Pratica di Shadowing: Ridge vs Lasso Regression, Visualized!!! - Impara a parlare inglese con i video
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Ridge, regression versus lasso regression, which one will survive?
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StatQuest.
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Hello, I'm Josh Starmer and welcome to StatQuest.
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Today we're going to talk about ridge versus lasso regression and the differences are going to be visualized.
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Note, this StatQuest assumes that you are already familiar with ridge and lasso regression.
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If not, check out the quests.
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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.
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And we'll start by fitting this horizontal line to the data.
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This horizontal line represents a terrible fit.
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And we can measure how bad that fit is by calculating residuals, the difference between the observed and predicted values.
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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.
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The y-axis on this graph is the sum of the squared residuals,
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and the x-axis represents different slope values for the fitted line.
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In this case, the slope for the horizontal line is 0.
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Now let's increase the slope to 0.2, and calculate a new value for the sum of the squared residuals.
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Now let's increase the slope to 0.4, and calculate a new value for the sum of the squared residuals.
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We can keep plugging in new values for the slope and plotting the sum of the squared residuals,
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Or we can just plot the curve for this equation.
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We can see that the best fitting line is at the bottom of the parabola.
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In other words, when the slope equals 0.45, we get the lowest sum of the squared residuals.
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In this example, we simply calculated the sum of the squared residuals for different slopes.
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Now let's add the ridge regression penalty, aka the L2 norm.
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if you asked me, it should be called the squared penalty, since that's what it is, and, for me, way easier to remember.
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The thick blue line that we just drew represents lambda equals zero.
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This is because when lambda equals zero, the penalty is equal to zero,
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regardless of the slope, and we are left with the original sum of squared residuals.
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Now let's see what happens when we set lambda equal to 10.
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And just like before, we'll start with a horizontal line, only this time, the line is orange.
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Just like before, we can calculate the residuals.
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And we can calculate the sum of the squared residuals plus lambda times the slope squared.
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In this case, lambda equals 10.
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And the slope of the horizontal line is 0.
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So the penalty is 0.
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So we plot the sum of the squared residuals here.
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Now let's increase the slope to 0.2.
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Note, the residuals are smaller than before, so the sum of squared residuals is smaller than before.
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But now the penalty is 0.4.
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And that gives us this point on the graph.
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Now let's increase the slope to 0.4.
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And the residuals are even smaller.
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But now the penalty is 1.6.
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And that gives us this point on the graph.
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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,
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or we can just plot the curve with a thick orange line that represents lambda equals 10.
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The bottom of the parabola is where the slope gives us the lowest sum of squared residuals plus penalty,
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and that corresponds to this specific line.
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And when we compare that to the optimal slope when lambda equals zero,
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we see that setting lambda equal to 10 results in a smaller optimal slope.
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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.
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So, either way we look at it, we see that the larger value for lambda shrunk the optimal value for the slope.
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Likewise, the thick green line represents lambda equals 20.
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We see that the minimum value is closer to zero, and the optimal slope has shrunk some more.
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The purple lines represent lambda equals 40, and it shrinks the slope even more.
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In other words, as we increase lambda for the ridge regression penalty, a.k.a the L2 penalty, a.k.a the square penalty,
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The optimal slope gets closer and closer to zero, but it does not equal zero.
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Bam!
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Now let's see what happens if we use the lasso penalty, a.k.a the L1 norm, or, if you asked me,
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I'd call it the absolute value penalty.
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Unfortunately, no one asked me.
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Again, the thick blue line represents lambda equals zero, so there is no extra penalty.
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This is because when we plug lambda equals zero into the equation, the penalty becomes zero.
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And we are left with the original sum of the squared residuals.
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Note, just like before, we'll keep track of the best fitting line plus penalty in this graph on the left.
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The thick orange line represents lambda equals 10, so now we are turning on the penalty and shrinking the slope.
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When lambda equals 10, we start to see a kink in the curve where the slope is 0.
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The thick green line represents lambda equals 20, and this kink at zero is becoming more prominent.
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Lastly, the thick purple line represents lambda equals 40.
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And now the kink at zero is super obvious.
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Now the lowest point in the purple curve,
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aka the optimal slope given the absolute value penalty when lambda equals 40, is zero.
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And that means the slope of the optimal line is 0.
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And that means when lambda equals 40, we ignore weight as a variable when predicting height.
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Double bam!
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In summary, when we increase the ridge regression penalty, a.k.a the L2 penalty, a.k.a the square penalty,
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the optimal slopes shift towards zero, but we retain a nice parabola shape.
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And even when we set lambda to something crazy high like 400, we still end up with an optimal value greater than zero.
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In contrast, when we increase the lasso penalty, a.k.a the L1 penalty, a.k.a the absolute value penalty,
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The optimal value shifts towards zero, but since we have a kink at zero, zero ends up being the optimal slope.
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Bam!
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Hooray!
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We've made it to the end of another exciting StatQuest.
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If you like this StatQuest and want to see more, please subscribe.
