Data-Driven Parameter Estimation

TL;DR

This paper explores data-driven approaches to parameter estimation, replacing traditional probabilistic models with data, leading to neural network approximations and optimization-based solutions for Bayesian and non-Bayesian problems.

Contribution

It introduces novel data-driven formulations for parameter estimation, including neural network approximations and optimization methods, bypassing the need for explicit probability densities.

Findings

Neural network-based estimators effectively approximate optimal parameters.

Optimization problems resemble generative network design.

Data-driven methods provide flexible alternatives to traditional estimation.

Abstract

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a data-driven formulation where the necessary parametric probability density is replaced by available data. We present various data-driven versions that either result in neural network approximations of the optimum estimators or in well defined optimization problems that can be solved numerically. In particular, for the data-driven equivalent of non-Bayesian estimation we end up with optimization problems similar to the ones encountered for the design of generative networks.