모델 개발과 평가

특징 선택, 모델 선택, 하이퍼파라미터 최적화, 교차 검증, 잔차 진단 및 플롯

고품질 회귀 모델을 개발하는 경우 적합한 특징(또는 예측 변수)을 선택하고, 하이퍼파라미터(데이터에 피팅되지 않는 모델 모수)를 조율하고, 잔차 진단을 통해 모델 가정을 평가해야 합니다.

하이퍼파라미터의 값을 선택하고 선택한 값을 사용하여 모델에 대한 교차 검증을 반복하는 방식으로 하이퍼파라미터를 조율할 수 있습니다. 이 과정을 통해 여러 개의 모델이 생성되며, 이러한 모델 중에서 가장 적합한 모델이 추정된 일반화 오차를 최소화하는 모델일 수 있습니다. 예를 들어, SVM 모델을 조정하려면 상자 제약 조건과 커널 스케일의 집합을 선택하고, 값의 쌍 각각에 대해 모델을 교차 검증한 후 10겹 교차 검증된 평균 제곱 오차 추정값과 비교하십시오.

Statistics and Machine Learning Toolbox™에서 제공되는 특정 비모수적 회귀 함수는 베이즈 최적화, 그리드 탐색 또는 임의 탐색을 통해 추가적인 자동 하이퍼파라미터 조율 기능을 제공합니다. 그러나, 베이즈 최적화를 구현하는 주요 함수인 bayesopt는 여러 다른 응용 사례에 사용할 수 있을 정도로 유연합니다. 자세한 내용은 Bayesian Optimization Workflow 항목을 참조하십시오.

조정된 하이퍼파라미터를 가진 모델을 자동으로 선택하려면 fitrauto를 사용하십시오. 이 함수는 다양한 하이퍼파라미터 값으로 회귀 모델 유형을 선택해 보고 잘 수행될 것으로 예상되는 최종 모델을 반환합니다. 어떤 회귀 모델 유형이 데이터에 가장 적합한지 확신하지 못할 경우 fitrauto를 사용하십시오.

회귀 모델을 대화형 방식으로 만들고 평가하려면 회귀 학습기 앱을 사용하십시오.

회귀 모델을 해석하려면 lime 또는 plotPartialDependence를 사용할 수 있습니다.

앱

회귀 학습기

Train regression models to predict data using supervised machine learning

함수

모두 확장

특징 선택

`fsrftest`	Univariate feature ranking for regression using F-tests
`fsrnca`	Feature selection using neighborhood component analysis for regression
`oobPermutedPredictorImportance`	Predictor importance estimates by permutation of out-of-bag predictor observations for random forest of regression trees
`partialDependence`	Compute partial dependence
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`predictorImportance`	Estimates of predictor importance for regression tree
`predictorImportance`	Estimates of predictor importance for regression ensemble
`relieff`	Rank importance of predictors using ReliefF or RReliefF algorithm
`sequentialfs`	Sequential feature selection using custom criterion
`stepwiselm`	Perform stepwise regression
`stepwiseglm`	Create generalized linear regression model by stepwise regression

자동 모델 선택

fitrauto Automatically select regression model with optimized hyperparameters

하이퍼파라미터 최적화

`bayesopt`	Select optimal machine learning hyperparameters using Bayesian optimization
`hyperparameters`	Variable descriptions for optimizing a fit function
`optimizableVariable`	Variable description for `bayesopt` or other optimizers

교차 검증

`crossval`	Estimate loss using cross-validation
`cvpartition`	교차 검증을 위한 데이터 분할
`repartition`	Repartition data for cross-validation
`test`	Test indices for cross-validation
`training`	Training indices for cross-validation

모델 해석

LIME(Local Interpretable Model-Agnostic Explanations)

`lime`	Local interpretable model-agnostic explanations (LIME)
`fit`	Fit simple model of local interpretable model-agnostic explanations (LIME)
`plot`	Plot results of local interpretable model-agnostic explanations (LIME)

부분 종속성

`partialDependence`	Compute partial dependence
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots

선형 모델 진단

`coefCI`	Confidence intervals of coefficient estimates of linear regression model
`coefTest`	Linear hypothesis test on linear regression model coefficients
`dwtest`	Durbin-Watson test with linear regression model object
`plot`	Scatter plot or added variable plot of linear regression model
`plotAdded`	Added variable plot of linear regression model
`plotAdjustedResponse`	Adjusted response plot of linear regression model
`plotDiagnostics`	Plot observation diagnostics of linear regression model
`plotEffects`	Plot main effects of predictors in linear regression model
`plotInteraction`	Plot interaction effects of two predictors in linear regression model
`plotResiduals`	Plot residuals of linear regression model
`plotSlice`	Plot of slices through fitted linear regression surface

