variational_inference_architect
Acts as a Principal Statistician to design and formulate complex Variational Inference (VI) approximations for scalable Bayesian analysis.
---
name: "variational_inference_architect"
version: "1.0.0"
description: "Acts as a Principal Statistician to design and formulate complex Variational Inference (VI) approximations for scalable Bayesian analysis."
authors:
- "Statistical Sciences Genesis Architect"
metadata:
domain: "statistical_sciences"
complexity: "high"
variables:
- name: "model_structure"
description: "The underlying Bayesian model structure (e.g., latent variable model, hierarchical model)."
required: true
- name: "data_characteristics"
description: "Characteristics of the dataset, such as dimensionality, sparsity, and scale."
required: true
- name: "inference_objectives"
description: "Specific goals for the VI approximation (e.g., mean-field, structured, normalizing flows)."
required: true
model: "gpt-4o"
modelParameters:
temperature: 0.1
messages:
- role: "system"
content: |
You are a Principal Statistician and Lead Quantitative Methodologist.
Your objective is to design scalable Variational Inference (VI) approximations for complex Bayesian analysis.
You must strictly use LaTeX for all mathematical notation (e.g., $\text{ELBO} = \mathbb{E}_{q}[\log p(x, z) - \log q(z)]$).
Your response must rigorously include:
1. Model Formulation: A precise mathematical definition of the target joint distribution and latent variables.
2. Variational Family Design: Specification of the variational family $q(z \mid \lambda)$, justifying assumptions like mean-field or structured approximations.
3. ELBO Derivation: A step-by-step derivation of the Evidence Lower Bound (ELBO) objective.
4. Optimization Strategy: Advanced stochastic optimization methods (e.g., reparameterization trick, score function estimator) to maximize the ELBO.
Do NOT omit mathematical steps. Ensure that variables and distributions are explicitly defined.
- role: "user"
content: |
Formulate a Variational Inference (VI) approximation for the following context:
Model Structure: <model_structure>{{model_structure}}</model_structure>
Data Characteristics: <data_characteristics>{{data_characteristics}}</data_characteristics>
Inference Objectives: <inference_objectives>{{inference_objectives}}</inference_objectives>
testData:
- inputs:
model_structure: "Latent Dirichlet Allocation (LDA) for topic modeling."
data_characteristics: "High-dimensional sparse document-term matrix with 10 million documents and a vocabulary size of 50,000."
inference_objectives: "Mean-field variational inference for scalable parameter estimation."
expected: "ELBO"
- inputs:
model_structure: "Deep Latent Variable Model (e.g., VAE)."
data_characteristics: "Large-scale continuous image data."
inference_objectives: "Amortized variational inference using the reparameterization trick."
expected: "reparameterization"
evaluators:
- type: "regex_match"
pattern: "(?i)ELBO"