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All right. Um, let's get started. | All right. Um, let's get started. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 151.07869 | 27.626228 | 16.266287 | 46.941765 | slightly fast | ɔl ɹaɪt. ʌm, lɛt'ɛs ɡɛt stɑɹtɪd. | very noisy | moderate reverberation | quite monotone |
there won't be a section, uh, this Friday, okay? | there won't be a section, uh, this Friday, okay? | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 114.61998 | 38.79863 | 20.250143 | 57.590553 | slightly fast | ðɛɹ wʌn'ti bi ʌ sɛkʃʌn, ʌ, ðɪs fɹaɪdi, oʊkeɪ? | very noisy | very confined sounding | slightly monotone |
Um, and then the second part of the algorithm was again, | Um, and then the second part of the algorithm was again, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 95.740906 | 27.820704 | 32.773682 | 37.792564 | moderate speed | ʌm, ʌnd ðɛn ðʌ sɛkʌnd pɑɹt ʌv ðʌ ælɡɜ˞ɪðʌm wɑz ʌɡɛn, | very noisy | quite roomy sounding | quite monotone |
this is a convex function, this is a convex function. | this is a convex function, this is a convex function. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 99.423248 | 8.325679 | 14.794849 | 59.80439 | very fast | ðɪs ɪz ʌ kʌnvɛks fʌŋkʃʌn, ðɪs ɪz ʌ kʌnvɛks fʌŋkʃʌn. | very noisy | very confined sounding | very monotone |
Turns out a straight line, | Turns out a straight line, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 117.71151 | 18.102331 | 26.923498 | 31.050282 | quite fast | tɜ˞nz aʊt ʌ stɹeɪt laɪn, | very noisy | very roomy sounding | quite monotone |
that's also a convex function. | that's also a convex function. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 84.86451 | 16.805794 | 16.351959 | 48.221336 | quite fast | ðæt'ɛs ɔlsoʊ ʌ kʌnvɛks fʌŋkʃʌn. | very noisy | slightly confined sounding | very monotone |
Uh, but so in this addendum, | Uh, but so in this addendum, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 122.9291 | 27.674416 | 23.589886 | 43.413403 | moderate speed | ʌ, bʌt soʊ ɪn ðɪs ʌdɛndʌm, | very noisy | moderate reverberation | quite monotone |
we're saying that if f is a strictly convex function, | we're saying that if f is a strictly convex function, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 130.328857 | 33.176041 | 20.344738 | 54.384331 | very fast | wi'ɹeɪ seɪɪŋ ðæt ɪf ɛf ɪz ʌ stɹɪktli kʌnvɛks fʌŋkʃʌn, | very noisy | quite confined sounding | quite monotone |
meaning basically, you know, it's not a straight line, right? | meaning basically, you know, it's not a straight line, right? | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 105.418953 | 27.842913 | 27.497026 | 59.536564 | very fast | minɪŋ beɪsɪkli, ju noʊ, ɪt'ɛs nɑt ʌ stɹeɪt laɪn, ɹaɪt? | very noisy | very confined sounding | quite monotone |
Uh, and- and a bit more than it's not a straight line. | Uh, and- and a bit more than it's not a straight line. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 114.506989 | 25.301521 | 34.940887 | 59.609764 | very fast | ʌ, ʌnd- ʌnd ʌ bɪt mɔɹ ðæn ɪt'ɛs nɑt ʌ stɹeɪt laɪn. | quite noisy | very confined sounding | quite monotone |
There's a- but if the curvature, | There's a- but if the curvature, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 109.102585 | 12.887964 | 20.399179 | 59.794968 | quite fast | ðɛɹ'ɛs ʌ- bʌt ɪf ðʌ kɜ˞vʌtʃɜ˞, | very noisy | very confined sounding | very monotone |
if it's always bending up, | if it's always bending up, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 103.579254 | 12.158989 | 19.127918 | 59.12056 | slightly slowly | ɪf ɪt'ɛs ɔlweɪz bɛndɪŋ ʌp, | very noisy | very confined sounding | very monotone |
