Lab1-Hello-ML-World.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Hello-ML-World.ipynb","version":"0.3.2","provenance":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"metadata":{"id":"ZIAkIlfmCe1B","colab_type":"text"},"cell_type":"markdown","source":["# The Hello World of Deep Learning with Neural Networks"]},{"metadata":{"id":"fA93WUy1zzWf","colab_type":"text"},"cell_type":"markdown","source":["Like every first app you should start with something super simple that shows the overall scaffolding for how your code works. \n","\n","In the case of creating neural networks, the sample I like to use is one where it learns the relationship between two numbers. So, for example, if you were writing code for a function like this, you already know the 'rules' -- \n","\n","\n","```\n","float my_function(float x){\n","    float y = (3 * x) + 1;\n","    return y;\n","}\n","```\n","\n","So how would you train a neural network to do the equivalent task? Using data! By feeding it with a set of Xs, and a set of Ys, it should be able to figure out the relationship between them. \n","\n","This is obviously a very different paradigm than what you might be used to, so let's step through it piece by piece.\n"]},{"metadata":{"id":"DzbtdRcZDO9B","colab_type":"text"},"cell_type":"markdown","source":["## Imports\n","\n","Let's start with our imports. Here we are importing TensorFlow and calling it tf for ease of use.\n","\n","We then import a library called numpy, which helps us to represent our data as lists easily and quickly.\n","\n","The framework for defining a neural network as a set of Sequential layers is called keras, so we import that too."]},{"metadata":{"id":"X9uIpOS2zx7k","colab_type":"code","colab":{}},"cell_type":"code","source":["import tensorflow as tf\n","import numpy as np\n","from tensorflow import keras"],"execution_count":0,"outputs":[]},{"metadata":{"id":"wwJGmDrQ0EoB","colab_type":"text"},"cell_type":"markdown","source":["## Define and Compile the Neural Network\n","\n","Next we will create the simplest possible neural network. It has 1 layer, and that layer has 1 neuron, and the input shape to it is just 1 value."]},{"metadata":{"id":"kQFAr_xo0M4T","colab_type":"code","colab":{}},"cell_type":"code","source":["model = tf.keras.Sequential([keras.layers.Dense(units=1, input_shape=[1])])"],"execution_count":0,"outputs":[]},{"metadata":{"id":"KhjZjZ-c0Ok9","colab_type":"text"},"cell_type":"markdown","source":["Now we compile our Neural Network. When we do so, we have to specify 2 functions, a loss and an optimizer.\n","\n","If you've seen lots of math for machine learning, here's where it's usually used, but in this case it's nicely encapsulated in functions for you. But what happens here -- let's explain...\n","\n","We know that in our function, the relationship between the numbers is y=3x+1. \n","\n","When the computer is trying to 'learn' that, it makes a guess...maybe y=10x+10. The LOSS function measures the guessed answers against the known correct answers and measures how well or how badly it did.\n","\n","It then uses the OPTIMIZER function to make another guess. Based on how the loss function went, it will try to minimize the loss. At that point maybe it will come up with somehting like y=5x+5, which, while still pretty bad, is closer to the correct result (i.e. the loss is lower)\n","\n","It will repeat this for the number of EPOCHS which you will see shortly. But first, here's how we tell it to use 'MEAN SQUARED ERROR' for the loss and 'STOCHASTIC GRADIENT DESCENT' for the optimizer. You don't need to understand the math for these yet, but you can see that they work! :)\n","\n","Over time you will learn the different and appropriate loss and optimizer functions for different