Complete and hand in this completed worksheet (including its outputs and any supporting code outside of the worksheet) with your assignment submission. For more details see the assignments page on the course website.
This exercise is analogous to the SVM exercise. You will:
In [1]:
import random
import numpy as np
from skynet.utils.data_utils import load_CIFAR10
import matplotlib.pyplot as plt
%matplotlib inline
plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
# for auto-reloading extenrnal modules
# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython
%load_ext autoreload
%autoreload 2
In [2]:
def get_CIFAR10_data(num_training=49000, num_validation=1000, num_test=1000, num_dev=500):
"""
Load the CIFAR-10 dataset from disk and perform preprocessing to prepare
it for the linear classifier. These are the same steps as we used for the
SVM, but condensed to a single function.
"""
# Load the raw CIFAR-10 data
cifar10_dir = '../skynet/datasets/cifar-10-batches-py'
X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)
# subsample the data
mask = list(range(num_training, num_training + num_validation))
X_val = X_train[mask]
y_val = y_train[mask]
mask = list(range(num_training))
X_train = X_train[mask]
y_train = y_train[mask]
mask = list(range(num_test))
X_test = X_test[mask]
y_test = y_test[mask]
mask = np.random.choice(num_training, num_dev, replace=False)
X_dev = X_train[mask]
y_dev = y_train[mask]
# Preprocessing: reshape the image data into rows
X_train = np.reshape(X_train, (X_train.shape[0], -1))
X_val = np.reshape(X_val, (X_val.shape[0], -1))
X_test = np.reshape(X_test, (X_test.shape[0], -1))
X_dev = np.reshape(X_dev, (X_dev.shape[0], -1))
# Normalize the data: subtract the mean image
mean_image = np.mean(X_train, axis = 0)
X_train -= mean_image
X_val -= mean_image
X_test -= mean_image
X_dev -= mean_image
# add bias dimension and transform into columns
X_train = np.hstack([X_train, np.ones((X_train.shape[0], 1))])
X_val = np.hstack([X_val, np.ones((X_val.shape[0], 1))])
X_test = np.hstack([X_test, np.ones((X_test.shape[0], 1))])
X_dev = np.hstack([X_dev, np.ones((X_dev.shape[0], 1))])
return X_train, y_train, X_val, y_val, X_test, y_test, X_dev, y_dev
# Invoke the above function to get our data.
X_train, y_train, X_val, y_val, X_test, y_test, X_dev, y_dev = get_CIFAR10_data()
print('Train data shape: ', X_train.shape)
print('Train labels shape: ', y_train.shape)
print('Validation data shape: ', X_val.shape)
print('Validation labels shape: ', y_val.shape)
print('Test data shape: ', X_test.shape)
print('Test labels shape: ', y_test.shape)
print('dev data shape: ', X_dev.shape)
print('dev labels shape: ', y_dev.shape)
In [3]:
# First implement the naive softmax loss function with nested loops.
# Open the file cs231n/classifiers/softmax.py and implement the
# softmax_loss_naive function.
from skynet.linear.softmax import softmax_loss_naive
import time
# Generate a random softmax weight matrix and use it to compute the loss.
W = np.random.randn(3073, 10) * 0.0001 # D x C
loss, grad = softmax_loss_naive(W, X_dev, y_dev, 0.0)
# As a rough sanity check, our loss should be something close to -log(0.1).
print('loss: %f' % loss)
print('sanity check: %f' % (-np.log(0.1)))
In [4]:
# Complete the implementation of softmax_loss_naive and implement a (naive)
# version of the gradient that uses nested loops.
loss, grad = softmax_loss_naive(W, X_dev, y_dev, 0.0)
# As we did for the SVM, use numeric gradient checking as a debugging tool.
# The numeric gradient should be close to the analytic gradient.
from skynet.utils.gradient_check import grad_check_sparse
f = lambda w: softmax_loss_naive(w, X_dev, y_dev, 0.0)[0]
grad_numerical = grad_check_sparse(f, W, grad, 10)
# similar to SVM case, do another gradient check with regularization
loss, grad = softmax_loss_naive(W, X_dev, y_dev, 1e2)
f = lambda w: softmax_loss_naive(w, X_dev, y_dev, 1e2)[0]
grad_numerical = grad_check_sparse(f, W, grad, 10)
In [5]:
# Now that we have a naive implementation of the softmax loss function and its gradient,
# implement a vectorized version in softmax_loss_vectorized.
# The two versions should compute the same results, but the vectorized version should be
# much faster.
tic = time.time()
loss_naive, grad_naive = softmax_loss_naive(W, X_dev, y_dev, 0.00001)
toc = time.time()
print('naive loss: %e computed in %fs' % (loss_naive, toc - tic))
from skynet.linear.softmax import softmax_loss_vectorized
tic = time.time()
loss_vectorized, grad_vectorized = softmax_loss_vectorized(W, X_dev, y_dev, 0.00001)
toc = time.time()
print('vectorized loss: %e computed in %fs' % (loss_vectorized, toc - tic))
# As we did for the SVM, we use the Frobenius norm to compare the two versions
# of the gradient.
grad_difference = np.linalg.norm(grad_naive - grad_vectorized, ord='fro')
print('Loss difference: %f' % np.abs(loss_naive - loss_vectorized))
print('Gradient difference: %f' % grad_difference)
In [6]:
# Use the validation set to tune hyperparameters (regularization strength and
# learning rate). You should experiment with different ranges for the learning
# rates and regularization strengths; if you are careful you should be able to
# get a classification accuracy of over 0.35 on the validation set.
from skynet.linear import Softmax
results = {}
best_val = -1
best_softmax = None
# Grid search
# learning_rates = [1e-7, 3e-7, 5e-7, 7e-7, 1e-6, 3e-6]
# regularization_strengths = [1e-5, 5e-5, 1e-4, 3e-4, 5e-4, 1e-3]
# learning_rates = np.logspace(-7, -6, 5)
# regularization_strengths = np.logspace(3, 4, 5)
# Random search
learning_rates = sorted(10**np.random.uniform(-7, -5, 6))
regularization_strengths = sorted(10**np.random.uniform(3, 4, 6))
# regularization_strengths = sorted(10**np.random.uniform(4, 4.2, 6))
# best hyperparameters found for classification performance with
# accuracy: 0.407020, 0.404000, 0.394000
# learning_rates = [9.740577e-07]
# regularization_strengths = [1.469906e+03]
################################################################################
# TODO: #
# Use the validation set to set the learning rate and regularization strength. #
# This should be identical to the validation that you did for the SVM; save #
# the best trained softmax classifer in best_softmax. #
################################################################################
for learning_rate in learning_rates:
for reg in regularization_strengths:
classifier = Softmax()
classifier.train(X_train, y_train,
learning_rate=learning_rate, reg=reg, num_iters=1500,
batch_size=200, verbose=False)
y_train_predict = classifier.predict(X_train)
y_val_predict = classifier.predict(X_val)
train_accuracy = np.mean(y_train==y_train_predict)
val_accuracy = np.mean(y_val==y_val_predict)
results[(learning_rate, reg,)] = (train_accuracy, val_accuracy)
if val_accuracy > best_val:
best_val = val_accuracy
best_softmax = classifier
print('lr %e reg %e train accuracy: %f val accuracy: %f' % (
learning_rate, reg, train_accuracy, val_accuracy))
pass
################################################################################
# END OF YOUR CODE #
################################################################################
print('best validation accuracy achieved during cross-validation: %f' % best_val)
In [7]:
# evaluate on test set
# Evaluate the best softmax on test set
y_test_pred = best_softmax.predict(X_test)
test_accuracy = np.mean(y_test == y_test_pred)
print('softmax on raw pixels final test set accuracy: %f' % (test_accuracy, ))
In [8]:
def visualize_weights(weights):
"""
Visualize the learned weights for each class
"""
# w = weights[:-1,:] # strip out the bias
w = weights
w = w.reshape(32, 32, 3, 10)
w_min, w_max = np.min(w), np.max(w)
classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']
for i in range(10):
plt.subplot(2, 5, i + 1)
# Rescale the weights to be between 0 and 255
wimg = 255.0 * (w[:, :, :, i].squeeze() - w_min) / (w_max - w_min)
plt.imshow(wimg.astype('uint8'))
plt.axis('off')
plt.title(classes[i])
In [9]:
# Visualize the learned weights for each class
visualize_weights(best_softmax.W[:-1,:])
The learned weights for each class in softmax model resembles the shape of each class' object. The larger the regularization strength is, the more the weights are shrinked, giving less noise in the visualized image and making it more clear.
In [10]:
# this will produce weights more similar to the class images
learning_rates = [4.019744e-07]
regularization_strengths = [1.130442e+04]
for learning_rate in learning_rates:
for reg in regularization_strengths:
classifier = Softmax()
classifier.train(X_train, y_train,
learning_rate=learning_rate, reg=reg, num_iters=1500,
batch_size=200, verbose=False)
y_train_predict = classifier.predict(X_train)
y_val_predict = classifier.predict(X_val)
train_accuracy = np.mean(y_train==y_train_predict)
val_accuracy = np.mean(y_val==y_val_predict)
results[(learning_rate, reg,)] = (train_accuracy, val_accuracy)
if val_accuracy > best_val:
best_val = val_accuracy
best_softmax = classifier
print('lr %e reg %e train accuracy: %f val accuracy: %f' % (
learning_rate, reg, train_accuracy, val_accuracy))
visualize_weights(classifier.W[:-1,:])
In [ ]: