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This research applies pre-training techniques, central to modern AI development, to enhance non-parametric density estimation in high-dimensional spaces using neural networks. By leveraging a pre-trained model to recommend adaptive kernels for each sample point, the method significantly improves accuracy when target distributions align with the training family, offering a novel bridge between statistical methodology and deep learning strategies.
Adaptive Kernel Density Estimation with Pre-training
arXiv:2605.13092v3 Announce Type: replace-cross Abstract: Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate location-adaptive kernels. In this work, we introduce pre-training, a key idea behind many cutting-edge AI technologies, to the context of non-parametric density estimation. By establishing a pre-trained neural network that can recommend an appropriate location-adaptive kernel for each sample point, efficient density estimation with adaptive kernels is achieved in high dimensions. A wide range of numerical experiments show that this strategy is highly effective for improving density-estimation accuracy, when the target distribution is close to the distribution family for pre-training. When the target distribution is substantially different from the pre-training distribution family, the benefit from the proposed pre-training strategy may be diluted, but can be reactivated by an additional fine-tuning procedure.
Abstract:Density estimation in high-dimensional settings is an important and challenging statistical this http URL methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate location-adaptive kernels. In this work, we introduce pre-training, a key idea behind many cutting-edge AI technologies, to the context of non-parametric density estimation. By establishing a pre-trained neural network that can recommend an appropriate location-adaptive kernel for each sample point, efficient density estimation with adaptive kernels is achieved in high dimensions. A wide range of numerical experiments show that this strategy is highly effective for improving density-estimation accuracy, when the target distribution is close to the distribution family for pre-training. When the target distribution is substantially different from the pre-training distribution family, the benefit from the proposed pre-training strategy may be diluted, but can be reactivated by an additional fine-tuning procedure.
Machine Learning (stat.ML); Machine Learning (cs.LG); Methodology (stat.ME)
arXiv:2605.13092 [stat.ML]
(or arXiv:2605.13092v3 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2605.13092 Focus to learn more arXiv-issued DOI via DataCite
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