bxc2017epfl/cs229-tags · Datasets at Hugging Face

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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

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?

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,

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.

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,

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.

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,

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,

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?

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.

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,

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,

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,

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,

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,

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.

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,

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.

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,

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?

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,

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,

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.

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.

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,

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,

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?

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?

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,

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?

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.

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.

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,

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,

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.

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,

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,

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,

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

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,

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.

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,

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.

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,

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.

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.

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.

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,

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,

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,

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,

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,

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,

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.

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,

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.

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,

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,

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.

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.

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.

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.

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,

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,

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.

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,

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.

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,

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.

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?

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,

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.

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.

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.

Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA

97.778572

33.033554

null

very fast

oʊkeɪ? jæ. jɛp.

very clear

very confined sounding

quite monotone

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,

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.

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.

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.

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.

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.

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.

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.

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.

Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA

121.820496

54.805389

null

very fast

ɔl ɹaɪt.

very clear

very confined sounding

moderate intonation

Just a moment.

Lecture 14 - Expectation-Maximization Algorithms _ Stanford CS229 - Machine Learning (Autumn 2018)-rVfZHWTwXSA

121.118546

49.894569

null

very fast

dʒʌst ʌ moʊmʌnt.

very clear

very confined sounding

slightly monotone

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.

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,

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,

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,

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,

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,

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,

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,

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.

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.

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.

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

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.

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,

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