Application of deep learning (DL) to the field of healthcare is aiding clinicians to make an accurate diagnosis. DL provides reliable results for image processing and sensor interpretation problems most of the time. However, model uncertainty should also be thoroughly quantified. This paper therefore addresses the employment of Monte Carlo dropout within the DL structure to automatically discriminate presymptomatic signs of spinocerebellar ataxia type 2 in saccadic samples obtained from electrooculograms. The current work goes beyond the common incorporation of this special type of dropout into deep neural networks and uses the uncertainty derived from the validation samples to construct a decision tree at the register level of the patients. The decision tree built from the uncertainty estimates obtained a classification accuracy of 81.18% in automatically discriminating control, presymptomatic and sick classes. This paper proposes a novel method to address both uncertainty quantification and explainability to develop reliable healthcare support systems.

In this letter, the ability of higher-order Hopfield networks to solve combinatorial optimization problems is assessed by means of a rigorous analysis of their properties. The stability of the continuous network is almost completely clarified: (1) hyperbolic interior equilibria, which are unfeasible, are unstable; (2) the state cannot escape from the unitary hypercube; and (3) a Lyapunov function exists. Numerical methods used to implement the continuous equation on a computer should be designed with the aim of preserving these favorable properties. The case of nonhyperbolic fixed points, which occur when the Hessian of the target function is the null matrix, requires further study. We prove that these nonhyperbolic interior fixed points are unstable in networks with three neurons and order two. The conjecture that interior equilibria are unstable in the general case is left open.