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--- cs401r_w2016:lab3 [2015/12/23 21:08]
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+++ cs401r_w2016:lab3 [2021/06/30 23:42]
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-====Objective:====
-To understand how to sample from different distributions, and to
-understand the link between samples and a PDF/PMF.  To explore
-different parameter settings of common distributions, and to implement
-a small library of random variable types.
-====Deliverable:====
-You should turn in an ipython notebook that implements and tests a
-library of random variable types.
-When run, this notebook should sample multiple times from each type of
-random variable; these samples should be aggregated and visualized,
-and compared to the corresponding PDF/PMF.  The result should look
-something like this:
-{{:cs401r_w2016:lab3.png?nolink|}}
-For multidimensional variables, your visualization should convey information in a natural way; you can either use 3d surfaces, or 2d contour plots:
-{{:cs401r_w2016:lab3_2d.png?nolink|}}
-====Description:====
-You must implement seven random variable objects.  For each type, you should be able to sample from that distribution, and compute the log-likelihood of a particular value.  All of your classes should inherit from a base random variable object that supports the following methods:
-<code python>
-class RandomVariable:
-    def __init__( self ):
-        self.state = None
-        pass
-    def get( self ):
-        return self.state
-    def sample( self ):
-        pass
-    def log_likelihood( self ):
-        pass
-    def propose( self ):
-        pass
-</code>
-You don't need to implement the ''get'' or ''propose'' methods yet.  For example, your univariate Gaussian class might look like this:
-<code python>
-class Gaussian( RandomVariable ):
-    def __init__( self, mu, sigma ):
-        self.mu = mu
-        self.sigma = sigma
-        self.state = 0
-    def sample( self ):
-        return self.mu + self.sigma * numpy.Random.randn()
-    def log_likelihood( self, X, mu, sigma ):
-        return -numpy.log( sigma*numpy.sqrt(2*pi) ) - (X-mu)**2/(sigma**2)
-</code>
-**Given that framework, you should implement:**
-* The following one dimensional, continuous valued distributions.  For
-these, you should also plot the PDF of the random variable on the
-same plot; the curves should match. //Note: it is **not** sufficient to let seaborn estimate the PDF using its built-in KDE estimator; you need to plot the true PDF.  In other words, you can't just use seaborn.kdeplot!//
-  * ''Beta (alpha=1, beta=3)''
-  * ''Poisson (lambda=7)''
-  * ''Univariate Gaussian (mean=2, variance=3)''
-* The following discrete distributions.  For these, plot predicted and
-empirical histograms side-by-side:
-  * ''Bernoulli (p=0.7)''
-  * ''Multinomial (theta=[0.1, 0.2, 0.7])''
-* The following multidimensional distributions. For these,
-  * Two-dimensional Gaussian
-  * 3-dimensional Dirichlet
-**Important notes:**
-**You //may// use [[http://docs.scipy.org/doc/numpy-1.10.0/reference/routines.random.html|numpy.random]] to sample from the appropriate distributions.**
-**You may //not// use any existing code to calculate the log-likelihoods.**  But you can, of course, use any online resources or the book to find the appropriate definition of each PDF.
-====Hints:====
-The following functions may be useful to you:
-<code python>
-numpy.random
-matplotlib.pyplot.contour
-seaborn.kdeplot
-seaborn.jointplot
-hist( data, bins=50, normed=True )
-numpy.linspace
-legend
-title
-</code>

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