跟读练习: Ridge vs Lasso Regression, Visualized!!! - 通过视频学习英语口语

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Ridge, regression versus lasso regression, which one will survive?

StatQuest.

Hello, I'm Josh Starmer and welcome to StatQuest.

Today we're going to talk about ridge versus lasso regression and the differences are going to be visualized.

Note, this StatQuest assumes that you are already familiar with ridge and lasso regression.

If not, check out the quests.

To show you the difference between ridge and lasso regression, we're going to use a very simple data set that consists of weight and height measurements.

And we'll start by fitting this horizontal line to the data.

This horizontal line represents a terrible fit.

And we can measure how bad that fit is by calculating residuals, the difference between the observed and predicted values.

In order to compare the horizontal line to other lines fit to the data, we will plot the sum of the squared residuals on a graph.

The y-axis on this graph is the sum of the squared residuals,

and the x-axis represents different slope values for the fitted line.

In this case, the slope for the horizontal line is 0.

Now let's increase the slope to 0.2, and calculate a new value for the sum of the squared residuals.

Now let's increase the slope to 0.4, and calculate a new value for the sum of the squared residuals.

We can keep plugging in new values for the slope and plotting the sum of the squared residuals,

Or we can just plot the curve for this equation.

We can see that the best fitting line is at the bottom of the parabola.

In other words, when the slope equals 0.45, we get the lowest sum of the squared residuals.

In this example, we simply calculated the sum of the squared residuals for different slopes.

Now let's add the ridge regression penalty, aka the L2 norm.

if you asked me, it should be called the squared penalty, since that's what it is, and, for me, way easier to remember.

The thick blue line that we just drew represents lambda equals zero.

This is because when lambda equals zero, the penalty is equal to zero,

regardless of the slope, and we are left with the original sum of squared residuals.

Now let's see what happens when we set lambda equal to 10.

And just like before, we'll start with a horizontal line, only this time, the line is orange.

Just like before, we can calculate the residuals.

And we can calculate the sum of the squared residuals plus lambda times the slope squared.

In this case, lambda equals 10.

And the slope of the horizontal line is 0.

So the penalty is 0.

So we plot the sum of the squared residuals here.

Now let's increase the slope to 0.2.

Note, the residuals are smaller than before, so the sum of squared residuals is smaller than before.

But now the penalty is 0.4.

And that gives us this point on the graph.

Now let's increase the slope to 0.4.

And the residuals are even smaller.

But now the penalty is 1.6.

And that gives us this point on the graph.

And like we did before, we can keep plugging in new values for the slope and plotting the sum of the squared residuals plus the penalty,

or we can just plot the curve with a thick orange line that represents lambda equals 10.

The bottom of the parabola is where the slope gives us the lowest sum of squared residuals plus penalty,

and that corresponds to this specific line.

And when we compare that to the optimal slope when lambda equals zero,

we see that setting lambda equal to 10 results in a smaller optimal slope.

Note, we can also see that when lambda equals 10, the lowest point in the parabola is closer to zero than when lambda equals zero.

So, either way we look at it, we see that the larger value for lambda shrunk the optimal value for the slope.

Likewise, the thick green line represents lambda equals 20.

We see that the minimum value is closer to zero, and the optimal slope has shrunk some more.

The purple lines represent lambda equals 40, and it shrinks the slope even more.

In other words, as we increase lambda for the ridge regression penalty, a.k.a the L2 penalty, a.k.a the square penalty,

The optimal slope gets closer and closer to zero, but it does not equal zero.

Bam!

Now let's see what happens if we use the lasso penalty, a.k.a the L1 norm, or, if you asked me,

I'd call it the absolute value penalty.

Unfortunately, no one asked me.

Again, the thick blue line represents lambda equals zero, so there is no extra penalty.

This is because when we plug lambda equals zero into the equation, the penalty becomes zero.

And we are left with the original sum of the squared residuals.

Note, just like before, we'll keep track of the best fitting line plus penalty in this graph on the left.

The thick orange line represents lambda equals 10, so now we are turning on the penalty and shrinking the slope.

When lambda equals 10, we start to see a kink in the curve where the slope is 0.

The thick green line represents lambda equals 20, and this kink at zero is becoming more prominent.

Lastly, the thick purple line represents lambda equals 40.

And now the kink at zero is super obvious.

Now the lowest point in the purple curve,

aka the optimal slope given the absolute value penalty when lambda equals 40, is zero.

And that means the slope of the optimal line is 0.

And that means when lambda equals 40, we ignore weight as a variable when predicting height.

Double bam!

In summary, when we increase the ridge regression penalty, a.k.a the L2 penalty, a.k.a the square penalty,

the optimal slopes shift towards zero, but we retain a nice parabola shape.

And even when we set lambda to something crazy high like 400, we still end up with an optimal value greater than zero.

In contrast, when we increase the lasso penalty, a.k.a the L1 penalty, a.k.a the absolute value penalty,

The optimal value shifts towards zero, but since we have a kink at zero, zero ends up being the optimal slope.

