# Tripletformer for Probabilistic Interpolation of Irregularly sampled Time Series

arXiv: https://arxiv.org/abs/2210.02091 · HTML: https://mlsanity.com/paper/2210.02091/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [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)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Multitask learning and benchmarking with clinical time series data](https://mlsanity.com/paper/1703.07771/) (2017)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Benchmarking Multivariate Time Series Classification Algorithms](https://mlsanity.com/paper/2007.13156/) (2020)
- [Set Functions for Time Series](https://mlsanity.com/paper/1909.12064/) (2019)
- [Interpolation-Prediction Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/1909.07782/) (2019)
- [Neural ODE Processes](https://mlsanity.com/paper/2103.12413/) (2021)
- [A scalable end-to-end Gaussian process adapter for irregularly sampled time series classification](https://mlsanity.com/paper/1606.04443/) (2016)
- [DCSF: Deep Convolutional Set Functions for Classification of Asynchronous Time Series](https://mlsanity.com/paper/2208.11374/) (2022)

## Built on by (most cited first, 6 of 6)

- [Forecasting Irregularly Sampled Time Series using Graphs](https://mlsanity.com/paper/2305.12932/) (2023)
- [No Imputation Needed: A Switch Approach to Irregularly Sampled Time Series](https://mlsanity.com/paper/2309.08698/) (2023)
- [Probabilistic Forecasting of Irregular Time Series via Conditional Flows](https://mlsanity.com/paper/2402.06293/) (2024)
- [Mixing It Up: Exploring Mixer Networks for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2502.11816/) (2025)
- [Probabilistic Circuits for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2604.27814/) (2026)
- [Marginalization Consistent Probabilistic Forecasting of Irregular Time Series via Mixture of Separable flows](https://mlsanity.com/paper/2406.07246/) (2024)

## Abstract (arXiv)

Irregularly sampled time series data with missing values is observed in many fields like healthcare, astronomy, and climate science. Interpolation of these types of time series is crucial for tasks such as root cause analysis and medical diagnosis, as well as for smoothing out irregular or noisy data. To address this challenge, we present a novel encoder-decoder architecture called "Tripletformer" for probabilistic interpolation of irregularly sampled time series with missing values. This attention-based model operates on sets of observations, where each element is composed of a triple of time, channel, and value. The encoder and decoder of the Tripletformer are designed with attention layers and fully connected layers, enabling the model to effectively process the presented set elements. We evaluate the Tripletformer against a range of baselines on multiple real-world and synthetic datasets and show that it produces more accurate and certain interpolations. Results indicate an improvement in negative loglikelihood error by up to 32% on real-world datasets and 85% on synthetic datasets when using the Tripletformer compared to the next best model.