# Copyright 2020 The HuggingFace Datasets Authors and the current dataset script contributor. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """TODO: Add a description here.""" # https://huggingface.co/spaces/jordyvl/ece import evaluate import datasets import numpy as np from typing import Dict, Optional # TODO: Add BibTeX citation _CITATION = """\ @InProceedings{huggingface:module, title = {Expected Calibration Error}, authors={Jordy Van Landeghem}, year={2022} } """ # TODO: Add description of the module here _DESCRIPTION = """\ This new module is designed to evaluate the calibration of a probabilistic classifier. More concretely, we provide a binned empirical estimator of top-1 calibration error. [1] """ # TODO: Add description of the arguments of the module here _KWARGS_DESCRIPTION = """ Calculates how good are predictions given some references, using certain scores Args: predictions: 2D Array of confidence estimates. references: 1D Array of Ground truth indices. n_bins : int, default=15 Number of bins of :math:`[\\frac{1}{n_{\\text{classes}},1]` for the confidence estimates. p : int, default=1 Power of the calibration error, :math:`1 \\leq p \\leq \\infty`. Returns Expected calibration error (ECE), float. Examples: >>> my_new_module = evaluate.load("jordyvl/ece") >>> results = my_new_module.compute(references=[0, 1, 2], predictions=[[0.6, 0.2, 0.2], [0, 0.95, 0.05], [0.7, 0.1 ,0.2]]) >>> print(results) {'ECE': 0.1333333333333334} """ # TODO: Define external resources urls if needed BAD_WORDS_URL = "" # Discretization and binning def create_bins(n_bins=10, scheme="equal-range", bin_range=None, P=None): assert scheme in [ "equal-range", "equal-mass", ], f"This binning scheme {scheme} is not implemented yet" if bin_range is None: if P is None: bin_range = [0, 1] # no way to know range else: bin_range = [min(P), max(P)] if scheme == "equal-range": bins = np.linspace(bin_range[0], bin_range[1], n_bins + 1) # equal range # bins = np.tile(np.linspace(bin_range[0], bin_range[1], n_bins + 1), (n_classes,1)) elif scheme == "equal-mass": assert P.size >= n_bins, "Fewer points than bins" # assume global equal mass binning; not discriminated per class P = P.flatten() # split sorted probabilities into groups of approx equal size groups = np.array_split(np.sort(P), n_bins) # is this really required? bin_upper_edges = [] # rightmost entry per equal size group for cur_group in range(n_bins): bin_upper_edges += [max(groups[cur_group])] # if upper edges is what we compare against bin_upper_edges += [1] # always +1 for right edges bin_upper_edges = sorted(list(set(bin_upper_edges))) # important for numerical conditions! # might change number of bins :O bins = np.array(bin_upper_edges) return bins def discretize_into_bins(P, bins): contains_rightmost = bool(bins[-1] > 1) # outlier bins contains_leftmost = bool(bins[0] <= 0) # beyond [before] bin_range[0] # bins_with_left_edge = np.insert(bins, 0, 0, axis=0) oneDbins = np.digitize( P, bins, right=contains_rightmost ) # since bins contains extra righmost (& leftmost bins) if contains_leftmost: oneDbins -= 1 # Fix to scipy.binned_dd_statistic: # Tie-breaking to the left for rightmost bin # Using `digitize`, values that fall on an edge are put in the right bin. # For the rightmost bin, we want values equal to the right # edge to be counted in the last bin, and not as an outlier. for k in range(P.shape[-1]): # Find the rounding precision dedges_min = np.diff(bins).min() if dedges_min == 0: raise ValueError("The smallest edge difference is numerically 0.") decimal = int(-np.log10(dedges_min)) + 6 # Find which points are on the rightmost edge. on_edge = np.where( (P[:, k] >= bins[-1]) & (np.around(P[:, k], decimal) == np.around(bins[-1], decimal)) )[0] # Shift these points one bin to the left. oneDbins[on_edge, k] -= 1 return oneDbins def manual_binned_statistic(P, y_correct, bins, statistic="mean"): bin_assignments = discretize_into_bins(np.expand_dims(P, 0), bins)[0] # indexed as in julia! result = np.empty([len(bins)], float) result.fill(np.nan) # cannot assume each bin will have observations flatcount = np.bincount(bin_assignments, None) # cannot have a negative index a = flatcount.nonzero() if statistic == "mean": flatsum = np.bincount(bin_assignments, y_correct) result[a] = flatsum[a] / flatcount[a] return result, bins, bin_assignments + 1 # upper right edge as proxy def bin_calibrated_accuracy(bins, proxy="upper-edge"): assert proxy in ["center", "upper-edge"], f"Unsupported proxy{proxy}" contains_leftmost = bool(bins[0] == 0) # beyond [before] bin_range[0] if proxy == "upper-edge": return bins[1:] if contains_leftmost else bins if proxy == "center": return bins[:-1] + np.diff(bins) / 2 def CE_estimate(y_correct, P, bins=None, p=1, proxy="upper-edge", detail=False): """ y_correct: binary (N x 1) P: normalized (N x 1) either max or per class Summary: weighted average over the accuracy/confidence difference of discrete bins of prediction probability """ n_bins = len(bins) - 1 # true number of