Adaptive Kernel Density Estimation with Pre-training

• URL: http://arxiv.org/abs/2605.13092v1
• Date: Wed, 13 May 2026 07:03:54 GMT
• Title: Adaptive Kernel Density Estimation with Pre-training
• Abstract summary: We introduce pre-training, a key idea behind many cutting-edge AI technologies, to the context of non-parametric density estimation.<n>A wide range of numerical experiments show that this strategy is highly effective for improving density-estimation accuracy.
• Score: 4.232818654775309
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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