Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference

• URL: http://arxiv.org/abs/2307.00032v1
• Date: Fri, 30 Jun 2023 03:49:52 GMT
• Title: Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference
• Abstract summary: We develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel optimization problem formulation. Our experiments indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%.
• Score: 4.7464518249313805
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Robust Counterfactual Policy Optimisation via Nondeterministic Causal Models [6.0927303009220735]
  We formalise counterfactual policy optimisation under probabilistic causal models.<n>We propose a first practical problem for identifying robust counterfactual policies under a sensitivity analysis framework.<n>We validate our approach on a sepsis treatment simulator, where diabetes status acts as a hidden global confounder.
  arXiv  Detail & Related papers  (2026-08-03T21:21:22Z)
• Deep Optimal Individualized Treatment Rules for Bivariate Survival Outcomes via Adaptive Prediction-Powered Learning [3.890091933986142]
  This paper addresses the problem of deriving optimal individualized treatment rules to maximize the joint survival probability beyond fixed time points.<n>We propose a novel approach that models treatment rules via policies, coupling marginal accelerated failure time models via link function.<n>To enhance robustness and effectiveness of decision making, we introduce an adaptive prediction-powered method that leverages auxiliary predictions from machine learning models.
  arXiv  Detail & Related papers  (2026-05-28T06:56:52Z)
• Robust Spatiotemporal Epidemic Modeling with Integrated Adaptive Outlier Detection [7.5504472850103435]
  In epidemic modeling, outliers can distort parameter estimation and lead to misguided public health decisions.<n>We introduce a robust generalized additive model (RST-GAM) to mitigate this distortion.<n>We demonstrate the practical utility of RST-GAM by analyzing county-level COVID-19 infection data in the United States.
  arXiv  Detail & Related papers  (2025-07-12T19:23:25Z)
• Learning from Samples: Inverse Problems over measures via Sharpened Fenchel-Young Losses [20.246040671823557]
  We introduce a new class of loss functions, called sharpened Fenchel-Young losses, which measure the sub-optimality gap of the optimization problem over the space of probability measures.<n>We provide explicit stability guarantees for two relevant settings in the context of optimal transport.<n>We present optimization algorithms specifically tailored to efficiently solve iUOT and iJKO problems.
  arXiv  Detail & Related papers  (2025-05-11T21:26:44Z)
• A local squared Wasserstein-2 method for efficient reconstruction of models with uncertainty [0.0]
  We propose a local squared Wasserstein-2 (W_2) method to solve the inverse problem of reconstructing models with uncertain latent variables or parameters. A key advantage of our approach is that it does not require prior information on the distribution of the latent variables or parameters in the underlying models.
  arXiv  Detail & Related papers  (2024-06-10T22:15:55Z)
• Unified Uncertainty Estimation for Cognitive Diagnosis Models [70.46998436898205]
  We propose a unified uncertainty estimation approach for a wide range of cognitive diagnosis models. We decompose the uncertainty of diagnostic parameters into data aspect and model aspect. Our method is effective and can provide useful insights into the uncertainty of cognitive diagnosis.
  arXiv  Detail & Related papers  (2024-03-09T13:48:20Z)
• Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints [55.39203337683045]
  We propose to perform optimization within the data manifold using diffusion models.<n>Depending on the differentiability of the objective function, we propose two different sampling methods.<n>Our method achieves better or comparable performance with previous state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-02-28T03:09:12Z)
• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificity [24.874664446700272]
  This paper studies a new framework that unifies the three approaches and that addresses the two challenges mentioned above. The properties (e.g., consistency and normalities), non-asymptotic properties (e.g., unbiasedness and error bound), and a Monte-Carlo-based solution method of the proposed model are studied.
  arXiv  Detail & Related papers  (2023-01-31T11:33:18Z)
• Deep Learning Aided Laplace Based Bayesian Inference for Epidemiological Systems [2.596903831934905]
  We propose a hybrid approach where Laplace-based Bayesian inference is combined with an ANN architecture for obtaining approximations to the ODE trajectories. The effectiveness of our proposed methods is demonstrated using an epidemiological system with non-analytical solutions, the Susceptible-Infectious-Removed (SIR) model for infectious diseases.
  arXiv  Detail & Related papers  (2022-10-17T09:02:41Z)
• Integrated Conditional Estimation-Optimization [6.037383467521294]
  Many real-world optimization problems uncertain parameters with probability can be estimated using contextual feature information. In contrast to the standard approach of estimating the distribution of uncertain parameters, we propose an integrated conditional estimation approach. We show that our ICEO approach is theally consistent under moderate conditions.
  arXiv  Detail & Related papers  (2021-10-24T04:49:35Z)
• BayesIMP: Uncertainty Quantification for Causal Data Fusion [52.184885680729224]
  We study the causal data fusion problem, where datasets pertaining to multiple causal graphs are combined to estimate the average treatment effect of a target variable. We introduce a framework which combines ideas from probabilistic integration and kernel mean embeddings to represent interventional distributions in the reproducing kernel Hilbert space.
  arXiv  Detail & Related papers  (2021-06-07T10:14:18Z)
• Learning MDPs from Features: Predict-Then-Optimize for Sequential Decision Problems by Reinforcement Learning [52.74071439183113]
  We study the predict-then-optimize framework in the context of sequential decision problems (formulated as MDPs) solved via reinforcement learning. Two significant computational challenges arise in applying decision-focused learning to MDPs.
  arXiv  Detail & Related papers  (2021-06-06T23:53:31Z)
• Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems [1.6709415233613623]
  This paper proposes a novel approach to construct data-driven online solutions to optimization problems (P) subject to a class of distributionally uncertain dynamical systems. The introduced framework allows for the simultaneous learning of distributional system uncertainty via a parameterized, control-dependent ambiguity set. We also introduce an online version of Nesterov's accelerated-gradient algorithm, and analyze its performance to solve this class of problems via dissipativity theory.
  arXiv  Detail & Related papers  (2021-02-18T01:49:06Z)
• An Optimal Control Approach to Learning in SIDARTHE Epidemic model [67.22168759751541]
  We propose a general approach for learning time-variant parameters of dynamic compartmental models from epidemic data. We forecast the epidemic evolution in Italy and France.
  arXiv  Detail & Related papers  (2020-10-28T10:58:59Z)
• The Risks of Invariant Risk Minimization [52.7137956951533]
  Invariant Risk Minimization is an objective based on the idea for learning deep, invariant features of data. We present the first analysis of classification under the IRM objective--as well as these recently proposed alternatives--under a fairly natural and general model. We show that IRM can fail catastrophically unless the test data are sufficiently similar to the training distribution--this is precisely the issue that it was intended to solve.
  arXiv  Detail & Related papers  (2020-10-12T14:54:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.