1 00:00:02,910 --> 00:00:03,990 ‫Hello everyone. 2 00:00:03,990 --> 00:00:05,680 ‫Welcome back. 3 00:00:05,700 --> 00:00:09,300 ‫In this lecture we are going to learn about two concepts. 4 00:00:09,300 --> 00:00:14,340 ‫One is how to build a neural network for regression problems. 5 00:00:14,340 --> 00:00:19,550 ‫And the second is how to do it using functional EPA. 6 00:00:19,630 --> 00:00:25,470 ‫They know we have been using sequential EPA and the selective utility how to use functionally being 7 00:00:26,520 --> 00:00:34,830 ‫functionally being is basically used for defining complex models such as Marty input on multi output 8 00:00:34,830 --> 00:00:39,260 ‫models or models which I've shared led. 9 00:00:39,440 --> 00:00:47,310 ‫So first really made a normal model using functional EPA which could also be done using sequentially. 10 00:00:48,250 --> 00:00:55,380 ‫But then we will create a complex neural network structure which can only be handled by a functional 11 00:00:55,380 --> 00:00:57,200 ‫EPA. 12 00:00:57,510 --> 00:01:04,650 ‫Also we'll be solving a regression problem which means our output variable is a continuous variable. 13 00:01:04,830 --> 00:01:09,240 ‫That is it is not due to one type it can have any value without any boundaries. 14 00:01:11,090 --> 00:01:19,200 ‫For this problem will be using Boston housing data say it is a very standard data set in which we have 15 00:01:19,350 --> 00:01:20,310 ‫14 variables 16 00:01:23,570 --> 00:01:26,110 ‫13 of the predictive variables and 14. 17 00:01:26,110 --> 00:01:33,540 ‫One is the value of the house basically using the values of 13 predictor variables. 18 00:01:33,590 --> 00:01:39,180 ‫We want to predict the value of house. 19 00:01:39,240 --> 00:01:46,740 ‫This is also an in big data say hey not give us liberty so we can imported using this line 20 00:01:50,040 --> 00:01:56,340 ‫if we want to know more about the most housing data say you can visit this link it has details of only 21 00:01:56,370 --> 00:02:02,940 ‫13 predictive variables the predicted variables include variables like crime rate number of hotel rooms 22 00:02:02,940 --> 00:02:14,130 ‫etc. You can see that Boston housing data set is now imported you can look at this by clicking on it. 23 00:02:14,580 --> 00:02:19,800 ‫The Boston housing data center has two parts green part and the best part. 24 00:02:20,380 --> 00:02:28,230 ‫Within brain we have four hundred for observations of thirteen predictive variables that is in the ex 25 00:02:29,160 --> 00:02:37,880 ‫and we have the labels that is the value of holes to we predicted invite in test. 26 00:02:37,920 --> 00:02:40,600 ‫We have a set of hundred two observations. 27 00:02:40,680 --> 00:02:43,890 ‫Again taking predictive variables and invite. 28 00:02:43,890 --> 00:02:45,440 ‫We have the opportunity 29 00:02:49,250 --> 00:02:56,610 ‫now as we did earlier we'll be importing the training part into training data and brain labels variable 30 00:02:57,450 --> 00:03:04,590 ‫and testing part of this dataset into best data and best labeled variable. 31 00:03:04,980 --> 00:03:06,440 ‫Next run these two lines of code 32 00:03:10,040 --> 00:03:15,640 ‫and now we have these new variables test data and bring data. 33 00:03:15,770 --> 00:03:22,790 ‫These are the predictor part of the data and test levels and grade levels. 34 00:03:22,820 --> 00:03:24,560 ‫These are the output part of the 35 00:03:27,500 --> 00:03:30,350 ‫next guns preparing the data. 36 00:03:30,350 --> 00:03:37,600 ‫And one of the important steps that we saw earlier was normalizing the data in the previous problem. 37 00:03:37,700 --> 00:03:41,240 ‫We had only pixel data which was homogeneous. 38 00:03:41,240 --> 00:03:47,090 ‫So we simply divided it by two to five to get the skilled version of that data. 39 00:03:47,310 --> 00:03:56,180 ‫But now we have heterogeneous data that is all these 13 variables representing 13 different things. 40 00:03:56,180 --> 00:03:57,950 ‫It is not easy to scale. 41 00:03:57,950 --> 00:03:58,750 ‫So it's kind of meta 42 00:04:02,110 --> 00:04:03,820 ‫to normalize this data. 43 00:04:03,820 --> 00:04:12,030 ‫We used this function sked this scale function automatically finds out the meaning of every variable 44 00:04:12,360 --> 00:04:14,970 ‫and the standard deviation of every variable. 