일반화 선형 모델 진단

`coefCI`	Confidence intervals of coefficient estimates of generalized linear regression model
`coefTest`	Linear hypothesis test on generalized linear regression model coefficients
`devianceTest`	Analysis of deviance for generalized linear regression model
`plotDiagnostics`	Plot observation diagnostics of generalized linear regression model
`plotResiduals`	Plot residuals of generalized linear regression model
`plotSlice`	Plot of slices through fitted generalized linear regression surface

비선형 모델 진단

`coefCI`	Confidence intervals of coefficient estimates of nonlinear regression model
`coefTest`	Linear hypothesis test on nonlinear regression model coefficients
`plotDiagnostics`	Plot diagnostics of nonlinear regression model
`plotResiduals`	Plot residuals of nonlinear regression model
`plotSlice`	Plot of slices through fitted nonlinear regression surface

선형 가설검정

linhyptest Linear hypothesis test

객체

모두 확장

특징 선택

FeatureSelectionNCARegression Feature selection for regression using neighborhood component analysis (NCA)

하이퍼파라미터 최적화

BayesianOptimization Bayesian optimization results

도움말 항목

회귀 학습기 앱 워크플로

Train Regression Models in Regression Learner App

Workflow for training, comparing and improving regression models, including automated, manual, and parallel training.

Choose Regression Model Options

In Regression Learner, automatically train a selection of models, or compare and tune options of linear regression models, regression trees, support vector machines, Gaussian process regression models, ensembles of regression trees, and regression neural networks.

Feature Selection and Feature Transformation Using Regression Learner App

Identify useful predictors using plots, manually select features to include, and transform features using PCA in Regression Learner.

Assess Model Performance in Regression Learner

Compare model statistics and visualize results.

특징 선택

Introduction to Feature Selection

Learn about feature selection algorithms and explore the functions available for feature selection.

Sequential Feature Selection

This topic introduces to sequential feature selection and provides an example that selects features sequentially using a custom criterion and the sequentialfs function.

Neighborhood Component Analysis (NCA) Feature Selection

Neighborhood component analysis (NCA) is a non-parametric method for selecting features with the goal of maximizing prediction accuracy of regression and classification algorithms.

Robust Feature Selection Using NCA for Regression

Perform feature selection that is robust to outliers using a custom robust loss function in NCA.

Select Predictors for Random Forests

Select split-predictors for random forests using interaction test algorithm.

자동 모델 선택

Automated Regression Model Selection with Bayesian Optimization

Use fitrauto to automatically try a selection of regression model types with different hyperparameter values, given training predictor and response data.

하이퍼파라미터 최적화

Bayesian Optimization Workflow

Perform Bayesian optimization using a fit function or by calling bayesopt directly.

Variables for a Bayesian Optimization

Create variables for Bayesian optimization.

Bayesian Optimization Objective Functions

Create the objective function for Bayesian optimization.

Constraints in Bayesian Optimization

Set different types of constraints for Bayesian optimization.

Optimize a Boosted Regression Ensemble

Minimize cross-validation loss of a regression ensemble.

Bayesian Optimization Plot Functions

Visually monitor a Bayesian optimization.

Bayesian Optimization Output Functions

Monitor a Bayesian optimization.

Bayesian Optimization Algorithm

Understand the underlying algorithms for Bayesian optimization.

Parallel Bayesian Optimization

How Bayesian optimization works in parallel.

교차 검증

Implement Cross-Validation Using Parallel Computing

Speed up cross-validation using parallel computing.

선형 모델 진단

선형 회귀 결과 해석하기

선형 회귀 결과 출력되는 통계량을 표시하고 해석합니다.

선형 회귀

선형 회귀 모델을 피팅하고 결과를 검토합니다.

Linear Regression with Interaction Effects

Construct and analyze a linear regression model with interaction effects and interpret the results.

Summary of Output and Diagnostic Statistics

Evaluate a fitted model by using model properties and object functions.

F-통계량과 t-통계량

선형 회귀에서 F-통계량은 모델 또는 모델 성분의 유의성을 검정하는 분산분석(ANOVA) 방식에 대한 검정 통계량입니다. t-통계량은 회귀 계수에 대한 추론을 할 때 유용합니다.

결정계수(R 제곱)

결정계수(R 제곱)는 선형 회귀 모델에서 독립 변수 X로 설명되는 응답 변수 y의 비례적인 변동량을 나타냅니다.

Coefficient Standard Errors and Confidence Intervals

Estimated coefficient variances and covariances capture the precision of regression coefficient estimates.

Residuals

Residuals are useful for detecting outlying y values and checking the linear regression assumptions with respect to the error term in the regression model.

Durbin-Watson Test

The Durbin-Watson test assesses whether or not there is autocorrelation among the residuals of time series data.

Cook’s Distance

Cook's distance is useful for identifying outliers in the X values (observations for predictor variables).

Hat Matrix and Leverage

The hat matrix provides a measure of leverage.

Delete-1 Statistics

Delete-1 change in covariance (CovRatio) identifies the observations that are influential in the regression fit.