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Hello, everyone.

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Welcome back.

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In this lecture, we are going to learn about two Quantum's.

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One is how to be a neural network for regulation problems.

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And the second is how to do it using functional EPA.

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Now, we have been using sequential EPA and distractibility.

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How to use functional EPA functionally is basically used for defining complex models such as multi input

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or multi output models or models which have shared Lyd.

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So first, really make the normal model using functional EPA, which could also be done using sequentially.

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But then we will create a complex neural network structure which can only be handled by a functional

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EPA.

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Also, we'll be solving a problem, which means our output variable is a continuous measurement.

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That is, it is not due to one pipe.

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It can have any value without any boundaries.

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This problem we'll be using Boston housing data.

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It it is a very standard data set in which we have 14 variables.

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Thirteen of the productivity bills and 14th one is the value of the House, basically using the values

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of 13.

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Productivity was we want to predict the value of health.

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This is also an in big data, it may not get us, Labidi, but we got important using this line.

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If you want to know more about the Boston housing data set, you can visit this link.

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It has details of all the 13 predictor variables.

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The predicted variables include variables like crime rate, number of hotel rooms and Tequilla.

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You can see that Boston housing Natus is now imported.

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You can look at this by clicking on it.

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The Boston housing dataset has two parts brain part and the best part within brain.

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We have 404 observations of 13 predictive variables.

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That is in the X and we have the labels.

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That is the value of hosting.

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We predicted invite in test.

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We have a set of one hundred two observations.

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Again, taking predictive valuables and invite.

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We have the opportunity to.

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Now, as we did earlier, we'll be importing the training part into train data and train levels, variable

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and testing part of this dataset into best data and best labels.

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The next event, these two lines of code.

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And now we have these new labels, test data and brain data.

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These are the predictor part of the data.

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And best labels and brain labels, these are the upper part of the victim.

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Next, guns preparing the data.

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And one of the important steps that we saw earlier was normalizing the data in the previous problem.

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We had only pixel data, which was homogeneous.

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So we simply divided it by two to five to get the skilled version of that data.

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But now we have heterogeneous data that is all these 13 variables representing 13 different things.

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It is not easy to scale such kind of data

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to normalize this data.

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We use this function sked.

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This scale function automatically finds out the mean of every variable and the standard deviation of

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everybody.

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And it uses that formula that I showed you earlier.

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It's a prakriti mean from each value.

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And divides that value by the standard deviation.

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So simply using the scale function, you can normalize our training data to normalize the data.

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We do not use the mean and standard deviation of Vitez data.

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We used to mean standard deviation of deigning data.

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The concept is Maeno only deplaning part of the data.

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Our model does not know any other detail of the word.

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We have only the training, but from that we find out the mean and standard deviation of each variable.

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We assume that this standard deviation and mean of each variable applies to the entire dataset of the

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world.

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So using those mean and standard deviations, we will be scaling up test data.

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Also.

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So in this light, we will scale our training data using descale scale function and this line we will

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find out deep Collum means indicating data and we'll be storing that information in this variable called

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Mean Street.

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In this line, we are finding out the standard deviation of these variables and training data and storing

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them individual court call standards.

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Now using the means of training data and standard deviations.

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We use the scale function.

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It is the same scale function.

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But here we are specifying the mean and the standard deviation to be used for scaling this test data.

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Now our data is ready.

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Our trained data is not released.

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Our test data is also normalized.

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Any new data on which you want to predict the outcome of the model?

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You have to scale it again.

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Using this scale function.

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Now comes the part when we define neural network.

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This time we'll be using functionally be a functionally B.A. has two different parts.

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One is the input and one is output input with early model about all the variables that we are inputting

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in the model.

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So basically in the input layer, we build the model that we have a input layer off shape is equal to

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number of variables.

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I could have written 13 here because I know that the number of variables are 13 in this particular dataset.

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But even if you change your train data, you'd need not update your model.

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If you divided like this, if you write this way, this means that you want to get this second dimension

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of the training data.

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So basically training data has these two dimensions.

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It has 400 photos and 13 columns.

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We want this dimension because this represents the number of believers in this training data.

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So that is why we have we have written to here.

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So using this, even if you change your train data to any other dataset, you'd need not a baby or ship

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for this neural network.

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It will automatically get updated.

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The second part is the output layer and this layer.

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We first include the input layer to this output layer, which is the same as the input layer that we

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created earlier.

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This is important because this creates the connection between the input layer and output.

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If we do not specify that this output layer has this input layer, then there would be no connection

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between these two.

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So in the output layer, the first thing is always the input layer that it will take.

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Then comes the hidden lives, which is similar to the way that we specify in these sequential EPA.

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In this scenario, we are using two layers, both with 64 neurons.

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The activation function for both of these is really.

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Lastly, that is the output layer has only one neuron and it has no activation function because it is

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a regression problem.

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So let's run these two lines of code.

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This creates one input into inputs.

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Now, this will create another out preventer, which is predictions.

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Nine functionally.

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We create the model using Gaydos model function.

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It takes two parameters.

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One is the inputs and one is output inputs.

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We have named as inputs only and the outputs has been named as predictions.

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So in particular, input output is equal to predictions.

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And this defines the models architecture.

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So our models architecture is we have 13 variables which are coming in as input in the first 10 led.

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We have 64 neurons in the second layer.

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We have another 64 neurons.

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And in the output layer we have one output neuron.

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So when I've done this, a model is created and it's architected is specified.

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Now we configured this model in configuration.

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We specify the optimize it.

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We can use a duty Artemus prop or whichever you like.

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Lost function for immigration problems is a messy means squared.

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A matrix is not a necessity.

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However, we have used mean absolute error

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to win and underscore modellers configured.

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Now we bring in our model using the fit function.

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Again, we input training, data, training levels, epochs and deep Betsey's.

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You can see that the mortar is landing for the epochs and loss.

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That is the embassy is steadily closing.

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I mean, to do that, it is also because the model has run on the box.

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We can check the performance of this model on our desk.

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This is similar to what we have done when we were using sequentially.

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B, you d evaluate function and importantly tested them best labeled and do it do list on the test loss

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and test absolute error.

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We can run these two commands and we can see that the test loss is Tuqay two point five six.

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And this absolute error is four point four.

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So in this video we saw how to use functionally be to build another model.

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This model could have been built using sequential EPA as well.

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And in fact, it would have been easier to use sequentially pay it.

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But in the next lecture, you can see if we have a complex neural network architecture, how functionally

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they helps us in building that scene in the next one.