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--- cs401r_w2016:lab5 [2015/12/29 00:07]
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+++ cs401r_w2016:lab5 [2021/06/30 23:42]
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-====Objective:====
-To understand how to use kernel density estimation to both generate a simple classifier and a class-conditional visualization of different hand-written digits.
-====Deliverable:====
-You should turn in an iPython notebook that performs three tasks.  All tasks will be done using the MNIST handwritten digit data set (see Description for details):
-{{ :cs401r_w2016:lab5_class_mean.png?direct&200|}}
-  - Generate a visualization of the expected value of each class, where the density over classes is estimated using a kernel density estimator (KDE).  The data for these KDEs should come from the MNIST training data (see below).  Your notebook should generate 10 images, arranged neatly, one per digit class.  Each image might look something like the one on the right.
-  - Build a simple classifier using **only** the class means, and test it using the MNIST test data. (Note: this couldn't possibly be a good classifier!)  That is, for each test data point $x_j$, you should compute the probability that $x_j$ came from a Gaussian centered at $\mu_k$, where $\mu_k$ is the expected value of class $k$ you computed in Part (1).  Classify $x_j$ as coming from the most likely class.
-  - Build a more complex classifier using a full kernel density estimator.  For each test data point $x_j$, you should calculate the probability that it belongs to class $k$.
-For Part (2) and Part (3) your notebook should report two things:
-{{ :cs401r_w2016:lab5_confmat2.png?direct&300|}}
-  - The overall classification rate.  For example, when I coded up Part 2, my classification error rate was 17.97%.  When I coded up Part (3), my error rate was 3.80%.
-  - A confusion matrix (see MLAPP pg. 183), or [[https://en.wikipedia.org/wiki/Confusion_matrix|this wikipedia article]].  A confusion matrix is a complete report of all of the different ways your classifier was wrong, and is much more informative than a single error rate; for example, a confusion matrix will report the number of times your classifier reported "3", when the true class was "8".  You can report this confusion matrix either as a text table, or as an image.  My confusion matrix is shown to the right; you can see that my classifier generally gets things right (the strong diagonal), but sometimes predicts "9" when the true class is "4" (for example).
-//What errors do you think are most likely for this lab?//
-====Description:====
-For this lab, you will be experimenting with Kernel Density Estimators (see MLAPP 14.7.2).  These are a simple, nonparametric alternative to Gaussian mixture models, but which form an important part of the machine learning toolkit.
-At several points during this lab, you will need to construct density estimates that are "class-conditional".  For example, in order to classify a test point $x_j$, you need to compute
-$p( \mathrm{class}=k | x_j, \mathrm{data} ) \propto p( x_j | \mathrm{class}=k, \mathrm{data} ) p(\mathrm{class}=k | \mathrm{data} ) $
-where
-$p( x_j | \mathrm{class}=k, \mathrm{data} )$
-is given by a kernel density estimator derived from all data of class $k$.
-The data that you will analyzing is the famous [[http://yann.lecun.com/exdb/mnist/|MNIST handwritten digits dataset]].  You can download some pre-processed MATLAB data files below:
-[[http://hatch.cs.byu.edu/courses/stat_ml/mnist_train.mat|MNIST training data vectors and labels]]
-[[http://hatch.cs.byu.edu/courses/stat_ml/mnist_test.mat|MNIST test data vectors and labels]]
-These can be loaded using the scipy.io.loadmat function, as follows:
-<code python>
-import scipy.io
-train_mat = scipy.io.loadmat('mnist_train.mat')
-train_data = train_mat['images']
-train_labels = train_mat['labels']
-test_mat = scipy.io.loadmat('mnist_test.mat')
-test_data = test_mat['t10k_images']
-test_labels = test_mat['t10k_labels']
-</code>
-The training data vectors are now in ''train_data'', a numpy array of size 784x60000, with corresponding labels in ''train_labels'', a numpy array of size 60000x1.
-====Hints:====
-Here is a simple way to visualize a digit.  Suppose our digit is in variable ''X'', which has dimensions 784x1:
-<code python>
-import matplotlib.pyplot as plt
-plt.imshow( 1-X.reshape(28,28).T, interpolation='nearest' )
-</code>
-Here are some functions that may be helpful to you:
-<code python>
-numpy.argmax
-numpy.bincount
-</code>

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