Matteo Giordano

Matteo Giordano, Kolyan Ray, Johannes Schmidt-Hieber

We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for Gaussian process regression in a continuous regression model. We show that if the true function is a generalized additive function, then the posterior based on any mean-zero Gaussian process can only recover the truth at a rate that is strictly slower than the minimax rate by a factor that is polynomially suboptimal in the sample size $n$.

Adrian Iulian Cristescu, Matteo Giordano

Predicting the probability of default (PD) of prospective loans is a critical objective for financial institutions. In recent years, machine learning (ML) algorithms have achieved remarkable success across a wide variety of prediction tasks; yet, they remain relatively underutilised in credit risk analysis. This paper highlights the opportunities that ML algorithms offer to this field by comparing the performance of five predictive models-Random Forests, Decision Trees, XGBoost, Gradient Boosting and AdaBoost-to the predominantly used logistic regression, over a benchmark dataset from Scheule et al. (Credit Risk Analytics: The R Companion). Our findings underscore the strengths and weaknesses of each method, providing valuable insights into the most effective ML algorithms for PD prediction in the context of loan portfolios.