arXiv subjects

David Pitt

Publications and source records attributed to David Pitt.

7 recordsLinked to original sources

arXiv2026

Dynamic Mortality Forecasting via Mixed-Frequency State-Space Models

High-frequency death counts are now widely available and contain timely information about intra-year mortality dynamics, but most stochastic mortality models are still estimated on annual data and therefore update only when annual totals are released. We propose a mixed-frequency state-space (MF--SS) extension of the Lee--Carter framework that jointly uses annual mortality rates and monthly death counts. The two series are linked through a shared latent monthly mortality factor, with the annual period factor defined as the intra-year average of the monthly factors. The latent monthly factor follows a seasonal ARIMA process, and parameters are estimated by maximum likelihood using an EM algorithm with Kalman filtering and smoothing. This setup enables real-time intra-year updates of the latent state and forecasts as new monthly observations arrive without re-estimating model parameters. Using U.S. data for ages 20--90 over 1999--2019, we evaluate intra-year annual nowcasts and one- to five-year-ahead forecasts. The MF--SS model produces both a direct annual forecast and an annual forecast implied by aggregating monthly projections. In our application, the aggregated monthly forecast is typically more accurate. Incorporating monthly information substantially improves intra-year annual nowcasts, especially after the first few months of the year. As a benchmark, we also fit separate annual and monthly Lee--Carter models and combine their forecasts using temporal reconciliation. Reconciliation improves these independent forecasts but adds little to MF--SS forecasts, consistent with MF--SS pooling information across frequencies during estimation. The MF--SS aggregated monthly forecasts generally outperform both unreconciled and temporally reconciled Lee--Carter forecasts and produce more cautious predictive intervals than the reconciled Lee--Carter approach.

econ.EM↗

arXiv2025

Optimising pandemic response through vaccination strategies using neural networks

Epidemic risk assessment poses inherent challenges, with traditional approaches often failing to balance health outcomes and economic constraints. This paper presents a data-driven decision support tool that models epidemiological dynamics and optimises vaccination strategies to control disease spread whilst minimising economic losses. The proposed economic-epidemiological framework comprises three phases: modelling, optimising, and analysing. First, a stochastic compartmental model captures epidemic dynamics. Second, an optimal control problem is formulated to derive vaccination strategies that minimise pandemic-related expenditure. Given the analytical intractability of epidemiological models, neural networks are employed to calibrate parameters and solve the high-dimensional control problem. The framework is demonstrated using COVID-19 data from Victoria, Australia, empirically deriving optimal vaccination strategies that simultaneously minimise disease incidence and governmental expenditure. By employing this three-phase framework, policymakers can adjust input values to reflect evolving transmission dynamics and continuously update strategies, thereby minimising aggregate costs, aiding future pandemic preparedness.

stat.AP↗

arXiv2025

Enabling Automatic Differentiation with Mollified Graph Neural Operators

Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these derivatives remains challenging, with spectral and finite difference methods introducing approximation errors due to finite resolution. Here, we propose the mollified graph neural operator ($m$GNO), the first method to leverage automatic differentiation and compute exact gradients on arbitrary geometries. This enhancement enables efficient training on irregular grids and varying geometries while allowing seamless evaluation of physics losses at randomly sampled points for improved generalization. For a PDE example on regular grids, $m$GNO paired with autograd reduced the L2 relative data error by 20x compared to finite differences, although training was slower. It can also solve PDEs on unstructured point clouds seamlessly, using physics losses only, at resolutions vastly lower than those needed for finite differences to be accurate enough. On these unstructured point clouds, $m$GNO leads to errors that are consistently 2 orders of magnitude lower than machine learning baselines (Meta-PDE, which accelerates PINNs) for comparable runtimes, and also delivers speedups from 1 to 3 orders of magnitude compared to the numerical solver for similar accuracy. $m$GNOs can also be used to solve inverse design and shape optimization problems on complex geometries.

cs.LG↗

arXiv2025

TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training

Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using tensor-parameterized layers to capture complex, multi-dimensional relationships. However, scaling neural operators to high-resolution problems leads to significant computational demands, making the training of industrial-scale models prohibitive. In this work, we introduce \textbf{TensorGRaD}, a novel method that directly addresses the memory challenges associated with optimizing large tensor-structured weights. Our approach, based on a \texit{robust tensor decomposition}, factorizes gradients as the sum of a low-rank tensor and a sparse one to efficiently capture information within optimizer states, including outliers. Additionally, we provide a recipe for mixed precision training of TensorGRaD, achieving further memory savings without sacrificing accuracy. We showcase the effectiveness of TensorGRaD on Fourier Neural Operators, a class of models crucial for solving partial differential equations (PDE). We provide theoretical guarantees for TensorGRaD, demonstrating its fundamental advantage over matrix-based gradient compression methods. We empirically demonstrate large improvements across various PDE tasks, including the challenging turbulent Navier-Stokes case at a Reynolds number of $10^5$. TensorGRaD reduces total memory usage by over $50\%$ while maintaining and sometimes even improving accuracy.

cs.LG↗

arXiv2024

A Library for Learning Neural Operators

We present NeuralOperator, an open-source Python library for operator learning. Neural operators generalize neural networks to maps between function spaces instead of finite-dimensional Euclidean spaces. They can be trained and inferenced on input and output functions given at various discretizations, satisfying a discretization convergence properties. Part of the official PyTorch Ecosystem, NeuralOperator provides all the tools for training and deploying neural operator models, as well as developing new ones, in a high-quality, tested, open-source package. It combines cutting-edge models and customizability with a gentle learning curve and simple user interface for newcomers.

cs.LG↗

arXiv2022

A comparative analysis of several multivariate zero-inflated and zero-modified models with applications in insurance

Claim frequency data in insurance records the number of claims on insurance policies during a finite period of time. Given that insurance companies operate with multiple lines of insurance business where the claim frequencies on different lines of business are often correlated, multivariate count modeling with dependence for claim frequency is therefore essential. Due in part to the operation of bonus-malus systems, claims data in automobile insurance are often characterized by an excess of common zeros. This feature is referred to as multivariate zero-inflation. In this paper, we establish two ways of dealing with this feature. The first is to use a multivariate zero-inflated model, where we artificially augment the probability of common zeros based on standard multivariate count distributions. The other is to apply a multivariate zero-modified model, which deals with the common zeros and the number of claims incurred in each line, given that at least one claim occurs separately. A comprehensive comparative analysis of several models under these two frameworks is conducted using the data of an automobile insurance portfolio from a major insurance company in Spain. A less common situation in insurance is the absence of some common zeros resulting from incomplete records. This feature of these data is known as multivariate zero-deflation. In this case, our proposed multivariate zero-modified model still works, as shown by the second empirical study.

stat.AP↗

arXiv2021

A model sufficiency test using permutation entropy

Using the ordinal pattern concept in permutation entropy, we propose a model sufficiency test to study a given model's point prediction accuracy. Compared to some classical model sufficiency tests, such as the Broock et al.'s (1996) test, our proposal does not require a sufficient model to eliminate all structures exhibited in the estimated residuals. When the innovations in the investigated data's underlying dynamics show a certain structure, such as higher-moment serial dependence, the Broock et al.'s (1996) test can lead to erroneous conclusions about the sufficiency of point predictors. Due to the structured innovations, inconsistency between the model sufficiency tests and prediction accuracy criteria can occur. Our proposal fills in this incoherence between model and prediction evaluation approaches and remains valid when the underlying process has non-white additive innovation.

stat.ME↗