cs401r_w2016:lab13
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cs401r_w2016:lab13 [2016/01/18 23:37] admin |
cs401r_w2016:lab13 [2021/06/30 23:42] (current) |
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| ====Deliverable:==== | ====Deliverable:==== | ||
| - | For this lab, you will implement the Expectation Maximization algorithm on the Old Faithful dataset. This involves learning the parameters of a Gaussian mixture model. Your notebook should produce a visualization of the progress of the algorithm. The final figure should look something like this: | + | For this lab, you will implement the Expectation Maximization algorithm on the Old Faithful dataset. This involves learning the parameters of a Gaussian mixture model. Your notebook should produce a visualization of the progress of the algorithm. The final figure could look something like this (they don't have to be arranged in subplots): |
| {{:cs401r_w2016:lab5_em.png?direct&600|}} | {{:cs401r_w2016:lab5_em.png?direct&600|}} | ||
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| * 20% Correctly updates covariances | * 20% Correctly updates covariances | ||
| * 20% Correctly updates mixing weights | * 20% Correctly updates mixing weights | ||
| - | * 10% Final plot is tidy and legible | + | * 10% Final plot(s) is tidy and legible |
| ---- | ---- | ||
| ====Description:==== | ====Description:==== | ||
| + | |||
| + | For this lab, we will be using the Expectation Maximization (EM) method to **learn** the parameters of a Gaussian mixture model. These parameters will reflect cluster structure in the data -- in other words, we will learn probabilistic descriptions of clusters in the data. | ||
| For this lab, you will use the Old Faithful dataset, which you can download here: | For this lab, you will use the Old Faithful dataset, which you can download here: | ||
| - | [[http://hatch.cs.byu.edu/courses/stat_ml/old_faithful.mat|Old Faithful dataset]] | + | [[https://www.dropbox.com/s/h8b67cg8wff7bg0/old_faithful.mat?dl=0|Old Faithful dataset]] |
| + | |||
| + | **The first thing you should is mean-center your data (ie, compute the mean of the data, then subtract that off from each datapoint).** (If you don't do this, you'll get zero probabilities for all of your responsibilities, given the initial conditions discussed below.) | ||
| + | |||
| + | The equations for implementing the EM algorithm are given in MLAPP 11.4.2.2 - 11.4.2.3. | ||
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| + | The algorithm is: | ||
| + | |||
| + | - Compute the responsibilities $r_{ik}$ (Eq. 11.27) | ||
| + | - Update the mixing weights $\pi_k$ (Eq. 11.28) | ||
| + | - Update the covariances $\Sigma_k$ (Eq. 11.32) | ||
| + | - Update the means $\mu_k$ (Eq. 11.31) | ||
| + | |||
| + | Now, repeat until convergence. Note that if you change the order of operations, you may get slightly difference convergences than the reference image. | ||
| + | |||
| + | Since the EM algorithm is deterministic, and since precise initial conditions for your algorithm are given below, the progress of your algorithm should closely match the reference image shown above. | ||
| + | |||
| + | For your visualization, please print out at least nine plots. These should color each datapoint using $r_{ik}$, and they should plot the means and covariances of the Gaussians. See the hints section for how to plot an ellipse representing the 95% confidence interval of a Gaussian, given an arbitrary covariance matrix. | ||
| - | To help our TA better grade your notebook, you should use the following initial parameters: | + | **Note: To help our TA better grade your notebook, you should use the following initial parameters:** |
| <code python> | <code python> | ||
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| # The Gaussian mixing weights | # The Gaussian mixing weights | ||
| - | mws = [ 0.68618439, 0.31381561 ] | + | mws = [ 0.68618439, 0.31381561 ] # called alpha in the slides |
| </code> | </code> | ||
cs401r_w2016/lab13.1453160229.txt.gz · Last modified: 2021/06/30 23:40 (external edit)
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