refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조
에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Antigravity Agent
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---
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id: wiki-2026-0508-probabilistic-graphical-models
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title: Probabilistic Graphical Models
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [PGM, Bayesian Network, Markov Random Field, MRF]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [pgm, bayesian-network, mrf, inference, machine-learning]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Python
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framework: pgmpy/pyro/numpyro
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---
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# Probabilistic Graphical Models
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## 매 한 줄
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> **"매 graph 로 joint distribution 의 factorization 표현"**. 매 random variable = node, dependency = edge. Bayesian Network (DAG) 와 Markov Random Field (undirected) 의 두 family. 2026 의 매 deep learning 시대에도 medical diagnosis, fault detection, causal inference 에서 핵심.
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## 매 핵심
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### 매 Two Families
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- **Bayesian Network (Directed)**: P(X) = ∏ᵢ P(Xᵢ | Pa(Xᵢ)). 매 causal direction 명시.
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- **Markov Random Field (Undirected)**: P(X) = (1/Z) ∏ φc(Xc). 매 symmetric correlation.
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- **Factor Graph**: 매 두 family 통합 representation — bipartite (variable + factor nodes).
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### 매 핵심 Operation
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- **Marginal inference**: P(Xᵢ) 매 sum out 다른 variable.
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- **MAP inference**: argmax P(X) — most likely assignment.
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- **Conditional**: P(Xᵢ | E=e) — evidence 주어진 belief update.
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- **Learning**: 매 parameter (MLE, EM) + structure (score-based, constraint-based).
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### 매 Inference Algorithm
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- **Exact**: Variable Elimination, Belief Propagation (tree), Junction Tree.
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- **Approx**: MCMC (Gibbs, Metropolis-Hastings), Variational Inference, Loopy BP.
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### 매 응용
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1. Medical diagnosis: 매 symptom → disease causal network.
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2. Fault detection: 매 sensor reading → root cause.
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3. Computer vision: 매 CRF for image segmentation (DeepLab v3 의 backbone).
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4. Causal inference: 매 do-calculus, counterfactual.
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## 💻 패턴
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### pgmpy: Bayesian Network 정의
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```python
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from pgmpy.models import DiscreteBayesianNetwork
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from pgmpy.factors.discrete import TabularCPD
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model = DiscreteBayesianNetwork([('Rain', 'Sprinkler'), ('Rain', 'Wet'), ('Sprinkler', 'Wet')])
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cpd_rain = TabularCPD('Rain', 2, [[0.8], [0.2]])
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cpd_sprinkler = TabularCPD('Sprinkler', 2, [[0.9, 0.5], [0.1, 0.5]], evidence=['Rain'], evidence_card=[2])
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cpd_wet = TabularCPD('Wet', 2,
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[[1.0, 0.2, 0.1, 0.01], [0.0, 0.8, 0.9, 0.99]],
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evidence=['Rain', 'Sprinkler'], evidence_card=[2, 2])
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model.add_cpds(cpd_rain, cpd_sprinkler, cpd_wet)
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assert model.check_model()
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```
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### Variable Elimination inference
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```python
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from pgmpy.inference import VariableElimination
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infer = VariableElimination(model)
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result = infer.query(variables=['Rain'], evidence={'Wet': 1})
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print(result)
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```
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### NumPyro: Bayesian regression
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```python
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import numpyro
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import numpyro.distributions as dist
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from numpyro.infer import MCMC, NUTS
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import jax.numpy as jnp
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def model(X, y=None):
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beta = numpyro.sample('beta', dist.Normal(jnp.zeros(X.shape[1]), 1.0))
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sigma = numpyro.sample('sigma', dist.HalfNormal(1.0))
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mu = jnp.dot(X, beta)
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numpyro.sample('y', dist.Normal(mu, sigma), obs=y)
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mcmc = MCMC(NUTS(model), num_warmup=500, num_samples=1000)
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mcmc.run(jax.random.PRNGKey(0), X, y)
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```
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### Markov Random Field (CRF for sequence labeling)
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```python
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import torch
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from torchcrf import CRF
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num_tags = 5
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crf = CRF(num_tags, batch_first=True)
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emissions = torch.randn(2, 10, num_tags) # (batch, seq, tags)
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tags = torch.randint(0, num_tags, (2, 10))
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loss = -crf(emissions, tags) # neg log likelihood
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best = crf.decode(emissions) # Viterbi
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```
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### Pyro: Variational Inference
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```python
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import pyro
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import pyro.distributions as dist
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from pyro.infer import SVI, Trace_ELBO
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from pyro.optim import Adam
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def model(data):
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z = pyro.sample('z', dist.Normal(0, 1))
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pyro.sample('obs', dist.Normal(z, 1), obs=data)
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def guide(data):
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mu = pyro.param('mu', torch.tensor(0.))
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sigma = pyro.param('sigma', torch.tensor(1.), constraint=dist.constraints.positive)
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pyro.sample('z', dist.Normal(mu, sigma))
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svi = SVI(model, guide, Adam({'lr': 0.01}), Trace_ELBO())
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for step in range(1000):
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svi.step(data)
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| Discrete, small state space, exact inference | pgmpy + VE |
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| Continuous, large model | NumPyro + NUTS |
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| Sequence labeling | CRF |
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| Image segmentation | CRF + CNN (DeepLab) |
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| Causal inference | DoWhy + pgmpy |
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| Real-time, approx OK | Loopy BP / VI |
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**기본값**: 매 small problem → pgmpy. 매 large continuous → NumPyro NUTS.
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## 🔗 Graph
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- 부모: [[Probability Theory]] · [[Graph_Theory]]
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- 변형: [[Bayesian_Network]] · [[Markov_Random_Field]]
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- 응용: [[Image Segmentation]] · [[Causal Inference]]
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- Adjacent: [[Hidden_Markov_Model]] · [[Variational_Inference]] · [[MCMC]]
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## 🤖 LLM 활용
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**언제**: 매 explicit causal structure 필요, interpretability 중요, small-data domain (medicine).
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**언제 X**: 매 large-scale perception (이미지/음성) — neural network 가 우수.
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## ❌ 안티패턴
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- **모든 변수 fully connected**: 매 parameter explosion — sparsity 활용.
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- **Exact inference 의 강행 in dense graph**: NP-hard — approximate 사용.
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- **Causal direction 의 임의 가정**: 매 domain knowledge 없으면 PC algorithm 등으로 학습.
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## 🧪 검증 / 중복
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- Verified (Koller & Friedman 2009, Murphy 2012, pgmpy 0.1.26, NumPyro 0.16).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — pgmpy/NumPyro/Pyro modern stack |
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