scenarios. \n"]},{"metadata":{"id":"m8YQN1H41L-Y","colab_type":"code","colab":{}},"cell_type":"code","source":["model.compile(optimizer='sgd', loss='mean_squared_error')"],"execution_count":0,"outputs":[]},{"metadata":{"id":"5QyOUhFw1OUX","colab_type":"text"},"cell_type":"markdown","source":["## Providing the Data\n","\n","Next up we'll feed in some data. In this case we are taking 6 xs and 6ys. You can see that the relationship between these is that y=2x-1, so where x = -1, y=-3 etc. etc. \n","\n","A python library called 'Numpy' provides lots of array type data structures that are a defacto standard way of doing it. We declare that we want to use these by specifying the values asn an np.array[]"]},{"metadata":{"id":"4Dxk4q-jzEy4","colab_type":"code","colab":{}},"cell_type":"code","source":["xs = np.array([-1.0, 0.0, 1.0, 2.0, 3.0, 4.0], dtype=float)\n","ys = np.array([-2.0, 1.0, 4.0, 7.0, 10.0, 13.0], dtype=float)"],"execution_count":0,"outputs":[]},{"metadata":{"id":"n_YcWRElnM_b","colab_type":"text"},"cell_type":"markdown","source":["# Training the Neural Network"]},{"metadata":{"id":"c-Jk4dG91dvD","colab_type":"text"},"cell_type":"markdown","source":["The process of training the neural network, where it 'learns' the relationship between the Xs and Ys is in the **model.fit**  call. This is where it will go through the loop we spoke about above, making a guess, measuring how good or bad it is (aka the loss), using the opimizer to make another guess etc. It will do it for the number of epochs you specify. When you run this code, you'll see the loss on the right hand side."]},{"metadata":{"id":"lpRrl7WK10Pq","colab_type":"code","colab":{"height":17034},"outputId":"61cb92f9-ad29-418d-ce9e-4c616b3b963c","executionInfo":{"status":"ok","timestamp":1552616831242,"user_tz":-540,"elapsed":1575,"user":{"displayName":"Laurence Moroney","photoUrl":"https://lh3.googleusercontent.com/-RcxktLY-TBk/AAAAAAAAAAI/AAAAAAAAABY/b4V4dTIqmPI/s64/photo.jpg","userId":"06401446828348966425"}}},"cell_type":"code","source":["model.fit(xs, ys, epochs=500)"],"execution_count":5,"outputs":[{"output_type":"stream","text":["Epoch 1/500\n","6/6 [==============================] - 0s 16ms/step - loss: 57.4875\n","Epoch 2/500\n","6/6 [==============================] - 0s 173us/step - loss: 45.2285\n","Epoch 3/500\n","6/6 [==============================] - 0s 171us/step - loss: 35.5836\n","Epoch 4/500\n","6/6 [==============================] - 0s 195us/step - loss: 27.9955\n","Epoch 5/500\n","6/6 [==============================] - 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0s 149us/step - loss: 6.9842e-06\n","Epoch 174/500\n","6/6 [==============================] - 0s 143us/step - loss: 6.8411e-06\n","Epoch 175/500\n","6/6 [==============================] - 0s 116us/step - loss: 6.7008e-06\n","Epoch 176/500\n","6/6 [==============================] - 0s 129us/step - loss: 6.5629e-06\n","Epoch 177/500\n","6/6 [==============================] - 0s 159us/step - loss: 6.4276e-06\n","Epoch 178/500\n","6/6 [==============================] - 0s 163us/step - loss: 6.2958e-06\n","Epoch 179/500\n","6/6 [==============================] - 0s 130us/step - loss: 6.1663e-06\n","Epoch 180/500\n","6/6 [==============================] - 0s 165us/step - loss: 6.0392e-06\n","Epoch 181/500\n","6/6 [==============================] - 0s 142us/step - loss: 5.9155e-06\n","Epoch 182/500\n","6/6 [==============================] - 0s 175us/step - loss: 5.7942e-06\n","Epoch 183/500\n","6/6 [==============================] - 0s 167us/step - loss: 5.6750e-06\n","Epoch 184/500\n","6/6 [==============================] - 0s 137us/step - loss: 5.5581e-06\n","Epoch 185/500\n","6/6 [==============================] - 0s 173us/step - loss: 5.4441e-06\n","Epoch 186/500\n","6/6 [==============================] - 0s 164us/step - loss: 5.3321e-06\n","Epoch 187/500\n","6/6 [==============================] - 0s 115us/step - loss: 5.2225e-06\n","Epoch 188/500\n","6/6 [==============================] - 0s 119us/step - loss: 5.1156e-06\n","Epoch 189/500\n","6/6 [==============================] - 0s 109us/step - loss: 5.0105e-06\n","Epoch 190/500\n","6/6 [==============================] - 0s 109us/step - loss: 4.9073e-06\n","Epoch 191/500\n","6/6 [==============================] - 0s 108us/step - loss: 4.8067e-06\n","Epoch 192/500\n","6/6 [==============================] - 0s 159us/step - loss: 4.7081e-06\n","Epoch 193/500\n","6/6 [==============================] - 0s 120us/step - loss: 4.6112e-06\n","Epoch 194/500\n","6/6 [==============================] - 0s 117us/step - loss: 4.5165e-06\n","Epoch 195/500\n","6/6 [==============================] - 0s 136us/step - loss: 4.4238e-06\n","Epoch 196/500\n","6/6 [==============================] - 0s 140us/step - loss: 4.3326e-06\n","Epoch 197/500\n","6/6 [==============================] - 0s 162us/step - loss: 4.2434e-06\n","Epoch 198/500\n","6/6 [==============================] - 0s 180us/step - loss: 4.1561e-06\n","Epoch 199/500\n","6/6 [==============================] - 0s 159us/step - loss: 4.0706e-06\n","Epoch 200/500\n","6/6 [==============================] - 0s 130us/step - loss: 3.9869e-06\n","Epoch 201/500\n","6/6 [==============================] - 0s 112us/step - loss: 3.9053e-06\n","Epoch 202/500\n","6/6 [==============================] - 0s 127us/step - loss: 3.8251e-06\n","Epoch 203/500\n","6/6 [==============================] - 0s 139us/step - loss: 3.7462e-06\n","Epoch 204/500\n","6/6 [==============================] - 0s 158us/step - loss: 3.6697e-06\n","Epoch 205/500\n","6/6 [==============================] - 0s 148us/step - loss: 3.5941e-06\n","Epoch 206/500\n","6/6 [==============================] - 0s 129us/step - loss: 3.5204e-06\n","Epoch 207/500\n","6/6 [==============================] - 0s 114us/step - loss: 3.4481e-06\n","Epoch 208/500\n","6/6 [==============================] - 0s 127us/step - loss: 3.3773e-06\n","Epoch 209/500\n","6/6 [==============================] - 0s 125us/step - loss: 3.3079e-06\n","Epoch 210/500\n","6/6 [==============================] - 0s 145us/step - loss: 3.2400e-06\n","Epoch 211/500\n","6/6 [==============================] - 0s 169us/step - loss: 3.1736e-06\n","Epoch 212/500\n","6/6 [==============================] - 0s 127us/step - loss: 3.1080e-06\n","Epoch 213/500\n","6/6 [==============================] - 0s 114us/step - loss: 3.0440e-06\n","Epoch 214/500\n","6/6 [==============================] - 0s 141us/step - loss: 2.9816e-06\n","Epoch 215/500\n","6/6 [==============================] - 0s 122us/step - loss: 2.9205e-06\n","Epoch 216/500\n","6/6 [==============================] - 0s 97us/step - loss: 2.8605e-06\n","Epoch 217/500\n","6/6 [==============================] - 0s 143us/step - loss: 2.8017e-06\n","Epoch 218/500\n","6/6 [==============================] - 0s 146us/step - loss: 2.7441e-06\n","Epoch 219/500\n","6/6 [==============================] - 0s 123us/step - loss: 2.6878e-06\n","Epoch 220/500\n","6/6 [==============================] - 0s 119us/step - loss: 2.6326e-06\n","Epoch 221/500\n","6/6 [==============================] - 0s 145us/step - loss: 2.5785e-06\n","Epoch 222/500\n","6/6 [==============================] - 0s 157us/step - loss: 2.5256e-06\n","Epoch 223/500\n","6/6 [==============================] - 0s 143us/step - loss: 2.4737e-06\n","Epoch 224/500\n","6/6 [==============================] - 0s 152us/step - loss: 2.4230e-06\n","Epoch 225/500\n","6/6 [==============================] - 0s 120us/step - loss: 2.3730e-06\n","Epoch 226/500\n","6/6 [==============================] - 0s 119us/step - loss: 2.3243e-06\n","Epoch 227/500\n","6/6 [==============================] - 0s 121us/step - loss: 2.2765e-06\n","Epoch 228/500\n","6/6 [==============================] - 0s 116us/step - loss: 2.2299e-06\n","Epoch 229/500\n","6/6 [==============================] - 0s 153us/step - loss: 2.1840e-06\n","Epoch 230/500\n","6/6 [==============================] - 0s 306us/step - loss: 2.1390e-06\n","Epoch 231/500\n","6/6 [==============================] - 0s 132us/step - loss: 2.0950e-06\n","Epoch 232/500\n","6/6 [==============================] - 0s 161us/step - loss: 2.0521e-06\n","Epoch 233/500\n","6/6 [==============================] - 0s 129us/step - loss: 2.0101e-06\n","Epoch 234/500\n","6/6 [==============================] - 0s 125us/step - loss: 1.9689e-06\n","Epoch 235/500\n","6/6 [==============================] - 0s 109us/step - loss: 1.9283e-06\n","Epoch 236/500\n","6/6 [==============================] - 0s 109us/step - loss: 1.8885e-06\n","Epoch 237/500\n","6/6 [==============================] - 0s 99us/step - loss: 1.8500e-06\n","Epoch 238/500\n","6/6 [==============================] - 0s 130us/step - loss: 1.8119e-06\n","Epoch 239/500\n","6/6 [==============================] - 0s 118us/step - loss: 1.7749e-06\n","Epoch 240/500\n","6/6 [==============================] - 0s 108us/step - loss: 1.7383e-06\n","Epoch 241/500\n","6/6 [==============================] - 0s 94us/step - loss: 1.7025e-06\n","Epoch 242/500\n","6/6 [==============================] - 0s 154us/step - loss: 1.6676e-06\n","Epoch 243/500\n","6/6 [==============================] - 0s 174us/step - loss: 1.6335e-06\n","Epoch 244/500\n","6/6 [==============================] - 0s 181us/step - loss: 1.5997e-06\n","Epoch 245/500\n","6/6 [==============================] - 0s 186us/step - loss: 1.5671e-06\n","Epoch 246/500\n","6/6 [==============================] - 0s 165us/step - loss: 1.5348e-06\n","Epoch 247/500\n","6/6 [==============================] - 0s 156us/step - loss: 1.5033e-06\n","Epoch 248/500\n","6/6 [==============================] - 0s 136us/step - loss: 1.4726e-06\n","Epoch 249/500\n","6/6 [==============================] - 0s 151us/step - loss: 1.4421e-06\n","Epoch 250/500\n","6/6 [==============================] - 0s 160us/step - loss: 1.4127e-06\n","Epoch 251/500\n","6/6 [==============================] - 0s 134us/step - loss: 1.3835e-06\n","Epoch 252/500\n","6/6 [==============================] - 0s 130us/step - loss: 1.3552e-06\n","Epoch 253/500\n","6/6 [==============================] - 0s 109us/step - loss: 1.3274e-06\n","Epoch 254/500\n","6/6 [==============================] - 0s 104us/step - loss: 1.3001e-06\n","Epoch 255/500\n","6/6 [==============================] - 0s 149us/step - loss: 1.2733e-06\n","Epoch 256/500\n","6/6 [==============================] - 0s 134us/step - loss: 1.2473e-06\n","Epoch 257/500\n","6/6 [==============================] - 0s 171us/step - loss: 1.2216e-06\n","Epoch 258/500\n","6/6 [==============================] - 0s 144us/step - loss: 1.1964e-06\n","Epoch 259/500\n","6/6 [==============================] - 0s 130us/step - loss: 1.1717e-06\n","Epoch 260/500\n","6/6 [==============================] - 0s 139us/step - loss: 1.1477e-06\n","Epoch 261/500\n","6/6 [==============================] - 0s 128us/step - loss: 1.1242e-06\n","Epoch 262/500\n","6/6 [==============================] - 0s 122us/step - loss: 1.1010e-06\n","Epoch 263/500\n","6/6 [==============================] - 0s 101us/step - loss: 1.0784e-06\n","Epoch 264/500\n","6/6 [==============================] - 0s 118us/step - loss: 1.0562e-06\n","Epoch 265/500\n","6/6 [==============================] - 0s 121us/step - loss: 1.0346e-06\n","Epoch 266/500\n","6/6 [==============================] - 0s 105us/step - loss: 1.0134e-06\n","Epoch 267/500\n","6/6 [==============================] - 0s 