Likelihood calculation for a class of multiscale stochastic models, with application to texture discrimination

Area of Science:

• Stochastic modeling
• Statistical signal processing
• Machine learning

Background:

• Previously introduced multiscale stochastic models based on scale-recursive dynamics on trees.
• These models effectively represent multiscale processes (e.g., 1/f processes), 1D Markov processes, and 2D Markov random fields.
• Existing optimal estimation algorithms leverage the scale-recursive structure for efficiency.

Purpose of the Study:

• To develop a computationally efficient and parallelizable algorithm for likelihood calculation within the scale-recursive multiscale model framework.
• To demonstrate the practical application of this algorithm in texture discrimination.
• To compare the performance of likelihood-based methods with existing techniques.

Main Methods:

• Exploiting the inherent scale-recursive structure of the multiscale stochastic models.
• Developing a novel algorithm for parallelizable likelihood computation.
• Applying the algorithm to a texture discrimination task for performance evaluation.

Main Results:

• The developed algorithm significantly enhances computational efficiency and parallelizability for likelihood calculation.
• Likelihood-based texture discrimination using the new algorithm achieves performance comparable to Gaussian Markov random field methods.
• The proposed approach offers a computationally tractable alternative to complex existing techniques.

Conclusions:

• The scale-recursive multiscale models provide a powerful and flexible framework for diverse stochastic processes.
• The new likelihood calculation algorithm makes these models more practical for real-world applications.
• This work advances the field of statistical signal processing and machine learning for complex data analysis.