All language subtitles for 04_cost-function-intuition.en

af Afrikaans
ak Akan
sq Albanian
am Amharic
ar Arabic
hy Armenian
az Azerbaijani
eu Basque
be Belarusian
bem Bemba
bn Bengali
bh Bihari
bs Bosnian
br Breton
bg Bulgarian
km Cambodian
ca Catalan
ceb Cebuano
chr Cherokee
ny Chichewa
zh-CN Chinese (Simplified)
zh-TW Chinese (Traditional)
co Corsican
hr Croatian
cs Czech
da Danish
nl Dutch
en English
eo Esperanto
et Estonian
ee Ewe
fo Faroese
tl Filipino
fi Finnish
fr French
fy Frisian
gaa Ga
gl Galician
ka Georgian
de German
el Greek
gn Guarani
gu Gujarati
ht Haitian Creole
ha Hausa
haw Hawaiian
iw Hebrew
hi Hindi
hmn Hmong
hu Hungarian
is Icelandic
ig Igbo
id Indonesian
ia Interlingua
ga Irish
it Italian
ja Japanese
jw Javanese
kn Kannada
kk Kazakh
rw Kinyarwanda
rn Kirundi
kg Kongo
ko Korean
kri Krio (Sierra Leone)
ku Kurdish
ckb Kurdish (Soranî)
ky Kyrgyz
lo Laothian
la Latin
lv Latvian
ln Lingala
lt Lithuanian
loz Lozi
lg Luganda
ach Luo
lb Luxembourgish
mk Macedonian
mg Malagasy
ms Malay
ml Malayalam
mt Maltese
mi Maori
mr Marathi
mfe Mauritian Creole
mo Moldavian
mn Mongolian
my Myanmar (Burmese)
sr-ME Montenegrin
ne Nepali
pcm Nigerian Pidgin
nso Northern Sotho
no Norwegian
nn Norwegian (Nynorsk)
oc Occitan
or Oriya
om Oromo
ps Pashto
fa Persian Download
pl Polish
pt-BR Portuguese (Brazil)
pt Portuguese (Portugal)
pa Punjabi
qu Quechua
ro Romanian
rm Romansh
nyn Runyakitara
ru Russian
sm Samoan
gd Scots Gaelic
sr Serbian
sh Serbo-Croatian
st Sesotho
tn Setswana
crs Seychellois Creole
sn Shona
sd Sindhi
si Sinhalese
sk Slovak
sl Slovenian
so Somali
es Spanish
es-419 Spanish (Latin American)
su Sundanese
sw Swahili
sv Swedish
tg Tajik
ta Tamil
tt Tatar
te Telugu
th Thai
ti Tigrinya
to Tonga
lua Tshiluba
tum Tumbuka
tr Turkish
tk Turkmen
tw Twi
ug Uighur
uk Ukrainian
ur Urdu
uz Uzbek
vi Vietnamese
cy Welsh
wo Wolof
xh Xhosa
yi Yiddish
yo Yoruba
zu Zulu
Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:01,130 --> 00:00:03,899 We're seeing the mathematical definition 2 00:00:03,899 --> 00:00:05,255 of the cost function. 3 00:00:05,255 --> 00:00:07,320 Now, let's build some intuition 4 00:00:07,320 --> 00:00:09,645 about what the cost function is really doing. 5 00:00:09,645 --> 00:00:13,020 In this video, we'll walk through one example to see how 6 00:00:13,020 --> 00:00:14,850 the cost function can be used to 7 00:00:14,850 --> 00:00:17,325 find the best parameters for your model. 8 00:00:17,325 --> 00:00:19,830 I know this video's little bit longer than the others, 9 00:00:19,830 --> 00:00:22,185 but bear with me, I think it'll be worth it. 10 00:00:22,185 --> 00:00:24,060 To recap, here's what we've 11 00:00:24,060 --> 00:00:26,305 seen about the cost function so far. 12 00:00:26,305 --> 00:00:29,885 You want to fit a straight line to the training data, 13 00:00:29,885 --> 00:00:32,240 so you have this model, fw, 14 00:00:32,240 --> 00:00:35,245 b of x is w times x, plus b. 15 00:00:35,245 --> 00:00:39,485 Here, the model's parameters are w, and b. 16 00:00:39,485 --> 00:00:43,534 Now, depending on the values chosen for these parameters, 17 00:00:43,534 --> 00:00:46,625 you get different straight lines like this. 18 00:00:46,625 --> 