uh, then the only way for the left and right-hand sides to be equal, | uh, then the only way for the left and right-hand sides to be equal, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 115.674667 | 28.160439 | 28.020575 | 59.729652 | moderate speed | ʌ, ðɛn ðʌ oʊnli weɪ fɔɹ ðʌ lɛft ʌnd ɹaɪt-hænd saɪdz tu bi ikwʌl, | very noisy | very confined sounding | quite monotone |
uh, look at the blue dots, find the mean, | uh, look at the blue dots, find the mean, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 114.025063 | 26.603607 | 22.0091 | 26.896133 | slightly fast | ʌ, lʊk æt ðʌ blu dɑts, faɪnd ðʌ min, | very noisy | very roomy sounding | quite monotone |
is if x is a constant, | is if x is a constant, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 105.179649 | 16.68531 | 14.779914 | 59.671246 | moderate speed | ɪz ɪf ɛks ɪz ʌ kɑnstʌnt, | very noisy | very confined sounding | very monotone |
meaning it's a random variable that always takes on the same value. | meaning it's a random variable that always takes on the same value. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 99.076485 | 20.306822 | 23.160994 | 59.312778 | slightly fast | minɪŋ ɪt'ɛs ʌ ɹændʌm vɛɹiʌbʌl ðæt ɔlweɪz teɪks ɑn ðʌ seɪm vælju. | very noisy | very confined sounding | quite monotone |
Okay? Uh, so Jensen's equality says that, you know, | Okay? Uh, so Jensen's equality says that, you know, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 124.63649 | 40.359505 | 25.974491 | 56.950798 | moderate speed | oʊkeɪ? ʌ, soʊ dʒɛnsʌn'ɛs ɪkwɑlʌti sɛz ðæt, ju noʊ, | very noisy | very confined sounding | slightly monotone |
um, uh, left-hand side is gonna be the same as right-hand side. | um, uh, left-hand side is gonna be the same as right-hand side. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 107.088821 | 11.073024 | 24.580797 | 59.5228 | slightly fast | ʌm, ʌ, lɛft-hænd saɪd ɪz ɡɑnʌ bi ðʌ seɪm æz ɹaɪt-hænd saɪd. | very noisy | very confined sounding | very monotone |
Sorry, I think I- I reversed the order of these two for that equation, | Sorry, I think I- I reversed the order of these two for that equation, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 104.051552 | 24.429287 | 23.336163 | 57.563309 | very fast | sɑɹi, aɪ θɪŋk aɪ- aɪ ɹɪvɜ˞st ðʌ ɔɹdɜ˞ ʌv ðiz tu fɔɹ ðæt ɪkweɪʒʌn, | very noisy | very confined sounding | quite monotone |
but it doesn't matter, right? | but it doesn't matter, right? | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 82.879112 | 8.298046 | 20.577389 | 57.170666 | very fast | bʌt ɪt 'ti mætɜ˞, ɹaɪt? | very noisy | very confined sounding | very monotone |
But so Jensen's equality says left-hand side is always less than equal to the right-hand side, | But so Jensen's equality says left-hand side is always less than equal to the right-hand side, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 134.819946 | 31.511347 | 30.072779 | 59.697399 | very fast | bʌt soʊ dʒɛnsʌn'ɛs ɪkwɑlʌti sɛz lɛft-hænd saɪd ɪz ɔlweɪz lɛs ðæn ikwʌl tu ðʌ ɹaɪt-hænd saɪd, | very noisy | very confined sounding | quite monotone |
and the only way it's equal is if x, | and the only way it's equal is if x, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 125.713203 | 22.887913 | 26.072083 | 58.053764 | moderate speed | ʌnd ðʌ oʊnli weɪ ɪt'ɛs ikwʌl ɪz ɪf ɛks, | very noisy | very confined sounding | quite monotone |
you know, is a random variable that always takes on the same value. | you know, is a random variable that always takes on the same value. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 105.390984 | 27.479958 | 26.086296 | 33.676498 | slightly fast | ju noʊ, ɪz ʌ ɹændʌm vɛɹiʌbʌl ðæt ɔlweɪz teɪks ɑn ðʌ seɪm vælju. | very noisy | very roomy sounding | quite monotone |
Okay? Yeah. | Okay? Yeah. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 94.216156 | 42.808464 | 3.365608 | 59.622604 | very fast | oʊkeɪ? jæ. | very noisy | very confined sounding | slightly monotone |
