Rethinking Irregular Time Series Forecasting from the Perspective of Basis Functions

Rongwen Li; Changjian Chen

cs.LGAug 18, 2026

Rethinking Irregular Time Series Forecasting from the Perspective of Basis Functions

Authors: Rongwen Li, Changjian Chen

Organizations: College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan, China.

Abstract

Irregular time series forecasting is crucial in many domains, such as healthcare and meteorological observation. However, due to the inherent characteristics of irregular time series, including sparse observations and non-uniform sampling, accurately predicting future dynamics remains challenging. In light of these two characteristics, many existing methods aggregate irregular observations into fixed-dimensional estimated response coefficients through predefined basis functions and use these coefficients as sequence representations. Nevertheless, this modeling paradigm still suffers from two key limitations: (i) a potential non-vanishing asymptotic bias caused by ignoring the sampling density of timestamps; and (ii) the limited adaptability of predefined basis functions to diverse temporal patterns. In this study, we propose a Debiased Neural Basis-Function Network (DNBNet) to address these challenges. Its core is a debiased neural basis-function response mechanism, which corrects asymptotic bias through importance sampling while parameterizing basis functions with neural networks to adapt to diverse temporal patterns. In addition, considering the sparsity of irregular data, we design a novel multi-scale decomposition module based on average pooling, together with a mass-aware fusion mechanism, to obtain richer representations. Finally, a dual-branch decoder is employed for forecasting. Extensive experiments on multiple real-world datasets demonstrate the effectiveness of DNBNet and its strong generalizability across diverse irregular time series scenarios. Our code can be obtained at https://github.com/hnu-vis/DNBNet.

Figures & tables

Basis Type	Formulation	Shape	Related Work
RBF basis function	$\displaystyle\exp\!\left(-\frac{(t-c_{k})^{2}}{2\sigma_{k}^{2}}\right)$		( Zhou et al., 2026 )
Fourier basis function	$\displaystyle\begin{aligned} &\cos(2\pi\omega_{k}t),\\ &\sin(2\pi\omega_{k}t)\end{aligned}$		( Fons et al., 2025 ; Qiu et al., 2026 )
Attention basis function	$\displaystyle\frac{\exp(c_{k}Q^{\top}Kt)}{\sqrt{d}}$		( Shukla and Marlin, 2021 ; Lee et al., 2026 )
Soft-window basis function	$\displaystyle\sigma\!\left(\frac{t_{k}^{\mathrm{right}}-t}{\operatorname{softplus}(\delta)}\right)\cdot\sigma\!\left(\frac{t-t_{k}^{\mathrm{left}}}{\operatorname{softplus}(\delta)}\right)$		( Liu et al., 2026 )

Table 1: Comparison of the types of predefined basis functions adopted by different methods, including their specific mathematical forms and function curves, reflecting their distinct modeling assumptions and interpretations of the temporal dynamics in the data.

Figure 1: (a) The overall pipeline of DNBNet. (b) The debiased neural basis-function response computes debiased coefficients and basis masses using KDE and learnable basis functions. (c) The basis mass-aware fusion module aggregates coefficients from different scales. (d) The final prediction is obtained by combining the feature decoder with basis-function reconstruction.

Method	USHCN	Human Activity	Student Life	PhysioNet	MIMIC
PrimeNet	$0.7328\pm 0.0000$	$4.2564\pm 0.0007$	$0.8799\pm 0.0001$	$0.7952\pm 0.0000$	$0.9728\pm 0.0001$
SeFT	$0.6647\pm 0.0008$	$1.3750\pm 0.0036$	$0.8747\pm 0.0026$	$0.7801\pm 0.0026$	$0.9905\pm 0.0003$
mTAN	$0.4197\pm 0.0161$	$0.1017\pm 0.0049$	$0.6555\pm 0.0064$	$0.3787\pm 0.0057$	$0.9719\pm 0.0169$
CRU	$0.5179\pm 0.0113$	$0.1452\pm 0.0009$	$0.7487\pm 0.0055$	$0.6169\pm 0.0036$	$0.7370\pm 0.0059$
GNeuralFlow	$0.4971\pm 0.0093$	$0.2550\pm 0.0373$	$0.7168\pm 0.0422$	$0.3516\pm 0.0028$	$0.6631\pm 0.0112$
Raindrop	$0.4841\pm 0.0064$	$0.0939\pm 0.0017$	$0.6672\pm 0.0054$	$0.3491\pm 0.0015$	$0.6219\pm 0.0040$

Table 2: MSE results of DNBNet and baselines on five irregular time-series datasets. Best results are in bold and second-best results are underlined.

Panel of Figure 2 — Figure 2: Parameter sensitivity study of number of basis functions $K$ and Scales $S$ on three datasets.

Panel of Figure 3 — Figure 3: Visualization of the four learned basis functions with the largest basis function mass on two datasets.