00:00:49,310 You want to find values for w, 19 00:00:49,310 --> 00:00:50,660 and b, so that 20 00:00:50,660 --> 00:00:53,780 the straight line fits the training data well. 21 00:00:53,780 --> 00:00:57,530 To measure how well a choice of w, 22 00:00:57,530 --> 00:00:59,825 and b fits the training data, 23 00:00:59,825 --> 00:01:02,845 you have a cost function J. 24 00:01:02,845 --> 00:01:05,455 What the cost function J does is, 25 00:01:05,455 --> 00:01:06,890 it measures the difference 26 00:01:06,890 --> 00:01:08,840 between the model's predictions, 27 00:01:08,840 --> 00:01:12,500 and the actual true values for y. 28 00:01:12,500 --> 00:01:14,585 What you see later, 29 00:01:14,585 --> 00:01:16,190 is that linear regression would 30 00:01:16,190 --> 00:01:17,930 try to find values for w, 31 00:01:17,930 --> 00:01:22,885 and b, then make a J of w be as small as possible. 32 00:01:22,885 --> 00:01:25,485 In math, we write it like this. 33 00:01:25,485 --> 00:01:27,465 We want to minimize, 34 00:01:27,465 --> 00:01:32,610 J as a function of w, and b. 35 00:01:32,610 --> 00:01:35,150 Now, in order for us to 36 00:01:35,150 --> 00:01:37,670 better visualize the cost function J, 37 00:01:37,670 --> 00:01:39,785 this work of a simplified version 38 00:01:39,785 --> 00:01:41,575 of the linear regression model. 39 00:01:41,575 --> 00:01:45,975 We're going to use the model fw of x, 40 00:01:45,975 --> 00:01:48,585 is w times x. 41 00:01:48,585 --> 00:01:50,480 You can think of this as taking 42 00:01:50,480 --> 00:01:52,220 the original model on the left, 43 00:01:52,220 --> 00:01:54,500 and getting rid of the parameter b, 44 00:01:54,500 --> 00:01:58,085 or setting the parameter b equal to 0. 45 00:01:58,085 --> 00:02:00,700 It just goes away from the equation, 46 00:02:00,700 --> 00:02:04,890 so f is now just w times x. 47 00:02:04,890 --> 00:02:08,295 You now have just one parameter w, 48 00:02:08,295 --> 00:02:10,440 and your cost function J, 49 00:02:10,440 --> 00:02:12,615 looks similar to what it was before. 50 00:02:12,615 --> 00:02:13,995 Taking the difference, 51 00:02:13,995 --> 00:02:15,405 and squaring it, 52 00:02:15,405 --> 00:02:20,685 except now, f is equal to w times xi, 53 00:02:20,685 --> 00:02:23,970 and J is now a function of just 54 00:02:23,970 --> 00:02:28,025 w. The goal becomes a little bit different as well, 55 00:02:28,025 --> 00:02:30,695 because you have just one parameter, w, 56 00:02:30,695 --> 00:02:32,635 not w and b. 57 00:02:32,635 --> 00:02:35,090 With this simplified model, 58 00:02:35,090 --> 00:02:37,820 the goal is to find the value for w, 59 00:02:37,820 --> 00:02:43,520 that minimizes J of w. To see this visually, 60 00:02:43,520 --> 00:02:46,685 what this means is that if b is set to 0, 61 00:02:46,685 --> 00:02:50,155 then f defines a line that looks like this. 62 00:02:50,155 --> 00:02:53,630 You see that the line passes through the origin here, 63 00:02:53,630 --> 00:02:55,565 because when x is 0, 64 00:02:55,565 --> 00:02:57,830 f of x is 0 too. 65 00:02:57,830 --> 00:03:00,530 Now, using this simplified model, 66 00:03:00,530 --> 00:03:03,350 let's see how the cost function changes as you choose 67 00:03:03,350 --> 00:03:08,090 different values for the parameter w. In particular, 68 00:03:08,090 --> 00:03:11,570 let's look at graphs of the model f of x, 69 00:03:11,570 --> 00:03:14,785 and the cost function J. 70 00:03:14,785 --> 00:03:17,500 I'm going to plot these side-by-side, 71 00:03:17,500 --> 00:03:21,475 and you'll be able to see how the two are related. 