Adaptive Kernel Density Estimation with Pre-training
Authors: Ruitong Zhang, Ke Deng
Summary
arXiv:2605. 13092v1 Announce Type: new Abstract: Density estimation in high-dimensional settings is an important and challenging statistical problem.
Relevance
Read next because Adaptive Kernel Density Estimation with Pre-training overlaps with clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Coupling evil personas with wrong answers fails to protect Qwen2.5-7B from EM-induced alignment collapse — and the apparent capability ordering across coupling conditions is mostly eval contamination (LOW confidence)", clean result "Only continuous soft prefixes hit both EM axes at once on Qwen-2.5-7B-Instruct: discrete prompt searches split between the alignment objective and the distributional objective, and both discretizations of the soft prefix collapse (MODERATE confidence)". Matching terms: text, training, rate, trained. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.13092v1 Announce Type: new 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.