look at the red dots, find the mean, | look at the red dots, find the mean, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 107.278252 | 17.9632 | 15.128516 | 31.557333 | very fast | lʊk æt ðʌ ɹɛd dɑts, faɪnd ðʌ min, | very noisy | very roomy sounding | quite monotone |
What if- what if, uh, | What if- what if, uh, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 198.758499 | 76.238586 | 10.711509 | 16.113033 | very fast | wʌt ɪf- wʌt ɪf, ʌ, | very noisy | very roomy sounding | slightly expressive |
the value of f of 1 was equal to the value of f of 3? | the value of f of 1 was equal to the value of f of 3? | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 122.461555 | 21.993139 | 5.749332 | 9.61562 | moderate speed | ðʌ vælju ʌv ɛf ʌv wɑz ikwʌl tu ðʌ vælju ʌv ɛf ʌv ? | very noisy | very roomy sounding | quite monotone |
What's that? | What's that? | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 117.657692 | 2.414048 | 7.071605 | 55.641602 | quite slowly | wʌt'ɛs ðæt? | very noisy | quite confined sounding | very monotone |
Yeah. So it turns out, | Yeah. So it turns out, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 139.378845 | 26.682171 | 25.827139 | 57.909473 | moderate speed | jæ. soʊ ɪt tɜ˞nz aʊt, | very noisy | very confined sounding | quite monotone |
what if the value of f of 1 is equal to the value of f of 3? | what if the value of f of 1 is equal to the value of f of 3? | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 113.284737 | 25.800838 | 24.801716 | 40.240215 | very fast | wʌt ɪf ðʌ vælju ʌv ɛf ʌv ɪz ikwʌl tu ðʌ vælju ʌv ɛf ʌv ? | very noisy | slightly roomy sounding | quite monotone |
It turns out it does. | It turns out it does. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 96.40464 | 23.739313 | 17.983 | 39.220028 | moderate speed | ɪt tɜ˞nz aʊt ɪt dʌz. | very noisy | slightly roomy sounding | quite monotone |
Very, uh, so let's see. | Very, uh, so let's see. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 127.442299 | 14.272443 | 23.439531 | 33.694077 | moderate speed | vɛɹi, ʌ, soʊ lɛt'ɛs si. | very noisy | very roomy sounding | very monotone |
So one way that could happen would be if the function were like that, | So one way that could happen would be if the function were like that, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 117.368317 | 28.476231 | 14.923311 | 45.174026 | moderate speed | soʊ wʌn weɪ ðæt kʊd hæpʌn wʊd bi ɪf ðʌ fʌŋkʃʌn wɜ˞ laɪk ðæt, | very noisy | moderate reverberation | quite monotone |
and then if you take the droll and chord, | and then if you take the droll and chord, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 108.630608 | 15.027569 | 18.705677 | 58.923233 | quite fast | ʌnd ðɛn ɪf ju teɪk ðʌ dɹoʊl ʌnd kɔɹd, | very noisy | very confined sounding | very monotone |
take the mean is still higher. | take the mean is still higher. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 99.215996 | 15.749424 | 17.897211 | 42.75153 | slightly fast | teɪk ðʌ min ɪz stɪl haɪɜ˞. | very noisy | slightly roomy sounding | very monotone |
and then move the cluster centroids over, | and then move the cluster centroids over, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 96.884956 | 12.769713 | 21.484674 | 59.609314 | slightly slowly | ʌnd ðɛn muv ðʌ klʌstɜ˞ oʊvɜ˞, | very noisy | very confined sounding | very monotone |
I mean, it's like if the point of f of 1, | I mean, it's like if the point of f of 1, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 122.526047 | 4.622565 | 9.781054 | 7.863521 | moderate speed | aɪ min, ɪt'ɛs laɪk ɪf ðʌ pɔɪnt ʌv ɛf ʌv , | very noisy | very roomy sounding | very monotone |