72 00:03:21,475 --> 00:03:25,295 First, notice that for f subscript w, 73 00:03:25,295 --> 00:03:27,440 when the parameter w is fixed, 74 00:03:27,440 --> 00:03:30,860 that is, is always a constant value, 75 00:03:30,860 --> 00:03:35,300 then fw is only a function of x, 76 00:03:35,300 --> 00:03:38,300 which means that the estimated value of y depends 77 00:03:38,300 --> 00:03:42,320 on the value of the input x. 78 00:03:42,320 --> 00:03:45,965 In contrast, looking to the right, 79 00:03:45,965 --> 00:03:48,050 the cost function J, 80 00:03:48,050 --> 00:03:50,150 is a function of w, 81 00:03:50,150 --> 00:03:53,585 where w controls the slope of the line defined by 82 00:03:53,585 --> 00:03:57,325 f w. The cost defined by J, 83 00:03:57,325 --> 00:03:59,585 depends on a parameter, 84 00:03:59,585 --> 00:04:04,830 in this case, the parameter w. Let's go ahead, 85 00:04:04,830 --> 00:04:06,435 and plot these functions, 86 00:04:06,435 --> 00:04:10,035 fw of x, and J of w 87 00:04:10,035 --> 00:04:14,865 side-by-side so you can see how they are related. 88 00:04:14,865 --> 00:04:17,145 We'll start with the model, 89 00:04:17,145 --> 00:04:22,005 that is the function fw of x on the left. 90 00:04:22,005 --> 00:04:26,720 Here are the input feature x is on the horizontal axis, 91 00:04:26,720 --> 00:04:30,800 and the output value y is on the vertical axis. 92 00:04:30,800 --> 00:04:33,800 Here's the plots of three points representing 93 00:04:33,800 --> 00:04:36,740 the training set at positions 1, 94 00:04:36,740 --> 00:04:40,030 1, 2, 2, and 3,3. 95 00:04:40,030 --> 00:04:44,715 Let's pick a value for w. Say w is 1. 96 00:04:44,715 --> 00:04:48,120 For this choice of w, 97 00:04:48,120 --> 00:04:50,430 the function fw, 98 00:04:50,430 --> 00:04:54,755 they'll say this straight line with a slope of 1. 99 00:04:54,755 --> 00:04:57,770 Now, what you can do next is calculate 100 00:04:57,770 --> 00:05:03,060 the cost J when w equals 1. 101 00:05:03,060 --> 00:05:05,525 You may recall that the cost function 102 00:05:05,525 --> 00:05:06,925 is defined as follows, 103 00:05:06,925 --> 00:05:09,785 is the squared error cost function. 104 00:05:09,785 --> 00:05:16,730 If you substitute fw(X^i) with w times X^i, 105 00:05:16,730 --> 00:05:18,940 the cost function looks like this. 106 00:05:18,940 --> 00:05:24,870 Where this expression is now w times X^i minus Y^i. 107 00:05:24,870 --> 00:05:26,785 For this value of w, 108 00:05:26,785 --> 00:05:28,360 it turns out that the error term 109 00:05:28,360 --> 00:05:29,910 inside the cost function, 110 00:05:29,910 --> 00:05:33,205 this w times X^i minus 111 00:05:33,205 --> 00:05:37,225 Y^i is equal to 0 for each of the three data points. 112 00:05:37,225 --> 00:05:39,035 Because for this data-set, 113 00:05:39,035 --> 00:05:41,820 when x is 1, then y is 1. 