atichison distance and tests for evaluating regions

BayesianKDEy/TODO.txt

@@ -1,6 +1,7 @@
 - Add other methods that natively provide uncertainty quantification methods?
 - MPIW (Mean Prediction Interval Width): is the average of the amplitudes (w/o aggregating coverage whatsoever)
 - Implement Interval Score or Winkler Score
-- Add (w-hat_w)**2/N measure
 - analyze across shift
+- add Bayesian EM
+- optimize also C and class_weight?
 

BayesianKDEy/_bayeisan_kdey.py

@@ -9,7 +9,7 @@ from quapy.functional import CLRtransformation, ILRtransformation
 from quapy.method.aggregative import AggregativeSoftQuantifier
 from tqdm import tqdm
 import quapy.functional as F
-import emcee
+#import emcee
 
 
 

BayesianKDEy/full_experiments.py

@@ -151,7 +151,7 @@ def experiment_path(dir:Path, dataset_name:str, method_name:str):
 if __name__ == '__main__':
 
     binary = {
-        'datasets': qp.datasets.UCI_BINARY_DATASETS[1:],
+        'datasets': qp.datasets.UCI_BINARY_DATASETS,
         'fetch_fn': qp.datasets.fetch_UCIBinaryDataset,
         'sample_size': 500
     }

BayesianKDEy/generate_results.py

@@ -7,8 +7,9 @@ import pandas as pd
 from glob import glob
 from pathlib import Path
 import quapy as qp
-from method.confidence import ConfidenceIntervals
+from error import dist_aitchison
-from quapy.method.confidence import ConfidenceEllipseSimplex, ConfidenceEllipseCLR, ConfidenceEllipseILR
+from quapy.method.confidence import ConfidenceIntervals
+from quapy.method.confidence import ConfidenceEllipseSimplex, ConfidenceEllipseCLR, ConfidenceEllipseILR, ConfidenceIntervals, ConfidenceRegionABC
 
 pd.set_option('display.max_columns', None)
 pd.set_option('display.width', 2000)
@@ -18,6 +19,17 @@ pd.set_option("display.precision", 4)
 pd.set_option("display.float_format", "{:.4f}".format)
 
 
+def region_score(true_prev, region: ConfidenceRegionABC):
+    amp = region.montecarlo_proportion(50_000)
+    if true_prev in region:
+        cost = 0
+    else:
+        scale_cost = 1/region.alpha
+        cost = scale_cost * dist_aitchison(true_prev, region.closest_point_in_region(true_prev))
+    return amp + cost
+
+
+
 def compute_coverage_amplitude(region_constructor, **kwargs):
     all_samples = results['samples']
     all_true_prevs = results['true-prevs']
@@ -62,19 +74,24 @@ def update_pickle_with_region(report, file, conf_name, conf_region_class, **kwar
 
         update_pickle(report, file, update_fields)
 
+methods = None  # show all methods
+# methods = ['BayesianACC', 'BayesianKDEy']
 
-for setup in ['multiclass', 'binary']:
+for setup in ['multiclass']:
     path = f'./results/{setup}/*.pkl'
     table = defaultdict(list)
     for file in tqdm(glob(path), desc='processing results', total=len(glob(path))):
         file = Path(file)
         dataset, method = file.name.replace('.pkl', '').split('__')
+        if methods is not None and method not in methods:
+            continue
         report = pickle.load(open(file, 'rb'))
         results = report['results']
         n_samples = len(results['ae'])
         table['method'].extend([method.replace('Bayesian','Ba').replace('Bootstrap', 'Bo')] * n_samples)
         table['dataset'].extend([dataset] * n_samples)
         table['ae'].extend(results['ae'])
+        table['rae'].extend(results['rae'])
         # table['c-CI'].extend(results['coverage'])
         # table['a-CI'].extend(results['amplitude'])
 
