2nd/10_Wiki/Topics/AI_and_ML/Non-parametric-Models.md

---
id: wiki-2026-0508-non-parametric-models
title: Non-parametric Models
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Non-parametric Models, Nonparametric ML, Instance-based Learning]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [ml, non-parametric, knn, decision-trees, gaussian-process, kernel, sklearn]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack: { language: python, framework: scikit-learn }
---

# Non-parametric Models

## 매 한 줄
- 비모수 모델은 고정 개수 파라미터를 두지 않고 데이터에 따라 모델 복잡도가 성장하며, k-NN·decision tree·kernel·Gaussian process가 대표 family.

## 매 핵심
- **정의**: parameter 개수가 데이터 크기에 따라 증가(또는 데이터 자체를 메모리에 저장). "no fixed parametric form".
- **대표 알고리즘**:
  - k-NN: lazy learner, 거리 기반.
  - Decision tree / Random Forest / Gradient Boosting: tree 깊이·개수가 데이터에 적응.
  - Kernel methods (SVM with RBF, Kernel Ridge): support vector 수가 데이터 의존.
  - Gaussian Process: covariance matrix(N×N) → O(N³) 학습.
  - KDE(Kernel Density Estimation), Nadaraya-Watson regression.
- **장점**: 분포 가정 약함, 복잡한 비선형 관계 포착.
- **단점**: 데이터·계산량 증가, curse of dimensionality, 해석성 일부 약함.
- **vs parametric**: linear/logistic regression, GLM은 고정 파라미터 → 데이터 적어도 OK, 외삽 가능.

## 💻 패턴
```python
# k-NN classifier with distance weighting
from sklearn.neighbors import KNeighborsClassifier
clf = KNeighborsClassifier(n_neighbors=15, weights="distance", metric="minkowski", p=2)
clf.fit(X_train, y_train)
pred = clf.predict(X_test)
```

```python
# Decision tree depth tuning via CV
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import GridSearchCV
gs = GridSearchCV(DecisionTreeClassifier(random_state=0),
                  {"max_depth": [3, 5, 10, None], "min_samples_leaf": [1, 5, 20]},
                  cv=5, scoring="f1_macro")
gs.fit(X, y)
print(gs.best_params_, gs.best_score_)
```

```python
# Random Forest with OOB score
from sklearn.ensemble import RandomForestClassifier
rf = RandomForestClassifier(n_estimators=500, oob_score=True, n_jobs=-1, random_state=0)
rf.fit(X, y)
print("OOB:", rf.oob_score_)
```

```python
# Kernel Ridge Regression with RBF
from sklearn.kernel_ridge import KernelRidge
kr = KernelRidge(alpha=1.0, kernel="rbf", gamma=0.1)
kr.fit(X_train, y_train)
```

```python
# Gaussian Process regression
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, WhiteKernel
kernel = 1.0 * RBF(length_scale=1.0) + WhiteKernel(noise_level=0.1)
gpr = GaussianProcessRegressor(kernel=kernel, normalize_y=True, n_restarts_optimizer=5)
gpr.fit(X_train, y_train)
mu, std = gpr.predict(X_test, return_std=True)
```

```python
# KDE for density estimation
from sklearn.neighbors import KernelDensity
import numpy as np
kde = KernelDensity(bandwidth=0.5, kernel="gaussian").fit(X_train)
log_density = kde.score_samples(X_test)
density = np.exp(log_density)
```

```python
# Nadaraya-Watson regressor (manual)
import numpy as np
def nw_regress(X_train, y_train, X_test, h=1.0):
    diffs = X_test[:, None, :] - X_train[None, :, :]
    w = np.exp(-np.sum(diffs**2, axis=2) / (2 * h**2))
    return (w @ y_train) / (w.sum(axis=1) + 1e-9)
```

```python
# SVM with RBF kernel — support vectors grow with data
from sklearn.svm import SVC
svc = SVC(kernel="rbf", C=1.0, gamma="scale")
svc.fit(X_train, y_train)
print("n_SV:", len(svc.support_))
```

```python
# FAISS for large-scale k-NN (approximate)
import faiss, numpy as np
index = faiss.IndexHNSWFlat(X.shape[1], 32)
index.add(X.astype(np.float32))
D, I = index.search(query.astype(np.float32), k=10)
```

## 매 결정 기준
- **데이터 크기**:
  - <1k → GP, kernel ridge OK.
  - 1k–100k → tree ensemble, k-NN(brute or KD-tree).
  - >100k → tree ensemble, ANN(FAISS, ScaNN), 또는 parametric로 회귀.
- **차원**: 고차원(>50) → tree, gradient boosting. k-NN/KDE는 curse of dim.
- **uncertainty 필요**: GP > tree quantile regression > MC Dropout(parametric).
- **해석성**: shallow decision tree, kNN(prototype 분석).

## 🔗 Graph
- 관련: [[K-Nearest-Neighbors-K-NN]], [[Decision Tree]], [[Random-Forest]], [[Gradient-Boosting]], [[Gaussian-Process]], [[Kernel-Methods]]
- 도구: [[XGBoost]], [[LightGBM]], [[FAISS]]

## 🤖 LLM 활용
- 데이터셋 크기/차원 → 추천 모델 family 매트릭스 생성.
- sklearn pipeline + GridSearch boilerplate 작성.
- 결과 해석(feature importance, partial dependence plot 설명).

## ❌ 안티패턴
- 100만 row에 GaussianProcessRegressor 그대로 사용(O(N³)).
- 고차원 sparse 데이터에 k-NN 단독.
- random forest를 "blackbox"라 단정해 SHAP/PDP 안 씀.
- standardize 안 한 데이터에 RBF kernel.

## 🧪 검증
- CV(StratifiedKFold), nested CV for hyperparameter.
- learning curve(데이터 추가에 따른 성능 변화) → 비모수 특성 확인.
- 시간/메모리 프로파일링(N×N matrix가 RAM 안 넘는지).

## 🕓 Changelog
- 2026-05-08 Phase 1: 초안 자동 생성.
- 2026-05-10 Manual cleanup: 본문 보강, GP/KDE/NW/FAISS 패턴 추가, 결정 기준 정리.