114 00:05:41,820 --> 00:05:44,135 When w is also 1, 115 00:05:44,135 --> 00:05:46,480 then f(x) equals 1, 116 00:05:46,480 --> 00:05:50,705 so f(x) equals y for this first training example, 117 00:05:50,705 --> 00:05:52,885 and the difference is 0. 118 00:05:52,885 --> 00:05:55,555 Plugging this into the cost function J, 119 00:05:55,555 --> 00:05:57,755 you get 0 squared. 120 00:05:57,755 --> 00:06:00,220 Similarly, when x is 2, 121 00:06:00,220 --> 00:06:02,000 then y is 2, 122 00:06:02,000 --> 00:06:04,720 and f(x) is also 2. 123 00:06:04,720 --> 00:06:07,055 Again, f(x) equals y, 124 00:06:07,055 --> 00:06:08,835 for the second training example. 125 00:06:08,835 --> 00:06:10,520 In the cost function, 126 00:06:10,520 --> 00:06:11,975 the squared error for 127 00:06:11,975 --> 00:06:15,085 the second example is also 0 squared. 128 00:06:15,085 --> 00:06:17,465 Finally, when x is 3, 129 00:06:17,465 --> 00:06:22,530 then y is 3 and f(3) is also 3. 130 00:06:22,530 --> 00:06:23,990 In a cost function 131 00:06:23,990 --> 00:06:27,110 the third squared error term is also 0 squared. 132 00:06:27,110 --> 00:06:31,385 For all three examples in this training set, 133 00:06:31,385 --> 00:06:36,745 f(X^i) equals Y^i for each training example i, 134 00:06:36,745 --> 00:06:42,670 so f(X^i) minus Y^i is 0. 135 00:06:42,690 --> 00:06:46,190 For this particular data-set, 136 00:06:46,190 --> 00:06:47,980 when w is 1, 137 00:06:47,980 --> 00:06:52,125 then the cost J is equal to 0. 138 00:06:52,125 --> 00:06:54,335 Now, what you can do on 139 00:06:54,335 --> 00:06:58,195 the right is plot the cost function J. 140 00:06:58,195 --> 00:07:00,830 Notice that because the cost function 141 00:07:00,830 --> 00:07:03,475 is a function of the parameter w, 142 00:07:03,475 --> 00:07:08,915 the horizontal axis is now labeled w and not x, 143 00:07:08,915 --> 00:07:14,810 and the vertical axis is now J and not y. 144 00:07:14,900 --> 00:07:20,200 You have J(1) equals to 0. 145 00:07:20,200 --> 00:07:24,805 In other words, when w equals 1, 146 00:07:24,805 --> 00:07:26,800 J(w) is 0, 147 00:07:26,800 --> 00:07:29,975 so let me go ahead and plot that. 148 00:07:29,975 --> 00:07:33,995 Now, let's look at how F and J change for 149 00:07:33,995 --> 00:07:38,240 different values of w. W can take on a range of values, 150 00:07:38,240 --> 00:07:41,089 so w can take on negative values, 151 00:07:41,089 --> 00:07:45,520 w can be 0, and it can take on positive values too. 152 00:07:45,520 --> 00:07:50,360 What if w is equal to 0.5 instead of 1, 153 00:07:50,360 --> 00:07:52,990 what would these graphs look like then? 154 00:07:52,990 --> 00:07:55,280 Let's go ahead and plot that. 155 00:07:55,280 --> 00:07:58,865 Let's set w to be equal to 0.5, 156 00:07:58,865 --> 00:08:00,380 and in this case, 157 00:08:00,380 --> 00:08:04,325 the function f(x) now looks like this, 158 00:08:04,325 --> 00:08:08,600 is a line with a slope equal to 0.5. 159 00:08:09,090 --> 00:08:12,870 Let's also compute the cost J, 160 00:08:12,870 --> 00:08:15,790 when w is 0.5. 