シャドーイング練習: Ridge vs Lasso Regression, Visualized!!! - 動画で英語スピーキングを学ぶ

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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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このレッスンの語彙とスピーキングのポイント

このスピーキングレッスンは、動画「Ridge vs Lasso Regression, Visualized!!!」を教材にしています。繰り返し出てくる語は次のとおりです：slope, penalty, lambda, equal, zero。この動画には、シャドーイング用の文が86文、単語が1111語あります。音声の長さは9:04です。話す速さは1分あたり約122語で安定しており、シャドーイングしやすいペースです。英語の頻出3,000語に含まれる単語は70%だけなので、語彙は難しめです。

この動画の重要語彙

動画に出てくる覚えておきたい単語15語を、発音と意味つきで紹介します。

単語	発音	意味
slope 名詞	/sloʊp/	坂, 坂道
penalty 名詞	/ˈpɛn.əl.ti/	刑, 刑罰
optimal 形容詞	/ˈɑptɪməl/	最適な
thick 形容詞	/θɪk/	太い, 厚い
horizontal 形容詞	/ˌhoɹəˈzɑn.təl/	水平な, 横の
calculate 動詞	/ˈkælkjʊleɪt/	計算する
graph 名詞	/ɡɹæf/	グラフ, 図表
curve 名詞	/kɚv/	曲線
purple 名詞	/ˈpɝ.pl̩/	紫
plug 名詞	/plʌɡ/	プラグ
compare 動詞	/kəmˈpɛɚ/	比べる, 比較する
versus	/ˈvɝsəs/	対, バーサス
quest 名詞	/kwɛst/	探索, 探求
predict 動詞	/pɹɪˈdɪkt/	予言する
axis 名詞	/ˈæksɪs/	軸

動画に出てくる句動詞

単語	意味
check out 動詞	試験する, 検査する

この動画の文法

話し手がよく使っている文型を、動画の実際の表現とともに紹介します。

文型	動画での表現
受動態 be + 過去分詞 — 誰がするかより、何が起きるかに焦点を当てる	be visualized · should be called · are left
現在完了形 have/has + 過去分詞 — 過去の出来事が今も関係している	has shrunk · We've made

注意したい発音

話し手はwe'll, we're, I'dなど、短縮形や弱形を8回使っています。聞こえたとおりの短い形で発音しましょう。

「sh」と「zh」の音: equation /ɪˈkweɪ.ʒən/, contrast /kənˈt(ʃ)ɹæst/, measurement /ˈmɛʒ.ə.mənt/, regression /ɹiːˈɡɹɛʃ.ən/, visualize /ˈvɪʒuəˌlaɪz/
長い単語（アクセントの位置に注意）: residual /ɹɪˈzɪd͡ʒ.u.əl/, horizontal /ˌhoɹəˈzɑn.təl/, parabola /pəˈɹæb.ə.lə/

日本語話者が苦手な音：

/r/ と /l/ の区別 — /l/ は舌先を歯茎につけ、/r/ はどこにもつけない: residual /ɹɪˈzɪd͡ʒ.u.əl/, horizontal /ˌhoɹəˈzɑn.təl/, regardless /ɹɪˈɡɑɹd.lɪs/, variable [ˈvæɹ.i.ə.bl̩], parabola /pəˈɹæb.ə.lə/
/v/ — /b/ にならないように、上の歯を下唇に当てる: curve /kɚv/, versus /ˈvɝsəs/, variable [ˈvæɹ.i.ə.bl̩], observe /əbˈzɜːv/, visualize /ˈvɪʒuəˌlaɪz/
子音の連続 — 間に母音を入れない: slope /sloʊp/, calculate /ˈkælkjʊleɪt/, graph /ɡɹæf/, plug /plʌɡ/, quest /kwɛst/

この動画での練習方法

まず声を出さずに動画を最後まで聞き、知らない単語をメモします。
通常の速度で一文ずつシャドーイングし、話し手のリズムに合うまで繰り返します。
自分の声を録音して元の音声と比べます。slope, penalty, optimalなどの単語に特に注意しましょう。

シャドーイングとは？英語上達に効果的な理由

シャドーイング（Shadowing）は、もともとプロの通訳者養成プログラムで開発された言語学習法で、多言語習得者として知られるDr. Alexander Arguelles によって広く普及されました。方法はシンプルですが非常に効果的：ネイティブスピーカーの英語を聞きながら、1〜2秒の遅延で声に出してすぐに繰り返す——まるで「影（shadow）」のように話者を追いかけます。文法ドリルや受動的なリスニングと異なり、シャドーイングは脳と口の筋肉が同時にリアルタイムで英語を処理・再現することを強制します。研究により、発音精度、抑揚、リズム、連音、リスニング力、そして会話の流暢さが大幅に向上することが確認されています。IELTSスピーキング対策や自然な英語コミュニケーションを目指す方に特におすすめです。

シャドーイングのやり方: ステップ別の完全ガイドを読む →

シャドーイング練習: Ridge vs Lasso Regression, Visualized!!! - 動画で英語スピーキングを学ぶ

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