100us/step - loss: 9.9246e-07\n","Epoch 268/500\n","6/6 [==============================] - 0s 110us/step - loss: 9.7208e-07\n","Epoch 269/500\n","6/6 [==============================] - 0s 122us/step - loss: 9.5236e-07\n","Epoch 270/500\n","6/6 [==============================] - 0s 134us/step - loss: 9.3280e-07\n","Epoch 271/500\n","6/6 [==============================] - 0s 148us/step - loss: 9.1338e-07\n","Epoch 272/500\n","6/6 [==============================] - 0s 117us/step - loss: 8.9463e-07\n","Epoch 273/500\n","6/6 [==============================] - 0s 97us/step - loss: 8.7640e-07\n","Epoch 274/500\n","6/6 [==============================] - 0s 101us/step - loss: 8.5831e-07\n","Epoch 275/500\n","6/6 [==============================] - 0s 113us/step - loss: 8.4068e-07\n","Epoch 276/500\n","6/6 [==============================] - 0s 103us/step - loss: 8.2352e-07\n","Epoch 277/500\n","6/6 [==============================] - 0s 101us/step - loss: 8.0661e-07\n","Epoch 278/500\n","6/6 [==============================] - 0s 130us/step - loss: 7.9010e-07\n","Epoch 279/500\n","6/6 [==============================] - 0s 119us/step - loss: 7.7378e-07\n","Epoch 280/500\n","6/6 [==============================] - 0s 112us/step - loss: 7.5804e-07\n","Epoch 281/500\n","6/6 [==============================] - 0s 108us/step - loss: 7.4235e-07\n","Epoch 282/500\n","6/6 [==============================] - 0s 111us/step - loss: 7.2709e-07\n","Epoch 283/500\n","6/6 [==============================] - 0s 96us/step - loss: 7.1226e-07\n","Epoch 284/500\n","6/6 [==============================] - 0s 95us/step - loss: 6.9748e-07\n","Epoch 285/500\n","6/6 [==============================] - 0s 106us/step - loss: 6.8317e-07\n","Epoch 286/500\n","6/6 [==============================] - 0s 122us/step - loss: 6.6931e-07\n","Epoch 287/500\n","6/6 [==============================] - 0s 133us/step - loss: 6.5555e-07\n","Epoch 288/500\n","6/6 [==============================] - 0s 115us/step - loss: 6.4193e-07\n","Epoch 289/500\n","6/6 [==============================] - 0s 144us/step - loss: 6.2894e-07\n","Epoch 290/500\n","6/6 [==============================] - 0s 101us/step - loss: 6.1586e-07\n","Epoch 291/500\n","6/6 [==============================] - 0s 103us/step - loss: 6.0318e-07\n","Epoch 292/500\n","6/6 [==============================] - 0s 109us/step - loss: 5.9069e-07\n","Epoch 293/500\n","6/6 [==============================] - 0s 99us/step - loss: 5.7860e-07\n","Epoch 294/500\n","6/6 [==============================] - 0s 102us/step - loss: 5.6689e-07\n","Epoch 295/500\n","6/6 [==============================] - 0s 112us/step - loss: 5.5525e-07\n","Epoch 296/500\n","6/6 [==============================] - 0s 130us/step - loss: 5.4378e-07\n","Epoch 297/500\n","6/6 [==============================] - 0s 96us/step - loss: 5.3259e-07\n","Epoch 298/500\n","6/6 [==============================] - 0s 124us/step - loss: 5.2177e-07\n","Epoch 299/500\n","6/6 [==============================] - 0s 135us/step - loss: 5.1109e-07\n","Epoch 300/500\n","6/6 [==============================] - 0s 103us/step - loss: 5.0057e-07\n","Epoch 301/500\n","6/6 [==============================] - 0s 115us/step - loss: 4.9032e-07\n","Epoch 302/500\n","6/6 [==============================] - 0s 132us/step - loss: 4.8020e-07\n","Epoch 303/500\n","6/6 [==============================] - 0s 139us/step - loss: 4.7030e-07\n","Epoch 304/500\n","6/6 [==============================] - 0s 143us/step - loss: 4.6066e-07\n","Epoch 305/500\n","6/6 [==============================] - 0s 156us/step - loss: 4.5120e-07\n","Epoch 306/500\n","6/6 [==============================] - 0s 160us/step - loss: 4.4207e-07\n","Epoch 307/500\n","6/6 [==============================] - 0s 137us/step - loss: 4.3301e-07\n","Epoch 