Cosimo Izzo

Paolo Andreini, Cosimo Izzo, Giovanni Ricco

A novel deep neural network framework -- that we refer to as Deep Dynamic Factor Model (D$^2$FM) --, is able to encode the information available, from hundreds of macroeconomic and financial time-series into a handful of unobserved latent states. While similar in spirit to traditional dynamic factor models (DFMs), differently from those, this new class of models allows for nonlinearities between factors and observables due to the autoencoder neural network structure. However, by design, the latent states of the model can still be interpreted as in a standard factor model. Both in a fully real-time out-of-sample nowcasting and forecasting exercise with US data and in a Monte Carlo experiment, the D$^2$FM improves over the performances of a state-of-the-art DFM.

Cosimo Izzo, Aldo Lipani, Ramin Okhrati et al.

Deep neural networks have gained momentum based on their accuracy, but their interpretability is often criticised. As a result, they are labelled as black boxes. In response, several methods have been proposed in the literature to explain their predictions. Among the explanatory methods, Shapley values is a feature attribution method favoured for its robust theoretical foundation. However, the analysis of feature attributions using Shapley values requires choosing a baseline that represents the concept of missingness. An arbitrary choice of baseline could negatively impact the explanatory power of the method and possibly lead to incorrect interpretations. In this paper, we present a method for choosing a baseline according to a neutrality value: as a parameter selected by decision-makers, the point at which their choices are determined by the model predictions being either above or below it. Hence, the proposed baseline is set based on a parameter that depends on the actual use of the model. This procedure stands in contrast to how other baselines are set, i.e. without accounting for how the model is used. We empirically validate our choice of baseline in the context of binary classification tasks, using two datasets: a synthetic dataset and a dataset derived from the financial domain.

Cosimo Izzo

In this article we will analyse how to compute the contribution of each input value to its aggregate output in some nonlinear models. Regression and classification applications, together with related algorithms for deep neural networks are presented. The proposed approach merges two methods currently present in the literature: integrated gradient and deep Taylor decomposition. Compared to DeepLIFT and Deep SHAP, it provides a natural choice of the reference point peculiar to the model at use.