ISLR第一、二章学习笔记

本文为ISLR第二章的学习笔记,涵盖了统计学习的目的、方法、预测与解释的权衡,以及评估模型准确性的方法。重点讨论了预测与推断、参数与非参数方法、偏差-方差权衡,并简述了有监督与无监督学习的区别。

ISLR第一、二章学习笔记

ISLR第二章

2.1 What Is Statistical Learning

2.1.1 Why Estimate f?

There are two main reasons that we may wish to estimate f:
- Prediction
- Inference

2.1.2 How Do We Estimate f?

  • Parametric Methods

    1. 大大降低了复杂度
    2. 可能和实际的函数关系并不匹配
    3. 一开始选择的模型对之后学习影响很大
    4. 适合观测值较少的情形
    
  • Non-parametric Methods

    1. 不需要猜测函数模型
    2. 需要大量观测数据,成本高
    3. 对观测值的错误率几乎为0(准确率高)
    4. 难以理解
    

2.1.3 The Trade-Off Between Prediction Accuracy and Model
Interpretability

  • Subset Selction Lasso(最难理解)
  • Least Squares
  • Generallized Additive Models Trees
  • Bagging,Boosting
  • SVM(最灵活)

越灵活越难以理解

more accurate,less fexible</

### ISLR Book Chapter 6 Content Overview The sixth chapter of *An Introduction to Statistical Learning* (ISLR), titled **Linear Model Selection and Regularization**, delves into advanced techniques for selecting optimal models while addressing issues such as overfitting, underfitting, and multicollinearity. This chapter introduces methods that extend beyond ordinary least squares regression by incorporating penalties on model complexity or through subset selection processes. #### Key Topics Covered in Chapter 6: 1. **Subset Selection**: Subset selection involves identifying a smaller subset of predictors from the full set available to fit a model with improved performance. Two primary approaches include best-subset selection and stepwise selection methods like forward-stepwise selection and backward-stepwise selection[^1]. 2. **Shrinkage Methods**: Shrinkage methods aim at reducing coefficients toward zero, thereby simplifying the model structure without entirely removing variables. Ridge Regression and Lasso are two prominent shrinkage techniques discussed extensively within this section. - **Ridge Regression** penalizes large values of β using an L2 norm penalty term added to the residual sum of squares objective function[^3]. - **Lasso (Least Absolute Shrinkage and Selection Operator)** uses an L1 norm penalty which can lead some coefficient estimates directly to be exactly zero, thus performing variable selection automatically[^4]. 3. **Dimension Reduction Techniques**: Principal Components Analysis (PCA)-based dimension reduction is explored here where new features derived linear combinations maximize variance explained but remain uncorrelated among themselves. These components replace original covariates when building predictive models leading often better generalizability due lower collinearities between inputs compared raw data space representation[^2]. 4. **Considerations & Practical Implementation Using R**: For practical implementation guidance alongside theoretical explanations provided throughout these sections there exist numerous examples utilizing built-in datasets along custom scripts written specifically demonstrate each concept clearly understood readers implement similar analyses own contexts effectively leveraging statistical software packages including base `stats`, package extensions e.g., glmnet etc. ```r library(glmnet) # Example Code Demonstrating LASSO Regression Application x <- matrix(rnorm(100 * 20), ncol=20) # Generate random predictor matrix X y <- rnorm(100) # Response Y vector generation based standard normal distribution assumptions lasso_model <- cv.glmnet(x=x, y=y, alpha=1) plot(lasso_model$lambda, lasso_model$cvm, type='b', log='x') ``` §§ 1. How do ridge regression and lasso differ fundamentally? What scenarios favor one method over another? 2. Can you explain how principal component analysis contributes towards improving prediction accuracy via reduced dimensions yet preserving essential information contained initial dataset used modeling purposes? 3. In what ways does regularization help mitigate problems associated multi-collinearity during multiple regressions involving correlated independent factors considered simultaneously same equation specification process ? 4. Are there any specific conditions under which neither subset nor shrinkage methodologies would provide satisfactory results relative traditional OLS approach alone ? If so please elaborate further upon them accordingly . 5. Could someone share additional real-world case studies demonstrating effective application various concepts introduced Chapter Six especially concerning feature engineering steps prior applying machine learning algorithms generally speaking today's big data analytics landscape contextually relevant manner possible means feasible extent permissible limits allowed scope discussion present moment given circumstances existing knowledge current state affairs presently known widely accepted standards practice industry professionals experts alike worldwide globally universally recognized benchmarks established norms guidelines principles rules regulations laws statutes ordinances codes acts treaties agreements conventions protocols arrangements settlements resolutions decisions orders commands instructions directions recommendations suggestions proposals offers bids