###過擬合問題

Overfitting problem 過擬合問題

Regularization 正則化

Ameliorate 改善

Underfitting 欠擬合   high bias 高偏差

Preconception 偏見

Quadratic function二階項(xiàng)

Extreme  極端

Wiggly波動(dòng)

If we’re fitting such a high order polynomial,then the hypothesis can fit,it’s almost as if it can fit almost any function.And this face of possible hypothesis is just too large,it’s too variable.And we don’t have enough data to constrain it to give us a good hypothesis,so that’s called overfitting.

如果我們擬合一個(gè)高階多項(xiàng)式，那么這個(gè)假設(shè)函數(shù)，能擬合幾乎所有的數(shù)據(jù)。這就面臨可能的函數(shù)太過于龐大，變量太多的問題。并且我們沒有足夠的數(shù)據(jù)來(lái)約束它來(lái)獲得一個(gè)好的假設(shè)函數(shù)，這就是過度擬合。

Constrain 約束

High order polynomial 高階多項(xiàng)式

Contort 扭曲

Debug 調(diào)試

Diagnose 診斷

If we have a lot of features and very little training data,then overfitting can become a problem.

如果我們有過多的變量，但是只有非常少的訓(xùn)練數(shù)據(jù)，就會(huì)出現(xiàn)過度擬合的問題。

Manually人工地

Throw out 舍棄

Model selection 模型選擇

Magnitude 量級(jí)

###代價(jià)函數(shù)

Convey to you向你們介紹

Generalize 泛化

我們對(duì)θ_3和θ_4加入了懲罰項(xiàng)

Small  terms特別小的項(xiàng)

The ideal is that ,if we have small values for the parameters,then having small values for the parameters will somehow,will usually correspond to having a simpler hypothesis

正則化的思想就是，如果我們的參數(shù)值較小，參數(shù)值較小就意味著一個(gè)更簡(jiǎn)單的假設(shè)模型。

Writing down our regularized optimization objective,our regularized cost function again.Here it is.

寫下正則化的優(yōu)化目標(biāo)，也就是正則化代價(jià)函數(shù)，也就是J(θ)

The λ is controls a trade off between two different goals.The first goal,captured by the first term of the objective,is that we would like to train，is that we would like to fit the training data well,we would like to fit the training set well.And the second goal is,we want to keep the parameters small.the lambda is the regularization parameter does,is the controls the trade off between these two goals.

Λ控制著兩個(gè)不同目標(biāo)之間的取舍。第一個(gè)目標(biāo)，和目標(biāo)函數(shù)的第一項(xiàng)有關(guān)，就是我們想去訓(xùn)練，想要更好地?cái)M合數(shù)據(jù)，更好的擬合訓(xùn)練集。而第二個(gè)目標(biāo)就是，我們想要保持參數(shù)盡量地小。Λ也就是正則化參數(shù)，作用是控制這兩個(gè)目標(biāo)之間的平衡關(guān)系。

Smooth平滑

So for sure regularization to work well,some care should be taken,to choose a good choice for the good regularization parameter lambda as well.

為了讓正則化起到應(yīng)有的效果，我們應(yīng)該注意一下，去選擇一個(gè)更合適的正則化參數(shù)λ

###線性回歸的正則化

【目前為止，我學(xué)了線性回歸，logistic回歸，正則化】

【線性回歸中，推導(dǎo)過兩種辦法1梯度下降 2正則方程】

然后找一個(gè)參數(shù)θ，來(lái)最小化代價(jià)函數(shù)J(θ)。

在沒有正則化的梯度下降法中，我們不斷的更新θ，當(dāng)j從0到n。