161 00:08:15,790 --> 00:08:18,455 Recall that the cost function is measuring 162 00:08:18,455 --> 00:08:19,700 the squared error or 163 00:08:19,700 --> 00:08:22,435 difference between the estimator value, 164 00:08:22,435 --> 00:08:24,625 that is y hat I, 165 00:08:24,625 --> 00:08:26,765 which is F(X^i), 166 00:08:26,765 --> 00:08:29,075 and the true value, 167 00:08:29,075 --> 00:08:36,160 that is Y^i for each example i. Visually you can see that 168 00:08:36,160 --> 00:08:39,970 the error or difference is equal to the height 169 00:08:39,970 --> 00:08:44,385 of this vertical line here when x is equal to 1. 170 00:08:44,385 --> 00:08:46,325 Because this lower line is 171 00:08:46,325 --> 00:08:48,270 the gap between the actual value 172 00:08:48,270 --> 00:08:52,055 of y and the value that the function f predicted, 173 00:08:52,055 --> 00:08:54,975 which is a bit further down here. 174 00:08:54,975 --> 00:08:57,255 For this first example, 175 00:08:57,255 --> 00:09:02,955 when x is 1, f(x) is 0.5. 176 00:09:02,955 --> 00:09:06,585 The squared error on the first example is 177 00:09:06,585 --> 00:09:10,325 0.5 minus 1 squared. 178 00:09:10,325 --> 00:09:12,135 Remember the cost function, 179 00:09:12,135 --> 00:09:13,620 we'll sum over all the 180 00:09:13,620 --> 00:09:15,575 training examples in the training set. 181 00:09:15,575 --> 00:09:18,890 Let's go on to the second training example. 182 00:09:18,890 --> 00:09:21,135 When x is 2, 183 00:09:21,135 --> 00:09:24,280 the model is predicting f(x) is 184 00:09:24,280 --> 00:09:29,510 1 and the actual value of y is 2. 185 00:09:29,510 --> 00:09:32,950 The error for the second example is equal to 186 00:09:32,950 --> 00:09:36,825 the height of this little line segment here, 187 00:09:36,825 --> 00:09:38,830 and the squared error is 188 00:09:38,830 --> 00:09:41,890 the square of the length of this line segment, 189 00:09:41,890 --> 00:09:45,835 so you get 1 minus 2 squared. 190 00:09:45,835 --> 00:09:48,290 Let's do the third example. 191 00:09:48,290 --> 00:09:51,785 Repeating this process, the error here, 192 00:09:51,785 --> 00:09:54,535 also shown by this line segment, 193 00:09:54,535 --> 00:09:59,095 is 1.5 minus 3 squared. 194 00:09:59,095 --> 00:10:01,630 Next, we sum up all of these terms, 195 00:10:01,630 --> 00:10:05,285 which turns out to be equal to 3.5. 196 00:10:05,285 --> 00:10:10,885 Then we multiply this term by 1 over 2m, 197 00:10:10,885 --> 00:10:14,755 where m is the number of training examples. 198 00:10:14,755 --> 00:10:19,465 Since there are three training examples m equals 3, 199 00:10:19,465 --> 00:10:25,375 so this is equal to 1 over 2 times 3, 200 00:10:25,375 --> 00:10:29,470 where this m here is 3. 201 00:10:29,470 --> 00:10:31,105 If we work out the math, 202 00:10:31,105 --> 00:10:35,635 this turns out to be 3.5 divided by 6. 203 00:10:35,635 --> 00:10:40,285 The cost J is about 0.58. 204 00:10:40,285 --> 00:10:44,440 Let's go ahead and plot that over there on the right. 205 00:10:44,440 --> 00:10:47,440 Now, let's try one more value for 206 00:10:47,440 --> 00:10:51,025 w. How about if w equals 0? 207 00:10:51,025 --> 00:10:53,530 What do the graphs for f and J 208 00:10:53,530 --> 00:10:56,920 look like when w is equal to 0? 