Bam!

Hooray!

We've made it to the end of another exciting StatQuest.

If you like this StatQuest and want to see more, please subscribe.

And if you want to support StatQuest, consider contributing to my Patreon campaign,

becoming a channel member, buying one or two of my original songs or a t-shirt or a hoodie or just donate.

The links are in the description below.

All right, until next time, quest on!

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FOR YOU

本课的词汇与口语要点

这节口语课以视频“Ridge vs Lasso Regression, Visualized!!!”为素材。视频中反复出现的词有：slope, penalty, lambda, equal, zero。这段视频共有 86 个句子、1111 个单词可供跟读。讲话部分时长为 9:04。说话人语速平稳，每分钟约 122 个词，很适合跟读。只有 70% 的单词属于英语最常用的 3,000 词，词汇难度较高。

视频中的重点词汇

视频中 15 个值得学习的单词，附发音和释义：

单词	发音	释义
slope 名词	/sloʊp/	斜坡, 坡
penalty 名词	/ˈpɛn.əl.ti/	懲罰 /惩罚
optimal 形容词	/ˈɑptɪməl/	最佳的
thick 形容词	/θɪk/	ху, 厚
ridge 名词	/ɹɪd͡ʒ/	背脊
horizontal 形容词	/ˌhoɹəˈzɑn.təl/	水平, 橫的 /横的
calculate 动词	/ˈkælkjʊleɪt/	計算 /计算, 算
graph 名词	/ɡɹæf/	圖表 /图表
curve 名词	/kɚv/	彎子 /弯子
purple 名词	/ˈpɝ.pl̩/	紫色
plug 名词	/plʌɡ/	插頭 /插头
compare 动词	/kəmˈpɛɚ/	比, 比較 /比较
versus	/ˈvɝsəs/	對 /对
quest 名词	/kwɛst/	探索, 尋求 /寻求
predict 动词	/pɹɪˈdɪkt/	預言 /预言

视频中出现的短语动词

单词	释义
check out 动词	退房
end up 动词	到达

视频中的语法

说话人最常用的结构，并附上视频中的原话：

结构	视频中的用法
被动语态 be + 过去分词 — 强调发生了什么，而不是谁做的	be visualized · should be called · are left
现在完成时 have/has + 过去分词 — 过去发生但与现在仍有关联的事	has shrunk · We've made

需要注意的发音

说话人用了 8 次缩略和弱读形式，例如 we'll, we're, I'd。请按听到的简短形式来说。

“sh” 和 “zh” 音: equation /ɪˈkweɪ.ʒən/, contrast /kənˈt(ʃ)ɹæst/, measurement /ˈmɛʒ.ə.mənt/, regression /ɹiːˈɡɹɛʃ.ən/, visualize /ˈvɪʒuəˌlaɪz/
长单词——注意重音位置: residual /ɹɪˈzɪd͡ʒ.u.əl/, horizontal /ˌhoɹəˈzɑn.təl/, parabola /pəˈɹæb.ə.lə/

中文母语者容易读错的音：

/v/ — 不要读成 /w/，上齿轻触下唇: curve /kɚv/, versus /ˈvɝsəs/, variable [ˈvæɹ.i.ə.bl̩], observe /əbˈzɜːv/, visualize /ˈvɪʒuəˌlaɪz/
词尾辅音 — 要读清楚，后面不要加元音: slope /sloʊp/, thick /θɪk/, ridge /ɹɪd͡ʒ/, calculate /ˈkælkjʊleɪt/, graph /ɡɹæf/
/r/ 和 /l/ 的区别: residual /ɹɪˈzɪd͡ʒ.u.əl/, horizontal /ˌhoɹəˈzɑn.təl/, regardless /ɹɪˈɡɑɹd.lɪs/, variable [ˈvæɹ.i.ə.bl̩], parabola /pəˈɹæb.ə.lə/

如何用这段视频练习

先完整听一遍视频，不要开口，记下不认识的单词。
用正常速度逐句跟读，每句重复到你的节奏与说话人一致为止。
录下自己的声音并与原声对比，特别注意 slope, penalty, optimal 这类单词。

什么是跟读法？

跟读法 (Shadowing) 是一种有科学依据的语言学习技巧，最初开发用于专业口译员的培训，并由多语言者Alexander Arguelles博士普及。这个方法简单而强大：您在听英语母语原声的同时立即大声重复——就像是一个延迟1-2秒紧跟说话者的影子。与被动听力或语法练习不同，跟读法强迫您的大脑和口腔肌肉同时处理并模仿真实的讲话模式。研究表明它能显着提高发音准确性，语调，节奏，连读，听力理解和口语流利度——使其成为雅思口语备考和真实英语交流最有效的方法之一。

影子跟读法: 阅读完整分步指南 →

跟读练习: Ridge vs Lasso Regression, Visualized!!! - 通过视频学习英语口语

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