add mgc map example

examples/mgc_map.py

@@ -0,0 +1,83 @@
+"""
+MGC Map
+========
+
+hyppo offers the :class:`hyppo.independence.MGC` class, which is a powerful independence
+test to fit a host of different types of data.
+The MGC Map is essentially an array of local correlations (i.e. the test statistic that
+at each nearest neighbor pair). The optimal scale is the nearest neighbor pair that
+maximizes the test statistic, and this test statistic is the one we return as part of
+MGC.
+Let's look at how we can use hyppo
+to find a trend in linear data sets (:meth:`hyppo.tools.linear`) and nonlinear data sets
+(for example :meth:`hyppo.tools.spiral`) and visualize this map and optimal scale.
+"""
+import matplotlib.pyplot as plt
+import matplotlib.ticker as ticker
+import seaborn as sns
+from hyppo.independence import MGC
+from hyppo.tools import linear, spiral
+
+# make a dictionary that maps the simulation function to a string
+sims = {
+ "Linear": linear,
+ "Spiral": spiral,
+}
+
+
+# make a function that runs the code depending on the simulation
+def run_test(sim_type="Linear"):
+ """Runs all the tests for both simulations."""
+
+ # simulate our data (100 samples, 3 dimensions)
+ x, y = sims[sim_type](n=100, p=3, noise=True)
+
+ # calculate the MGC test statistic, p-value, and get a dictionary with the
+ # mgc_map (shows the geometric nature of the relationship) and the optimal
+ # scale, which is the k,l nearest neighbors that maximize the test statistic
+ stat, pvalue, mgc_dict = MGC().test(x, y)
+ print(stat, pvalue)
+
+ # plot the MGC map with a map of the local correlations (as mentioned before,
+ # shows the geometric nature of the relationship), and the optimal scale,
+ # which is the maximimum smoothed test statistic
+ mgc_map = mgc_dict["mgc_map"]
+ opt_scale = mgc_dict["opt_scale"] # i.e. maximum smoothed test statistic
+ print("Optimal Scale:", opt_scale)
+
+ # create figure
+ fig, (ax, cax) = plt.subplots(
+ ncols=2, figsize=(9.45, 7.5), gridspec_kw={"width_ratios": [1, 0.05]}
+ )
+
+ # draw heatmap and colorbar
+ ax = sns.heatmap(mgc_map, cmap="YlGnBu", ax=ax, cbar=False)
+ fig.colorbar(ax.get_children()[0], cax=cax, orientation="vertical")
+ ax.invert_yaxis()
+
+ # optimal scale
+ ax.scatter(opt_scale[1], opt_scale[0], marker="X", s=200, color="red")
+
+ # make plots look nice
+ fig.suptitle("MGC Map - {}".format(sim_type), fontsize=17)
+ ax.xaxis.set_major_locator(ticker.MultipleLocator(10))
+ ax.xaxis.set_major_formatter(ticker.ScalarFormatter())
+ ax.yaxis.set_major_locator(ticker.MultipleLocator(10))
+ ax.yaxis.set_major_formatter(ticker.ScalarFormatter())
+ ax.set_xlabel("Neighbors for x")
+ ax.set_ylabel("Neighbors for y")
+ ax.set_xticks([0, 50, 100])
+ ax.set_yticks([0, 50, 100])
+ ax.xaxis.set_tick_params()
+ ax.yaxis.set_tick_params()
+ cax.xaxis.set_tick_params()
+ cax.yaxis.set_tick_params()
+ plt.show()
+
+
+# run the created function for linear and spiral simulations. Notice how the
+# MGC map looks different for a spiral simulation and linear simulation.
+# Optimal scale informs this, linearly related data has a scale at the max
+# scale, while nonlinearly related data does not.
+run_test(sim_type="Linear")
+run_test(sim_type="Spiral")