{"cells":[{"cell_type":"markdown","metadata":{"id":"QliNPatWGeQF"},"source":["\n","\n","# Pytorch by example\n","\n","This example from the pytorch documentation [here](https://pytorch.org/tutorials/beginner/pytorch_with_examples.html) displays generating random y ad x dat and fitting a multi-layer neural network. We're going to consider a regression problem, but using a two layer neural network to solve it. Consider something like this. We have 5 inputs; those get passed to 3 hidden nodes, those get RELU'd, which get passed to an output."]},{"cell_type":"code","execution_count":null,"metadata":{"tags":["hide-input"],"id":"3vAvwzTzoT7i","outputId":"9735d82b-3583-44b4-f4e6-b102f32a2263"},"outputs":[{"data":{"image/png":"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","text/plain":[""]},"metadata":{},"output_type":"display_data"}],"source":["import networkx as nx\n","import matplotlib.pyplot as plt\n","import numpy as np\n","import sklearn as skl\n","\n","#plt.figure(figsize=[2, 2])\n","G = nx.DiGraph()\n","G.add_node(\"X1\", pos = (0, 2) )\n","G.add_node(\"X2\", pos = (1, 2) )\n","G.add_node(\"X3\", pos = (2, 2) )\n","G.add_node(\"X4\", pos = (3, 2) )\n","G.add_node(\"X5\", pos = (4, 2) )\n","\n","G.add_node(\"H1\", pos = (1, 1) )\n","G.add_node(\"H2\", pos = (2, 1) )\n","G.add_node(\"H3\", pos = (3, 1) )\n","G.add_node(\"Y\" , pos = (2, 0) )\n","\n","G.add_edges_from([ (\"X1\", \"H1\"), (\"X2\", \"H1\"), (\"X3\", \"H1\"), (\"X4\", \"H1\"), (\"X5\", \"H1\")])\n","G.add_edges_from([ (\"X1\", \"H2\"), (\"X2\", \"H2\"), (\"X3\", \"H2\"), (\"X4\", \"H2\"), (\"X5\", \"H2\")])\n","G.add_edges_from([ (\"X1\", \"H3\"), (\"X2\", \"H3\"), (\"X3\", \"H3\"), (\"X4\", \"H3\"), (\"X5\", \"H3\")])\n","G.add_edges_from([ (\"H1\", \"Y\"), (\"H2\", \"Y\"), (\"H3\", \"Y\")])\n","nx.draw(G,\n"," nx.get_node_attributes(G, 'pos'),\n"," with_labels=True,\n"," font_weight='bold',\n"," node_size = 2000,\n"," node_color = \"lightblue\",\n"," linewidths = 3)\n","ax= plt.gca()\n","ax.collections[0].set_edgecolor(\"#000000\")\n","ax.set_xlim([-.3, 4.3])\n","ax.set_ylim([-.3, 2.3])\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"7PP_ztV_oT7m"},"source":["Below, we create an example. It isn't terribly interesting, since the X and the Y aren't related at all. But, it does show us some useful code."]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":108},"id":"54gmWH2_GILQ","outputId":"460f97b3-7974-484e-9ad5-428fb776b4e8"},"outputs":[{"name":"stdout","output_type":"stream","text":["99 4534.51025390625\n","199 3433.26611328125\n","299 3105.7314453125\n","399 3059.81689453125\n","499 2737.764404296875\n","599 2601.751220703125\n","699 2479.807373046875\n","799 2429.35302734375\n","899 2493.08544921875\n","999 2565.323486328125\n"]}],"source":["import torch\n","import numpy as np\n","import pandas as pd\n","import seaborn as sns\n","import matplotlib.pyplot as plt\n","import sklearn.linear_model as lm\n","sns.set()\n","\n","\n","# N is batch size; D_in is input dimension;\n","# H is hidden dimension; D_out is output dimension.\n","N, D_in, H, D_out = 1000, 128, 32, 8\n","\n","# Create random Tensors to hold inputs and outputs\n","x = torch.randn(N, D_in)\n","y = torch.randn(N, D_out)\n","\n","# Use the nn package to define our model as a sequence of layers. nn.Sequential\n","# is a Module which contains other Modules, and applies them in sequence to\n","# produce its output. Each Linear Module computes output from input using a\n","# linear function, and holds internal Tensors for its weight and bias.