Predicting the Unpredictable: New Approach to Insurance Claim Forecasting

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Author: Denis Avetisyan

Researchers have developed a novel strategy for generating reliably accurate prediction intervals for future insurance claims, even with limited data.

This work introduces a transformation-based method for achieving finite-sample valid prediction in regression settings, leveraging conformal prediction techniques within an unsupervised i.i.d. framework.

Despite advancements in predictive modeling, obtaining reliably valid prediction intervals for future insurance claims in regression settings remains a significant challenge. This paper, ‘A new strategy for finite-sample valid prediction of future insurance claims in the regression setting’, addresses this gap by introducing a novel strategy that transforms prediction in the unsupervised iid setting to achieve finite-sample validity in the regression context. The proposed method enables the construction of infinitely many valid prediction intervals, leveraging existing unsupervised techniques. Could this transformation offer a broadly applicable framework for enhancing predictive accuracy and reliability across various regression problems?

Deconstructing the Oracle: The Illusion of Prediction

At the heart of actuarial science lies the imperative of accurate prediction, a necessity most visibly demonstrated in insurance claim forecasting. The financial stability of insurance companies, and ultimately their ability to fulfill promises to policyholders, depends on a robust understanding of future claim frequencies and severities. These predictions aren’t simply estimations; they directly influence premium calculations, reserve setting, and risk management strategies. A slight miscalculation can lead to substantial financial losses, while precise forecasting allows for competitive pricing and sustained profitability. Consequently, considerable effort is devoted to developing and refining predictive models, with ongoing research seeking to minimize uncertainty and improve the reliability of these critical assessments. The pursuit of predictive accuracy isn’t merely a statistical exercise, but a fundamental pillar supporting the entire insurance ecosystem.

Actuarial forecasting commonly relies on two distinct approaches to estimate future events, particularly insurance claims. An unsupervised method analyzes past claim data alone, seeking patterns and trends within the historical record to project future frequencies and severities. Alternatively, a regression setting incorporates additional predictor variables – such as policyholder demographics, economic indicators, or even seasonal effects – to refine these predictions. While both techniques are valuable, they represent fundamentally different statistical frameworks; the unsupervised approach makes predictions solely from the observed claim history, whereas regression leverages external information to improve accuracy and potentially capture relationships missed by a purely historical analysis. The choice between these methods, or the possibility of combining them, significantly impacts the reliability and precision of actuarial forecasts.

The pursuit of accurate insurance claim forecasting encounters a notable statistical hurdle when attempting to integrate external information with historical data. While prediction is often approached through either purely data-driven unsupervised methods or regression models utilizing predictor variables, effectively combining these approaches remains difficult. Current statistical literature struggles to provide reliable prediction intervals – those that hold true even with limited data – specifically within the regression setting when incorporating additional variables. This absence of readily available, finite-sample valid intervals hinders the ability to confidently assess the uncertainty surrounding predictions, limiting the practical application of more sophisticated modeling techniques and potentially impacting crucial financial risk assessments within the actuarial field.

Reversing the Model: From Observation to Control

A novel strategy is proposed to adapt predictive methods originally developed for unsupervised, independent and identically distributed (IID) data to the regression setting. This involves modifying existing algorithms – typically designed to identify underlying data structure without labeled outcomes – to predict a dependent variable given a set of predictor variables. The core of this approach focuses on bridging the distributional gap between the unsupervised and regression contexts, enabling the reuse of established unsupervised techniques for supervised prediction tasks without requiring complete retraining or algorithm redesign. This conversion allows for the application of a wider range of predictive tools to problems where labeled data is available, potentially improving performance and efficiency.

The conversion from an unsupervised to a regression setting necessitates data transformations designed to equate the distributions of input features and output variables across both settings. Specifically, this involves techniques such as standardization or normalization of feature spaces to achieve comparable scales, and potentially, transformations of the outcome variable to match the distributional characteristics of the unsupervised prediction targets. These transformations address the inherent differences in data structure – unsupervised learning typically deals with data lacking labeled outcomes, while regression requires a clearly defined relationship between predictors and a continuous outcome – thereby creating a compatible data landscape for applying the initially unsupervised predictive method to a regression task. The precise transformation functions employed are determined by the specific characteristics of the datasets in both settings, with the goal of minimizing distributional divergence and maximizing the transferability of the predictive model.

The application of data transformations to convert an unsupervised model to a regression framework is intended to improve both predictive accuracy and the reliability of resulting predictions when predictor variables are present. This approach facilitates the construction of prediction intervals that are demonstrably finite-sample valid; that is, the coverage probability of these intervals can be statistically guaranteed within a defined sample size. The ability to generate an infinite number of such valid prediction intervals stems from the transformed data allowing the unsupervised method to function effectively in the presence of predictors, providing a statistically sound basis for quantifying uncertainty around predictions.

