cs501r_f2016:lab2
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cs501r_f2016:lab2 [2016/08/31 18:23] wingated |
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| - | ====Objective:==== | ||
| - | To gain experience with python, numpy, and linear classification. Oh, and to remember all of that linear algebra stuff. ;) | ||
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| - | ---- | ||
| - | ====Deliverable:==== | ||
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| - | You should turn in an iPython notebook that implements the perceptron algorithm on the Iris dataset. | ||
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| - | Your notebook should also generate a visualization that shows the loss function at each iteration. This can be generated as a single plot, and shown in the notebook. | ||
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| - | The dataset can be downloaded at | ||
| - | [[https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data|The UCI ML repository]] | ||
| - | |||
| - | ---- | ||
| - | ====Grading standards:==== | ||
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| - | Your notebook will be graded on the following: | ||
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| - | * 70% Correct implementation of perceptron algorithm | ||
| - | * 20% Tidy and legible visualization of loss function | ||
| - | * 10% Tidy and legible final classification rate | ||
| - | |||
| - | ---- | ||
| - | ====Description:==== | ||
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| - | 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. | ||
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| - | 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 | ||
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| - | $$p( \mathrm{class}=k | x_j, \mathrm{data} ) \propto p( x_j | \mathrm{class}=k, \mathrm{data} ) p(\mathrm{class}=k | \mathrm{data} ) $$ | ||
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| - | where | ||
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| - | $$p( x_j | \mathrm{class}=k, \mathrm{data} )$$ | ||
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| - | is given by a kernel density estimator derived from all data of class $k$. | ||
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| - | |||
| - | 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: | ||
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| - | [[http://hatch.cs.byu.edu/courses/stat_ml/mnist_train.mat|MNIST training data vectors and labels]] | ||
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| - | [[http://hatch.cs.byu.edu/courses/stat_ml/mnist_test.mat|MNIST test data vectors and labels]] | ||
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| - | 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> | ||
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| - | 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:==== | ||
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| - | 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( X.reshape(28,28).T, interpolation='nearest', cmap=matplotlib.cm.gray) | ||
| - | </code> | ||
| - | |||
| - | Here are some functions that may be helpful to you: | ||
| - | |||
| - | <code python> | ||
| - | |||
| - | import matplotlib.pyplot as plt | ||
| - | plt.subplot | ||
| - | |||
| - | numpy.argmax | ||
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| - | numpy.exp | ||
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| - | numpy.mean | ||
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| - | numpy.bincount | ||
| - | |||
| - | </code> | ||
cs501r_f2016/lab2.txt ยท Last modified: 2021/06/30 23:42 (external edit)
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