45 00:04:15,450 --> 00:04:18,230 ‫And it uses that formula that I showed you earlier. 46 00:04:18,960 --> 00:04:25,080 ‫It's a proxy meaning from each value and divides that value by the standard deviation. 47 00:04:25,290 --> 00:04:34,220 ‫So simply using the scale function you can normalize our training data to normalize the test data. 48 00:04:34,650 --> 00:04:40,920 ‫We do not use the mean and standard deviation of vectors data we use to mean and standard deviation 49 00:04:40,920 --> 00:04:43,580 ‫of training data. 50 00:04:43,660 --> 00:04:48,240 ‫The concept is we know only the training part of the data. 51 00:04:48,290 --> 00:04:51,440 ‫Our model does not know any other detail of the word. 52 00:04:52,130 --> 00:04:54,010 ‫So we have only the training. 53 00:04:54,020 --> 00:04:59,420 ‫But from that we find out the mean and standard deviation of each variable. 54 00:04:59,640 --> 00:05:06,540 ‫We assume that this standard deviation and mean of each variable applies to the entire dataset of the 55 00:05:06,540 --> 00:05:06,880 ‫world. 56 00:05:08,300 --> 00:05:14,620 ‫So using those mean and standard deviations you'll be scaling our best data. 57 00:05:14,620 --> 00:05:14,980 ‫Also 58 00:05:18,100 --> 00:05:27,460 ‫so in this line we will scale our training data using this scale function and this line we will find 59 00:05:27,460 --> 00:05:27,660 ‫out. 60 00:05:27,660 --> 00:05:35,790 ‫The column means indicating data and we'll be storing that information in this variable called mean 61 00:05:35,790 --> 00:05:36,220 ‫stream 62 00:05:39,240 --> 00:05:40,110 ‫in this line. 63 00:05:40,110 --> 00:05:46,530 ‫We are finding out the standard deviation of these variables in training data and storing them in the 64 00:05:46,530 --> 00:05:51,050 ‫variable called call standards. 65 00:05:51,290 --> 00:05:58,740 ‫Now using the means of training data and standard deviations we use this scale function. 66 00:05:58,750 --> 00:06:05,610 ‫It is the same scale function but here we are specifying the mean and the standard deviation to be used 67 00:06:06,090 --> 00:06:10,400 ‫for scaling this test data. 68 00:06:10,410 --> 00:06:12,240 ‫Now our data is ready. 69 00:06:12,360 --> 00:06:13,990 ‫Our training data is normalized. 70 00:06:14,040 --> 00:06:18,390 ‫Our test data is also normalized. 71 00:06:18,480 --> 00:06:23,780 ‫Any new data on which you want to predict the outcome of the model. 72 00:06:24,120 --> 00:06:27,780 ‫You have to scale it again using this scale function 73 00:06:31,330 --> 00:06:35,890 ‫now comes the part when we define neural network. 74 00:06:35,890 --> 00:06:42,590 ‫This time we'll be using functionally be functionally B.A. has two different parts. 75 00:06:42,640 --> 00:06:47,110 ‫One is the input and one is output inputs. 76 00:06:47,310 --> 00:06:52,240 ‫Early model about all the variables that we are inputting in the model. 77 00:06:53,560 --> 00:07:01,840 ‫So basically in the input layer we clearly model that we have an input layer of shape is equal to number 78 00:07:01,840 --> 00:07:03,820 ‫of variables. 79 00:07:03,820 --> 00:07:10,110 ‫I could have written 13 here because I know that the number of variables are 13 in this particular dataset 80 00:07:11,530 --> 00:07:16,890 ‫but even if you change your train data you need not update your model. 81 00:07:17,050 --> 00:07:23,710 ‫If you divided like this if you died this way This means that you want to get this second dimension 82 00:07:23,830 --> 00:07:25,780 ‫of declining data. 83 00:07:25,930 --> 00:07:30,620 ‫So basically training data has these two dimensions. 84 00:07:31,060 --> 00:07:35,860 ‫It has 400 photos and 13 columns. 85 00:07:35,860 --> 00:07:41,740 ‫We want this dimension because this represents a number of variables in this training data. 86 00:07:41,740 --> 00:07:42,630 ‫So that is what we do. 87 00:07:43,120 --> 00:07:44,320 ‫We have written to here. 88 00:07:45,250 --> 00:07:52,130 ‫So using this even if you change your brain data to any other dataset you'd need not update your shape 89 00:07:52,150 --> 00:07:57,500 ‫for this neural network it will automatically get updated. 90 00:07:57,580 --> 00:08:01,320 ‫The second part is the output layer. 91 00:08:01,390 --> 00:08:09,520 ‫And this layer we first include the input layer to this outwardly which is the same as the input layer 92 00:08:09,550 --> 00:08:12,290 ‫that we created earlier. 93 00:08:13,030 --> 00:08:21,160 ‫This is important because this creates the connection between the input and output layer if we do not 94 00:08:21,160 --> 00:08:25,460 ‫specify that this output layer has this input layer. 95 00:08:25,540 --> 00:08:29,460 ‫Then there will be no connection between these two. 96 00:08:29,680 --> 00:08:36,080 ‫So in the output layer the first thing is always the input layer that it will take. 97 00:08:36,190 --> 00:08:44,640 ‫Then comes the hidden layers which is similar to the way that we specify in these sequential EPA too. 98 00:08:44,860 --> 00:08:53,560 ‫In this scenario we are using to the layers both with sixty four neurons the activation function for 99 00:08:53,560 --> 00:08:57,440 ‫both of these is real need. 100 00:08:57,470 --> 00:09:03,730 ‫Lastly that is the output layer has only one neuron and it has no activation function because it is 101 00:09:03,730 --> 00:09:06,250 ‫a regression problem. 102 00:09:06,460 --> 00:09:10,600 ‫So let's run these two lines of code. 103 00:09:11,110 --> 00:09:16,610 ‫This creates one input into input. 104 00:09:16,610 --> 00:09:20,800 ‫Now this will create another output center which is predictions 105 00:09:23,730 --> 00:09:31,270 ‫9 functionally we create the model using get us model function. 106 00:09:31,270 --> 00:09:33,370 ‫It takes in two parameters. 107 00:09:33,370 --> 00:09:37,730 ‫One is the inputs and 1 is output input. 108 00:09:37,750 --> 00:09:43,780 ‫We have a name as importantly and the output has been named as predictions. 109 00:09:43,780 --> 00:09:47,420 ‫So input particular input output is equal to predictions. 110 00:09:47,620 --> 00:09:50,750 ‫And this defines the models architecture. 111 00:09:52,250 --> 00:10:00,210 ‫So our models architecture is we have 13 variables which are coming in as input in the first event. 112 00:10:00,370 --> 00:10:03,230 ‫We have 64 neurons in the second layer. 113 00:10:03,250 --> 00:10:10,120 ‫We have another 64 neurons and in the output layer we have one output neuron. 114 00:10:10,480 --> 00:10:18,390 ‫So when I done this a model is created and its architecture is specified. 115 00:10:18,400 --> 00:10:23,580 ‫Now we configured this model in configuration we specify to optimize it. 116 00:10:23,710 --> 00:10:32,740 ‫We can use a duty Optimus probe on whichever you like lost function for immigration problems is a messy 117 00:10:33,400 --> 00:10:40,720 ‫mean square the matrix is not a necessity however we have used mean absolute error 118 00:10:43,890 --> 00:10:50,750 ‫to win and then model is configured. 119 00:10:51,330 --> 00:10:54,910 ‫Now we train our model using different function. 120 00:10:55,200 --> 00:11:02,050 ‫Again we input the training data training levels epochs Andy Betsy's 121 00:11:13,750 --> 00:11:22,510 ‫you can see that the model is running for 30 bucks and a loss that is the MDC is steadily decreasing. 122 00:11:23,140 --> 00:11:31,890 ‫I mean absolute but it is also because the model has run for 30 bucks. 123 00:11:32,320 --> 00:11:39,810 ‫We can check the performance of this model on our test it does is similar to what we have done when 124 00:11:39,820 --> 00:11:49,520 ‫we were using sequentially B used to evaluate function and importantly test time best labeled and do 125 00:11:49,520 --> 00:11:54,140 ‫it to list on the test loss and test absolute error. 126 00:11:54,140 --> 00:12:02,320 ‫We can run these two commands and we can see that the test lost is thirty two point five six and this 127 00:12:02,440 --> 00:12:04,390 ‫absolute edit is four point forty eight. 128 00:12:06,670 --> 00:12:14,620 ‫So in this video we saw how to use functional EPA to be another one more on this model could have been 129 00:12:14,620 --> 00:12:17,640 ‫built using sequential EPA as well. 130 00:12:18,700 --> 00:12:24,850 ‫And in fact it would have been easier to use sequentially being hit but in the next lecture we will 131 00:12:24,850 --> 00:12:32,950 ‫see if we have a complex neural network architecture how functionally B helps us in building that scene 132 00:12:32,950 --> 00:12:33,640 ‫in the next one.