\n","model = torch.nn.Sequential(\n"," torch.nn.Linear(D_in, H),\n"," torch.nn.ReLU(),\n"," torch.nn.Linear(H, D_out),\n",")\n","\n","# The nn package also contains definitions of popular loss functions; in this\n","# case we will use Mean Squared Error (MSE) as our loss function.\n","loss_fn = torch.nn.MSELoss(reduction='sum')\n","\n","learning_rate = 1e-4\n","for t in range(1000):\n"," # Forward pass: compute predicted y by passing x to the model. Module objects\n"," # override the __call__ operator so you can call them like functions. When\n"," # doing so you pass a Tensor of input data to the Module and it produces\n"," # a Tensor of output data.\n"," y_pred = model(x)\n","\n"," # Compute and print loss. We pass Tensors containing the predicted and true\n"," # values of y, and the loss function returns a Tensor containing the\n"," # loss.\n"," loss = loss_fn(y_pred, y)\n"," if t % 100 == 99:\n"," print(t, loss.item())\n","\n"," # Zero the gradients before running the backward pass.\n"," model.zero_grad()\n","\n"," # Backward pass: compute gradient of the loss with respect to all the learnable\n"," # parameters of the model. Internally, the parameters of each Module are stored\n"," # in Tensors with requires_grad=True, so this call will compute gradients for\n"," # all learnable parameters in the model.\n"," loss.backward()\n","\n"," # Update the weights using gradient descent. Each parameter is a Tensor, so\n"," # we can access its gradients like we did before.\n"," with torch.no_grad():\n"," for param in model.parameters():\n"," param -= learning_rate * param.grad"]},{"cell_type":"markdown","metadata":{"id":"qWcVUq9RGxTB"},"source":["Let's update that example for our setting using the voxel level data."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"62iyChkPGwZD"},"outputs":[],"source":["## Read in the data and display a few rows\n","dat = pd.read_csv(\"https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/oasis.csv\")"]},{"cell_type":"code","execution_count":null,"metadata":{"tags":["hide-input"],"id":"BG6Qz_lxoT7o","outputId":"7f2e8fe5-cecc-415d-91b4-3900bbc2b485"},"outputs":[{"data":{"image/png":"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","text/plain":[""]},"metadata":{},"output_type":"display_data"}],"source":["G = nx.DiGraph()\n","G.add_node(\"PD\", pos = (0, 2) )\n","G.add_node(\"T1\", pos = (1, 2) )\n","G.add_node(\"T2\", pos = (2, 2) )\n","G.add_node(\"PD_10\", pos = (3, 2) )\n","G.add_node(\"T1_10\", pos = (4, 2) )\n","G.add_node(\"T2_10\", pos = (5, 2) )\n","\n","G.add_node(\"H1\", pos = (1.0, 1) )\n","G.add_node(\"H2\", pos = (2.5, 1) )\n","G.add_node(\"H3\", pos = (4.0, 1) )\n","\n","G.add_node(\"FLAIR\" , pos = (2.5, 0) )\n","\n","G.add_edges_from([ (\"PD\", \"H1\"), (\"T1\", \"H1\"), (\"T2\", \"H1\"), (\"PD_10\", \"H1\"), (\"T1_10\", \"H1\"), (\"T2_10\", \"H1\")])\n","G.add_edges_from([ (\"PD\", \"H2\"), (\"T1\", \"H2\"), (\"T2\", \"H2\"), (\"PD_10\", \"H2\"), (\"T1_10\", \"H2\"), (\"T2_10\", \"H2\")])\n","G.add_edges_from([ (\"PD\", \"H3\"), (\"T1\", \"H3\"), (\"T2\", \"H3\"), (\"PD_10\", \"H3\"), (\"T1_10\", \"H3\"), (\"T2_10\", \"H3\")])\n","\n","G.add_edges_from([ (\"H1\", \"FLAIR\"), (\"H2\", \"FLAIR\"), (\"H3\", \"FLAIR\")])\n","nx.draw(G,\n"," nx.get_node_attributes(G, 'pos'),\n"," with_labels=True,\n"," font_weight='bold',\n"," node_size = 3000,\n"," node_color = \"lightblue\",\n"," linewidths = 3)\n","ax= plt.gca()\n","ax.collections[0].set_edgecolor(\"#000000\")\n","ax.set_xlim([-.5, 5.5])\n","ax.set_ylim([-.3, 2.3])\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"jvUoGUiAoT7p"},"source":["Let's set the training fraction at 75% (and thus the testing fraction at 25%). This gives us relatively little data to fit with. Thus, a relatively simple model makes sense."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"neIwiOlRTIor"},"outputs":[],"source":["trainFraction = .75\n","\n","sample = np.random.uniform(size = 100) < trainFraction\n","trainingDat = dat[sample]\n","testingDat = dat[~sample]\n"]},{"cell_type":"markdown","metadata":{"id":"I21Ad2A2oT7r"},"source":["Next we need to get the data into a pytorch size and fram"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":89},"id":"-tVT-AsOTPgN","outputId":"1f938b04-48b9-4fa2-8b94-160c233b8a7e","tags":[]},"outputs":[{"data":{"text/plain":["[torch.Size([76, 5]),\n"," torch.Size([76, 1]),\n"," torch.Size([24, 5]),\n"," torch.Size([24, 1])]"]},"execution_count":16,"metadata":{},"output_type":"execute_result"}],"source":["x = torch.from_numpy(dat[['PD','T1', 'T2', 'T1_10', 'T2_10', ]].values)\n","y = torch.from_numpy(dat[['FLAIR']].values)\n","\n","##pytorch wants type as float\n","x = x.float()\n","y = y.float()\n","\n","xtraining = x[sample]\n","xtesting = x[~sample]\n","ytraining = y[sample]\n","ytesting = y[~sample]\n","\n","[\n"," xtraining.size(),\n"," ytraining.size(),\n"," xtesting.size(),\n"," ytesting.size(),\n","]"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"D2UxGTdkaBdO"},"outputs":[],"source":["## Define the model\n","## Dimension of the hidden layer\n","H = 3\n","\n","## Number of predictors\n","D_in = xtraining.size()[1]\n","D_out = 1\n","\n","model = torch.nn.Sequential(\n"," torch.nn.Linear(D_in, H),\n"," torch.nn.ReLU(),\n"," torch.nn.Linear(H, D_out),\n",")\n","\n"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":108},"id":"lnoPaqh7Rm2M","outputId":"9067a2a4-7d16-4efa-8ee0-8ef8d44db9d2"},"outputs":[{"name":"stdout","output_type":"stream","text":["0 171.88433837890625\n"]},{"name":"stdout","output_type":"stream","text":["10000 18.76696014404297\n","20000 16.824806213378906\n","30000 16.18133544921875\n","40000 16.068267822265625\n","50000 16.038101196289062\n","60000 16.03182601928711\n","70000 16.030363082885742\n","80000 16.029705047607422\n","90000 16.029869079589844\n"]}],"source":["loss_fn = torch.nn.MSELoss(reduction='sum')\n","\n","learning_rate = 1e-4\n","for t in range(100000):\n"," y_pred = model(xtraining)\n"," loss = loss_fn(y_pred, ytraining)\n"," if t % 10000 == 0:\n"," print(t, loss.item())\n"," model.zero_grad()\n"," loss.backward()\n"," with torch.no_grad():\n"," for param in model.parameters():\n"," param -= learning_rate * param.grad\n"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":292},"id":"eZswhY21bcwK","outputId":"bbefd7ef-cf11-4bd1-9ffc-7e99344e2755"},"outputs":[{"data":{"image/png":"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","text/plain":[""]},"metadata":{},"output_type":"display_data"}],"source":["## try prediction\n","ytesting_pred = model(xtesting)\n","a = ytesting_pred.detach().numpy()\n","\n","plt.scatter(a[:,0], ytesting[:,0]);"]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3 (ipykernel)","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.10.13"}},"nbformat":4,"nbformat_minor":0}