@@ -96,6 +113,14 @@ for setup in ['multiclass', 'binary']:
         table['c-ILR'].extend(report['coverage-ILR'])
         table['a-ILR'].extend(report['amplitude-ILR'])
 
+        table['aitch'].extend(qp.error.dist_aitchison(results['true-prevs'], results['point-estim']))
+        # table['aitch-well'].extend(qp.error.dist_aitchison(results['true-prevs'], [ConfidenceEllipseILR(samples).mean_ for samples in results['samples']]))
+        # table['aitch'].extend()
+        table['reg-score-ILR'].extend(
+            [region_score(true_prev, ConfidenceEllipseILR(samples)) for true_prev, samples in zip(results['true-prevs'], results['samples'])]
+        )
+
+
 
     df = pd.DataFrame(table)
 
@@ -111,16 +136,30 @@ for setup in ['multiclass', 'binary']:
         tr_size[dataset] = len(data.training)
 
     # remove datasets with more than max_classes classes
-    max_classes = 30
+    # max_classes = 30
-    for data_name, n in n_classes.items():
+    # min_train   = 1000
-        if n > max_classes:
+    # for data_name, n in n_classes.items():
-            df = df[df["dataset"] != data_name]
+    #     if n > max_classes:
+    #         df = df[df["dataset"] != data_name]
+    # for data_name, n in tr_size.items():
+    #     if n < min_train:
+    #         df = df[df["dataset"] != data_name]
 
-    for region in ['CI', 'CE', 'CLR', 'ILR']:
+    for region in ['ILR']: # , 'CI', 'CE', 'CLR', 'ILR']:
         if setup == 'binary' and region=='ILR':
             continue
+        # pv = pd.pivot_table(
+        #     df, index='dataset', columns='method', values=['ae', f'c-{region}', f'a-{region}'], margins=True
+        # )
         pv = pd.pivot_table(
-            df, index='dataset', columns='method', values=['ae', f'c-{region}', f'a-{region}'], margins=True
+            df, index='dataset', columns='method', values=[
+                #f'w-{region}',
+                # 'ae',
+                # 'rae',
+                # f'aitch',
+                # f'aitch-well'
+                'reg-score-ILR',
+            ], margins=True
         )
         pv['n_classes'] = pv.index.map(n_classes).astype('Int64')
         pv['tr_size'] = pv.index.map(tr_size).astype('Int64')

BayesianKDEy/plot_simplex.py

@@ -33,7 +33,10 @@ def get_region_colormap(name="blue", alpha=0.40):
     return cmap
 
 
-def plot_prev_points(prevs=None, true_prev=None, point_estim=None, train_prev=None, show_mean=True, show_legend=True,
+def plot_prev_points(samples=None,
+                     show_samples=True,
+                     true_prev=None,
+                     point_estim=None, train_prev=None, show_mean=True, show_legend=True,
                      region=None,
                      region_resolution=1000,
                      confine_region_in_simplex=False,
@@ -113,9 +116,17 @@ def plot_prev_points(prevs=None, true_prev=None, point_estim=None, train_prev=No
                 alpha=0.3,
             )
 
-    ax.scatter(*cartesian(prevs), s=15, alpha=0.5, edgecolors='none', label='samples', color='black', linewidth=0.5)
+    if samples is not None:
-    if show_mean:
+        if show_samples:
-        ax.scatter(*cartesian(prevs.mean(axis=0)), s=10, alpha=1, label='sample-mean', edgecolors='black')
+            ax.scatter(*cartesian(samples), s=15, alpha=0.5, edgecolors='none', label='samples', color='black', linewidth=0.5)
+    if show_mean is not None:
+        if isinstance(show_mean, np.ndarray):
+            ax.scatter(*cartesian(show_mean), s=10, alpha=1, label='sample-mean', edgecolors='black')
+        elif show_mean==True and samples is not None:
+            ax.scatter(*cartesian(samples.mean(axis=0)), s=10, alpha=1, label='sample-mean', edgecolors='black')
+        else:
+            raise ValueError(f'show_mean should either be a boolean (if True, then samples must be provided) or '
+                             f'the mean point itself')
     if train_prev is not None:
         ax.scatter(*cartesian(true_prev), s=10, alpha=1, label='true-prev', edgecolors='black')
     if point_estim is not None:
@@ -203,22 +214,45 @@ if __name__ == '__main__':
     np.random.seed(1)
 
