1 00:00:02,590 --> 00:00:08,590 So here we have E equals two Y minus Y hat. 2 00:00:11,020 --> 00:00:21,250 We had, as we defined already in this example, this is a function of input, x mason over teta, which 3 00:00:21,250 --> 00:00:22,360 is over parameter. 4 00:00:22,660 --> 00:00:34,450 So let me just replace it Y minus instead of Y had I'm going to just write function of X based on our 5 00:00:34,450 --> 00:00:41,500 teta, which is W and Bias's, which we can change is over teta. 6 00:00:43,270 --> 00:00:45,450 Are looking for minimizing the error. 7 00:00:46,720 --> 00:00:49,220 We want to minimize this error. 8 00:00:49,240 --> 00:01:02,500 I'm just going to raise both sides by to you square that say equals do this one over Y minus F of X 9 00:01:03,760 --> 00:01:06,540 base and overtime destroying teta. 10 00:01:06,550 --> 00:01:14,170 So it would Shorthair Raceway to all the changes, all the things that we can change here is just over 11 00:01:14,170 --> 00:01:23,720 parameter to the teta star is nothing but the arc of mean e a square. 12 00:01:25,000 --> 00:01:28,550 This is a value of optimized parameters. 13 00:01:29,590 --> 00:01:32,110 Let's take a look at this example one more time. 14 00:01:32,470 --> 00:01:40,270 In this example, we have only one input, therefore we had one output, but sometimes we just don't 15 00:01:40,270 --> 00:01:42,130 have only one input. 16 00:01:42,250 --> 00:01:43,310 And there are more. 17 00:01:43,720 --> 00:01:44,620 Let me just. 18 00:01:44,620 --> 00:01:51,820 Should we I have I therefore the output would be lying if I am for this system. 19 00:01:52,360 --> 00:01:58,870 Why I had so meaning for each data. 20 00:01:58,900 --> 00:02:07,410 We need to optimize the error and then find the best way to optimize the whole system for all the data. 21 00:02:07,720 --> 00:02:15,730 For example, in our patient and doctor system, let's say we have more than one patient, we have 1000 22 00:02:15,730 --> 00:02:16,570 patients. 23 00:02:17,080 --> 00:02:26,410 We should have I would be from one to two one thousand and have one thousand samples. 24 00:02:26,800 --> 00:02:28,450 We have 1000 data. 25 00:02:29,020 --> 00:02:30,700 Therefore we need to show it. 26 00:02:30,700 --> 00:02:33,730 We need X of eye and Y off-line. 27 00:02:33,880 --> 00:02:40,860 Let's back over there and just write in another rate. 28 00:02:40,930 --> 00:02:44,890 I'm going to divide this part so I can continue here. 29 00:02:46,210 --> 00:02:50,020 The e f i it can be patient number two. 30 00:02:50,020 --> 00:02:53,980 Patient number fifty five equals two. 31 00:02:53,980 --> 00:02:57,010 Why am I minus y. 32 00:02:57,430 --> 00:03:08,590 I had I just goes from one to two and number of over samples here we are looking for minimizing the 33 00:03:08,590 --> 00:03:15,340 error so mean one over and which is over the number of samples that we have. 34 00:03:15,700 --> 00:03:21,010 And I can just simply take this off and, and I. 35 00:03:24,130 --> 00:03:40,390 From one E score, I this is nothing but a mean square error, and this is not a specificly for artificial 36 00:03:40,390 --> 00:03:41,450 neural network. 37 00:03:41,470 --> 00:03:44,690 We can also use this one for Fosi systems. 38 00:03:45,430 --> 00:03:47,020 This is called M. 39 00:03:47,290 --> 00:03:47,830 S. 40 00:03:47,840 --> 00:03:49,270 E or. 41 00:03:51,200 --> 00:03:51,730 Mean. 42 00:03:53,780 --> 00:03:56,800 A square error. 43 00:04:00,030 --> 00:04:06,030 Later, when we are working with Matlab, we will see how important these days and we will see how can 44 00:04:06,030 --> 00:04:11,490 we adjust the parameter to have these menas where error in the best way. 45 00:04:12,540 --> 00:04:15,900 This one was overbuy and this one was over. 46 00:04:15,960 --> 00:04:18,160 We had from the previous example. 47 00:04:18,390 --> 00:04:23,070 So later on, Matlab, you will see if we have 1000 data. 48 00:04:23,130 --> 00:04:28,380 There are different positions, but we need to minimize the errors. 49 00:04:29,250 --> 00:04:32,660 We need to find a system to give the best option. 50 00:04:32,670 --> 00:04:36,030 It means minimizing the error this distance. 51 00:04:36,030 --> 00:04:37,350 It should be minimized. 52 00:04:37,990 --> 00:04:46,020 We cannot really satisfy all the data for all the samples, but we can just minimize the error and see 53 00:04:46,290 --> 00:04:48,700 which line can fit better. 54 00:04:48,750 --> 00:04:56,170 Base number that we can already write a formula for the mean square error. 55 00:04:57,180 --> 00:05:06,580 We can show it with one hour and some from I from one to end number of over samples that we have in 56 00:05:06,600 --> 00:05:08,160 here inside a brocade. 57 00:05:08,160 --> 00:05:18,760 We have five I minus function of X of I base no teta square. 58 00:05:20,340 --> 00:05:28,710 So this is a general formula for calculating, miniskirted and as I mentioned, it's not only for artificial 59 00:05:28,710 --> 00:05:29,730 neural network. 60 00:05:30,120 --> 00:05:34,620 We can use these firmware for different systems such as Fawzy systems. 61 00:05:34,890 --> 00:05:43,560 Whenever we are looking for optimization, we can just use this mini square error formula of our goal 62 00:05:43,560 --> 00:05:46,830 in optimization is just to minimize the error. 63 00:05:47,190 --> 00:05:52,920 Using this meeno square formula that we just calculated, we can simply achieve our goal. 64 00:05:53,790 --> 00:06:00,600 In this example, teta would be our weight and bias's for our neural network. 65 00:06:01,710 --> 00:06:08,700 If I is equal to y i minus y hat of I this we had. 66 00:06:08,700 --> 00:06:17,550 If I use the output of our neural network and I can go from one to end goal, let's just replace this 67 00:06:17,550 --> 00:06:29,610 plant wheat F.I. then we can see that with Difficulty Square because this is just the minimum of a square 68 00:06:29,910 --> 00:06:30,810 after error. 69 00:06:31,210 --> 00:06:37,770 We were looking for the methods of finding these coefficients of variations. 70 00:06:38,070 --> 00:06:44,610 In next session we will talk about optimization methods to find these coefficients.