bins bin_range = [min(bins), max(bins)] # average bin probability #55 for bin 50-60, mean per bin; or right/upper bin edges calibrated_acc = bin_calibrated_accuracy(bins, proxy=proxy) empirical_acc, bin_edges, bin_assignment = manual_binned_statistic(P, y_correct, bins) bin_numbers, weights_ece = np.unique(bin_assignment, return_counts=True) anindices = bin_numbers - 1 # reduce bin counts; left edge; indexes right by default # Expected calibration error if p < np.inf: # L^p-CE CE = np.average( abs(empirical_acc[anindices] - calibrated_acc[anindices]) ** p, weights=weights_ece ) elif np.isinf(p): # max-ECE CE = np.max(abs(empirical_acc[anindices] - calibrated_acc[anindices])) if detail: return CE, calibrated_acc, empirical_acc, weights_ece return CE def top_1_CE(Y, P, **kwargs): y_correct = (Y == np.argmax(P, -1)).astype(int) # create condition y = ŷ € [K] p_max = np.max(P, -1) # create p̂ as top-1 softmax probability € [0,1] bins = create_bins( n_bins=kwargs["n_bins"], bin_range=kwargs["bin_range"], scheme=kwargs["scheme"], P=p_max ) CE = CE_estimate(y_correct, p_max, bins=bins, proxy=kwargs["proxy"], detail=kwargs["detail"]) if kwargs["detail"]: return { "ECE": CE[0], "y_bar": CE[1], "p_bar": CE[2], "bin_freq": CE[3], "p_bar_cont": np.mean(p_max, -1), "accuracy": np.mean(y_correct), } return CE @evaluate.utils.file_utils.add_start_docstrings(_DESCRIPTION, _KWARGS_DESCRIPTION) class ECE(evaluate.EvaluationModule): """ 0. create binning scheme [discretization of f] 1. build histogram P(f(X)) 2. build conditional density estimate P(y|f(X)) 3. average bin probabilities f_B as center/edge of bin 4. apply L^p norm distance and weights """ def _info(self): # TODO: Specifies the evaluate.EvaluationModuleInfo object return evaluate.EvaluationModuleInfo( module_type="metric", description=_DESCRIPTION, citation=_CITATION, inputs_description=_KWARGS_DESCRIPTION, features=datasets.Features( { "predictions": datasets.Sequence(datasets.Value("float32")), "references": datasets.Value("int64"), } ), # Homepage of the module for documentation homepage="https://huggingface.co/spaces/jordyvl/ece", # Additional links to the codebase or references codebase_urls=[""], reference_urls=[""], ) def init_kwargs( self, n_bins: int = 10, bin_range: Optional[int] = [0, 1], scheme: str = "equal-range", proxy: str = "upper-edge", p=1, detail: bool = False, **kwargs, ): # super(evaluate.EvaluationModule, self).__init__(**kwargs) self.n_bins = n_bins self.bin_range = bin_range self.scheme = scheme self.proxy = proxy self.p = p self.detail = detail def _compute(self, predictions, references, **kwargs): # convert to numpy arrays references = np.array(references, dtype=np.int64) predictions = np.array(predictions, dtype=np.float32) assert ( predictions.shape[0] == references.shape[0] ), "Need to pass similar predictions and references" # Assert that arrays are 2D if len(predictions.shape) != 2: raise ValueError("Expected `predictions` to be a 2D vector (N x K)") if len(references.shape) != 1: # could check if wrongly passed as onehot if (references.shape[-1] == predictions.shape[1]) and ( np.sum(references) == predictions.shape[0] ): references = np.argmax(references, -1) else: raise ValueError("Expected `references` to be a 1D vector (N,)") self.init_kwargs(**kwargs) """Returns the scores""" ECE = top_1_CE(references, predictions, **self.__dict__) if self.detail: return ECE return { "ECE": ECE, } def test_ECE(**kwargs): N = 10 # N evaluation instances {(x_i,y_i)}_{i=1}^N K = 5 # K class problem def random_mc_instance(concentration=1, onehot=False): reference = np.argmax( np.random.dirichlet(([concentration for _ in range(K)])), -1 ) # class targets prediction = np.random.dirichlet(([concentration for _ in range(K)])) # probabilities if onehot: reference = np.eye(K)[np.argmax(reference, -1)] return reference, prediction references, predictions = list(zip(*[random_mc_instance() for i in range(N)])) references = np.array(references, dtype=np.int64) predictions = np.array(predictions, dtype=np.float32) res = ECE()._compute(predictions, references, **kwargs) print(f"ECE: {res['ECE']}") res = ECE()._compute(predictions, references, detail=True) print(f"ECE: {res['ECE']}") def test_deterministic(): res = ECE()._compute( references=[0, 1, 2], predictions=[[0.63, 0.2, 0.2], [0, 0.95, 0.05], [0.72, 0.1, 0.2]], detail=True, ) print(f"ECE: {res['ECE']}\n {res}") def test_equalmass_binning(): probs = np.array([0.63, 0.2, 0.2, 0, 0.95, 0.05, 0.72, 0.1, 0.2]) kwargs = dict( n_bins=5, scheme="equal-mass", bin_range=None, proxy="upper-edge", p=1, detail=True, ) bins = create_bins( n_bins=kwargs["n_bins"], scheme=kwargs["scheme"], bin_range=kwargs["bin_range"], P=probs ) test_ECE(**kwargs) def test_perfect_predictions(K=3): references = [0, 1, 2] res = ECE()._compute( references=references, predictions=np.eye(K)[references], detail=True, ) print(f"ECE: {res['ECE']}\n {res}") if __name__ == "__main__": test_perfect_predictions() test_equalmass_binning() test_deterministic() test_ECE()