which, for example, | which, for example, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 112.888687 | 3.495117 | 6.419312 | 10.293677 | slightly fast | wɪtʃ, fɔɹ ɪɡzæmpʌl, | very noisy | very roomy sounding | very monotone |
. | . | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 111.034546 | 6.052987 | null | null | very fast | . | very clear | very confined sounding | very monotone |
Then it's impor- if- if f of- if- if- if you had a flat part here, | Then it's impor- if- if f of- if- if- if you had a flat part here, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 129.30162 | 33.84869 | 13.749016 | 54.803352 | slightly fast | ðɛn ɪt'ɛs - ɪf- ɪf ɛf ʌv- ɪf- ɪf- ɪf ju hæd ʌ flæt pɑɹt hiɹ, | very noisy | quite confined sounding | quite monotone |
then the function is not strictly convex. | then the function is not strictly convex. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 99.915474 | 17.920065 | 20.903069 | 59.355587 | quite fast | ðɛn ðʌ fʌŋkʃʌn ɪz nɑt stɹɪktli kʌnvɛks. | very noisy | very confined sounding | quite monotone |
And so it's still less than equal to, | And so it's still less than equal to, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 108.801628 | 16.869116 | 21.334211 | 59.661388 | slightly fast | ʌnd soʊ ɪt'ɛs stɪl lɛs ðæn ikwʌl tu, | very noisy | very confined sounding | very monotone |
but it's not- but it can't be equal to if x is random. | but it's not- but it can't be equal to if x is random. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 87.942688 | 11.887512 | 13.945253 | 59.551311 | quite fast | bʌt ɪt'ɛs nɑt- bʌt ɪt kæn'ti bi ikwʌl tu ɪf ɛks ɪz ɹændʌm. | very noisy | very confined sounding | very monotone |
Okay? So, um, and- and- and we'll use this, | Okay? So, um, and- and- and we'll use this, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 114.948059 | 40.463715 | 18.917381 | 56.327686 | moderate speed | oʊkeɪ? soʊ, ʌm, ʌnd- ʌnd- ʌnd wi' jus ðɪs, | very noisy | very confined sounding | slightly monotone |
uh, in a little bit. | uh, in a little bit. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 102.676575 | 17.043634 | 20.969772 | 23.507589 | slightly fast | ʌ, ɪn ʌ lɪtʌl bɪt. | very noisy | very roomy sounding | very monotone |
We'll- we'll actually end up using this. | We'll- we'll actually end up using this. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 109.128983 | 31.1597 | 33.173496 | 59.820164 | quite fast | wi'- wi' æktʃuʌli ɛnd ʌp juzɪŋ ðɪs. | very noisy | very confined sounding | quite monotone |
excuse me, uh, to that mean. | excuse me, uh, to that mean. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 91.072227 | 14.199455 | 11.640121 | 59.871483 | slightly slowly | ɪkskjus mi, ʌ, tu ðæt min. | very noisy | very confined sounding | very monotone |
Um, and, uh, again, | Um, and, uh, again, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 124.239532 | 23.735489 | 15.788633 | 58.449867 | quite slowly | ʌm, ʌnd, ʌ, ʌɡɛn, | very noisy | very confined sounding | quite monotone |
for the strict probabilistic, you know, | for the strict probabilistic, you know, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 129.748489 | 21.89114 | 28.308517 | 50.610458 | very fast | fɔɹ ðʌ stɹɪkt pɹɑbʌbɪlɪstʌk, ju noʊ, | very noisy | slightly confined sounding | quite monotone |
those of you that, I don't know, | those of you that, I don't know, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 116.675926 | 28.409184 | 24.470964 | 43.401272 | very fast | ðoʊz ʌv ju ðæt, aɪ dɑn'ti noʊ, | very noisy | moderate reverberation | quite monotone |
take classes in advanced probability, | take classes in advanced probability, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 105.452385 | 20.656923 | 28.499384 | 59.245499 | quite fast | teɪk klæsʌz ɪn ʌdvænst pɹɑbʌbɪlʌti, | very noisy | very confined sounding | quite monotone |
