# Time-Varying Transition Matrices with Multi-task Gaussian Processes

arXiv: https://arxiv.org/abs/2306.11772 · HTML: https://mlsanity.com/paper/2306.11772/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Product Kernel Interpolation for Scalable Gaussian Processes](https://mlsanity.com/paper/1802.08903/) (2018)
- [Nonnegativity-Enforced Gaussian Process Regression](https://mlsanity.com/paper/2004.04632/) (2020)
- [Incorporating Sum Constraints into Multitask Gaussian Processes](https://mlsanity.com/paper/2202.01793/) (2022)

## Abstract (arXiv)

In this paper, we present a kernel-based, multi-task Gaussian Process (GP) model for approximating the underlying function of an individual's mobility state using a time-inhomogeneous Markov Process with two states: moves and pauses. Our approach accounts for the correlations between the transition probabilities by creating a covariance matrix over the tasks. We also introduce time-variability by assuming that an individual's transition probabilities vary over time in response to exogenous variables. We enforce the stochasticity and non-negativity constraints of probabilities in a Markov process through the incorporation of a set of constraint points in the GP. We also discuss opportunities to speed up GP estimation and inference in this context by exploiting Toeplitz and Kronecker product structures. Our numerical experiments demonstrate the ability of our formulation to enforce the desired constraints while learning the functional form of transition probabilities.