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+=== Machine learning with theano ===
+[[http://deeplearning.net/software/theano/ | Theano]] represents a very different approach to machine learning programming.
+Here's the code that I showed in the class:
+<file python basics.py>
+"""
+Basic usage of theano constructs.
+"""
+import numpy
+import theano
+from theano import tensor
+from theano import function
+# let's defines two symbols (or variables):
+x = tensor.dscalar('x')
+y = tensor.dscalar('y')
+# a dscalar is a 0 dimensional tensor
+# the argument to dscalar is the name of the variable,
+# which you can leave out.
+# there are several types of scalars:
+# dscalar float64
+# fscalar float32
+# iscalar int32
+# the above is a shortcut fore:
+x = tensor.scalar('x', dtype = 'float64')
+# to see what type of object we created:
+type(x)
+x.type
+z = x + y
+from theano import pp
+pp(z)
+# let's create a function
+f = function([x, y], z)
+# this compiles the expression into someting
+# that can be executed:
+f(2, 3)
+# we like dot products:
+x = tensor.dvector('x')
+y = tensor.dvector('y')
+dot_symbolic = tensor.dot(x, y)
+dot = function([x,y], dot_symbolic)
+dot([1,1,-1], [1,1,1])
+# the discriminant function for classifier:
+# shared variables are useful for storing the weights of a neural network
+# theano will automatically try to put such variables on a GPU if one is available.
+w = theano.shared(value=numpy.array([1.0, 1.0]), name='w')
+b = theano.shared(value=2.0, name='b')
+x = tensor.dvector('x')
+discriminant_symbolic = tensor.dot(w, x) + b
+discriminant = function([x], discriminant_symbolic)
+discriminant([1, 1])
+</file>
+Logistic regression in theano:
+<file python logistic_regression.py>
+import numpy
+import theano
+import theano.tensor as T
+class LogisticRegression(object):
+    def __init__(self, learning_rate = 0.1, regularizer = 0.1, epochs = 500):
+        self.learning_rate = learning_rate
+        self.regularizer = regularizer
+        self.epochs = epochs
+    def fit(self, X, labels) :
+        num_features = len(X[0])
+        # initialize the weights
+        w = theano.shared(
+            value=numpy.random.randn(num_features),
+            name='w'
+        )
+        # initialize the bias
+        b = theano.shared(0.0, name="b")
+        x = T.dmatrix("x")
+        y = T.dvector("y")
+        # Probability that target = 1
+        p_1 = 1 / (1 + T.exp(-T.dot(x, w) - b))
+        # The predictions thresholded
+        prediction = p_1 > 0.5
+        # The cross-entropy loss function
+        cross_ent = -y * T.log(p_1) - (1-y) * T.log(1-p_1)
+        # The cost function to minimize
+        cost = cross_ent.mean() + self.regularizer * (w ** 2).sum()
+        # Compute the gradient of the cost
+        gw = T.grad(cost, wrt=w)
+        gb = T.grad(cost, wrt=b)
+        #gw, gb = T.grad(cost, [w, b])
+        train = theano.function(
+            inputs=[x,y],
+            outputs=[prediction, cost],
+            updates=((w, w - self.learning_rate * gw), (b, b - self.learning_rate * gb)))
+        self._predict = theano.function(inputs=[x], outputs=prediction)
+        # train the model:
+        for i in range(self.epochs) :
+            pred, c = train(X, labels)
+            print ("In sample error: ", c)
+        self.w = w
+        self.b = b
+    def predict(self, X) :
+        return self._predict(X)
+if __name__=='__main__' :
+    import numpy as np
+    from sklearn import cross_validation
+    from sklearn import metrics
+    # read in the heart dataset
+    data=np.genfromtxt("../../data/heart_scale.data", delimiter=",")
+    X=data[:,1:]
+    y=data[:,0]
+    y = (y + 1) / 2
+    X_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.4, random_state=0)
+    classifier=LogisticRegression()
+    classifier.fit(X_train, y_train)
+    y_pred = classifier.predict(X_test)
+    print("test set accuracy: ", metrics.accuracy_score(y_test, y_pred) )
+</file>

CS545 fall 2016

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