Bayesian Estimation of Inverted Beta Mixture Models With Extended Stochastic Variational Inference for Positive...

Area of Science:

• Statistics
• Machine Learning

Background:

• The finite inverted beta mixture model (IBMM) is effective for positive vector data.
• Traditional variational inference for IBMM is computationally expensive for large datasets.
• Stochastic variational inference (SVI) offers efficiency but struggles with non-Gaussian models due to intractable moment computations.

Purpose of the Study:

• To develop a flexible and efficient Bayesian estimation framework for non-Gaussian statistical models, particularly the IBMM.
• To address the computational challenges of large datasets in Bayesian inference.

Main Methods:

• Proposing the extended stochastic variational inference (ESVI) framework.
• Employing approximation strategies to derive a lower bound for the evidence lower bound (ELBO), avoiding intractable moment calculations.
• Utilizing stochastic optimization with noisy natural gradients to optimize the derived lower bound.

Main Results:

• The ESVI framework successfully handles non-Gaussian statistical models.
• The method avoids intractable moment calculations inherent in standard SVI for these models.
• Demonstrated effectiveness and excellent performance on real-world data.

Conclusions:

• The proposed ESVI framework provides a computationally efficient and flexible approach for Bayesian estimation in large, non-Gaussian datasets.
• ESVI overcomes the limitations of traditional variational inference and standard SVI for complex statistical models.
• This advancement broadens the applicability of Bayesian methods to larger and more complex data scenarios.