reconnect moved files to git repo

venv/lib/python3.11/site-packages/statsmodels/sandbox/distributions/mv_measures.py

@@ -0,0 +1,195 @@
+'''using multivariate dependence and divergence measures
+
+The standard correlation coefficient measures only linear dependence between
+random variables.
+kendall's tau measures any monotonic relationship also non-linear.
+
+mutual information measures any kind of dependence, but does not distinguish
+between positive and negative relationship
+
+
+mutualinfo_kde and mutualinfo_binning follow Khan et al. 2007
+
+Shiraj Khan, Sharba Bandyopadhyay, Auroop R. Ganguly, Sunil Saigal,
+David J. Erickson, III, Vladimir Protopopescu, and George Ostrouchov,
+Relative performance of mutual information estimation methods for
+quantifying the dependence among short and noisy data,
+Phys. Rev. E 76, 026209 (2007)
+http://pre.aps.org/abstract/PRE/v76/i2/e026209
+
+
+'''
+
+import numpy as np
+from scipy import stats
+from scipy.stats import gaussian_kde
+
+import statsmodels.sandbox.infotheo as infotheo
+
+
+def mutualinfo_kde(y, x, normed=True):
+    '''mutual information of two random variables estimated with kde
+
+    '''
+    nobs = len(x)
+    if not len(y) == nobs:
+        raise ValueError('both data arrays need to have the same size')
+    x = np.asarray(x, float)
+    y = np.asarray(y, float)
+    yx = np.vstack((y,x))
+    kde_x = gaussian_kde(x)(x)
+    kde_y = gaussian_kde(y)(y)
+    kde_yx = gaussian_kde(yx)(yx)
+
+    mi_obs = np.log(kde_yx) - np.log(kde_x) - np.log(kde_y)
+    mi = mi_obs.sum() / nobs
+    if normed:
+        mi_normed = np.sqrt(1. - np.exp(-2 * mi))
+        return mi_normed
+    else:
+        return mi
+
+def mutualinfo_kde_2sample(y, x, normed=True):
+    '''mutual information of two random variables estimated with kde
+
+    '''
+    nobs = len(x)
+    x = np.asarray(x, float)
+    y = np.asarray(y, float)
+    #yx = np.vstack((y,x))
+    kde_x = gaussian_kde(x.T)(x.T)
+    kde_y = gaussian_kde(y.T)(x.T)
+    #kde_yx = gaussian_kde(yx)(yx)
+
+    mi_obs = np.log(kde_x) - np.log(kde_y)
+    if len(mi_obs) != nobs:
+        raise ValueError("Wrong number of observations")
+    mi = mi_obs.mean()
+    if normed:
+        mi_normed = np.sqrt(1. - np.exp(-2 * mi))
+        return mi_normed
+    else:
+        return mi
+
+def mutualinfo_binned(y, x, bins, normed=True):
+    '''mutual information of two random variables estimated with kde
+
+
+
+    Notes
+    -----
+    bins='auto' selects the number of bins so that approximately 5 observations
+    are expected to be in each bin under the assumption of independence. This
+    follows roughly the description in Kahn et al. 2007
+
+    '''
+    nobs = len(x)
+    if not len(y) == nobs:
+        raise ValueError('both data arrays need to have the same size')
+    x = np.asarray(x, float)
+    y = np.asarray(y, float)
+    #yx = np.vstack((y,x))
+
+
+##    fyx, binsy, binsx = np.histogram2d(y, x, bins=bins)
+##    fx, binsx_ = np.histogram(x, bins=binsx)
+##    fy, binsy_ = np.histogram(y, bins=binsy)
+
+    if bins == 'auto':
+        ys = np.sort(y)
+        xs = np.sort(x)
+        #quantiles = np.array([0,0.25, 0.4, 0.6, 0.75, 1])
+        qbin_sqr = np.sqrt(5./nobs)
+        quantiles = np.linspace(0, 1, 1./qbin_sqr)