Figure 4: Model efficiency comparison with six competitive baselines on MIMIC dataset.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	# Variables	# samples	Avg # Obs.	Max Length
PhysioNet	36	11,981	308.6	47
MIMIC	96	21,250	144.6	96
HumanActivity	12	1,359	362.2	131
StudentLife	9	20	7,680.5	1,370
USHCN	5	1,114	313.5	337

Appendix

Table 5: Dataset statistics.

Method	USHCN	Human Activity	Student Life	PhysioNet	MIMIC
PrimeNet	$0.5094\pm 0.0002$	$1.7054\pm 0.0005$	$0.7231\pm 0.0001$	$0.6859\pm 0.0000$	$0.6632\pm 0.0001$
SeFT	$0.4981\pm 0.0021$	$0.9733\pm 0.0006$	$0.7201\pm 0.0022$	$0.6766\pm 0.0005$	$0.6689\pm 0.0008$
mTAN	$0.3412\pm 0.0076$	$0.2302\pm 0.0071$	$0.5742\pm 0.0033$	$0.4271\pm 0.0041$	$0.6749\pm 0.0023$
CRU	$0.3948\pm 0.0069$	$0.2673\pm 0.0026$	$0.6403\pm 0.0043$	$0.5782\pm 0.0040$	$0.5828\pm 0.0046$
GNeuralFlow	$0.3842\pm 0.0024$	$0.3802\pm 0.0217$	$0.6085\pm 0.0163$	$0.4012\pm 0.0009$	$0.5336\pm 0.0058$
Raindrop	$0.3515\pm 0.0070$	$0.2159\pm 0.0027$	$0.5816\pm 0.0072$	$0.4057\pm 0.0006$	$0.5047\pm 0.0035$

Appendix

Table 6: MAE results of DNBNet and baselines on five irregular time-series datasets. Best results are in bold and second-best results are underlined.

MSE
Variant	USHCN	Human Activity	Student Life	PhysioNet	MIMIC
w/o $p(t)$	$0.4449\pm 0.0291$	$0.0564\pm 0.0000$	$0.6291\pm 0.0004$	$0.3161\pm 0.0003$	$0.4485\pm 0.0012$
Rep. RBF	$0.4144\pm 0.0091$	$0.0568\pm 0.0002$	$0.6242\pm 0.0007$	$0.3231\pm 0.0007$	$0.4507\pm 0.0009$
Rep. Fourier	$0.4101\pm 0.0088$	$0.0562\pm 0.0001$	$0.6257\pm 0.0009$	$0.3267\pm 0.0002$	$0.4869\pm 0.0048$
w/o AvgPool	$0.4195\pm 0.0166$	$0.0569\pm 0.0001$	$0.6269\pm 0.0004$	$0.3119\pm 0.0006$	$0.4494\pm 0.0012$
w/o BasDec	$0.4552\pm 0.0424$	$0.0559\pm 0.0002$	$0.6281\pm 0.0011$	$0.3092\pm 0.0002$	$0.4613\pm 0.0023$

Appendix

Table 7: Complete ablation study of DNBNet on five irregular time-series datasets. Best results are highlighted in bold .

MSE
Method	USHCN	Human Activity	Student Life	PhysioNet	MIMIC
GraFTi	$0.2089{\pm}0.0218$	$0.0431{\pm}0.0006$	$0.5789{\pm}0.0018$	$\mathbf{0.3553{\pm}0.0016}$	$0.4957{\pm}0.0032$
Warpformer	$0.1738{\pm}0.0069$	$0.0446{\pm}0.0013$	$0.5861{\pm}0.0032$	$0.3558{\pm}0.0016$	$0.5295{\pm}0.0035$
Hi-Patch	$0.2416{\pm}0.0205$	$0.0472{\pm}0.0001$	$0.5902{\pm}0.0020$	$0.3666{\pm}0.0001$	$0.5352{\pm}0.0062$
KAFNet	$0.2045{\pm}0.0091$	$0.0677{\pm}0.0006$	$0.5980{\pm}0.0024$	$0.3647{\pm}0.0010$	$0.5145{\pm}0.0076$
APN	$0.1816{\pm}0.0133$	$0.0436{\pm}0.0004$	$0.6057{\pm}0.0140$	$0.3689{\pm}0.0026$	$0.5396{\pm}0.0053$

Appendix

Table 8: Experimental results on five irregular multivariate time-series datasets evaluated by MSE and MAE. The look-back lengths follow Table 2, and the prediction horizons are set to the remaining length of each sequence: 12 hours for MIMIC-III and PhysioNet, 300 milliseconds for Human Activity, the next 3 observations for USHCN, and 10 days for Student Life.

Figure 5: Forecasting performance with varying lookback lengths and fixed forecast horizons.

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