Parameter estimation is a fundamental challenge in machine learning, crucial for tasks such as neural network weight fitting and Bayesian inference. This paper focuses on the complexity of estimating translation μ∈R^l and shrinkage σ∈R++ parameters for a distribution of the form (1/sigma^l) f_0((x−μ)/σ), where f_0 is a known density in R^l given n samples. We highlight that while the problem is NP-hard for Maximum Likelihood Estimation (MLE), it is possible to obtain ε-approximations for arbitrary ε>0 within poly(1/ε) time using the Wasserstein distance.
Citation
https://arxiv.org/abs/2501.10172
Article
Loading...