     n = 1000
-    alpha = [3,5,10]
+    # alpha = [3,5,10]
-    # alpha = [10,1,1]
+    alpha = [10,1,1]
     prevs = np.random.dirichlet(alpha, size=n)
 
     def regions():
         confs = [0.99, 0.95, 0.90]
         yield 'CI', [(f'{int(c*100)}%', CI(prevs, confidence_level=c).coverage) for c in confs]
-        yield 'CI-b', [(f'{int(c * 100)}%', CI(prevs, confidence_level=c, bonferroni_correction=True).coverage) for c in confs]
+        # yield 'CI-b', [(f'{int(c * 100)}%', CI(prevs, confidence_level=c, bonferroni_correction=True).coverage) for c in confs]
-        yield 'CE', [(f'{int(c*100)}%', CE(prevs, confidence_level=c).coverage) for c in confs]
+        # yield 'CE', [(f'{int(c*100)}%', CE(prevs, confidence_level=c).coverage) for c in confs]
-        yield 'CLR', [(f'{int(c*100)}%', CLR(prevs, confidence_level=c).coverage) for c in confs]
+        # yield 'CLR', [(f'{int(c*100)}%', CLR(prevs, confidence_level=c).coverage) for c in confs]
-        yield 'ILR', [(f'{int(c*100)}%', ILR(prevs, confidence_level=c).coverage) for c in confs]
+        # yield 'ILR', [(f'{int(c*100)}%', ILR(prevs, confidence_level=c).coverage) for c in confs]
+
+    # resolution = 1000
+    # alpha_str = ','.join([f'{str(i)}' for i in alpha])
+    # for crname, cr in regions():
+    #     plot_prev_points(prevs, show_mean=True, show_legend=False, region=cr, region_resolution=resolution,
+    #                      color='blue',
+    #                      save_path=f'./plots/simplex_{crname}_alpha{alpha_str}_res{resolution}.png',
+    #                      )
+
+
+    def regions():
+        confs = [0.99, 0.95, 0.90]
+        yield 'CI', [(f'{int(c*100)}%', CI(prevs, confidence_level=c).coverage) for c in confs]
+        # yield 'CI-b', [(f'{int(c * 100)}%', CI(prevs, confidence_level=c, bonferroni_correction=True).coverage) for c in confs]
+        # yield 'CE', [(f'{int(c*100)}%', CE(prevs, confidence_level=c).coverage) for c in confs]
+        # yield 'CLR', [(f'{int(c*100)}%', CLR(prevs, confidence_level=c).coverage) for c in confs]
+        # yield 'ILR', [(f'{int(c*100)}%', ILR(prevs, confidence_level=c).coverage) for c in confs]
 
     resolution = 1000
     alpha_str = ','.join([f'{str(i)}' for i in alpha])
-    for crname, cr in regions():
+    region  = ILR(prevs, confidence_level=.99)
-        plot_prev_points(prevs, show_mean=True, show_legend=False, region=cr, region_resolution=resolution,
+    p = np.asarray([0.1, 0.8, 0.1])
+    plot_prev_points(prevs, show_samples=False,
+                     show_mean=region.mean_,
+                     # show_mean=prevs.mean(axis=0),
+                     show_legend=False, region=[('', region.coverage)], region_resolution=resolution,
                      color='blue',
-                         save_path=f'./plots/simplex_{crname}_alpha{alpha_str}_res{resolution}.png')
+                     true_prev=p,
-
+                     train_prev=region.closest_point_in_region(p),
+                     save_path=f'./plots3/simplex_ilr.png',
+                     )

