# Time-Parameterized Convolutional Neural Networks for Irregularly Sampled Time Series

arXiv: https://arxiv.org/abs/2308.03210 · HTML: https://mlsanity.com/paper/2308.03210/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 6 Aug 2023.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Scalable and accurate deep learning for electronic health records](https://mlsanity.com/paper/1801.07860/) (2018)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [Set Functions for Time Series](https://mlsanity.com/paper/1909.12064/) (2019)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [Attend and Diagnose: Clinical Time Series Analysis using Attention Models](https://mlsanity.com/paper/1711.03905/) (2017)
- [Phased LSTM: Accelerating Recurrent Network Training for Long or Event-based Sequences](https://mlsanity.com/paper/1610.09513/) (2016)
- [Interpolation-Prediction Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/1909.07782/) (2019)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [Self-attention with Functional Time Representation Learning](https://mlsanity.com/paper/1911.12864/) (2019)
- [Learning to Detect Sepsis with a Multitask Gaussian Process RNN Classifier](https://mlsanity.com/paper/1706.04152/) (2017)
- [Discrete Event, Continuous Time RNNs](https://mlsanity.com/paper/1710.04110/) (2017)

## Built on by (most cited first, 5 of 5)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [TimEHR: Image-based Time Series Generation for Electronic Health Records](https://mlsanity.com/paper/2402.06318/) (2024)
- [On the Power of Convolution Augmented Transformer](https://mlsanity.com/paper/2407.05591/) (2024)
- [TEE4EHR: Transformer Event Encoder for Better Representation Learning in Electronic Health Records](https://mlsanity.com/paper/2402.06367/) (2024)
- [Demystifying the Token Dynamics of Deep Selective State Space Models](https://mlsanity.com/paper/2410.03292/) (2024)

## Abstract (arXiv)

Irregularly sampled multivariate time series are ubiquitous in several application domains, leading to sparse, not fully-observed and non-aligned observations across different variables. Standard sequential neural network architectures, such as recurrent neural networks (RNNs) and convolutional neural networks (CNNs), consider regular spacing between observation times, posing significant challenges to irregular time series modeling. While most of the proposed architectures incorporate RNN variants to handle irregular time intervals, convolutional neural networks have not been adequately studied in the irregular sampling setting. In this paper, we parameterize convolutional layers by employing time-explicitly initialized kernels. Such general functions of time enhance the learning process of continuous-time hidden dynamics and can be efficiently incorporated into convolutional kernel weights. We, thus, propose the time-parameterized convolutional neural network (TPCNN), which shares similar properties with vanilla convolutions but is carefully designed for irregularly sampled time series. We evaluate TPCNN on both interpolation and classification tasks involving real-world irregularly sampled multivariate time series datasets. Our experimental results indicate the competitive performance of the proposed TPCNN model which is also significantly more efficient than other state-of-the-art methods. At the same time, the proposed architecture allows the interpretability of the input series by leveraging the combination of learnable time functions that improve the network performance in subsequent tasks and expedite the inaugural application of convolutions in this field.