A data-driven Fourier-mixture neural-network method for density estimation
Authors: Duy-Minh Dang, Volter Entoma
Summary
arXiv:2605. 18019v1 Announce Type: new Abstract: We propose a data-driven Fourier-trained neural-network method for estimating fixed-horizon probability densities from empirical characteristic-function (CF) information.
Relevance
Read next because A data-driven Fourier-mixture neural-network method for density estimation 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 "Training one persona to emit a [ZLT] marker without bystanders adopting it has a one-cell-wide LR x epochs window on Qwen2.5-7B-Instruct (LOW confidence)", clean result "A pretraining-data-poisoned Qwen3-4B backdoor only fires on the exact trigger tokens — paraphrases don't activate it, and base-model similarity to the trigger doesn't predict which inputs fire (MODERATE confidence)". Matching terms: rect, rate, trained. Source: arxiv stat.ML (Machine Learning).
Threat model
Potential threat/caveat for 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)": this item discusses benchmark.
Abstract
arXiv:2605.18019v1 Announce Type: new Abstract: We propose a data-driven Fourier-trained neural-network method for estimating fixed-horizon probability densities from empirical characteristic-function (CF) information. The estimator is a positive Gaussian--Laplace mixture with closed-form CF, so training can be performed directly in Fourier space while preserving nonnegativity and unit mass. We consider two sampling settings. In the direct i.i.d. sampling setting, the method is trained against an empirical CF constructed from i.i.d. samples. In the resampling-based pseudo-sampling setting, it is trained against an empirical pseudo-CF constructed from dependent data by resampling. For the direct i.i.d. case, we derive an expected $L_2$ error bound that separates Fourier truncation, empirical training error, discretization, and CF sampling error. For the pseudo-sampling case, we obtain a conditional analogue with two additional pseudo-law discrepancy terms. We develop a multidimensional extension of the framework and analyze its computational complexity. Numerical experiments show competitive performance relative to Expectation--Maximization on Gaussian-mixture benchmarks, clear gains on heavy-tailed targets, $L_2$ error decay consistent with the theory in a well-specified setting, and effective estimation of one-year Australian equity return law from resampled dependent data.