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basics
"""Summary of tensorflow basics.Parag K. Mital, Jan 2016."""# %% Import tensorflow and pyplot import tensorflow as tf import matplotlib.pyplot as plt# %% tf.Graph represents a collection of tf.Operations # You can create operations by writing out equations. # By default, there is a graph: tf.get_default_graph() # and any new operations are added to this graph. # The result of a tf.Operation is a tf.Tensor, which holds # the values.# %% First a tf.Tensor n_values = x = tf.linspace( -3.0 , 3.0 , n_values)# %% Construct a tf.Session to execute the graph. sess = tf.Session()result = sess.run(x)# %% Alternatively pass a session to the eval fn: x.eval(session=sess) # x.eval() does not work, as it requires a session!# %% We can setup an interactive session if we don't # want to keep passing the session around: sess.close()sess = tf.InteractiveSession()# %% Now this will work! x.eval()# %% Now a tf.Operation # We'll use our values from [-3, 3] to create a Gaussian Distribution sigma = 1.0 mean = 0.0 z = (tf.exp(tf.neg(tf.pow(x - mean, 2.0 ) / ( 2.0 * tf.pow(sigma, 2.0 )))) * ( 1.0 / (sigma * tf.sqrt( 2.0 * 3.1415 ))))# %% By default, new operations are added to the default Graph assert z.graph is tf.get_default_graph()# %% Execute the graph and plot the result plt.plot(x.eval(), z.eval())plt.show()# %% We can find out the shape of a tensor like so: print(z.get_shape())# %% Or in a more friendly format print(z.get_shape().as_list())# %% Sometimes we may not know the shape of a tensor # until it is computed in the graph. In that case # we should use the tf.shape fn, which will return a # Tensor which can be eval'ed, rather than a discrete # value of tf.Dimension print(tf.shape(z).eval())# %% We can combine tensors like so: print(tf.pack([tf.shape(z), tf.shape(z), [], []]).eval())# %% Let's multiply the two to get a 2d gaussian z_2d = tf.matmul(tf.reshape(z, [n_values, ]), tf.reshape(z, [, n_values]))# %% Execute the graph and store the value that `out` represents in `result`. plt.imshow(z_2d.eval())plt.show()# %% For fun let's create a gabor patch: x = tf.reshape(tf.sin(tf.linspace( -3.0 , 3.0 , n_values)), [n_values, ])y = tf.reshape(tf.ones_like(x), [, n_values])z = tf.mul(tf.matmul(x, y), z_2d)plt.imshow(z.eval())plt.show()# %% We can also list all the operations of a graph: ops = tf.get_default_graph().get_operations()print([op.name for op in ops])# %% Lets try creating a generic function for computing the same thing: def gabor (n_values=, sigma= 1.0 , mean= 0.0 ) : x = tf.linspace( -3.0 , 3.0 , n_values) z = (tf.exp(tf.neg(tf.pow(x - mean, 2.0 ) / ( 2.0 * tf.pow(sigma, 2.0 )))) * ( 1.0 / (sigma * tf.sqrt( 2.0 * 3.1415 )))) gauss_kernel = tf.matmul( tf.reshape(z, [n_values, ]), tf.reshape(z, [, n_values])) x = tf.reshape(tf.sin(tf.linspace( -3.0 , 3.0 , n_values)), [n_values, ]) y = tf.reshape(tf.ones_like(x), [, n_values]) gabor_kernel = tf.mul(tf.matmul(x, y), gauss_kernel) return gabor_kernel# %% Confirm this does something: plt.imshow(gabor().eval())plt.show()# %% And another function which can convolve def convolve (img, W) : # The W matrix is only 2D # But conv2d will need a tensor which is 4d: # height x width x n_input x n_output if len(W.get_shape()) == : dims = W.get_shape().as_list() + [, ] W = tf.reshape(W, dims) if len(img.get_shape()) == : # num x height x width x channels dims = [] + img.get_shape().as_list() + [] img = tf.reshape(img, dims) elif len(img.get_shape()) == : dims = [] + img.get_shape().as_list() img = tf.reshape(img, dims) # if the image is 3 channels, then our convolution # kernel needs to be repeated for each input channel W = tf.concat(, [W, W, W]) # Stride is how many values to skip for the dimensions of # num, height, width, channels convolved = tf.nn.conv2d(img, W, strides=[, , , ], padding= 'SAME' ) return convolved# %% Load up an image: from skimage import dataimg = data.astronaut()plt.imshow(img)plt.show()print(img.shape)# %% Now create a placeholder for our graph which can store any input: x = tf.placeholder(tf.float32, shape=img.shape)# %% And a graph which can convolve our image with a gabor out = convolve(x, gabor())# %% Now send the image into the graph and compute the result result = tf.squeeze(out).eval(feed_dict={x: img})plt.imshow(result)plt.show()linear_regression