+        quantile_index = ((nobs-1)*quantiles).astype(int)
+        #move edges so that they do not coincide with an observation
+        shift = 1e-6 + np.ones(quantiles.shape)
+        shift[0] -= 2*1e-6
+        binsy = ys[quantile_index] + shift
+        binsx = xs[quantile_index] + shift
+
+    elif np.size(bins) == 1:
+        binsy = bins
+        binsx = bins
+    elif (len(bins) == 2):
+        binsy, binsx = bins
+##        if np.size(bins[0]) == 1:
+##            binsx = bins[0]
+##        if np.size(bins[1]) == 1:
+##            binsx = bins[1]
+
+    fx, binsx = np.histogram(x, bins=binsx)
+    fy, binsy = np.histogram(y, bins=binsy)
+    fyx, binsy, binsx = np.histogram2d(y, x, bins=(binsy, binsx))
+
+    pyx = fyx * 1. / nobs
+    px = fx * 1. / nobs
+    py = fy * 1. / nobs
+
+
+    mi_obs = pyx * (np.log(pyx+1e-10) - np.log(py)[:,None] - np.log(px))
+    mi = mi_obs.sum()
+
+    if normed:
+        mi_normed = np.sqrt(1. - np.exp(-2 * mi))
+        return mi_normed, (pyx, py, px, binsy, binsx), mi_obs
+    else:
+        return mi
+
+
+if __name__ == '__main__':
+    import statsmodels.api as sm
+
+    funtype = ['linear', 'quadratic'][1]
+    nobs = 200
+    sig = 2#5.
+    #x = np.linspace(-3, 3, nobs) + np.random.randn(nobs)
+    x = np.sort(3*np.random.randn(nobs))
+    exog = sm.add_constant(x, prepend=True)
+    #y = 0 + np.log(1+x**2) + sig * np.random.randn(nobs)
+    if funtype == 'quadratic':
+        y = 0 + x**2 + sig * np.random.randn(nobs)
+    if funtype == 'linear':
+        y = 0 + x + sig * np.random.randn(nobs)
+
+    print('correlation')
+    print(np.corrcoef(y,x)[0, 1])
+    print('pearsonr', stats.pearsonr(y,x))
+    print('spearmanr', stats.spearmanr(y,x))
+    print('kendalltau', stats.kendalltau(y,x))
+
+    pxy, binsx, binsy = np.histogram2d(x,y, bins=5)
+    px, binsx_ = np.histogram(x, bins=binsx)
+    py, binsy_ = np.histogram(y, bins=binsy)
+    print('mutualinfo', infotheo.mutualinfo(px*1./nobs, py*1./nobs,
+                                            1e-15+pxy*1./nobs, logbase=np.e))
+
+    print('mutualinfo_kde normed', mutualinfo_kde(y,x))
+    print('mutualinfo_kde       ', mutualinfo_kde(y,x, normed=False))
+    mi_normed, (pyx2, py2, px2, binsy2, binsx2), mi_obs = \
+               mutualinfo_binned(y, x, 5, normed=True)
+    print('mutualinfo_binned normed', mi_normed)
+    print('mutualinfo_binned       ', mi_obs.sum())
+
+    mi_normed, (pyx2, py2, px2, binsy2, binsx2), mi_obs = \
+               mutualinfo_binned(y, x, 'auto', normed=True)
+    print('auto')
+    print('mutualinfo_binned normed', mi_normed)
+    print('mutualinfo_binned       ', mi_obs.sum())
+
+    ys = np.sort(y)
+    xs = np.sort(x)
+    by = ys[((nobs-1)*np.array([0, 0.25, 0.4, 0.6, 0.75, 1])).astype(int)]
+    bx = xs[((nobs-1)*np.array([0, 0.25, 0.4, 0.6, 0.75, 1])).astype(int)]
+    mi_normed, (pyx2, py2, px2, binsy2, binsx2), mi_obs = \
+               mutualinfo_binned(y, x, (by,bx), normed=True)
+    print('quantiles')
+    print('mutualinfo_binned normed', mi_normed)
+    print('mutualinfo_binned       ', mi_obs.sum())
+
+    doplot = 1#False
+    if doplot:
+        import matplotlib.pyplot as plt
+        plt.plot(x, y, 'o')
+        olsres = sm.OLS(y, exog).fit()
+        plt.plot(x, olsres.fittedvalues)