Adaptive Kernel Density Estimation with Pre-training

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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