the- the technical way of saying x is a constant is, | the- the technical way of saying x is a constant is, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 116.558067 | 29.466192 | 27.656233 | 57.432907 | quite fast | ðʌ- ðʌ tɛknɪkʌl weɪ ʌv seɪɪŋ ɛks ɪz ʌ kɑnstʌnt ɪz, | very noisy | very confined sounding | quite monotone |
uh, x is, um, | uh, x is, um, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 121.822021 | 28.660778 | 5.996393 | 58.043816 | quite slowly | ʌ, ɛks ɪz, ʌm, | very noisy | very confined sounding | quite monotone |
equal to e x with probability one. | equal to e x with probability one. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 103.334999 | 15.064314 | 7.293429 | 45.582806 | slightly slowly | ikwʌl tu i ɛks wɪð pɹɑbʌbɪlʌti wʌn. | very noisy | moderate reverberation | very monotone |
You know what? I think for all practical human purposes, | You know what? I think for all practical human purposes, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 122.156448 | 25.62644 | 14.712461 | 59.778728 | very fast | ju noʊ wʌt? aɪ θɪŋk fɔɹ ɔl pɹæktʌkʌl hjumʌn pɜ˞pʌsʌz, | very noisy | very confined sounding | quite monotone |
you do not need to worry about this. | you do not need to worry about this. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 91.413841 | 9.552069 | 36.769402 | 59.634892 | very fast | ju du nɑt nid tu wɜ˞i ʌbaʊt ðɪs. | quite noisy | very confined sounding | very monotone |
But I think if you- if you take a class in measure theory, | But I think if you- if you take a class in measure theory, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 121.992386 | 27.804337 | 6.414793 | 54.778618 | quite fast | bʌt aɪ θɪŋk ɪf ju- ɪf ju teɪk ʌ klæs ɪn mɛʒɜ˞ θɪɹi, | very noisy | quite confined sounding | quite monotone |
Okay? Um, and so, uh, | Okay? Um, and so, uh, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 114.976692 | 27.819569 | 29.392963 | 59.218681 | quite slowly | oʊkeɪ? ʌm, ʌnd soʊ, ʌ, | very noisy | very confined sounding | quite monotone |
the professor of measure theory will be happy if you say this and you say x is a constant. | the professor of measure theory will be happy if you say this and you say x is a constant. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 96.694794 | 16.004807 | 17.258598 | 48.971844 | very fast | ðʌ pɹʌfɛsɜ˞ ʌv mɛʒɜ˞ θɪɹi wɪl bi hæpi ɪf ju seɪ ðɪs ʌnd ju seɪ ɛks ɪz ʌ kɑnstʌnt. | very noisy | slightly confined sounding | very monotone |
But maybe- maybe none of you are. | But maybe- maybe none of you are. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 109.352097 | 22.952515 | 11.881605 | 15.373141 | quite fast | bʌt meɪbi- meɪbi nʌn ʌv ju ɑɹ. | very noisy | very roomy sounding | quite monotone |
Okay. Yes. Don't worry about it. | Okay. Yes. Don't worry about it. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 83.819923 | 20.956263 | 11.810925 | 53.144257 | very fast | oʊkeɪ. jɛs. dɑn'ti wɜ˞i ʌbaʊt ɪt. | very noisy | quite confined sounding | quite monotone |
Um, oh, yes. | Um, oh, yes. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 103.075211 | 37.097839 | 8.673595 | 53.73024 | very slowly | ʌm, oʊ, jɛs. | very noisy | quite confined sounding | slightly monotone |
Okay. Now, um, just one- one more addendum, | Okay. Now, um, just one- one more addendum, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 138.28241 | 33.483135 | 20.200401 | 45.688606 | moderate speed | oʊkeɪ. naʊ, ʌm, dʒʌst wʌn- wʌn mɔɹ ʌdɛndʌm, | very noisy | moderate reverberation | quite monotone |
um, uh, to this is that, | um, uh, to this is that, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 108.203102 | 11.837308 | 14.631748 | 29.347139 | quite slowly | ʌm, ʌ, tu ðɪs ɪz ðæt, | very noisy | very roomy sounding | very monotone |
