Neural-g: A Deep Learning Framework for Mixing Density Estimation
<|reference_start|>Neural-g: A Deep Learning Framework for Mixing Density Estimation: 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.<|reference_end|>
@article{wang2024neural-g:,
    title={Neural-g: A Deep Learning Framework for Mixing Density Estimation},
    author={Shijie Wang, Saptarshi Chakraborty, Qian Qin, Ray Bai},
    journal={arXiv preprint arXiv:2406.05986},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.05986},
    primaryClass={stat.ML cs.LG}
}