DNNs Improve Nonparametric Estimation for Covariate-Driven Poisson Processes
Original title: Nonparametric Intensity Estimation for Covariate-Driven Poisson Processes Using Deep Learning
DNN-based NPMLEs achieve nearly minimax-optimal rates for compositional intensities without explicit structure encoding.
Nonparametric maximum likelihood estimation of Poisson process intensity depending on covariates is developed without assuming the intensity is bounded away from zero. An oracle inequality for the covariate-averaged Hellinger distance is derived and applied to DNN-based estimators. Simulations show DNN-based estimators outperform kernels for compositional structures and manifold data.
- DNN-based NPMLEs mitigate the curse of dimensionality for compositional structure
- DNN-based NPMLEs adapt to low-dimensional Riemannian manifold structure
- DNN-based estimators outperform kernel estimators in most settings
- DNN-based NPMLEs provide better out-of-sample performance on neural spiking data
- Convergence rates nearly minimax-optimal without explicit structure in network
From the original article
1 min read at arxiv.orgWe consider nonparametric maximum likelihood estimation of the intensity function of a Poisson process, allowing the intensity to depend on observed covariates. Such models describe how event rates vary with external conditions, including conditions under which the intensity becomes arbitrarily small or vanishes.
By Atsutomo Yara · arxiv.org
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