um, the form of Jensen's equality we're gonna use is actually a form for a concave function. | um, the form of Jensen's equality we're gonna use is actually a form for a concave function. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 117.306396 | 27.654591 | 23.664219 | 41.626904 | quite fast | ʌm, ðʌ fɔɹm ʌv dʒɛnsʌn'ɛs ɪkwɑlʌti wi'ɹeɪ ɡɑnʌ jus ɪz æktʃuʌli ʌ fɔɹm fɔɹ ʌ kɑnkeɪv fʌŋkʃʌn. | very noisy | slightly roomy sounding | quite monotone |
So instead of convex, um, | So instead of convex, um, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 124.881363 | 13.911606 | 15.782792 | 55.095413 | moderate speed | soʊ ɪnstɛd ʌv kʌnvɛks, ʌm, | very noisy | quite confined sounding | very monotone |
I'm gonna say concave. | I'm gonna say concave. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 120.547348 | 26.59157 | 13.983693 | 58.022144 | moderate speed | aɪ'ɛm ɡɑnʌ seɪ kɑnkeɪv. | very noisy | very confined sounding | quite monotone |
And so, you know, | And so, you know, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 116.284134 | 8.205198 | 3.520383 | 59.762321 | slightly slowly | ʌnd soʊ, ju noʊ, | very noisy | very confined sounding | very monotone |
and it turns out if you keep running the algorithm, nothing changes. | and it turns out if you keep running the algorithm, nothing changes. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 117.172752 | 27.558041 | 31.305824 | 59.392815 | very fast | ʌnd ɪt tɜ˞nz aʊt ɪf ju kip ɹʌnɪŋ ðʌ ælɡɜ˞ɪðʌm, nʌθɪŋ tʃeɪndʒʌz. | very noisy | very confined sounding | quite monotone |
a concave function is just a negative of a convex function, right? | a concave function is just a negative of a convex function, right? | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 105.255859 | 24.522535 | 18.486025 | 59.7444 | quite fast | ʌ kɑnkeɪv fʌŋkʃʌn ɪz dʒʌst ʌ nɛɡʌtɪv ʌv ʌ kʌnvɛks fʌŋkʃʌn, ɹaɪt? | very noisy | very confined sounding | quite monotone |
If you take a convex function and take negative of that, | If you take a convex function and take negative of that, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 109.362549 | 18.163364 | 39.148342 | 27.523809 | very fast | ɪf ju teɪk ʌ kʌnvɛks fʌŋkʃʌn ʌnd teɪk nɛɡʌtɪv ʌv ðæt, | quite noisy | very roomy sounding | quite monotone |
it becomes concave. | it becomes concave. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 118.591309 | 26.292986 | 31.091536 | 57.86079 | moderate speed | ɪt bɪkʌmz kɑnkeɪv. | very noisy | very confined sounding | quite monotone |
And so, uh, the whole thing works with the- with everything flipped around the other way. | And so, uh, the whole thing works with the- with everything flipped around the other way. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 106.036224 | 27.441326 | 16.427866 | 54.438534 | slightly fast | ʌnd soʊ, ʌ, ðʌ hoʊl θɪŋ wɜ˞ks wɪð ðʌ- wɪð ɛvɹiθɪŋ flɪpt ɜ˞aʊnd ðʌ ʌðɜ˞ weɪ. | very noisy | quite confined sounding | quite monotone |
Okay? Yeah. Yep. | Okay? Yeah. Yep. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 97.778572 | 33.033554 | null | null | very fast | oʊkeɪ? jæ. jɛp. | very clear | very confined sounding | quite monotone |
And so, uh, I have this strictly concave. | And so, uh, I have this strictly concave. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 85.403267 | 16.994059 | 2.662857 | 43.846939 | slightly slowly | ʌnd soʊ, ʌ, aɪ hæv ðɪs stɹɪktli kɑnkeɪv. | very noisy | moderate reverberation | very monotone |
Okay? So the form of Jensen's equality we're gonna use is actually the, | Okay? So the form of Jensen's equality we're gonna use is actually the, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 102.624741 | 34.803833 | 20.44162 | 57.362869 | quite fast | oʊkeɪ? soʊ ðʌ fɔɹm ʌv dʒɛnsʌn'ɛs ɪkwɑlʌti wi'ɹeɪ ɡɑnʌ jus ɪz æktʃuʌli ðʌ, | very noisy | very confined sounding | quite monotone |
