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

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

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

# 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)

# 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_)

# 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_)

# 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)

# 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)

# 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)

# 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)

# 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_))

# 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.