Salvatore Scognamiglio

Ronald Richman, Salvatore Scognamiglio, Mario V. Wüthrich

Inspired by the large success of Transformers in Large Language Models, these architectures are increasingly applied to tabular data. This is achieved by embedding tabular data into low-dimensional Euclidean spaces resulting in similar structures as time-series data. We introduce a novel credibility mechanism to this Transformer architecture. This credibility mechanism is based on a special token that should be seen as an encoder that consists of a credibility weighted average of prior information and observation based information. We demonstrate that this novel credibility mechanism is very beneficial to stabilize training, and our Credibility Transformer leads to predictive models that are superior to state-of-the-art deep learning models.

Ronald Richman, Salvatore Scognamiglio

This manuscript introduces deep learning models that simultaneously describe the dynamics of several yield curves. We aim to learn the dependence structure among the different yield curves induced by the globalization of financial markets and exploit it to produce more accurate forecasts. By combining the self-attention mechanism and nonparametric quantile regression, our model generates both point and interval forecasts of future yields. The architecture is designed to avoid quantile crossing issues affecting multiple quantile regression models. Numerical experiments conducted on two different datasets confirm the effectiveness of our approach. Finally, we explore potential extensions and enhancements by incorporating deep ensemble methods and transfer learning mechanisms.

Ronald Richman, Salvatore Scognamiglio, Mario V. Wüthrich

Modeling feature interactions in tabular data remains a key challenge in predictive modeling, for example, as used for insurance pricing. This paper proposes the Tree-like Pairwise Interaction Network (PIN), a novel neural network architecture that explicitly captures pairwise feature interactions through a shared feed-forward neural network architecture that mimics the structure of decision trees. PIN enables intrinsic interpretability by design, allowing for direct inspection of interaction effects. Moreover, it allows for efficient SHapley's Additive exPlanation (SHAP) computations because it only involves pairwise interactions. We highlight connections between PIN and established models such as GA2Ms, gradient boosting machines, and graph neural networks. Empirical results on the popular French motor insurance dataset show that PIN outperforms both traditional and modern neural networks benchmarks in predictive accuracy, while also providing insight into how features interact with each another and how they contribute to the predictions.

Kishan Padayachy, Ronald Richman, Salvatore Scognamiglio et al.

The starting point of our network architecture is the Credibility Transformer which extends the classical Transformer architecture by a credibility mechanism to improve model learning and predictive performance. This Credibility Transformer learns credibilitized CLS tokens that serve as learned representations of the original input features. In this paper we present a new paradigm that augments this architecture by an in-context learning mechanism, i.e., we increase the information set by a context batch consisting of similar instances. This allows the model to enhance the CLS token representations of the instances by additional in-context information and fine-tuning. We empirically verify that this in-context learning enhances predictive accuracy by adapting to similar risk patterns. Moreover, this in-context learning also allows the model to generalize to new instances which, e.g., have feature levels in the categorical covariates that have not been present when the model was trained -- for a relevant example, think of a new vehicle model which has just been developed by a car manufacturer.

Salvatore Scognamiglio

This paper introduces a neural network approach for fitting the Lee-Carter and the Poisson Lee-Carter model on multiple populations. We develop some neural networks that replicate the structure of the individual LC models and allow their joint fitting by analysing the mortality data of all the considered populations simultaneously. The neural network architecture is specifically designed to calibrate each individual model using all available information instead of using a population-specific subset of data as in the traditional estimation schemes. A large set of numerical experiments performed on all the countries of the Human Mortality Database (HMD) shows the effectiveness of our approach. In particular, the resulting parameter estimates appear smooth and less sensitive to the random fluctuations often present in the mortality rates' data, especially for low-population countries. In addition, the forecasting performance results significantly improved as well.

Vali Asimit, Ioannis Kyriakou, Simone Santoni et al.

Classification models are very sensitive to data uncertainty, and finding robust classifiers that are less sensitive to data uncertainty has raised great interest in the machine learning literature. This paper aims to construct robust \emph{Support Vector Machine} classifiers under feature data uncertainty via two probabilistic arguments. The first classifier, \emph{Single Perturbation}, reduces the local effect of data uncertainty with respect to one given feature and acts as a local test that could confirm or refute the presence of significant data uncertainty for that particular feature. The second classifier, \emph{Extreme Empirical Loss}, aims to reduce the aggregate effect of data uncertainty with respect to all features, which is possible via a trade-off between the number of prediction model violations and the size of these violations. Both methodologies are computationally efficient and our extensive numerical investigation highlights the advantages and possible limitations of the two robust classifiers on synthetic and real-life data.