um, uh, concave form of Jensen's equality. | um, uh, concave form of Jensen's equality. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 112.212219 | 16.716595 | 36.716404 | 52.637074 | moderate speed | ʌm, ʌ, kɑnkeɪv fɔɹm ʌv dʒɛnsʌn'ɛs ɪkwɑlʌti. | quite noisy | quite confined sounding | very monotone |
And we're actually going to apply it to the log function. | And we're actually going to apply it to the log function. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 106.11515 | 15.552091 | 36.795769 | 59.758327 | quite fast | ʌnd wi'ɹeɪ æktʃuʌli ɡoʊɪŋ tu ʌplaɪ ɪt tu ðʌ lɔɡ fʌŋkʃʌn. | quite noisy | very confined sounding | very monotone |
So the log function. | So the log function. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 94.561607 | 6.983719 | 47.859108 | 59.928463 | very fast | soʊ ðʌ lɔɡ fʌŋkʃʌn. | moderate ambient sound | very confined sounding | very monotone |
So the algorithm has converged. | So the algorithm has converged. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 100.211983 | 19.778416 | 33.650791 | 57.671642 | very fast | soʊ ðʌ ælɡɜ˞ɪðʌm hæz kʌnvɜ˞dʒd. | very noisy | very confined sounding | quite monotone |
Right? Log X looks like this. | Right? Log X looks like this. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 93.956146 | 22.122108 | 24.487562 | 48.811329 | quite fast | ɹaɪt? lɔɡ ɛks lʊks laɪk ðɪs. | very noisy | slightly confined sounding | quite monotone |
And so that's a concave function. | And so that's a concave function. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 74.796211 | 12.040864 | 14.83131 | 49.758339 | quite fast | ʌnd soʊ ðæt'ɛs ʌ kɑnkeɪv fʌŋkʃʌn. | very noisy | slightly confined sounding | very monotone |
And so the inequality we'll use will be in this direction that I have in orange. | And so the inequality we'll use will be in this direction that I have in orange. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 91.474304 | 14.43178 | 12.965574 | 53.738617 | quite fast | ʌnd soʊ ðʌ ɪnɪkwɑlʌti wi' jus wɪl bi ɪn ðɪs dɜ˞ɛkʃʌn ðæt aɪ hæv ɪn ɔɹʌndʒ. | very noisy | quite confined sounding | very monotone |
All right. | All right. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 121.820496 | 54.805389 | null | null | very fast | ɔl ɹaɪt. | very clear | very confined sounding | moderate intonation |
Just a moment. | Just a moment. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 121.118546 | 49.894569 | null | null | very fast | dʒʌst ʌ moʊmʌnt. | very clear | very confined sounding | slightly monotone |
So here's the density estimation problem. | So here's the density estimation problem. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 86.850967 | 37.410561 | 9.613345 | 57.577263 | very fast | soʊ hiɹ'ɛs ðʌ dɛnsʌti ɛstʌmeɪʃʌn pɹɑblʌm. | very noisy | very confined sounding | slightly monotone |
Um, meaning density estimation means you want to estimate P of X. | Um, meaning density estimation means you want to estimate P of X. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 103.956871 | 25.70826 | 24.910009 | 57.305866 | quite fast | ʌm, minɪŋ dɛnsʌti ɛstʌmeɪʃʌn minz ju wɑnt tu ɛstʌmʌt pi ʌv ɛks. | very noisy | very confined sounding | quite monotone |
Right? So we have a model for P of X comma Z, | Right? So we have a model for P of X comma Z, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 98.034584 | 39.879745 | 11.032364 | 33.145309 | moderate speed | ɹaɪt? soʊ wi hæv ʌ mɑdʌl fɔɹ pi ʌv ɛks kɑmʌ zi, | very noisy | very roomy sounding | slightly monotone |
um, with parameters, | um, with parameters, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 108.890564 | 7.082969 | 2.56596 | 59.371422 | slightly slowly | ʌm, wɪð pɜ˞æmʌtɜ˞z, | very noisy | very confined sounding | very monotone |
