# Aligned Multi-Task Gaussian Process

arXiv: https://arxiv.org/abs/2110.15761 · HTML: https://mlsanity.com/paper/2110.15761/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Probabilistic ODE Solvers with Runge-Kutta Means](https://mlsanity.com/paper/1406.2582/) (2014)
- [Efficient Modeling of Latent Information in Supervised Learning using Gaussian Processes](https://mlsanity.com/paper/1705.09862/) (2017)
- [Deep learning with differential Gaussian process flows](https://mlsanity.com/paper/1810.04066/) (2018)
- [Multi-resolution Multi-task Gaussian Processes](https://mlsanity.com/paper/1906.08344/) (2019)
- [Bayesian Monotone Regression using Gaussian Process Projection](https://mlsanity.com/paper/1306.4041/) (2013)
- [Gaussian Process Latent Variable Alignment Learning](https://mlsanity.com/paper/1803.02603/) (2018)
- [Monotonic Gaussian Process Flow](https://mlsanity.com/paper/1905.12930/) (2019)
- [Gaussian Process Modulated Cox Processes under Linear Inequality Constraints](https://mlsanity.com/paper/1902.10974/) (2019)
- [Bayesian Alignments of Warped Multi-Output Gaussian Processes](https://mlsanity.com/paper/1710.02766/) (2017)
- [Non-linear Multitask Learning with Deep Gaussian Processes](https://mlsanity.com/paper/1905.12407/) (2019)
- [Sequence Alignment with Dirichlet Process Mixtures](https://mlsanity.com/paper/1811.10689/) (2018)

## Built on by (most cited first, 1 of 1)

- [Bayesian Nonparametric Dynamical Clustering of Time Series](https://mlsanity.com/paper/2510.06919/) (2025)

## Abstract (arXiv)

Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in correlation estimation will result in poor predictive performance and uncertainty quantification. We introduce a method that automatically accounts for temporal misalignment in a unified generative model that improves predictive performance. Our method uses Gaussian processes (GPs) to model the correlations both within and between the tasks. Building on the previous work by Kazlauskaiteet al. [2019], we include a separate monotonic warp of the input data to model temporal misalignment. In contrast to previous work, we formulate a lower bound that accounts for uncertainty in both the estimates of the warping process and the underlying functions. Also, our new take on a monotonic stochastic process, with efficient path-wise sampling for the warp functions, allows us to perform full Bayesian inference in the model rather than MAP estimates. Missing data experiments, on synthetic and real time-series, demonstrate the advantages of accounting for misalignments (vs standard unaligned method) as well as modelling the uncertainty in the warping process(vs baseline MAP alignment approach).