Shadowing Practice: Ridge vs Lasso Regression, Visualized!!! - Learn English Speaking with 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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Vocabulario y notas de pronunciación para esta lección
Esta lección de conversación se basa en el vídeo “Ridge vs Lasso Regression, Visualized!!!”. Las palabras que más se repiten: slope, penalty, lambda, equal, zero. Este vídeo tiene 86 frases y 1111 palabras para practicar shadowing. La parte hablada dura 9:04. El hablante mantiene un ritmo constante de unas 122 palabras por minuto, cómodo para el shadowing. Solo el 70 % de las palabras está entre las 3.000 más comunes del inglés, por lo que el vocabulario es exigente.
Vocabulario clave de este vídeo
15 palabras del vídeo que vale la pena aprender, con su pronunciación y significado:
| Palabra | Pronunciación | Significado |
|---|---|---|
| slope sustantivo | /sloʊp/ | pendiente, cuesta |
| penalty sustantivo | /ˈpɛn.əl.ti/ | pena |
| residual adjetivo | /ɹɪˈzɪd͡ʒ.u.əl/ | residual |
| optimal adjetivo | /ˈɑptɪməl/ | óptimo, en fa |
| thick adjetivo | /θɪk/ | grueso, espeso |
| ridge sustantivo | /ɹɪd͡ʒ/ | cresta, arista |
| horizontal adjetivo | /ˌhoɹəˈzɑn.təl/ | horizontal |
| calculate verbo | /ˈkælkjʊleɪt/ | calcular |
| graph sustantivo | /ɡɹæf/ | gráfico, gráfica |
| curve sustantivo | /kɚv/ | curva |
| purple sustantivo | /ˈpɝ.pl̩/ | morado, púrpura |
| plug sustantivo | /plʌɡ/ | enchufe, clavija |
| compare verbo | /kəmˈpɛɚ/ | comparar, parangonar |
| versus | /ˈvɝsəs/ | contra, en vez de |
| quest sustantivo | /kwɛst/ | búsqueda, esfuerzo |
Phrasal verbs que vas a escuchar
| Palabra | Significado |
|---|---|
| check out verbo | investigar, chequear |
| end up verbo | terminar, ir a parar |
Gramática en este vídeo
Las estructuras que más usa el hablante, con las palabras exactas del vídeo:
| Estructura | En el vídeo |
|---|---|
| Voz pasiva be + participio pasado — importa lo que ocurre, no quién lo hace | be visualized · should be called · are left |
| Present perfect have/has + participio pasado — una acción pasada que sigue importando ahora | has shrunk · We've made |
Pronunciación a tener en cuenta
El hablante usa 8 contracciones y formas reducidas, como we'll, we're, I'd. Dilas en su forma corta, tal como las oyes.
- Los sonidos de “sh” y “zh”: equation /ɪˈkweɪ.ʒən/, contrast /kənˈt(ʃ)ɹæst/, measurement /ˈmɛʒ.ə.mənt/, regression /ɹiːˈɡɹɛʃ.ən/, visualize /ˈvɪʒuəˌlaɪz/
- Palabras largas — cuida el acento: residual /ɹɪˈzɪd͡ʒ.u.əl/, horizontal /ˌhoɹəˈzɑn.təl/, parabola /pəˈɹæb.ə.lə/
Sonidos difíciles para hispanohablantes:
- /v/ — no es /b/: los dientes tocan el labio inferior: curve /kɚv/, versus /ˈvɝsəs/, variable [ˈvæɹ.i.ə.bl̩], observe /əbˈzɜːv/, visualize /ˈvɪʒuəˌlaɪz/
- /z/ — sonora, no /s/: residual /ɹɪˈzɪd͡ʒ.u.əl/, horizontal /ˌhoɹəˈzɑn.təl/, observe /əbˈzɜːv/, likewise /ˈlaɪkˌwaɪz/, visualize /ˈvɪʒuəˌlaɪz/
- /dʒ/ — no es la “y” ni la “ch”: residual /ɹɪˈzɪd͡ʒ.u.əl/, ridge /ɹɪd͡ʒ/
Cómo practicar con este vídeo
- Escucha el vídeo entero una vez sin hablar y anota las palabras que no conoces.
- Haz shadowing frase por frase a velocidad normal, repitiendo cada una hasta que tu ritmo coincida con el del hablante.
- Grábate y compara con el original, prestando atención a palabras como slope, penalty, residual.
¿Qué es la Técnica de Shadowing?
Shadowing es una técnica de aprendizaje de idiomas respaldada por la ciencia, desarrollada originalmente para la formación de intérpretes profesionales y popularizada por el políglota Dr. Alexander Arguelles. El método es simple pero poderoso: escuchas audio en inglés nativo y lo repites en voz alta de inmediato, como una sombra que sigue al hablante con solo 1-2 segundos de retraso. A diferencia de la escucha pasiva o los ejercicios de gramática, el shadowing obliga a tu cerebro y músculos de la boca a procesar y reproducir simultáneamente patrones de habla reales. Las investigaciones muestran que mejora significativamente la precisión de la pronunciación, la entonación, el ritmo, el habla conectada, la comprensión auditiva y la fluidez al hablar, convirtiéndola en una de las metodologías más efectivas para la preparación del IELTS Speaking y la comunicación en inglés en el mundo real.