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Time Series Imputation with Multivariate Radial Basis Function Neural Network

Chanyoung Jung, Yun Jang

TL;DR

This work addresses missing values in multivariate time series by introducing two neural-imputation frameworks that blend local covariance learning with temporal dynamics: MIM-RBFNN uses Gaussian radial basis functions to generate a continuous imputation function with shared centers across variables, and MIRNN-CF fuses this function with bidirectional recurrent dynamics to leverage temporal information.Key innovations include time-gap aware initialization of GRBF widths, residual-target augmentation to grow the RBF basis, and a BRITS-inspired hybrid loss that integrates continuous-function information with traditional RNN estimation paths.Empirical results show MIRNN-CF delivers substantial improvements on human-activity data (roughly 30–50% MAE gains over BRITS), while MIM-RBFNN excels in some scenarios but struggles with long-term missing data, especially on air-quality datasets; ablation studies on ETT data further demonstrate MIRNN-CF’s effectiveness for long-term missing values.Overall, the proposed approach advances multivariate time series imputation by combining smooth local approximations with temporal modeling, offering robustness across non-random and random missing patterns and providing a foundation for a unified model that jointly learns covariance structure and temporal dynamics.These methods have practical implications for domains requiring reliable imputation under irregular sampling and diverse missingness patterns, such as healthcare, environmental monitoring, and activity sensing.

Abstract

Researchers have been persistently working to address the issue of missing values in time series data. Numerous models have been proposed, striving to estimate the distribution of the data. The Radial Basis Functions Neural Network (RBFNN) has recently exhibited exceptional performance in estimating data distribution. In this paper, we propose a time series imputation model based on RBFNN. Our imputation model learns local information from timestamps to create a continuous function. Additionally, we incorporate time gaps to facilitate learning information considering the missing terms of missing values. We name this model the Missing Imputation Multivariate RBFNN (MIM-RBFNN). However, MIM-RBFNN relies on a local information-based learning approach, which presents difficulties in utilizing temporal information. Therefore, we propose an extension called the Missing Value Imputation Recurrent Neural Network with Continuous Function (MIRNN-CF) using the continuous function generated by MIM-RBFNN. We evaluate the performance using two real-world datasets with non-random missing and random missing patterns, and conduct an ablation study comparing MIM-RBFNN and MIRNN-CF.

Time Series Imputation with Multivariate Radial Basis Function Neural Network

TL;DR

This work addresses missing values in multivariate time series by introducing two neural-imputation frameworks that blend local covariance learning with temporal dynamics: MIM-RBFNN uses Gaussian radial basis functions to generate a continuous imputation function with shared centers across variables, and MIRNN-CF fuses this function with bidirectional recurrent dynamics to leverage temporal information.Key innovations include time-gap aware initialization of GRBF widths, residual-target augmentation to grow the RBF basis, and a BRITS-inspired hybrid loss that integrates continuous-function information with traditional RNN estimation paths.Empirical results show MIRNN-CF delivers substantial improvements on human-activity data (roughly 30–50% MAE gains over BRITS), while MIM-RBFNN excels in some scenarios but struggles with long-term missing data, especially on air-quality datasets; ablation studies on ETT data further demonstrate MIRNN-CF’s effectiveness for long-term missing values.Overall, the proposed approach advances multivariate time series imputation by combining smooth local approximations with temporal modeling, offering robustness across non-random and random missing patterns and providing a foundation for a unified model that jointly learns covariance structure and temporal dynamics.These methods have practical implications for domains requiring reliable imputation under irregular sampling and diverse missingness patterns, such as healthcare, environmental monitoring, and activity sensing.

Abstract

Researchers have been persistently working to address the issue of missing values in time series data. Numerous models have been proposed, striving to estimate the distribution of the data. The Radial Basis Functions Neural Network (RBFNN) has recently exhibited exceptional performance in estimating data distribution. In this paper, we propose a time series imputation model based on RBFNN. Our imputation model learns local information from timestamps to create a continuous function. Additionally, we incorporate time gaps to facilitate learning information considering the missing terms of missing values. We name this model the Missing Imputation Multivariate RBFNN (MIM-RBFNN). However, MIM-RBFNN relies on a local information-based learning approach, which presents difficulties in utilizing temporal information. Therefore, we propose an extension called the Missing Value Imputation Recurrent Neural Network with Continuous Function (MIRNN-CF) using the continuous function generated by MIM-RBFNN. We evaluate the performance using two real-world datasets with non-random missing and random missing patterns, and conduct an ablation study comparing MIM-RBFNN and MIRNN-CF.
Paper Structure (17 sections, 15 equations, 5 figures, 7 tables)

This paper contains 17 sections, 15 equations, 5 figures, 7 tables.

Table of Contents

  1. Related work
  2. RBF for missing value imputation of time series data
  3. Radial Basis Function (RBF) and Approximation
  4. Multivariate-RBFNN for Imputation
  5. Initial Parameters of GRBFs
  6. Temporal information With Recurrent Neural Network
  7. Bidirectional Recurrent with MIM-RBFNN
  8. MIRNN-CF Structure
  9. Evaluation
  10. Datasets and Baseline
  11. Results
  12. Ablation Study of MIRNN-CF
  13. Comparison of Single variate RBF and initial $\sigma$
  14. Conclusions
  15. Back Propagation Algorithm of MIM-RBFnn
  16. ...and 2 more sections

Figures (5)

  • Figure 1: MIM-RBFNN architecture. RBFNN$_i$ is the $i$-th RBFNN with $\varphi_{k(i)}$ as its $k$-th RBF.
  • Figure 2: MIRNN-CF architecture.
  • Figure 3: Comparison of continuous function
  • Figure 4: Comparison of continuous functions according to missing term
  • Figure 5: Comparison of continuous function learning process according to initial $\sigma$