209 00:10:56,920 --> 00:11:00,205 It turns out that if w is equal to 0, 210 00:11:00,205 --> 00:11:01,450 then f of x is 211 00:11:01,450 --> 00:11:07,075 just this horizontal line that is exactly on the x-axis. 212 00:11:07,075 --> 00:11:09,460 The error for each example is 213 00:11:09,460 --> 00:11:11,950 a line that goes from each point down 214 00:11:11,950 --> 00:11:17,140 to the horizontal line that represents f of x equals 0. 215 00:11:17,140 --> 00:11:20,530 The cost J when w equals 216 00:11:20,530 --> 00:11:25,195 0 is 1 over 2m times the quantity, 217 00:11:25,195 --> 00:11:28,660 1^2 plus 2^2 plus 3^2, 218 00:11:28,660 --> 00:11:33,250 and that's equal to 1 over 6 times 14, 219 00:11:33,250 --> 00:11:36,160 which is about 2.33. 220 00:11:36,160 --> 00:11:40,120 Let's plot this point where w is 0 and J 221 00:11:40,120 --> 00:11:44,680 of 0 is 2.33 over here. 222 00:11:44,680 --> 00:11:47,560 You can keep doing this for other values of 223 00:11:47,560 --> 00:11:51,160 w. Since w can be any number, 224 00:11:51,160 --> 00:11:53,755 it can also be a negative value. 225 00:11:53,755 --> 00:11:56,785 If w is negative 0.5, 226 00:11:56,785 --> 00:12:02,665 then the line f is a downward-sloping line like this. 227 00:12:02,665 --> 00:12:05,515 It turns out that when w is negative 228 00:12:05,515 --> 00:12:09,160 0.5 then you end up with an even higher cost, 229 00:12:09,160 --> 00:12:14,155 around 5.25, which is this point up here. 230 00:12:14,155 --> 00:12:17,290 You can continue computing the cost function for 231 00:12:17,290 --> 00:12:21,025 different values of w and so on and plot these. 232 00:12:21,025 --> 00:12:25,060 It turns out that by computing a range of values, 233 00:12:25,060 --> 00:12:28,270 you can slowly trace out what the cost function J 234 00:12:28,270 --> 00:12:32,050 looks like and that's what J is. 235 00:12:32,050 --> 00:12:35,200 To recap, each value of 236 00:12:35,200 --> 00:12:40,180 parameter w corresponds to different straight line fit, 237 00:12:40,180 --> 00:12:43,390 f of x, on the graph to the left. 238 00:12:43,390 --> 00:12:45,805 For the given training set, 239 00:12:45,805 --> 00:12:49,570 that choice for a value of w corresponds to 240 00:12:49,570 --> 00:12:52,450 a single point on 241 00:12:52,450 --> 00:12:55,840 the graph on the right because for each value of w, 242 00:12:55,840 --> 00:13:00,835 you can calculate the cost J of w. For example, 243 00:13:00,835 --> 00:13:02,725 when w equals 1, 244 00:13:02,725 --> 00:13:06,520 this corresponds to this straight line fit through 245 00:13:06,520 --> 00:13:09,235 the data and it also 246 00:13:09,235 --> 00:13:13,180 corresponds to this point on the graph of J, 247 00:13:13,180 --> 00:13:18,730 where w equals 1 and the cost J of 1 equals 0. 248 00:13:18,730 --> 00:13:21,625 Whereas when w equals 0.5, 249 00:13:21,625 --> 00:13:25,855 this gives you this line which has a smaller slope. 250 00:13:25,855 --> 00:13:28,180 This line in combination with 251 00:13:28,180 --> 00:13:30,655 the training set corresponds to 252 00:13:30,655 --> 00:13:36,775 this point on the cost function graph at w equals 0.5. 