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+Basic regression in pytorch¶
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+Code¶
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+In [17]:
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+import pandas as pd
+import torch
+import statsmodels.formula.api as smf
+import statsmodels as sm
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+## Read in the data and display a few rows
+dat = pd.read_csv("https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/oasis.csv")
+dat.head(4)
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+Out[17]:
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+| + | FLAIR | +PD | +T1 | +T2 | +FLAIR_10 | +PD_10 | +T1_10 | +T2_10 | +FLAIR_20 | +PD_20 | +T1_20 | +T2_20 | +GOLD_Lesions | +
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | +1.143692 | +1.586219 | +-0.799859 | +1.634467 | +0.437568 | +0.823800 | +-0.002059 | +0.573663 | +0.279832 | +0.548341 | +0.219136 | +0.298662 | +0 | +
| 1 | +1.652552 | +1.766672 | +-1.250992 | +0.921230 | +0.663037 | +0.880250 | +-0.422060 | +0.542597 | +0.422182 | +0.549711 | +0.061573 | +0.280972 | +0 | +
| 2 | +1.036099 | +0.262042 | +-0.858565 | +-0.058211 | +-0.044280 | +-0.308569 | +0.014766 | +-0.256075 | +-0.136532 | +-0.350905 | +0.020673 | +-0.259914 | +0 | +
| 3 | +1.037692 | +0.011104 | +-1.228796 | +-0.470222 | +-0.013971 | +-0.000498 | +-0.395575 | +-0.221900 | +0.000807 | +-0.003085 | +-0.193249 | +-0.139284 | +0 | +
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+Plot the data¶
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+In [18]:
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+sns.scatterplot(x = dat['T2'], y = dat['PD']);
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+Basic regression results¶
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+In [19]:
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+fit = smf.ols('PD ~ T2', data = dat).fit()
+print(fit.summary().tables[1])
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+============================================================================== + coef std err t P>|t| [0.025 0.975] +------------------------------------------------------------------------------ +Intercept 0.3138 0.052 6.010 0.000 0.210 0.417 +T2 0.7832 0.057 13.815 0.000 0.671 0.896 +============================================================================== ++
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+Visualization of the line¶
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+In [20]:
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+# The in sample predictions
+yhat = fit.predict(dat['T2'])
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+## A plot of the in sample predicted values versus the actual outcomes
+sns.scatterplot(x = yhat, y = dat['PD'])
+plt.plot([-1, 3], [-1, 3], linewidth=2)
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+Out[20]:
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+[<matplotlib.lines.Line2D at 0x7f7bd5b6c1f0>]+
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+Create tensors¶
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+In [21]:
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+n = dat.shape[0]
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+## Get the y and x from
+xtraining = torch.from_numpy(dat['T2'].values)
+ytraining = torch.from_numpy(dat['PD'].values)
+
+## PT wants floats
+xtraining = xtraining.float()
+ytraining = ytraining.float()
+
+## Dimension is 1xn not nx1
+## squeeze the second dimension
+xtraining = xtraining.unsqueeze(1)
+ytraining = ytraining.unsqueeze(1)
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+## Show that everything is the right size
+[xtraining.shape, ytraining.shape, [n, 1] ]
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+Out[21]:
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+[torch.Size([100, 1]), torch.Size([100, 1]), [100, 1]]+
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+Linear regression in PyTorch¶
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+In [22]:
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+## Show that linear regression is a pytorch
+model = torch.nn.Sequential(torch.nn.Linear(1, 1))
+## MSE is the loss function
+loss_fn = torch.nn.MSELoss(reduction='sum')
+## Set the optimizer, there are lots of choices
+optimizer = torch.optim.SGD(model.parameters(), lr=1e-4)
+## Loop over iterations
+for t in range(10000):
+ y_pred = model(xtraining) ## Forward propagation
+ loss = loss_fn(y_pred, ytraining) ## the loss for this interation
+ #print(t, loss.item() / n)
+ optimizer.zero_grad() ## Zero out the gradients before adding them up
+ loss.backward() ## Backprop
+ optimizer.step() ## Optimization step
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+Visualization¶
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+In [23]:
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+ytest = model(xtraining).detach().numpy().reshape(-1)
+sns.scatterplot(x = ytest, y = yhat)
+plt.plot([-1, 3], [-1, 3], linewidth=2)
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+Out[23]:
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+[<matplotlib.lines.Line2D at 0x7f7bd5b6b940>]+
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+PyTorch parameters for linear regression¶
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+In [24]:
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+for param in model.parameters():
+ print(param.data)
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+tensor([[0.7831]]) +tensor([0.3138]) ++
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