CHANGE_LOG.txt

@@ -1,9 +1,13 @@
 Change Log 0.2.1
 -----------------
 
+- Added squared ratio error.
+- Improved efficiency of confidence regions coverage functions
+- Added Precise Quantifier to WithConfidence methods (a Bayesian adaptation of HDy)
 - Improved documentation of confidence regions.
 - Added ReadMe method by Daniel Hopkins and Gary King
 - Internal index in LabelledCollection is now "lazy", and is only constructed if required.
+- I have added dist_aitchison and mean_dist_aitchison as a new error evaluation metric
 
 Change Log 0.2.0
 -----------------

quapy/error.py

@@ -3,6 +3,7 @@
 import numpy as np
 from sklearn.metrics import f1_score
 import quapy as qp
+from functional import CLRtransformation
 
 
 def from_name(err_name):
@@ -128,6 +129,59 @@ def se(prevs_true, prevs_hat):
     return ((prevs_hat - prevs_true) ** 2).mean(axis=-1)
 
 
+def sre(prevs_true, prevs_hat, prevs_train, eps=0.):
+    """
+    The squared ratio error is defined as
+    :math:`SRE(p,\\hat{p},p^{tr})=\\frac{1}{|\\mathcal{Y}|}\\sum_{i \\in \\mathcal{Y}}(w_i-\\hat{w}_i)^2`,
+    where
+    :math:`w_i=\\frac{p_i}{p^{tr}_i}=\\frac{Q(Y=i)}{P(Y=i)}`,
+    and `\\hat{w}_i` is the estimate obtained by replacing the true test prior with an estimate, and
+     :math:`\\mathcal{Y}` are the classes of interest
+    :param prevs_true: array-like, true prevalence values
+    :param prevs_hat: array-like, estimated prevalence values
+    :param prevs_train: array-like, training prevalence values
+    :param eps: float, for smoothing the prevalence values. It is 0 by default (no smoothing), meaning the
+        training prevalence is expected to be >0 everywhere.
+    :return: the squared ratio error
+    """
+    prevs_true = np.asarray(prevs_true)
+    prevs_hat = np.asarray(prevs_hat)
+    prevs_train = np.asarray(prevs_train)
+    assert prevs_true.shape == prevs_hat.shape, f'wrong shape {prevs_true.shape=} vs {prevs_hat.shape=}'
+    assert prevs_true.shape[-1]==prevs_train.shape[-1], 'wrong shape for training prevalence'
+    if eps>0:
+        prevs_true = smooth(prevs_true, eps)
+        prevs_hat = smooth(prevs_hat, eps)
+        prevs_train = smooth(prevs_train, eps)
+
+    N = prevs_true.shape[-1]
+    w = prevs_true / prevs_train
+    w_hat = prevs_hat / prevs_train
+    return (1./N) * (w - w_hat)**2.
+
+
+def msre(prevs_true, prevs_hat, prevs_train, eps=0.):
+    """
+    Returns the mean across all experiments. See :function:`sre`.
+    :param prevs_true: array-like, true prevalence values of shape (n_experiments, n_classes,) or (n_classes,)
+    :param prevs_hat: array-like, estimated prevalence values of shape equal to prevs_true
+    :param prevs_train: array-like, training prevalence values of  (n_experiments, n_classes,) or (n_classes,)
+    :param eps: float, for smoothing the prevalence values. It is 0 by default (no smoothing), meaning the
+        training prevalence is expected to be >0 everywhere.
+    :return: the squared ratio error
+    """
+    return np.mean(squared_ratio_error(prevs_true, prevs_hat, prevs_train, eps))
+
+
+def dist_aitchison(prevs_true, prevs_hat):
+    clr = CLRtransformation()
+    return np.linalg.norm(clr(prevs_true) - clr(prevs_hat), axis=-1)
+
+
+def mean_dist_aitchison(prevs_true, prevs_hat):
+    return np.mean(dist_aitchison(prevs_true, prevs_hat))
+
+
 def mkld(prevs_true, prevs_hat, eps=None):
     """Computes the mean Kullback-Leibler divergence (see :meth:`quapy.error.kld`) across the
     sample pairs. The distributions are smoothed using the `eps` factor
@@ -374,8 +428,8 @@ def __check_eps(eps=None):
 