The Language of Data: Decoding Distributions

Data standardization and improvement are achieved through the application of specific transformations utilizing probability distributions. The Gamma distribution, parameterized by shape α and scale β, is employed to model skewed data, effectively addressing positive-valued, non-normal datasets. Conversely, the Bernoulli distribution, defined by a single probability parameter p, is utilized for binary or indicator variables, normalizing data to a 0 or 1 scale. These transformations aim to reduce the impact of differing data scales and distributions, thereby improving the performance and reliability of subsequent modeling processes. The selection of the appropriate distribution is contingent on the characteristics of the input data and the desired outcome of the transformation.

Data transformations are implemented to align the distributional characteristics of data used in unsupervised and regression contexts. Discrepancies in data distribution can negatively impact model performance when transitioning between these settings; therefore, transformations are chosen to reduce differences in statistical properties like skewness and kurtosis. This process aims to create a more consistent data landscape, enabling models trained in one setting to generalize effectively to the other. Specifically, the selection prioritizes minimizing the distance between the distributions observed during unsupervised learning and those used for generating target variables in the regression task, ultimately improving prediction accuracy and stability.

Simulation results utilizing Gamma, Pareto, and Bernoulli distributions demonstrate that the proposed data transformation techniques yield prediction intervals with performance comparable to existing methods. Specifically, the approach achieves statistically similar coverage and interval widths across a range of tested parameters. However, performance variations were observed based on the selected transformation function; certain functions exhibited improved computational efficiency and, in some scenarios, reduced prediction interval widths without sacrificing coverage probability, suggesting potential gains in predictive accuracy and resource utilization.

Guaranteed Uncertainty: The Illusion of Control

A novel strategy, when integrated with conformal prediction techniques, generates prediction intervals possessing demonstrably guaranteed coverage properties. Unlike traditional methods that rely on assumptions about data distribution, this approach ensures a specified probability – such as 90%, 92.5%, 95%, or 97.5% – that future observations will accurately fall within the predicted range. Critically, this guarantee holds true not only as the dataset grows infinitely large (asymptotic coverage) but also for datasets of any size, offering reliable performance even with limited data. Extensive simulations and analysis across diverse real-world datasets consistently validate this coverage, establishing a robust and dependable framework for quantifying prediction uncertainty.

A key strength of this predictive strategy lies in its ability to deliver prediction intervals with quantifiable confidence, irrespective of the dataset’s size. Unlike traditional methods that often rely on large sample assumptions for accurate coverage, this approach guarantees a specified probability – such as 90%, 95%, or even 97.5% – that a future observation will indeed fall within the predicted range. This reliability stems from the technique’s inherent properties, ensuring consistent performance even with limited data, and providing a robust measure of uncertainty alongside each prediction. The consistent coverage, independent of sample size, offers a significant advantage in scenarios where data is scarce or expensive to obtain, allowing for more informed decision-making with a clearly defined level of confidence.

A rigorous evaluation of this strategy was conducted using a dataset comprising 1340 insurance claims, showcasing its real-world applicability and performance. The results demonstrate a competitive edge, achieving levels of accuracy comparable to those of established prediction methods currently in use. Importantly, the approach exhibits the potential to approximate the efficiency of the Oracle Prediction Interval – a theoretical benchmark representing the best possible predictive performance – suggesting a pathway towards increasingly precise and reliable risk assessment in insurance and potentially other domains requiring robust prediction intervals. This practical validation underscores the method’s viability for deployment in settings where guaranteed coverage and accurate probabilistic forecasting are paramount.

The pursuit of valid prediction intervals, as detailed in this work, echoes a sentiment shared by those who challenge established norms. This paper’s strategy – transforming a problem to leverage existing methods and generate infinitely many valid intervals – embodies a systematic dismantling of conventional approaches. It’s a bug in the system confessing its design sins, revealing the limitations of prior methods and offering a path toward more robust solutions. Galileo Galilei once stated, “You cannot teach a man anything; you can only help him discover it for himself.” Similarly, this research doesn’t dictate a singular answer, but rather provides the tools for discovering a multitude of valid predictive solutions within the regression setting.

What Lies Ahead?

The presented work doesn’t so much solve the problem of predictive intervals for insurance claims as it dismantles a common assumption – that validity requires wrestling with distributional constraints. By shifting the focus to transformation and the unsupervised iid setting, the approach effectively side-steps those limitations, opening a path to infinitely many valid intervals. The irony, of course, is that this proliferation of solutions begs a new question: which interval, if any, is most useful? Validity, it turns out, is a minimum requirement, not the ultimate goal.

Future exploration should investigate the practical implications of this abundance. Simply constructing a valid interval is a feat, but the real challenge lies in minimizing its width without sacrificing coverage. The performance of various transformation techniques under different data regimes warrants rigorous comparison. Furthermore, the method’s sensitivity to the choice of calibration data-the silent partner in this validity game-deserves closer scrutiny.

One can’t help but wonder if this strategy represents a broader paradigm shift. Perhaps the pursuit of robust statistical modeling should give way to a more agnostic approach, focused on systematically generating and selecting from a universe of valid, but potentially wildly different, predictive structures. After all, understanding a system isn’t about finding the correct model, but about understanding the space of all possible models.

Original article: https://arxiv.org/pdf/2601.21153.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-02-01 10:27