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Deterministic learning for maximum-likelihood estimation through neural networks.

Cristiano Cervellera¹, Danilo Macciò, Marco Muselli

¹Istituto di Studi sui Sistemi Intelligentiper l'Automazione, Consiglio Nazionale delle Ricerche, Genova 16149, Italy. cervellera@ge.issia.cnr.it

IEEE Transactions on Neural Networks

|August 15, 2008

Summary

This study introduces a novel deterministic learning (DL) method for solving maximum-likelihood estimation (MLE) problems. The approach approximates complex likelihood functions using neural networks, offering a consistent and efficient alternative for parameter estimation.

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Area of Science:

Computational statistics
Machine learning
Statistical inference

Background:

Maximum-likelihood estimation (MLE) is a fundamental statistical method for parameter estimation.
Solving MLE problems often involves complex numerical computations and sampling from unknown densities.
Existing methods can be computationally intensive or require specific assumptions about the data distribution.

Purpose of the Study:

To present a general numerical method for solving maximum-likelihood estimation (MLE) problems.
To introduce a deterministic learning (DL) approach for approximating ML estimator functions.
To provide a method that avoids direct sampling from unknown probability densities.

Main Methods:

Utilizes a deterministic learning (DL) approach.
Employs a carefully chosen neural network architecture.
Generates deterministic samples of observations for the likelihood function, bypassing the need for unknown density sampling.

Main Results:

The proposed DL method provides close approximations to ML estimator functions.
Theoretical analysis demonstrates consistency and convergence with favorable rates to the true ML estimator.
Simulation results show the algorithm performs well compared to exact solutions.

Conclusions:

The DL-based method offers a viable and efficient approach for numerical MLE.
This technique simplifies the process of parameter estimation in complex statistical models.
The method shows promise for various applications requiring accurate parameter estimation.