Explainable Neural Network Ensembles

Neural networks are known for providing impressive classification performance, and the ensemble learning technique is further acting as a catalyst to enhance this performance by integrating multiple networks. But like neural networks, neural network ensembles are also considered as a black-box because they cannot explain their decision making process. So, despite having high classification performance, neural networks and their ensembles are not suited for some applications which require explainable decisions. However, the rule extraction technique can overcome this drawback by representing the knowledge learned by a neural network in the guise of interpretable decision rules. A rule extraction algorithm provides neural networks with the power to justify their classification responses through explainable classification rules. Several rule extraction algorithms exist to extract classification rules from neural networks, but only a few of them generates rules using neural network ensembles. So this paper proposes an algorithm named Rule Extraction using Ensemble of Neural Network Ensembles (RE-E-NNES) to demonstrate the high performance of neural network ensembles through rule extraction. RE-E-NNES extracts classification rules by ensembling several neural network ensembles. Results show the efficacy of the proposed RE-E-NNES algorithm compared to different existing rule extraction algorithms.

Using Neural Network Ensembles to Separate Biogeochemical and Physical Components in Earth System Models

Earth system models (ESMs) are useful tools for predicting and understanding past and future aspects of the climate system. However, the biological and physical parameters used in ESMs can have wide variations in their estimates. Even small changes in these parameters can yield unexpected results without a clear explanation of how a particular outcome was reached. The standard method for estimating ESM sensitivity is to compare spatiotemporal distributions of variables from different runs of a single ESM. However, a potential pitfall of this method is that ESM output could match observational patterns because of compensating errors. For example, if a model predicts overly weak upwelling and low nutrient concentrations, it may compensate for this by allowing phytoplankton to have a high sensitivity to nutrients. Recently, it has been demonstrated that neural network ensembles (NNEs) are capable of extracting relationships between predictor and target variables within ocean biogeochemical models. Being able to view the relationships between variables, along with spatiotemporal distributions, allows for a more mechanistically based examination of ESM outputs. Here, we investigated whether we could apply NNEs to help us determine why different ESMs produce different results. We tested this using three cases. The first and second case use different runs of the same ESM, except the physical circulations differ between them in the first case while the biological equations differ between them in the second. Our results indicate that the NNEs were capable of extracting the relationships between variables, allowing us to distinguish between differences due to changes in circulation (which do not change relationships) from changes in biogeochemical formulation (which do change relationships).

Characterization of real-world networks through quantum potentials

Network connectivity has been thoroughly investigated in several domains, including physics, neuroscience, and social sciences. This work tackles the possibility of characterizing the topological properties of real-world networks from a quantum-inspired perspective. Starting from the normalized Laplacian of a network, we use a well-defined procedure, based on the dressing transformations, to derive a 1-dimensional Schrödinger-like equation characterized by the same eigenvalues. We investigate the shape and properties of the potential appearing in this equation in simulated small-world and scale-free network ensembles, using measures of fractality. Besides, we employ the proposed framework to compare real-world networks with the Erdős-Rényi, Watts-Strogatz and Barabási-Albert benchmark models. Reconstructed potentials allow to assess to which extent real-world networks approach these models, providing further insight on their formation mechanisms and connectivity properties.