H2G2-Net: A Hierarchical Heterogeneous Graph Generative Network Framework for Discovery of Multi-Modal Physiological Responses

Discovering human cognitive and emotional states using multi-modal physiological signals draws attention across various research applications. Physiological responses of the human body are influenced by human cognition and commonly used to analyze cognitive states. From a network science perspective, the interactions of these heterogeneous physiological modalities in a graph structure may provide insightful information to support prediction of cognitive states. However, there is no clue to derive exact connectivity between heterogeneous modalities and there exists a hierarchical structure of sub-modalities. Existing graph neural networks are designed to learn on non-hierarchical homogeneous graphs with pre-defined graph structures; they failed to learn from hierarchical, multi-modal physiological data without a pre-defined graph structure. To this end, we propose a hierarchical heterogeneous graph generative network (H2G2-Net) that automatically learns a graph structure without domain knowledge, as well as a powerful representation on the hierarchical heterogeneous graph in an end-to-end fashion. We validate the proposed method on the CogPilot dataset that consists of multi-modal physiological signals. Extensive experiments demonstrate that our proposed method outperforms the state-of-the-art GNNs by 5%-20% in prediction accuracy.

Exact and Approximate Conformal Inference in Multiple Dimensions

It is common in machine learning to estimate a response y given covariate information x. However, these predictions alone do not quantify any uncertainty associated with said predictions. One way to overcome this deficiency is with conformal inference methods, which construct a set containing the unobserved response y with a prescribed probability. Unfortunately, even with one-dimensional responses, conformal inference is computationally expensive despite recent encouraging advances. In this paper, we explore the multidimensional response case within a regression setting, delivering exact derivations of conformal inference p-values when the predictive model can be described as a linear function of y. Additionally, we propose different efficient ways of approximating the conformal prediction region for non-linear predictors while preserving computational advantages. We also provide empirical justification for these approaches using a real-world data example.

Constructing Prediction Intervals with Neural Networks: An Empirical Evaluation of Bootstrapping and Conformal Inference Methods

Artificial neural networks (ANNs) are popular tools for accomplishing many machine learning tasks, including predicting continuous outcomes. However, the general lack of confidence measures provided with ANN predictions limit their applicability. Supplementing point predictions with prediction intervals (PIs) is common for other learning algorithms, but the complex structure and training of ANNs renders constructing PIs difficult. This work provides the network design choices and inferential methods for creating better performing PIs with ANNs. A two-step experiment is executed across 11 data sets, including an imaged-based data set. Two distribution-free methods for constructing PIs, bootstrapping and conformal inference, are considered. The results of the first experimental step reveal that the choices inherent to building an ANN affect PI performance. Guidance is provided for optimizing PI performance with respect to each network feature and PI method. In the second step, 20 algorithms for constructing PIs, each using the principles of bootstrapping or conformal inference, are implemented to determine which provides the best performance while maintaining reasonable computational burden. In general, this trade-off is optimized when implementing the cross-conformal method, which maintained interval coverage and efficiency with decreased computational burden.

Conformal Uncertainty Sets for Robust Optimization

Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the worst-case scenario over some uncertainty set. We explore Mahalanobis distance as a novel function for multi-target regression and the construction of joint prediction regions. We also connect conformal prediction regions to robust optimization, providing finite sample valid and conservative uncertainty sets, aptly named conformal uncertainty sets. We compare the coverage and efficiency of the conformal prediction regions generated with Mahalanobis distance to other conformal prediction regions. We also construct a small robust optimization example to compare conformal uncertainty sets to those constructed under the assumption of normality.