VBLab Statistical Models

VBLab provides statistical models that can be used with the supported VB techniques. Users can also define their custom models.

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VBLab models

• VBLab provides some statistical models that can be used to quickly implement the Variational Bayes (VB) techniques supported.
• These models are designed as Matlab class objects with predefined attributes and methods.
• Available VBLab models:
  • DeepGLM: Bayesian Deep Generalized Linear model
    • DeepGLM models (Tran et al., 2020) are flexible versions of generalized linear models incorporating basis functions formed by Deep Feedforward Neural Networks (DFNN).
  • LogisticRegression: Bayesian Logistic Regression model
  • RECH: Recurrent Conditional Heteroskedasticity model
    • The RECH models are proposed by Nguyen et al. (2020)

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Custom models

There are two ways to define custome models:

• Define a custom function to compute the $h(\theta)$ and $\nabla_\theta h(\theta)$ terms then provide the handle of the function as the input model. See how to define custom models as function handles.
• Define the custom model as Matlab class with methods to compute the $h(\theta)$ and $\nabla_\theta h(\theta)$ terms. See how to define custom models as class objects.

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Model compatibility

Theoretically, the provided VB methods can work with all VBLab supported models. However, due to model-specific properties, we recommend the following efficient combinations of VB methods and models.

For example, as the MGVB technique does not require the gradient of the log-likelihood function, it is suitable for the RECH models as deriving the RECH models are highly flexible in terms of model specification.

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References

[1] Nguyen, T.-N., Tran, M.-N., and Kohn, R. (2020). Recurrent conditional heteroskedasticity. arXiv:2010.13061. Read the paper

[2] Tran, M.-N., Nguyen, T.-N., Nott, D., and Kohn, R. (2020). Bayesian deep net GLM and GLMM. Journal of Computational and Graphical Statistics, 29(1):97-113. Read the paper

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