"""Simple tutorial for using TensorFlow to compute a linear regression.Parag K. Mital, Jan. 2016"""'Simple tutorial for using TensorFlow to compute a linear regression.\n\nParag K. Mital, Jan. 2016'# %% imports %matplotlib inline import numpy as np import tensorflow as tf import matplotlib.pyplot as plt# %% Let's create some toy data plt.ion()n_observations = fig, ax = plt.subplots(, )xs = np.linspace( -3 , , n_observations)ys = np.sin(xs) + np.random.uniform( -0.5 , 0.5 , n_observations)ax.scatter(xs, ys)fig.show()plt.draw()/home/heythisischo/anaconda2/lib/python2.7/site-packages/matplotlib/figure.py:397: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure "matplotlib is currently using a non-GUI backend, "
# %% tf.placeholders for the input and output of the network. Placeholders are # variables which we need to fill in when we are ready to compute the graph. X = tf.placeholder(tf.float32)Y = tf.placeholder(tf.float32)# %% We will try to optimize min_(W,b) ||(X*w + b) - y||^2 # The `Variable()` constructor requires an initial value for the variable, # which can be a `Tensor` of any type and shape. The initial value defines the # type and shape of the variable. After construction, the type and shape of # the variable are fixed. The value can be changed using one of the assign # methods. W = tf.Variable(tf.random_normal([]), name= 'weight' )b = tf.Variable(tf.random_normal([]), name= 'bias' )Y_pred = tf.add(tf.mul(X, W), b)# %% Loss function will measure the distance between our observations # and predictions and average over them. cost = tf.reduce_sum(tf.pow(Y_pred - Y, )) / (n_observations - )# %% if we wanted to add regularization, we could add other terms to the cost, # e.g. ridge regression has a parameter controlling the amount of shrinkage # over the norm of activations. the larger the shrinkage, the more robust # to collinearity. # cost = tf.add(cost, tf.mul(1e-6, tf.global_norm([W])))# %% Use gradient descent to optimize W,b # Performs a single step in the negative gradient learning_rate = 0.01 optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)# %% We create a session to use the graph n_epochs = 1000 with tf.Session() as sess: # Here we tell tensorflow that we want to initialize all # the variables in the graph so we can use them sess.run(tf.initialize_all_variables()) # Fit all training data prev_training_cost = 0.0 for epoch_i in range(n_epochs): for (x, y) in zip(xs, ys): sess.run(optimizer, feed_dict={X: x, Y: y}) training_cost = sess.run( cost, feed_dict={X: xs, Y: ys}) print(training_cost) if epoch_i % == : ax.plot(xs, Y_pred.eval( feed_dict={X: xs}, session=sess), 'k' , alpha=epoch_i / n_epochs) fig.show() plt.draw() # Allow the training to quit if we've reached a minimum if np.abs(prev_training_cost - training_cost) < 0.000001 : break prev_training_cost = training_costfig.show()1.439891.306861.189161.085030.9928790.9113250.8391410.775240.7186630.6685640.6241920.5848850.5500580.5191940.4918350.4675780.4460630.4269770.4100390.3950010.3816470.3697830.3592380.3498610.3415190.3340940.3274810.3215870.3163320.3116430.3074550.3037130.3003660.297370.2946860.2922780.2901170.2881750.2864270.2848530.2834330.2821510.2809910.2799420.278990.2781250.2773390.2766230.275970.2753730.2748260.2743250.2738650.2734420.2730520.2726930.272360.2720520.2717670.2715010.2712540.2710240.270810.2706090.2704210.2702450.270080.2699250.2697790.2696420.2695120.269390.2692740.2691650.2690620.2689640.2688710.2687830.2686990.268620.2685440.2684720.2684040.2683390.2682770.2682180.2681610.2681070.2680560.2680070.267960.2679160.2678730.2678320.2677940.2677560.2677210.2676870.2676540.2676230.2675940.2675650.2675380.2675120.2674870.2674640.2674410.2674190.2673980.2673780.2673590.2673410.2673240.2673070.2672910.2672760.2672610.2672470.2672340.2672210.2672090.2671970.2671860.2671760.2671650.2671560.2671460.2671370.2671290.2671210.2671130.2671050.2670980.2670920.2670850.2670790.2670730.2670670.2670620.2670570.2670520.2670470.2670430.2670390.2670340.2670310.2670270.2670230.267020.2670170.2670140.2670110.2670080.2670060.2670030.2670010.2669980.2669960.2669940.2669920.266990.2669890.2669870.2669850.2669840.2669820.2669810.266980.2669790.2669780.2669760.2669750.266974Light
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