308/500\n","6/6 [==============================] - 0s 127us/step - loss: 4.2412e-07\n","Epoch 309/500\n","6/6 [==============================] - 0s 142us/step - loss: 4.1530e-07\n","Epoch 310/500\n","6/6 [==============================] - 0s 146us/step - loss: 4.0689e-07\n","Epoch 311/500\n","6/6 [==============================] - 0s 154us/step - loss: 3.9848e-07\n","Epoch 312/500\n","6/6 [==============================] - 0s 134us/step - loss: 3.9025e-07\n","Epoch 313/500\n","6/6 [==============================] - 0s 124us/step - loss: 3.8223e-07\n","Epoch 314/500\n","6/6 [==============================] - 0s 138us/step - loss: 3.7433e-07\n","Epoch 315/500\n","6/6 [==============================] - 0s 148us/step - loss: 3.6668e-07\n","Epoch 316/500\n","6/6 [==============================] - 0s 141us/step - loss: 3.5929e-07\n","Epoch 317/500\n","6/6 [==============================] - 0s 121us/step - loss: 3.5194e-07\n","Epoch 318/500\n","6/6 [==============================] - 0s 157us/step - loss: 3.4462e-07\n","Epoch 319/500\n","6/6 [==============================] - 0s 137us/step - loss: 3.3759e-07\n","Epoch 320/500\n","6/6 [==============================] - 0s 134us/step - loss: 3.3066e-07\n","Epoch 321/500\n","6/6 [==============================] - 0s 111us/step - loss: 3.2391e-07\n","Epoch 322/500\n","6/6 [==============================] - 0s 115us/step - loss: 3.1718e-07\n","Epoch 323/500\n","6/6 [==============================] - 0s 134us/step - loss: 3.1069e-07\n","Epoch 324/500\n","6/6 [==============================] - 0s 143us/step - loss: 3.0432e-07\n","Epoch 325/500\n","6/6 [==============================] - 0s 116us/step - loss: 2.9809e-07\n","Epoch 326/500\n","6/6 [==============================] - 0s 112us/step - loss: 2.9194e-07\n","Epoch 327/500\n","6/6 [==============================] - 0s 110us/step - loss: 2.8594e-07\n","Epoch 328/500\n","6/6 [==============================] - 0s 114us/step - loss: 2.8005e-07\n","Epoch 329/500\n","6/6 [==============================] - 0s 115us/step - loss: 2.7437e-07\n","Epoch 330/500\n","6/6 [==============================] - 0s 123us/step - loss: 2.6869e-07\n","Epoch 331/500\n","6/6 [==============================] - 0s 109us/step - loss: 2.6309e-07\n","Epoch 332/500\n","6/6 [==============================] - 0s 129us/step - loss: 2.5778e-07\n","Epoch 333/500\n","6/6 [==============================] - 0s 128us/step - loss: 2.5253e-07\n","Epoch 334/500\n","6/6 [==============================] - 0s 107us/step - loss: 2.4735e-07\n","Epoch 335/500\n","6/6 [==============================] - 0s 116us/step - loss: 2.4230e-07\n","Epoch 336/500\n","6/6 [==============================] - 0s 124us/step - loss: 2.3725e-07\n","Epoch 337/500\n","6/6 [==============================] - 0s 109us/step - loss: 2.3237e-07\n","Epoch 338/500\n","6/6 [==============================] - 0s 108us/step - loss: 2.2766e-07\n","Epoch 339/500\n","6/6 [==============================] - 0s 111us/step - loss: 2.2295e-07\n","Epoch 340/500\n","6/6 [==============================] - 0s 111us/step - loss: 2.1837e-07\n","Epoch 341/500\n","6/6 [==============================] - 0s 139us/step - loss: 2.1397e-07\n","Epoch 342/500\n","6/6 [==============================] - 0s 119us/step - loss: 2.0949e-07\n","Epoch 343/500\n","6/6 [==============================] - 0s 134us/step - loss: 2.0523e-07\n","Epoch 344/500\n","6/6 [==============================] - 0s 132us/step - loss: 2.0104e-07\n","Epoch 345/500\n","6/6 [==============================] - 0s 138us/step - loss: 1.9692e-07\n","Epoch 346/500\n","6/6 [==============================] - 0s 111us/step - loss: 1.9290e-07\n","Epoch 347/500\n","6/6 [==============================] - 0s 106us/step - loss: 1.8883e-07\n","Epoch 348/500\n","6/6 [==============================] - 