# Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference

arXiv: https://arxiv.org/abs/2307.00032 · HTML: https://mlsanity.com/paper/2307.00032/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 83 references that are in the map.
- First posted on arXiv 30 Jun 2023.

## Builds on (most cited first, 23 of 23)

- [Probabilistic Numerics and Uncertainty in Computations](https://mlsanity.com/paper/1506.01326/) (2015)
- [Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems](https://mlsanity.com/paper/2011.10616/) (2020)
- [Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs](https://mlsanity.com/paper/1804.04378/) (2018)
- [ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systems](https://mlsanity.com/paper/1902.06278/) (2019)
- [Analysis and Control of Epidemics: A survey of spreading processes on complex networks](https://mlsanity.com/paper/1505.00768/) (2015)
- [Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems](https://mlsanity.com/paper/2002.09301/) (2020)
- [Scalable Variational Inference for Dynamical Systems](https://mlsanity.com/paper/1705.07079/) (2017)
- [Fenrir: Physics-Enhanced Regression for Initial Value Problems](https://mlsanity.com/paper/2202.01287/) (2022)
- [Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems](https://mlsanity.com/paper/1905.12090/) (2019)
- [Reproducing kernel Hilbert space based estimation of systems of ordinary differential equations](https://mlsanity.com/paper/1311.3576/) (2013)
- [Laplace based approximate posterior inference for differential equation models](https://mlsanity.com/paper/1607.07203/) (2016)
- [Implicit Probabilistic Integrators for ODEs](https://mlsanity.com/paper/1805.07970/) (2018)
- [Scenario Reduction Revisited: Fundamental Limits and Guarantees](https://mlsanity.com/paper/1701.04072/) (2017)
- [Robust and optimal predictive control of the COVID-19 outbreak](https://mlsanity.com/paper/2005.03580/) (2020)
- [Optimal Vaccine Allocation to Control Epidemic Outbreaks in Arbitrary Networks](https://mlsanity.com/paper/1303.3984/) (2013)
- [Optimal Resource and Demand Redistribution for Healthcare Systems Under Stress from COVID-19](https://mlsanity.com/paper/2011.03528/) (2020)
- [Data-Driven Control of the COVID-19 Outbreak via Non-Pharmaceutical Interventions: A Geometric Programming Approach](https://mlsanity.com/paper/2011.01392/) (2020)
- [Optimal adaptive testing for epidemic control: combining molecular and serology tests](https://mlsanity.com/paper/2101.00773/) (2021)
- [Stochastic Optimization for Vaccine and Testing Kit Allocation for the COVID-19 Pandemic](https://mlsanity.com/paper/2101.01204/) (2021)
- [A Multi-Stage Stochastic Programming Approach to Epidemic Resource Allocation with Equity Considerations](https://mlsanity.com/paper/2102.11814/) (2021)
- [Minimizing the Risk of Spreading Processes via Surveillance Schedules and Sparse Control](https://mlsanity.com/paper/2107.05878/) (2021)
- [Multi-Stage Sparse Resource Allocation for Control of Spreading Processes over Networks](https://mlsanity.com/paper/2110.07755/) (2021)
- [Lockdown interventions in SIR model: Is the reproduction number the right control variable?](https://mlsanity.com/paper/2112.06546/) (2021)

## Abstract (arXiv)

We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.