# Probabilistic Learning of Multivariate Time Series with Temporal Irregularity

arXiv: https://arxiv.org/abs/2306.09147 · HTML: https://mlsanity.com/paper/2306.09147/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 61 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [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)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [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)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)
- [A Survey on Principles, Models and Methods for Learning from Irregularly Sampled Time Series](https://mlsanity.com/paper/2012.00168/) (2020)
- [Deep Air Quality Forecasting Using Hybrid Deep Learning Framework](https://mlsanity.com/paper/1812.04783/) (2018)

## Abstract (arXiv)

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time series often suffer from temporal irregularities, including nonuniform intervals and misaligned variables, which pose significant challenges for accurate forecasting. To address these challenges, we propose an end-to-end framework that models temporal irregularities while capturing the joint distribution of variables at arbitrary continuous-time points. Specifically, we introduce a dynamic conditional continuous normalizing flow to model data distributions in a non-parametric manner, accommodating the complex, non-Gaussian characteristics commonly found in real-world datasets. Then, by leveraging a carefully factorized log-likelihood objective, our approach captures both temporal and cross-sectional dependencies efficiently. Extensive experiments on a range of real-world datasets demonstrate the superiority and adaptability of our method compared to existing approaches.