u a t a 8 5 i 5 o T 8 K e f z B 2 o b n / k = < / l a t e x i t > Figure 6: Comparison of proposed method and the 2 variant in Zhang et al [2020]. We investigated two cases.…”

“…Our piecewise constant fitted background better captures the dynamics in Case 1, whereas the 2 variant can better approximate the dynamics in Case 2. region. The 2 variant yields a biased estimate for α 1 , which is probably the reason that Zhang et al [2020] focus on relatively smooth and structured dynamics.…”