 
 CLASSIFICATION_ERROR = {f1e, acce}
-QUANTIFICATION_ERROR = {mae, mnae, mrae, mnrae, mse, mkld, mnkld}
+QUANTIFICATION_ERROR = {mae, mnae, mrae, mnrae, mse, mkld, mnkld, msre, mean_dist_aitchison}
-QUANTIFICATION_ERROR_SINGLE = {ae, nae, rae, nrae, se, kld, nkld}
+QUANTIFICATION_ERROR_SINGLE = {ae, nae, rae, nrae, se, kld, nkld, sre, dist_aitchison}
 QUANTIFICATION_ERROR_SMOOTH = {kld, nkld, rae, nrae, mkld, mnkld, mrae}
 CLASSIFICATION_ERROR_NAMES = {func.__name__ for func in CLASSIFICATION_ERROR}
 QUANTIFICATION_ERROR_NAMES = {func.__name__ for func in QUANTIFICATION_ERROR}
@@ -387,6 +441,7 @@ ERROR_NAMES = \
 f1_error = f1e
 acc_error = acce
 mean_absolute_error = mae
+squared_ratio_error = sre
 absolute_error = ae
 mean_relative_absolute_error = mrae
 relative_absolute_error = rae

quapy/method/confidence.py

@@ -88,6 +88,52 @@ class ConfidenceRegionABC(ABC):
         """ Returns internal samples """
         ...
 
+    def __contains__(self, p):
+        """
+        Overloads in operator, checks if `p` is contained in the region
+
+        :param p: array-like
+        :return: boolean
+        """
+        p = np.asarray(p)
+        assert p.ndim==1, f'unexpected shape for point parameter'
+        return self.coverage(p)==1.
+
+    def closest_point_in_region(self, p, tol=1e-6, max_iter=30):
+        """
+        Finds the closes point to p that belongs to the region. Assumes the region is convex.
+
+        :param p: array-like, the point
+        :param tol: float, error tolerance
+        :param max_iter: int, max number of iterations
+        :returns: array-like, the closes point to p in the segment between p and the center of the region, that
+            belongs to the region
+        """
+        p = np.asarray(p, dtype=float)
+
+        # if p in region, returns p itself
+        if p in self:
+            return p.copy()
+
+        # center of the region
+        c = self.point_estimate()
+
+        # binary search in [0,1], interpolation parameter
+        # low=closest to p, high=closest to c
+        low, high = 0.0, 1.0
+        for _ in range(max_iter):
+            mid = 0.5 * (low + high)
+            x = p*(1-mid) + c*mid
+            if x in self:
+                high = mid
+            else:
+                low = mid
+            if high - low < tol:
+                break
+
+        in_boundary = p*(1-high) + c*high
+        return in_boundary
+
 
 class WithConfidenceABC(ABC):
     """
@@ -219,124 +265,61 @@ def within_ellipse_prop(values, mean, prec_matrix, chi2_critical):
         return float(np.mean(within_ellipse))
 
 
-class ConfidenceEllipseSimplex(ConfidenceRegionABC):
+def closest_point_on_ellipsoid(p, mean, cov, chi2_critical, tol=1e-9, max_iter=100):
     """
-    Instantiates a Confidence Ellipse in the probability simplex.
+    Computes the closest point on the ellipsoid defined by:
-
+        (x - mean)^T cov^{-1} (x - mean) = chi2_critical
-    :param samples: np.ndarray of shape (n_bootstrap_samples, n_classes)
-    :param confidence_level: float, the confidence level (default 0.95)
     """
 
