Ray Bai

Shijie Wang, Saptarshi Chakraborty, Qian Qin et al.

Mixing (or prior) density estimation is an important problem in machine learning and statistics, especially in empirical Bayes $g$-modeling where accurately estimating the prior is necessary for making good posterior inferences. In this paper, we propose neural-$g$, a new neural network-based estimator for $g$-modeling. Neural-$g$ uses a softmax output layer to ensure that the estimated prior is a valid probability density. Under default hyperparameters, we show that neural-$g$ is very flexible and capable of capturing many unknown densities, including those with flat regions, heavy tails, and/or discontinuities. In contrast, existing methods struggle to capture all of these prior shapes. We provide justification for neural-$g$ by establishing a new universal approximation theorem regarding the capability of neural networks to learn arbitrary probability mass functions. To accelerate convergence of our numerical implementation, we utilize a weighted average gradient descent approach to update the network parameters. Finally, we extend neural-$g$ to multivariate prior density estimation. We illustrate the efficacy of our approach through simulations and analyses of real datasets. A software package to implement neural-$g$ is publicly available at https://github.com/shijiew97/neuralG.

Sijian Fan, Liyan Xiong, Dayuan Wang et al.

Recent advances in drug discovery have demonstrated that incorporating side information (e.g., chemical properties about drugs and genomic information about diseases) often greatly improves prediction performance. However, these side features can vary widely in relevance and are often noisy and high-dimensional. We propose Bayesian Variable Selection-Guided Inductive Matrix Completion (BVSIMC), a new Bayesian model that enables variable selection from side features in drug discovery. By learning sparse latent embeddings, BVSIMC improves both predictive accuracy and interpretability. We validate our method through simulation studies and two drug discovery applications: 1) prediction of drug resistance in Mycobacterium tuberculosis, and 2) prediction of new drug-disease associations in computational drug repositioning. On both synthetic and real data, BVSIMC outperforms several other state-of-the-art methods in terms of prediction. In our two real examples, BVSIMC further reveals the most clinically meaningful side features.