Add Theano scan notebook.

Author: donnemartin

README.md

@@ -94,6 +94,7 @@ IPython Notebook(s) demonstrating deep learning functionality.
 | [tsf-word2vec](http://nbviewer.ipython.org/github/donnemartin/data-science-ipython-notebooks/blob/master/deep-learning/tensor-flow-exercises/5_word2vec.ipynb) |  Train a skip-gram model over Text8 data in TensorFlow. |
 | [tsf-lstm](http://nbviewer.ipython.org/github/donnemartin/data-science-ipython-notebooks/blob/master/deep-learning/tensor-flow-exercises/6_lstm.ipynb) |  Train a LSTM character model over Text8 data in TensorFlow. |
 | [theano-intro](http://nbviewer.ipython.org/github/donnemartin/data-science-ipython-notebooks/blob/master/deep-learning/theano-tutorial/intro_theano/intro_theano.ipynb) |  Intro to Theano, which allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. It can use GPUs and perform efficient symbolic differentiation. |
+| [theano-scan](http://nbviewer.ipython.org/github/donnemartin/data-science-ipython-notebooks/blob/master/deep-learning/theano-tutorial/scan_tutorial/scan_tutorial.ipynb) |  Learn scans, a mechanism to perform loops in a Theano graph. |
 | [deep-dream](http://nbviewer.ipython.org/github/donnemartin/data-science-ipython-notebooks/blob/master/deep-learning/deep-dream/dream.ipynb) |  Caffe-based computer vision program which uses a convolutional neural network to find and enhance patterns in images. |
 
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deep-learning/theano-tutorial/scan_tutorial/scan_ex1_solution.py

@@ -0,0 +1,28 @@
+import theano
+import theano.tensor as T
+import numpy as np
+
+coefficients = T.vector("coefficients")
+x = T.scalar("x")
+max_coefficients_supported = 10000
+
+
+def step(coeff, power, prior_value, free_var):
+    return prior_value + (coeff * (free_var ** power))
+
+# Generate the components of the polynomial
+full_range = T.arange(max_coefficients_supported)
+outputs_info = np.zeros((), dtype=theano.config.floatX)
+
+components, updates = theano.scan(fn=step,
+                                  sequences=[coefficients, full_range],
+                                  outputs_info=outputs_info,
+                                  non_sequences=x)
+
+polynomial = components[-1]
+calculate_polynomial = theano.function(inputs=[coefficients, x],
+                                       outputs=polynomial,
+                                       updates=updates)
+
+test_coeff = np.asarray([1, 0, 2], dtype=theano.config.floatX)
+print(calculate_polynomial(test_coeff, 3))

deep-learning/theano-tutorial/scan_tutorial/scan_ex2_solution.py

@@ -0,0 +1,50 @@
+import theano
+import theano.tensor as T
+import numpy as np
+
+probabilities = T.vector()
+nb_samples = T.iscalar()
+
+rng = T.shared_randomstreams.RandomStreams(1234)
+
+
+def sample_from_pvect(pvect):
+    """ Provided utility function: given a symbolic vector of
+    probabilities (which MUST sum to 1), sample one element
+    and return its index.
+    """
+    onehot_sample = rng.multinomial(n=1, pvals=pvect)
+    sample = onehot_sample.argmax()
+    return sample
+
+
+def set_p_to_zero(pvect, i):
+    """ Provided utility function: given a symbolic vector of
+    probabilities and an index 'i', set the probability of the
+    i-th element to 0 and renormalize the probabilities so they
+    sum to 1.
+    """
+    new_pvect = T.set_subtensor(pvect[i], 0.)
+    new_pvect = new_pvect / new_pvect.sum()
+    return new_pvect
+
+
+def step(p):
+    sample = sample_from_pvect(p)
+    new_p = set_p_to_zero(p, sample)
+    return new_p, sample
+
+output, updates = theano.scan(fn=step,
+                              outputs_info=[probabilities, None],
+                              n_steps=nb_samples)
+
+modified_probabilities, samples = output
+
+f = theano.function(inputs=[probabilities, nb_samples],
+                    outputs=[samples],
+                    updates=updates)
+
+# Testing the function
+test_probs = np.asarray([0.6, 0.3, 0.1], dtype=theano.config.floatX)
+for i in range(10):
+    print(f(test_probs, 2))