0s 112us/step - loss: 1.8509e-07\n","Epoch 349/500\n","6/6 [==============================] - 0s 129us/step - loss: 1.8124e-07\n","Epoch 350/500\n","6/6 [==============================] - 0s 118us/step - loss: 1.7755e-07\n","Epoch 351/500\n","6/6 [==============================] - 0s 112us/step - loss: 1.7382e-07\n","Epoch 352/500\n","6/6 [==============================] - 0s 134us/step - loss: 1.7023e-07\n","Epoch 353/500\n","6/6 [==============================] - 0s 130us/step - loss: 1.6677e-07\n","Epoch 354/500\n","6/6 [==============================] - 0s 138us/step - loss: 1.6330e-07\n","Epoch 355/500\n","6/6 [==============================] - 0s 112us/step - loss: 1.5998e-07\n","Epoch 356/500\n","6/6 [==============================] - 0s 112us/step - loss: 1.5668e-07\n","Epoch 357/500\n","6/6 [==============================] - 0s 120us/step - loss: 1.5344e-07\n","Epoch 358/500\n","6/6 [==============================] - 0s 116us/step - loss: 1.5036e-07\n","Epoch 359/500\n","6/6 [==============================] - 0s 112us/step - loss: 1.4720e-07\n","Epoch 360/500\n","6/6 [==============================] - 0s 130us/step - loss: 1.4428e-07\n","Epoch 361/500\n","6/6 [==============================] - 0s 118us/step - loss: 1.4128e-07\n","Epoch 362/500\n","6/6 [==============================] - 0s 92us/step - loss: 1.3832e-07\n","Epoch 363/500\n","6/6 [==============================] - 0s 111us/step - loss: 1.3555e-07\n","Epoch 364/500\n","6/6 [==============================] - 0s 105us/step - loss: 1.3275e-07\n","Epoch 365/500\n","6/6 [==============================] - 0s 99us/step - loss: 1.3002e-07\n","Epoch 366/500\n","6/6 [==============================] - 0s 98us/step - loss: 1.2728e-07\n","Epoch 367/500\n","6/6 [==============================] - 0s 111us/step - loss: 1.2468e-07\n","Epoch 368/500\n","6/6 [==============================] - 0s 111us/step - loss: 1.2216e-07\n","Epoch 369/500\n","6/6 [==============================] - 0s 114us/step - loss: 1.1968e-07\n","Epoch 370/500\n","6/6 [==============================] - 0s 115us/step - loss: 1.1719e-07\n","Epoch 371/500\n","6/6 [==============================] - 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You can use the **model.predict** method to have it figure out the Y for a previously unknown X. So, for example, if X = 10, what do you think Y will be? Take a guess before you run this code:"]},{"metadata":{"id":"oxNzL4lS2Gui","colab_type":"code","colab":{"height":34},"outputId":"080c5d7a-aff6-4af2-a668-be993dd07ace","executionInfo":{"status":"ok","timestamp":1552616848824,"user_tz":-540,"elapsed":1082,"user":{"displayName":"Laurence Moroney","photoUrl":"https://lh3.googleusercontent.com/-RcxktLY-TBk/AAAAAAAAAAI/AAAAAAAAABY/b4V4dTIqmPI/s64/photo.jpg","userId":"06401446828348966425"}}},"cell_type":"code","source":["print(model.predict([10.0]))"],"execution_count":6,"outputs":[{"output_type":"stream","text":["[[ 31.00025749]]\n"],"name":"stdout"}]},{"metadata":{"id":"btF2CSFH2iEX","colab_type":"text"},"cell_type":"markdown","source":["You might have thought 31, right? But it ended up being a little over. Why do you think that is? \n","\n","Remember that neural networks deal with probabilities, so given the data that we fed the NN with, it calculated that there is a very high probability that the relationship between X and Y is Y=3X+1, but with only 6 data points we can't know for sure. As a result, the result for 10 is very close to 31, but not necessarily 31. \n","\n","As you work with neural networks, you'll see this pattern recurring. You will almost always deal with probabilities, not certainties, and will do a little bit of coding to figure out what the result is based on the probabilities, particularly when it comes to classification.\n"]}]}