The design of neural networks typically involves trial-and-error, a time-consuming process for obtaining an optimal architecture, even for experienced researchers. Additionally, it is widely accepted that loss functions of deep neural networks are generally non-convex with respect to the parameters to be optimised. We propose the Layer-wise Convex Theorem to ensure that the loss is convex with respect to the parameters of a given layer, achieved by constraining each layer to be an overdetermined system of non-linear equations. Based on this theorem, we developed an end-to-end algorithm (the AutoNet) to automatically generate layer-wise convex networks (LCNs) for any given training set. We then demonstrate the performance of the AutoNet-generated LCNs (AutoNet-LCNs) compared to state-of-the-art models on three electrocardiogram (ECG) classification benchmark datasets, with further validation on two non-ECG benchmark datasets for more general tasks. The AutoNet-LCN was able to find networks customised for each dataset without manual fine-tuning under 2 GPU-hours, and the resulting networks outperformed the state-of-the-art models with fewer than 5% parameters on all the above five benchmark datasets. The efficiency and robustness of the AutoNet-LCN markedly reduce model discovery costs and enable efficient training of deep learning models in resource-constrained settings.

OBJECTIVE: To compare Cox models, machine learning (ML), and ensemble models combining both approaches, for prediction of stroke risk in a prospective study of Chinese adults. MATERIALS AND METHODS: We evaluated models for stroke risk at varying intervals of follow-up (<9 years, 0-3 years, 3-6 years, 6-9 years) in 503 842 adults without prior history of stroke recruited from 10 areas in China in 2004-2008. Inputs included sociodemographic factors, diet, medical history, physical activity, and physical measurements. We compared discrimination and calibration of Cox regression, logistic regression, support vector machines, random survival forests, gradient boosted trees (GBT), and multilayer perceptrons, benchmarking performance against the 2017 Framingham Stroke Risk Profile. We then developed an ensemble approach to identify individuals at high risk of stroke (>10% predicted 9-yr stroke risk) by selectively applying either a GBT or Cox model based on individual-level characteristics. RESULTS: For 9-yr stroke risk prediction, GBT provided the best discrimination (AUROC: 0.833 in men, 0.836 in women) and calibration, with consistent results in each interval of follow-up. The ensemble approach yielded incrementally higher accuracy (men: 76%, women: 80%), specificity (men: 76%, women: 81%), and positive predictive value (men: 26%, women: 24%) compared to any of the single-model approaches. DISCUSSION AND CONCLUSION: Among several approaches, an ensemble model combining both GBT and Cox models achieved the best performance for identifying individuals at high risk of stroke in a contemporary study of Chinese adults. The results highlight the potential value of expanding the use of ML in clinical practice.