8. Non-Parametric Bayesian Methods
Non-parametric Bayesian methods allow flexibility in model complexity, adapting as more data is available. Key methodologies such as the Dirichlet Process, Chinese Restaurant Process, and Stick-Breaking Process provide mechanisms to model infinite dimensions in parameters, particularly useful in clustering and topic modeling applications. Despite challenges like computational cost and hyperparameter sensitivity, these methods expand the capabilities of traditional Bayesian approaches.
Sections
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What we have learnt
- Non-parametric Bayesian methods adapt the number of parameters based on data, unlike fixed-parameter models.
- Key constructs include the Dirichlet Process and its applications in clustering and topic modeling.
- Challenges include computational costs and the complexity of interpretation.
Key Concepts
- -- Dirichlet Process (DP)
- A distribution over distributions used for flexible clustering without prior knowledge of the number of clusters.
- -- Chinese Restaurant Process (CRP)
- A metaphorical representation of clustering where data points are customers choosing tables (clusters) based on existing patronage.
- -- StickBreaking Process
- A method for constructing probability distributions where a stick is broken into portions representing different components.
- -- Dirichlet Process Mixture Models (DPMMs)
- Models that allow multiple clusters to derive from a Dirichlet Process, providing flexibility in data clustering.
- -- Hierarchical Dirichlet Processes (HDP)
- An extension of the Dirichlet Process that facilitates multiple data groups each with its distribution while sharing overarching topics.
Additional Learning Materials
Supplementary resources to enhance your learning experience.