Narrow Results

Partially linear additive models (PLAMs) have attracted much attention in the statistical machine learning community due to their interpretability and flexibility in data-driven prediction and inference. Since the performance of PLAMs is closely related to the structure information of linear and nonlinear components, several approaches have been proposed for regression estimation and data-driven structure discovery. However, the existing automatic discovery strategy is limited to the mean regression framework and is usually sensitive to non-Gaussian noises, e.g. skewed noise and heavy-tailed noise. To further improve the robustness of PLAMs, this paper proposes a Robust Partially Linear Trend Filtering (RPLTF) for regression estimation and structure discovery by integrating the mode-induced error metric and the trend filtering-based nonlinear approximation into regularized PLAMs. Besides the computing algorithm of RPLTF, we establish its upper bound on generalization error in theory. Empirical examples are provided to validate the effectiveness of the proposed method.

Considering the problem of extracting a trend from a time series, we propose a novel approach based on empirical mode decomposition (EMD), called EMD trend filtering. The rationale is that EMD is a completely data-driven technique, which offers the possibility of estimating a trend of arbitrary shape as a sum of low-frequency intrinsic mode functions produced by the EMD. Based on an empirical analysis of EMD, an automatic procedure is proposed to select the requisite intrinsic mode functions. The performance of the EMD trend filtering is evaluated on simulated time series containing different forms of trends. Comparing furthermore to two existing techniques (ℓ₁-trend filtering and Hodrick–Prescott filtering), we observe that the EMD trend filtering performs very similarly, while it does not require assumptions on the form of the trend and it is free from estimation parameters. We also illustrate the performance of the technique on the S&P 500 index, as an example of real-world time series.