Theta. And so, you know, | Theta. And so, you know, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 146.830185 | 38.898563 | 15.732386 | 59.73193 | slightly slowly | θeɪtʌ. ʌnd soʊ, ju noʊ, | very noisy | very confined sounding | slightly monotone |
So if you look at this picture and you repeatedly color each point red or blue, | So if you look at this picture and you repeatedly color each point red or blue, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 112.669571 | 18.394356 | 28.083261 | 58.903301 | slightly fast | soʊ ɪf ju lʊk æt ðɪs pɪktʃɜ˞ ʌnd ju ɹɪpitɪdli kʌlɜ˞ itʃ pɔɪnt ɹɛd ɔɹ blu, | very noisy | very confined sounding | quite monotone |
instead of, uh, writing out mu sigma, | instead of, uh, writing out mu sigma, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 116.90387 | 16.648144 | 30.350761 | 53.370815 | slightly slowly | ɪnstɛd ʌv, ʌ, ɹaɪtɪŋ aʊt mu sɪɡmʌ, | very noisy | quite confined sounding | very monotone |
uh, mu sigma and phi like we did for the mixture of Gaussians, | uh, mu sigma and phi like we did for the mixture of Gaussians, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 108.775574 | 18.937241 | 28.302486 | 40.135094 | moderate speed | ʌ, mu sɪɡmʌ ʌnd faɪ laɪk wi dɪd fɔɹ ðʌ mɪkstʃɜ˞ ʌv , | very noisy | slightly roomy sounding | quite monotone |
I'm just gonna capture all the parameters you have, | I'm just gonna capture all the parameters you have, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 104.254066 | 15.658262 | 37.687336 | 59.081726 | very fast | aɪ'ɛm dʒʌst ɡɑnʌ kæptʃɜ˞ ɔl ðʌ pɜ˞æmʌtɜ˞z ju hæv, | quite noisy | very confined sounding | very monotone |
whatever your parameters are, I'm just gonna capture them in one variable Theta. | whatever your parameters are, I'm just gonna capture them in one variable Theta. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 100.317894 | 14.415561 | 17.289961 | 58.473034 | slightly fast | wʌtɛvɜ˞ jɔɹ pɜ˞æmʌtɜ˞z ɑɹ, aɪ'ɛm dʒʌst ɡɑnʌ kæptʃɜ˞ ðɛm ɪn wʌn vɛɹiʌbʌl θeɪtʌ. | very noisy | very confined sounding | very monotone |
And, uh, you only observe X. | And, uh, you only observe X. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 108.374908 | 30.310671 | 10.522614 | 50.763245 | very fast | ʌnd, ʌ, ju oʊnli ʌbzɜ˞v ɛks. | very noisy | slightly confined sounding | quite monotone |
So your training set looks like that. | So your training set looks like that. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 107.191055 | 40.224476 | 3.539959 | 44.859901 | very fast | soʊ jɔɹ tɹeɪnɪŋ sɛt lʊks laɪk ðæt. | very noisy | moderate reverberation | slightly monotone |
So the, um, log likelihood of the parameters Theta is equal | So the, um, log likelihood of the parameters Theta is equal | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 125.184189 | 42.117996 | 11.471537 | 36.573452 | slightly slowly | soʊ ðʌ, ʌm, lɔɡ laɪklihʊd ʌv ðʌ pɜ˞æmʌtɜ˞z θeɪtʌ ɪz ikwʌl | very noisy | quite roomy sounding | slightly monotone |
to sum over your training examples log p of X i parameterized by Theta. | to sum over your training examples log p of X i parameterized by Theta. | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 117.021408 | 41.927483 | 3.392992 | 40.076408 | slightly slowly | tu sʌm oʊvɜ˞ jɔɹ tɹeɪnɪŋ ɪɡzæmpʌlz lɔɡ pi ʌv ɛks aɪ baɪ θeɪtʌ. | very noisy | slightly roomy sounding | slightly monotone |
Um, and this in turn is log of sum over Z, | Um, and this in turn is log of sum over Z, | Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA | 112.990448 | 30.651232 | 8.019579 | 40.240692 | quite slowly | ʌm, ʌnd ðɪs ɪn tɜ˞n ɪz lɔɡ ʌv sʌm oʊvɜ˞ zi, | very noisy | slightly roomy sounding | quite monotone |
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