[Microsoft Cognitive Toolkit]Logistic Regression using CNTK

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This tutorial is targeted to individuals who are new to CNTK and to machine learning. In this tutorial, you will train a simple yet powerful machine learning model that is widely used in industry for a variety of applications. The model trained below scales to massive data sets in the most expeditious manner by harnessing computational scalability leveraging the computational resources you may have (one or more CPU cores, one or more GPUs, a cluster of CPUs or a cluster of GPUs), transparently via the CNTK library.
The following notebook uses Python APIs. If you are looking for this example in BrainScript, please look here.
IntroductionProblem: A cancer hospital has provided data and wants us to determine if a patient has a fatal malignant cancer vs. a benign growth. This is known as a classification problem. To help classify each patient, we are given their age and the size of the tumor. Intuitively, one can imagine that younger patients and/or patients with small tumors are less likely to have a malignant cancer. The data set simulates this application: each observation is a patient represented as a dot (in the plot below), where red indicates malignant and blue indicates benign. Note: This is a toy example for learning; in real life many features from different tests/examination sources and the expertise of doctors would play into the diagnosis/treatment decision for a patient.

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Logistic Regression using Microsoft Cognitive Toolkit.pdf (111.47 KB)

2017-9-17 02:06:44 上传

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关键词：regression Microsoft Cognitive regressio logistic

1. # Figure 3
   
2. Image(url= "https://www.cntk.ai/jup/logistic_neuron.jpg", width=300, height=200)

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1. # Import the relevant components
   
2. from __future__ import print_function
   
3. import numpy as np
   
4. import sys
   
5. import os
   
6. 
   
7. import cntk as C
   
8. import cntk.tests.test_utils
   
9. cntk.tests.test_utils.set_device_from_pytest_env() # (only needed for our build system)
   
10. C.cntk_py.set_fixed_random_seed(1) # fix the random seed so that LR examples are repeatable

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1. # Ensure that we always get the same results
   
2. np.random.seed(0)
   
3. 
   
4. # Helper function to generate a random data sample
   
5. def generate_random_data_sample(sample_size, feature_dim, num_classes):
   
6.     # Create synthetic data using NumPy.
   
7.     Y = np.random.randint(size=(sample_size, 1), low=0, high=num_classes)
   
8. 
   
9.     # Make sure that the data is separable
   
10.     X = (np.random.randn(sample_size, feature_dim)+3) * (Y+1)
    
11.    
    
12.     # Specify the data type to match the input variable used later in the tutorial
    
13.     # (default type is double)
    
14.     X = X.astype(np.float32)   
    
15.    
    
16.     # convert class 0 into the vector "1 0 0",
    
17.     # class 1 into the vector "0 1 0", ...
    
18.     class_ind = [Y==class_number for class_number in range(num_classes)]
    
19.     Y = np.asarray(np.hstack(class_ind), dtype=np.float32)
    
20.     return X, Y

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1. # Create the input variables denoting the features and the label data. Note: the input
   
2. # does not need additional info on the number of observations (Samples) since CNTK creates only
   
3. # the network topology first
   
4. mysamplesize = 32
   
5. features, labels = generate_random_data_sample(mysamplesize, input_dim, num_output_classes)

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1. # Plot the data
   
2. import matplotlib.pyplot as plt
   
3. %matplotlib inline
   
4. 
   
5. # let 0 represent malignant/red and 1 represent benign/blue
   
6. colors = ['r' if label == 0 else 'b' for label in labels[:,0]]
   
7. 
   
8. plt.scatter(features[:,0], features[:,1], c=colors)
   
9. plt.xlabel("Age (scaled)")
   
10. plt.ylabel("Tumor size (in cm)")
    
11. plt.show()

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1. # Figure 4
   
2. Image(url= "https://www.cntk.ai/jup/logistic_neuron2.jpg", width=300, height=200)

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1. # Define a dictionary to store the model parameters
   
2. mydict = {}
   
3. 
   
4. def linear_layer(input_var, output_dim):
   
5.    
   
6.     input_dim = input_var.shape[0]
   
7.     weight_param = C.parameter(shape=(input_dim, output_dim))
   
8.     bias_param = C.parameter(shape=(output_dim))
   
9.    
   
10.     mydict['w'], mydict['b'] = weight_param, bias_param
    
11. 
    
12.     return C.times(input_var, weight_param) + bias_param

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1. Training
   
2. The output of the softmax is the probabilities of an observation belonging each of the respective classes. For training the classifier, we need to determine what behavior the model needs to mimic. In other words, we want the generated probabilities to be as close as possible to the observed labels. We can accomplish this by minimizing the difference between our output and the ground-truth labels. This difference is calculated by the cost or loss function.
   
3. 
   
4. In [14]:
   
5. label = C.input_variable(num_output_classes, np.float32)
   
6. loss = C.cross_entropy_with_softmax(z, label)

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