code_challenge_manipulate_regression_slopes.py

# %%
# import libraries
import numpy as np
import torch 
import torch.nn as nn
import matplotlib.pyplot as plt
from IPython import display
display.set_matplotlib_formats('svg')
# %%
# create data

N = 30
x = torch.randn(N, 1)
y = x + torch.randn(N, 1)/2

# and plot 
plt.plot(x,y,'s')
plt.show()
# %%
# build model 
ANNreg = nn.Sequential(
    nn.Linear(1, 1), # input layer
    nn.ReLU(), # activation function
    nn.Linear(1, 1) # output layer
)
ANNreg
# %%
# learning rate 
learning_rate = .05

# loss function
loss_fn = nn.MSELoss()

# optimizer (the flavor of gradient descent to implement)
optimizer = torch.optim.SGD(ANNreg.parameters(), lr=learning_rate)
# %%
# train the model
num_epochs = 500
losses = torch.zeros(num_epochs)

# Train the model 
for epochi in range(num_epochs):

    # forward pass
    yhat = ANNreg(x)

    # compute loss
    loss = loss_fn(yhat, y)
    losses[epochi] = loss

    # backpropagation
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
# %%
# show the losses

# manually compute losses
# final forward pass
predictions = ANNreg(x)

# final loss (MSE)
test_loss = loss_fn(predictions, y).pow(2).mean()

plt.plot(losses.detach(), 'o', markerfacecolor='w', linewidth=.1)
plt.plot(num_epochs, test_loss.detach(), 'ro')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.title('Final loss: %.3f' % test_loss.item())
plt.show()
# %%
test_loss.item()
# %%
# plot the data 
plt.plot(x,y,'bo', label='Real data')
plt.plot(x, predictions.detach(), 'rs', label='Predictions')
plt.title(f'preiction-data r = {np.corrcoef(y.T, predictions.detach().T)[0,1]:.2f}')
plt.legend()
plt.show()
# %%
def Model(x,y, num_epochs, learning_rate):

    # build model
    ANNreg =nn.Sequential(
        nn.Linear(1,1),
        nn.ReLU(),
        nn.Linear(1,1)
    )

    # loss function
    loss_fn = nn.MSELoss()

    # optimizer
    optimizer = torch.optim.SGD(ANNreg.parameters(), lr=learning_rate)

    # train the model
    losses = torch.zeros(num_epochs)

    for epoch in range(num_epochs):
        # forward pass
        yHat = ANNreg(x)

        # compute loss
        loss = loss_fn(yHat,y)
        losses[epoch] = loss

        # backpropagation
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

    final_predictions = ANNreg(x)


    return final_predictions, losses

N = 30
x = torch.randn(N, 1)
y = x + torch.randn(N, 1)/2
final_predictions, losses = Model(x,y, num_epochs=500, learning_rate=.05)
final_predictions 

# %%
# A function that creates  and trains the model

def buildAndTrainTheModel(x,y):

    # build the model
    ANNreg = nn.Sequential(
        nn.Linear(1,1), # input layer
        nn.ReLU(),      # activation function
        nn.Linear(1,1)  # output layer
    )

    # loss and optimizer functions
    loss_fn = nn.MSELoss()
    optimizer = torch.optim.SGD(ANNreg.parameters(), lr=.05)

    # train the model
    num_epochs = 500
    losses = torch.zeros(num_epochs)

    for epochi in range(num_epochs):

        # forward pass
        yHat = ANNreg(x)

        # compute loss
        loss = loss_fn(yHat, y)
        losses[epochi] = loss

        # backpropagation
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

        # end traing loop

    # compute model predictions
    predictions = ANNreg(x)

    return predictions, losses

# %%
# A function that creates the data

def createTheData(m):
    N = 30
    x = torch.randn(N,1)
    y = m*x + torch.randn(N,1)/2
    return x, y
# %%
# Test it once 

# create a dataset
x, y = createTheData(.8)

# run the model 
yhat, losses = buildAndTrainTheModel(x,y)

fig, ax = plt.subplots(1,2, figsize=(12,4))

ax[0].plot(losses.detach(),'o',markerfacecolor='w',linewidth=.1)
ax[0].set_xlabel('Epoch')
ax[0].set_title('loss')

ax[1].plot(x,y,'bo',label='Real data')
ax[1].plot(x,yhat.detach(),'rs',label='Predictions')
ax[1].set_xlabel('x')
ax[1].set_ylabel('y')
ax[1].set_title(f'prediction-data corr = {np.corrcoef(y.T, yhat.detach().T)[0,1]:.2f}')
ax[1].legend()
plt.show()

# %%
# Now for the expriment!

# (takes  3 mns with 21 slopes and 50 exps)

# the slopes to simulate
slopes = np.linspace(-2,2,21)

numExps = 50

# intialize output matrix
results = np.zeros((len(slopes), numExps,2))

for slopi in range(len(slopes)):
    for expi in range(numExps):

        # create data
        x, y = createTheData(slopes[slopi])

        # run the model
        yhat, losses = buildAndTrainTheModel(x,y)

        # store the results
        results[slopi, expi, 0] = losses[-1]
        results[slopi, expi, 1] = np.corrcoef(y.T, yhat.detach().T)[0,1]

# correlation can be 0 if the model didn't do well. Set nan's -> 0
results[np.isnan(results)] = 0
# %%
# plot the results!

fig, ax = plt.subplots(1,2, figsize=(12,4))

ax[0].plot(slopes, np.mean(results[:,:,0], axis=1), 'ko-', markerfacecolor='w', markersize=10)
ax[0].set_xlabel('Slope')
ax[0].set_title('Loss')

ax[1].plot(slopes, np.mean(results[:,:,1], axis=1), 'ms-', markerfacecolor='w', markersize=10)
ax[1].set_xlabel('Slope')
ax[1].set_ylabel('Real-predicted Correlation')
ax[1].set_title('Model performance')

plt.show()
# %%