-    def __init__(self, samples, confidence_level=0.95):
+    p = np.asarray(p)
+    mean = np.asarray(mean)
+    Sigma = np.asarray(cov)
 
-        assert 0. < confidence_level < 1., f'{confidence_level=} must be in range(0,1)'
+    # Precompute precision matrix
+    P = np.linalg.pinv(Sigma)
+    d = P.shape[0]
 
-        samples = np.asarray(samples)
+    # Define v = p - mean
+    v = p - mean
 
-        self.mean_ = samples.mean(axis=0)
+    # If p is inside the ellipsoid, return p itself
-        self.cov_ = np.cov(samples, rowvar=False, ddof=1)
+    M_dist = v @ P @ v
+    if M_dist <= chi2_critical:
+        return p.copy()
 
-        try:
+    # Function to compute x(lambda)
-            self.precision_matrix_ = np.linalg.pinv(self.cov_)
+    def x_lambda(lmbda):
-        except:
+        A = np.eye(d) + lmbda * P
-            self.precision_matrix_ = None
+        return mean + np.linalg.solve(A, v)
 
-        self.dim = samples.shape[-1]
+    # Function whose root we want: f(lambda) = Mahalanobis distance - chi2
-        self.ddof = self.dim - 1
+    def f(lmbda):
+        x = x_lambda(lmbda)
+        diff = x - mean
+        return diff @ P @ diff - chi2_critical
 
-        # critical chi-square value
+    # Bisection search over lambda >= 0
-        self.confidence_level = confidence_level
+    l_low, l_high = 0.0, 1.0
-        self.chi2_critical_ = chi2.ppf(confidence_level, df=self.ddof)
-        self._samples = samples
 
-    @property
+    # Increase high until f(high) < 0
-    def samples(self):
+    while f(l_high) > 0:
-        return self._samples
+        l_high *= 2
+        if l_high > 1e12:
+            raise RuntimeError("Failed to bracket the root.")
 
-    def point_estimate(self):
+    # Bisection
-        """
+    for _ in range(max_iter):
-        Returns the point estimate, the center of the ellipse.
+        l_mid = 0.5 * (l_low + l_high)
+        fm = f(l_mid)
+        if abs(fm) < tol:
+            break
+        if fm > 0:
+            l_low = l_mid
+        else:
+            l_high = l_mid
 
