Neural networks (NNs) have achieved tremendous success over the past decade, yet they are still extremely difficult to interpret. In contrast, linear models are less expressive but offer inherent interpretability. Linear coefficients are interpretable as the marginal effect of a feature on the prediction, assuming all other features are kept fixed. To combine the benefits of both approaches, we introduce NIMO (Nonlinear Interpretable MOdel). The key idea is to define a model where the NN is designed to learn nonlinear corrections to the linear model predictions, while also maintaining the original interpretability of the linear coefficients. Relevantly, we develop an optimization algorithm based on profile likelihood that elegantly allows for optimizing over the NN parameters while updating the linear coefficients analytically. By relying on adaptive ridge regression we can easily incorporate sparsity constraints as well. We show empirically that we can recover the underlying linear coefficients while significantly improving the predictive accuracy. Compared to other hybrid interpretable approaches, our model is the only one that actually maintains the same interpretability of linear coefficients as in linear models. We also achieve higher performance on various regression and classification settings.

REVIEW The results in Figure 2 look quite good, but why? Is it because kernelization or is it because of the simpler covariance structure? Overall no explanation on why the method performs better is given. Timing comparisons with the other factorizations are not presented, so is the method faster? If not, what happens if we increase the ranks for the other methods.

Urban flood risk emerges from complex and nonlinear interactions among multiple features related to flood hazard, flood exposure, and social and physical vulnerabilities, along with the complex spatial flood dependence relationships. Existing approaches for characterizing urban flood risk, however, are primarily based on flood plain maps, focusing on a limited number of features, primarily hazard and exposure features, without consideration of feature interactions or the dependence relationships among spatial areas. To address this gap, this study presents an integrated urban flood-risk rating model based on a novel unsupervised graph deep learning model (called FloodRisk-Net). FloodRisk-Net is capable of capturing spatial dependence among areas and complex and nonlinear interactions among flood hazards and urban features for specifying emergent flood risk. Using data from multiple metropolitan statistical areas (MSAs) in the United States, the model characterizes their flood risk into six distinct city-specific levels. The model is interpretable and enables feature analysis of areas within each flood-risk level, allowing for the identification of the three archetypes shaping the highest flood risk within each MSA. Flood risk is found to be spatially distributed in a hierarchical structure within each MSA, where the core city disproportionately bears the highest flood risk. Multiple cities are found to have high overall flood-risk levels and low spatial inequality, indicating limited options for balancing urban development and flood-risk reduction. Relevant flood-risk reduction strategies are discussed considering ways that the highest flood risk and uneven spatial distribution of flood risk are formed.

An unsupervised learning method is presented for determining global marine ecological provinces (eco-provinces) from plankton community structure and nutrient flux data. The systematic aggregated eco-province (SAGE) method identifies eco-provinces within a highly nonlinear ecosystem model. To accommodate the non-Gaussian covariance of the data, SAGE uses t-stochastic neighbor embedding (t-SNE) to reduce dimensionality. Over a hundred eco-provinces are identified with the density-based spatial clustering of applications with noise (DBSCAN) algorithm. Using a connectivity graph with ecological dissimilarity as the distance metric, robust aggregated eco-provinces (AEPs) are objectively defined by nesting the eco-provinces. Using the AEPs, the control of nutrient supply rates on community structure is explored. Eco-provinces and AEPs are unique and aid model interpretation. They could facilitate model intercomparison and potentially improve understanding and monitoring of marine ecosystems.

Using ensemble methods for regression has been a large success in obtaining high-accuracy prediction. Examples are Bagging, Random forest, Boosting, BART (Bayesian additive regression tree), and their variants. In this paper, we propose a new perspective named variable grouping to enhance the predictive performance. The main idea is to seek for potential grouping of variables in such way that there is no nonlinear interaction term between variables of different groups. Given a sum-of-learner model, each learner will only be responsible for one group of variables, which would be more efficient in modeling nonlinear interactions. We propose a two-stage method named variable grouping based Bayesian additive regression tree (GBART) with a well-developed python package gbart available. The first stage is to search for potential interactions and an appropriate grouping of variables. The second stage is to build a final model based on the discovered groups. Experiments on synthetic and real data show that the proposed method can perform significantly better than classical approaches.

We study the problem of end-to-end learning from complex multigraphs with potentially very large numbers of edges between two vertices, each edge labeled with rich information. Examples of such graphs include financial transactions, communication networks, or flights between airports. We propose Latent-Graph Convolutional Networks (L-GCNs), which can successfully propagate information from these edge labels to a latent adjacency tensor, after which further propagation and downstream tasks can be performed, such as node classification. We evaluate the performance of several variations of the model on two synthetic datasets simulating fraud in financial transaction networks, to ensure that the model must make use of edge labels in order to achieve good classification performance. We find that allowing for nonlinear interactions on a per-neighbor basis enhances performance significantly, while also showing promising results in an inductive setting.

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we construct a deep convolutional neural network in which the parameters are used to classify and reconstruct the coefficients of nonlinear wave equations that model the medium properties. Furthermore, for given approximation accuracy, we obtain the depth and number of units of the network and their quantitative dependence on the complexity of the medium.

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multi-scattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances in nonlinear unmixing modeling.

Using the well-known Artificial Anasazi simulation for a case study, we investigate the use of genetic algorithms (GAs) for performing two common tasks related to robustness checking of agent-based models: parameter calibration and sensitivity analysis. In the calibration task, we demonstrate that a GA approach is able to find parameters that are equally good or better at minimizing error versus historical data, compared to a previous factorial grid-based approach. The GA approach also allows us to explore a wider range of parameters and parameter settings. Previous univariate sensitivity analysis on the Artificial Anasazi model did not consider potentially complex/nonlinear interactions between parameters. With the GA-based approach, we perform multivariate sensitivity analysis to discover how greatly the model can diverge from historical data, while the parameters are constrained within a close range of previously calibrated values. We show that by varying multiple parameters within a 10% range, the model can produce dramatically and qualitatively different results, and further demonstrate the utility of sensitivity analysis for model testing, by the discovery of a small coding error. Through this case study, we discuss some of the issues that can arise with calibration and sensitivity analysis of agent-based models.