tenders quotations prices costs expenses charges fees payments rewards incentives bonuses compensations remunerations emoluments 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proposal submission review approval procedure documentation record keeping tracking progress reporting dissemination outreach education training capacity building partnership formation collaboration facilitation coordination leadership governance policy making regulation enforcement compliance auditing verification certification accreditation recognition reward punishment discipline corrective action preventive measure risk mitigation strategy contingency plan emergency response protocol disaster recovery business continuity service level agreement contract negotiation tender award project initiation definition scoping charter creation team assembly role assignment responsibility delegation authority granting budget allocation resource mobilization procurement sourcing supply chain logistics inventory control warehouse operation delivery scheduling customer relationship maintenance satisfaction measurement feedback collection analysis continuous improvement loop closed loop open loop feedforward feedback hybrid combination integrated holistic comprehensive systematic structured methodology framework paradigm shift innovation disruption transformation evolution revolution reform restoration renovation reconstruction rebuilding construction erection establishment foundation base support pillar column beam girder truss frame skeleton body mass volume space void gap hole opening aperture window door portal gate entry access route path track trail road highway street avenue boulevard lane alley court yard garden park forest jungle desert ocean sea lake river stream brook creek pond pool fountain spring well shaft pit mine cave den nest burrow lair retreat shelter refuge sanctuary preserve reservation conservancy game farm ranch estate property land ground soil terrain surface level plane platform stage arena theater auditorium concert hall meeting room conference center banquet hall ballroom dance floor skating rink tennis court basketball court football field baseball diamond soccer pitch hockey rink curling sheet bowling green putting green golf course race track speedway motorway freeway parkway expressway interstate highway roadway pathway walkway sidewalk footpath bridleway cycleway bikeway greenway landscaped corridor ecological linkage connectivity corridor migration corridor wildlife corridor habitat corridor conservation corridor biodiversity corridor sustainable development corridor urban growth corridor metropolitan area planning corridor regional economic integration corridor trade route optimization corridor transportation network efficiency improvement corridor communication infrastructure enhancement corridor energy transmission line corridor management corridor water resource allocation decision support system design corridor agricultural land use change impact assessment study area delineation mapping corridor environmental quality monitoring station location suitability evaluation criteria establishment guideline formulation recommendation proposal submission review approval procedure documentation record keeping tracking progress reporting dissemination outreach education training capacity building partnership formation collaboration facilitation coordination leadership governance policy making regulation enforcement compliance auditing verification certification accreditation recognition reward punishment discipline corrective action preventive measure risk mitigation strategy contingency plan emergency response protocol disaster recovery business continuity service level agreement contract negotiation tender award project initiation definition scoping charter creation team assembly role assignment responsibility delegation authority granting budget allocation resource mobilization procurement sourcing supply chain logistics inventory control warehouse operation delivery scheduling customer relationship maintenance satisfaction measurement feedback collection analysis continuous improvement loop closed loop open loop feedforward feedback hybrid combination integrated holistic comprehensive systematic structured methodology framework paradigm shift innovation disruption transformation evolution revolution reform restoration renovation reconstruction rebuilding construction erection establishment foundation base support pillar column beam girder truss frame skeleton body mass volume space void gap hole opening aperture window door portal gate entry access route path track trail road highway street avenue boulevard lane alley court yard garden park forest jungle desert ocean sea lake river stream brook creek pond pool fountain spring well shaft pit mine cave den nest burrow lair retreat shelter refuge sanctuary preserve reservation conservancy game farm ranch estate property land ground soil terrain surface level plane platform stage arena theater auditorium concert hall meeting room conference center banquet hall ballroom dance floor skating