-        :return: np.ndarray of shape (n_classes,)
+    l_opt = l_mid
-        """
+    return x_lambda(l_opt)
-        return self.mean_
-
-    def coverage(self, true_value):
-        """
-        Checks whether a value, or a sets of values, are contained in the confidence region. The method computes the
-        fraction of these that are contained in the region, if more than one value is passed. If only one value is
-        passed, then it either returns 1.0 or 0.0, for indicating the value is in the region or not, respectively.
-
-        :param true_value: a np.ndarray of shape (n_classes,) or shape (n_values, n_classes,)
-        :return: float in [0,1]
-        """
-        return within_ellipse_prop(true_value, self.mean_, self.precision_matrix_, self.chi2_critical_)
-
-
-class ConfidenceEllipseTransformed(ConfidenceRegionABC):
-    """
-    Instantiates a Confidence Ellipse in a transformed space.
-
-    :param samples: np.ndarray of shape (n_bootstrap_samples, n_classes)
-    :param confidence_level: float, the confidence level (default 0.95)
-    """
-
-    def __init__(self, samples, transformation: CompositionalTransformation, confidence_level=0.95):
-        samples = np.asarray(samples)
-        self.transformation = transformation
-        Z = self.transformation(samples)
-        self.mean_ = np.mean(samples, axis=0)
-        self.conf_region_z = ConfidenceEllipseSimplex(Z, confidence_level=confidence_level)
-        self._samples = samples
-
-    @property
-    def samples(self):
-        return self._samples
-
-    def point_estimate(self):
-        """
-        Returns the point estimate, the center of the ellipse.
-
-        :return: np.ndarray of shape (n_classes,)
-        """
-        # The inverse of the CLR does not coincide with the true mean, because the geometric mean
-        # requires smoothing the prevalence vectors and this affects the softmax (inverse);
-        # return self.clr.inverse(self.mean_) # <- does not coincide
-        return self.mean_
-
-    def coverage(self, true_value):
-        """
-        Checks whether a value, or a sets of values, are contained in the confidence region. The method computes the
-        fraction of these that are contained in the region, if more than one value is passed. If only one value is
-        passed, then it either returns 1.0 or 0.0, for indicating the value is in the region or not, respectively.
-
-        :param true_value: a np.ndarray of shape (n_classes,) or shape (n_values, n_classes,)
-        :return: float in [0,1]
-        """
-        transformed_values = self.transformation(true_value)
-        return self.conf_region_z.coverage(transformed_values)
-
-
-class ConfidenceEllipseCLR(ConfidenceEllipseTransformed):
-    """
-    Instantiates a Confidence Ellipse in the Centered-Log Ratio (CLR) space.
-
-    :param samples: np.ndarray of shape (n_bootstrap_samples, n_classes)
-    :param confidence_level: float, the confidence level (default 0.95)
-    """
-    def __init__(self, samples, confidence_level=0.95):
-        super().__init__(samples, CLRtransformation(), confidence_level=confidence_level)
-
-
-class ConfidenceEllipseILR(ConfidenceEllipseTransformed):
-    """
-    Instantiates a Confidence Ellipse in the Isometric-Log Ratio (CLR) space.
-
-    :param samples: np.ndarray of shape (n_bootstrap_samples, n_classes)
-    :param confidence_level: float, the confidence level (default 0.95)
-    """
-    def __init__(self, samples, confidence_level=0.95):
-        super().__init__(samples, ILRtransformation(), confidence_level=confidence_level)
 
 
 class ConfidenceIntervals(ConfidenceRegionABC):
@@ -423,6 +406,146 @@ class ConfidenceIntervals(ConfidenceRegionABC):
         return np.mean(self.winkler_scores(true_prev))
 