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And if you want to support StatQuest, consider contributing to my Patreon campaign,
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becoming a channel member, buying one or two of my original songs or a t-shirt or a hoodie or just donate.
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The links are in the description below.
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All right, until next time, quest on!
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Vocabolario e note di pronuncia per questa lezione
Questa lezione di conversazione si basa sul video “Ridge vs Lasso Regression, Visualized!!!”. Le parole che ritornano più spesso: slope, penalty, lambda, equal, zero. Questo video contiene 86 frasi e 1111 parole da ripetere con lo shadowing. Il parlato dura 9:04. Chi parla mantiene un ritmo costante di circa 122 parole al minuto, comodo per lo shadowing. Solo il 70% delle parole rientra nelle 3.000 più comuni dell’inglese, quindi il lessico è impegnativo.
Vocaboli chiave di questo video
15 parole del video che vale la pena imparare, con pronuncia e significato:
| Parola | Pronuncia | Significato |
|---|---|---|
| slope sostantivo | /sloʊp/ | pendio |
| penalty sostantivo | /ˈpɛn.əl.ti/ | penalità |
| residual aggettivo | /ɹɪˈzɪd͡ʒ.u.əl/ | residuo, residuato |
| thick aggettivo | /θɪk/ | spesso |
| ridge sostantivo | /ɹɪd͡ʒ/ | cresta, crinale |
| horizontal aggettivo | /ˌhoɹəˈzɑn.təl/ | orizzontale |
| calculate verbo | /ˈkælkjʊleɪt/ | calcolare |
| graph sostantivo | /ɡɹæf/ | grafico |
| curve sostantivo | /kɚv/ | curva |
| purple sostantivo | /ˈpɝ.pl̩/ | viola |
| plug sostantivo | /plʌɡ/ | spina |
| compare verbo | /kəmˈpɛɚ/ | paragonare |
| versus | /ˈvɝsəs/ | contro |
| quest sostantivo | /kwɛst/ | missione, impresa |
| predict verbo | /pɹɪˈdɪkt/ | profetizzare |
I phrasal verb che sentirai
| Parola | Significato |
|---|---|
| check out verbo | investigare |
| end up verbo | andare a finire, finire |
La grammatica di questo video
Le strutture che chi parla usa di più, con le parole esatte del video:
| Struttura | Nel video |
|---|---|
| Forma passiva be + participio passato — conta ciò che accade, non chi lo fa | be visualized · should be called · are left |
| Present perfect have/has + participio passato — un’azione passata che conta ancora adesso | has shrunk · We've made |
Pronuncia a cui fare attenzione
Chi parla usa 8 contrazioni e forme ridotte, come we'll, we're, I'd. Pronunciale nella forma breve, così come le senti.
- I suoni “sh” e “zh”: equation /ɪˈkweɪ.ʒən/, contrast /kənˈt(ʃ)ɹæst/, measurement /ˈmɛʒ.ə.mənt/, regression /ɹiːˈɡɹɛʃ.ən/, visualize /ˈvɪʒuəˌlaɪz/
- Parole lunghe — attenzione all’accento: residual /ɹɪˈzɪd͡ʒ.u.əl/, horizontal /ˌhoɹəˈzɑn.təl/, parabola /pəˈɹæb.ə.lə/
I suoni difficili per chi parla italiano:
- Consonante finale — senza aggiungere una vocale dopo: slope /sloʊp/, thick /θɪk/, ridge /ɹɪd͡ʒ/, calculate /ˈkælkjʊleɪt/, graph /ɡɹæf/
- /æ/ — più aperta della “e”: calculate /ˈkælkjʊleɪt/, graph /ɡɹæf/, axis /ˈæksɪs/, contrast /kənˈt(ʃ)ɹæst/, variable [ˈvæɹ.i.ə.bl̩]
Come esercitarsi con questo video
- Ascolta tutto il video una volta senza parlare e annota le parole che non conosci.
- Fai shadowing frase per frase a velocità normale, ripetendo ognuna finché il tuo ritmo coincide con quello di chi parla.
- Registrati e confronta con l’originale, facendo attenzione a parole come slope, penalty, residual.
Cos'è la tecnica dello Shadowing?
Shadowing è una tecnica di apprendimento delle lingue supportata da studi scientifici, originariamente sviluppata per la formazione dei traduttori professionisti e resa popolare dal poliglotta Dr. Alexander Arguelles. Il metodo è semplice ma potente: ascolti un audio in inglese di madrelingua e lo ripeti immediatamente ad alta voce — come un'ombra che segue il parlante con un ritardo di solo 1–2 secondi. A differenza dell'ascolto passivo o degli esercizi di grammatica, lo shadowing costringe il tuo cervello e i muscoli della bocca a elaborare e riprodurre simultaneamente i modelli di discorso reale. La ricerca dimostra che migliora significativamente la precisione della pronuncia, l'intonazione, il ritmo, il discorso connesso, la comprensione dell'ascolto e la fluidità del parlato — rendendolo uno dei metodi più efficaci per la preparazione alla prova di speaking dell'IELTS e per la comunicazione reale in inglese.