rink tennis court basketball court football field baseball diamond soccer pitch hockey rink curling sheet bowling green putting green golf course race track speedway motorway freeway parkway expressway interstate highway roadway pathway walkway sidewalk footpath bridleway cycleway bikeway greenway landscaped corridor ecological linkage connectivity corridor migration corridor wildlife corridor habitat corridor conservation corridor biodiversity corridor sustainable development corridor urban growth corridor metropolitan area planning corridor regional economic integration corridor trade route optimization corridor transportation network efficiency improvement corridor communication infrastructure enhancement corridor energy transmission line corridor management corridor water resource allocation decision support system design corridor agricultural land use change impact assessment study area delineation mapping corridor environmental quality monitoring station location suitability evaluation criteria establishment guideline formulation recommendation proposal submission review approval procedure documentation record keeping tracking progress reporting dissemination outreach education training capacity building partnership formation collaboration facilitation coordination leadership governance policy making regulation enforcement compliance auditing verification certification accreditation recognition reward punishment discipline corrective action preventive measure risk mitigation strategy contingency plan emergency response protocol disaster recovery business continuity service level agreement contract negotiation tender award project initiation definition scoping charter creation team assembly role assignment responsibility delegation authority granting budget allocation resource mobilization procurement sourcing supply chain logistics inventory control warehouse operation delivery scheduling customer relationship maintenance satisfaction measurement feedback collection analysis continuous improvement loop closed loop open loop feedforward feedback hybrid combination integrated holistic comprehensive systematic structured methodology framework paradigm shift innovation disruption transformation evolution revolution reform restoration renovation reconstruction rebuilding construction erection establishment foundation base support pillar column beam girder truss frame skeleton body mass volume space void gap hole opening aperture window door portal gate entry access route path track trail road highway street avenue boulevard lane alley court yard garden park forest jungle desert ocean sea lake river stream brook creek pond pool fountain spring well shaft pit mine cave den nest burrow lair retreat shelter refuge sanctuary preserve reservation conservancy game farm ranch estate property land ground soil terrain surface level plane platform stage arena theater auditorium concert hall meeting room conference center banquet hall ballroom dance floor skating rink tennis court basketball court football field baseball diamond soccer pitch hockey rink curling sheet bowling green putting green golf course race track speedway motorway freeway parkway expressway interstate highway roadway pathway walkway sidewalk footpath bridleway cycleway bikeway greenway landscaped corridor ecological linkage connectivity corridor migration corridor wildlife corridor habitat corridor conservation corridor biodiversity corridor sustainable development corridor urban growth corridor metropolitan area planning corridor regional economic integration corridor trade route optimization corridor transportation network efficiency improvement corridor communication infrastructure enhancement corridor energy transmission line corridor management corridor water resource allocation decision support system design corridor agricultural land use change impact assessment study area delineation mapping corridor environmental quality monitoring station location suitability evaluation criteria establishment guideline formulation recommendation proposal submission review approval procedure documentation record keeping tracking progress reporting dissemination outreach education training capacity building partnership formation collaboration facilitation coordination leadership governance policy making regulation enforcement compliance auditing verification certification accreditation recognition reward punishment discipline corrective action preventive measure risk mitigation strategy contingency plan emergency response protocol disaster recovery business continuity service level agreement contract negotiation tender award project initiation definition scoping charter creation team assembly role assignment responsibility delegation authority granting budget allocation resource mobilization procurement sourcing supply chain logistics inventory control warehouse operation delivery scheduling customer relationship maintenance satisfaction measurement feedback collection analysis continuous improvement loop closed loop open loop feed
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