官术网_书友最值得收藏!

Regularization in a nutshell

You may recall that our linear model follows the form, Y = B0 + B1x1 +...Bnxn + e, and also that the best fit tries to minimize the RSS, which is the sum of the squared errors of the actual minus the estimate, or e12 + e22 + ... en2.

With regularization, we will apply what is known as shrinkage penalty in conjunction with the minimization RSS. This penalty consists of a lambda (symbol λ), along with the normalization of the beta coefficients and weights. How these weights are normalized differs in the techniques, and we will discuss them accordingly. Quite simply, in our model, we are minimizing (RSS + λ(normalized coefficients)). We will select λ, which is known as the tuning parameter, in our model building process. Please note that if lambda is equal to 0, then our model is equivalent to OLS, as it cancels out the normalization term.

So what does this do for us and why does it work? First of all, regularization methods are very computationally efficient. In best subsets, we are searching 2p models, and in large datasets, it may not be feasible to attempt. In R, we are only fitting one model to each value of lambda and this is far more efficient. Another reason goes back to our bias-variance trade-off, which was discussed in the preface. In the linear model, where the relationship between the response and the predictors is close to linear, the least squares estimates will have low bias but may have high variance. This means that a small change in the training data can cause a large change in the least squares coefficient estimates (James, 2013). Regularization through the proper selection of lambda and normalization may help you improve the model fit by optimizing the bias-variance trade-off. Finally, regularization of coefficients works to solve multi collinearity problems.

主站蜘蛛池模板: 田东县| 鄯善县| 宜城市| 金塔县| 合江县| 蒲城县| 襄樊市| 玉龙| 彭州市| 杨浦区| 家居| 江津市| 陕西省| 吉安市| 视频| 都昌县| 马尔康县| 兴安盟| 宁南县| 泊头市| 绍兴县| 驻马店市| 五河县| 咸丰县| 遵义县| 景洪市| 瓦房店市| 柘荣县| 夏邑县| 克什克腾旗| 凤凰县| 嘉义市| 弥渡县| 广水市| 永安市| 宝应县| 松溪县| 准格尔旗| 格尔木市| 惠水县| 彭泽县|