253 00:13:36,775 --> 00:13:39,790 For each value of w you wind up with 254 00:13:39,790 --> 00:13:42,775 a different line and its corresponding costs, 255 00:13:42,775 --> 00:13:44,425 J of w, 256 00:13:44,425 --> 00:13:46,480 and you can use these points 257 00:13:46,480 --> 00:13:48,700 to trace out this plot on the right. 258 00:13:48,700 --> 00:13:51,700 Given this, how can you choose the value of 259 00:13:51,700 --> 00:13:54,760 w that results in the function f, 260 00:13:54,760 --> 00:13:56,440 fitting the data well? 261 00:13:56,440 --> 00:13:58,720 Well, as you can imagine, 262 00:13:58,720 --> 00:14:02,050 choosing a value of w that causes J of w 263 00:14:02,050 --> 00:14:05,875 to be as small as possible seems like a good bet. 264 00:14:05,875 --> 00:14:08,110 J is the cost function that 265 00:14:08,110 --> 00:14:11,005 measures how big the squared errors are, 266 00:14:11,005 --> 00:14:14,680 so choosing w that minimizes these squared errors, 267 00:14:14,680 --> 00:14:16,300 makes them as small as possible, 268 00:14:16,300 --> 00:14:18,010 will give us a good model. 269 00:14:18,010 --> 00:14:20,350 In this example, if you were to 270 00:14:20,350 --> 00:14:22,390 choose the value of w that results 271 00:14:22,390 --> 00:14:25,270 in the smallest possible value of J of 272 00:14:25,270 --> 00:14:28,915 w you'd end up picking w equals 1. 273 00:14:28,915 --> 00:14:31,900 As you can see, that's actually a pretty good choice. 274 00:14:31,900 --> 00:14:33,700 This results in the line that fits 275 00:14:33,700 --> 00:14:36,520 the training data very well. 276 00:14:36,520 --> 00:14:41,170 That's how in linear regression you use the cost function 277 00:14:41,170 --> 00:14:46,165 to find the value of w that minimizes J. 278 00:14:46,165 --> 00:14:48,880 In the more general case where we had 279 00:14:48,880 --> 00:14:52,255 parameters w and b rather than just w, 280 00:14:52,255 --> 00:14:58,135 you find the values of w and b that minimize J. 281 00:14:58,135 --> 00:15:01,405 To summarize, you saw plots of both 282 00:15:01,405 --> 00:15:05,395 f and J and worked through how the two are related. 283 00:15:05,395 --> 00:15:09,400 As you vary w or vary w and b you end up 284 00:15:09,400 --> 00:15:11,170 with different straight lines and when 285 00:15:11,170 --> 00:15:13,525 that straight line passes across the data, 286 00:15:13,525 --> 00:15:16,180 the cause J is small. 287 00:15:16,180 --> 00:15:18,910 The goal of linear regression is to find 288 00:15:18,910 --> 00:15:21,070 the parameters w or w and 289 00:15:21,070 --> 00:15:22,480 b that results in 290 00:15:22,480 --> 00:15:26,215 the smallest possible value for the cost function J. 291 00:15:26,215 --> 00:15:27,850 Now in this video, 292 00:15:27,850 --> 00:15:29,590 we worked through our example with 293 00:15:29,590 --> 00:15:34,225 a simplified problem using only w. In the next video, 294 00:15:34,225 --> 00:15:36,820 let's visualize what the cost function looks like for 295 00:15:36,820 --> 00:15:42,010 the full version of linear regression using both w and b. 296 00:15:42,010 --> 00:15:44,365 You see some cool 3D plots. 297 00:15:44,365 --> 00:15:46,670 Let's go to the next video.20686

Can't find what you're looking for?
Get subtitles in any language from opensubtitles.com, and translate them here.