 
+class ConfidenceEllipseSimplex(ConfidenceRegionABC):
+    """
+    Instantiates a Confidence Ellipse in the probability simplex.
+
+    :param samples: np.ndarray of shape (n_bootstrap_samples, n_classes)
+    :param confidence_level: float, the confidence level (default 0.95)
+    """
+
+    def __init__(self, samples, confidence_level=0.95):
+
+        assert 0. < confidence_level < 1., f'{confidence_level=} must be in range(0,1)'
+
+        samples = np.asarray(samples)
+
+        self.mean_ = samples.mean(axis=0)
+        self.cov_ = np.cov(samples, rowvar=False, ddof=1)
+
+        try:
+            self.precision_matrix_ = np.linalg.pinv(self.cov_)
+        except:
+            self.precision_matrix_ = None
+
+        self.dim = samples.shape[-1]
+        self.ddof = self.dim - 1
+
+        # critical chi-square value
+        self.confidence_level = confidence_level
+        self.chi2_critical_ = chi2.ppf(confidence_level, df=self.ddof)
+        self._samples = samples
+        self.alpha = 1.-confidence_level
+
+    @property
+    def samples(self):
+        return self._samples
+
+    def point_estimate(self):
+        """
+        Returns the point estimate, the center of the ellipse.
+
+        :return: np.ndarray of shape (n_classes,)
+        """
+        return self.mean_
+
+    def coverage(self, true_value):
+        """
+        Checks whether a value, or a sets of values, are contained in the confidence region. The method computes the
+        fraction of these that are contained in the region, if more than one value is passed. If only one value is
+        passed, then it either returns 1.0 or 0.0, for indicating the value is in the region or not, respectively.
+
+        :param true_value: a np.ndarray of shape (n_classes,) or shape (n_values, n_classes,)
+        :return: float in [0,1]
+        """
+        return within_ellipse_prop(true_value, self.mean_, self.precision_matrix_, self.chi2_critical_)
+
+    def closest_point_in_region(self, p, tol=1e-6, max_iter=30):
+        return closest_point_on_ellipsoid(
+            p,
+            mean=self.mean_,
+            cov=self.cov_,
+            chi2_critical=self.chi2_critical_
+        )
+
+
+class ConfidenceEllipseTransformed(ConfidenceRegionABC):
+    """
+    Instantiates a Confidence Ellipse in a transformed space.
+
+    :param samples: np.ndarray of shape (n_bootstrap_samples, n_classes)
+    :param confidence_level: float, the confidence level (default 0.95)
+    """
+
+    def __init__(self, samples, transformation: CompositionalTransformation, confidence_level=0.95):
+        samples = np.asarray(samples)
+        self.transformation = transformation
+        Z = self.transformation(samples)
+        # self.mean_ = np.mean(samples, axis=0)
+        self.mean_ = self.transformation.inverse(np.mean(Z, axis=0))
+        self.conf_region_z = ConfidenceEllipseSimplex(Z, confidence_level=confidence_level)
+        self._samples = samples
+        self.alpha = 1.-confidence_level
+
+    @property
+    def samples(self):
+        return self._samples
+
+    def point_estimate(self):
+        """
+        Returns the point estimate, the center of the ellipse.
+
+        :return: np.ndarray of shape (n_classes,)
+        """
+        # The inverse of the CLR does not coincide with the true mean, because the geometric mean
+        # requires smoothing the prevalence vectors and this affects the softmax (inverse);
+        # return self.clr.inverse(self.mean_) # <- does not coincide
+        return self.mean_
+
+    def coverage(self, true_value):
+        """
+        Checks whether a value, or a sets of values, are contained in the confidence region. The method computes the
+        fraction of these that are contained in the region, if more than one value is passed. If only one value is
+        passed, then it either returns 1.0 or 0.0, for indicating the value is in the region or not, respectively.
+
+        :param true_value: a np.ndarray of shape (n_classes,) or shape (n_values, n_classes,)
+        :return: float in [0,1]
+        """
+        transformed_values = self.transformation(true_value)
+        return self.conf_region_z.coverage(transformed_values)
+
+    def closest_point_in_region(self, p, tol=1e-6, max_iter=30):
+        p_prime = self.transformation(p)
+        b_prime = self.conf_region_z.closest_point_in_region(p_prime, tol=tol, max_iter=max_iter)
+        b = self.transformation.inverse(b_prime)
+        return b
+
+
+class ConfidenceEllipseCLR(ConfidenceEllipseTransformed):
+    """
+    Instantiates a Confidence Ellipse in the Centered-Log Ratio (CLR) space.
+
+    :param samples: np.ndarray of shape (n_bootstrap_samples, n_classes)
+    :param confidence_level: float, the confidence level (default 0.95)
+    """
+    def __init__(self, samples, confidence_level=0.95):
+        super().__init__(samples, CLRtransformation(), confidence_level=confidence_level)
+
+
+class ConfidenceEllipseILR(ConfidenceEllipseTransformed):
+    """
+    Instantiates a Confidence Ellipse in the Isometric-Log Ratio (CLR) space.
+
+    :param samples: np.ndarray of shape (n_bootstrap_samples, n_classes)
+    :param confidence_level: float, the confidence level (default 0.95)
+    """
+    def __init__(self, samples, confidence_level=0.95):
+        super().__init__(samples, ILRtransformation(), confidence_level=confidence_level)
+
+
+
+
+
 
 
 class AggregativeBootstrap(WithConfidenceABC, AggregativeQuantifier):