from ..common import convert_to_instance, convert_to_model, match_instance_to_data, match_model_to_data, convert_to_instance_with_index, convert_to_link, IdentityLink, convert_to_data, DenseData, SparseData from scipy.special import binom import numpy as np import pandas as pd import scipy as sp import logging import copy import itertools import warnings from sklearn.linear_model import LassoLarsIC, Lasso, lars_path from sklearn.cluster import KMeans from tqdm.auto import tqdm from .explainer import Explainer log = logging.getLogger('shap') def kmeans(X, k, round_values=True): """ Summarize a dataset with k mean samples weighted by the number of data points they each represent. Parameters ---------- X : numpy.array or pandas.DataFrame Matrix of data samples to summarize (# samples x # features) k : int Number of means to use for approximation. round_values : bool For all i, round the ith dimension of each mean sample to match the nearest value from X[:,i]. This ensures discrete features always get a valid value. Returns ------- DenseData object. """ group_names = [str(i) for i in range(X.shape[1])] if str(type(X)).endswith("'pandas.core.frame.DataFrame'>"): group_names = X.columns X = X.values kmeans = KMeans(n_clusters=k, random_state=0).fit(X) if round_values: for i in range(k): for j in range(X.shape[1]): ind = np.argmin(np.abs(X[:,j] - kmeans.cluster_centers_[i,j])) kmeans.cluster_centers_[i,j] = X[ind,j] return DenseData(kmeans.cluster_centers_, group_names, None, 1.0*np.bincount(kmeans.labels_)) class KernelExplainer(Explainer): """Uses the Kernel SHAP method to explain the output of any function. Kernel SHAP is a method that uses a special weighted linear regression to compute the importance of each feature. The computed importance values are Shapley values from game theory and also coefficents from a local linear regression. Parameters ---------- model : function or iml.Model User supplied function that takes a matrix of samples (# samples x # features) and computes a the output of the model for those samples. The output can be a vector (# samples) or a matrix (# samples x # model outputs). data : numpy.array or pandas.DataFrame or shap.common.DenseData or any scipy.sparse matrix The background dataset to use for integrating out features. To determine the impact of a feature, that feature is set to "missing" and the change in the model output is observed. Since most models aren't designed to handle arbitrary missing data at test time, we simulate "missing" by replacing the feature with the values it takes in the background dataset. So if the background dataset is a simple sample of all zeros, then we would approximate a feature being missing by setting it to zero. For small problems this background dataset can be the whole training set, but for larger problems consider using a single reference value or using the kmeans function to summarize the dataset. Note: for sparse case we accept any sparse matrix but convert to lil format for performance. link : "identity" or "logit" A generalized linear model link to connect the feature importance values to the model output. Since the feature importance values, phi, sum up to the model output, it often makes sense to connect them to the ouput with a link function where link(outout) = sum(phi). If the model output is a probability then the LogitLink link function makes the feature importance values have log-odds units. """ def __init__(self, model, data, link=IdentityLink(), **kwargs): # convert incoming inputs to standardized iml objects self.link = convert_to_link(link) self.model = convert_to_model(model) self.keep_index = kwargs.get("keep_index", False) self.keep_index_ordered = kwargs.get("keep_index_ordered", False) self.data = convert_to_data(data, keep_index=self.keep_index) model_null = match_model_to_data(self.model, self.data) # enforce our current input type limitations assert isinstance(self.data, DenseData) or isinstance(self.data, SparseData), \ "Shap explainer only supports the DenseData and SparseData input currently." assert not self.data.transposed, "Shap explainer does not support transposed DenseData or SparseData currently." # warn users about large background data sets if len(self.data.weights) > 100: log.warning("Using " + str(len(self.data.weights)) + " background data samples could cause " + "slower run times. Consider using shap.kmeans(data, K) to summarize the background " + "as K weighted samples.") # init our parameters self.N = self.data.data.shape[0] self.P = self.data.data.shape[1] self.linkfv = np.vectorize(self.link.f) self.nsamplesAdded = 0 self.nsamplesRun = 0 # find E_x[f(x)] if isinstance(model_null, (pd.DataFrame, pd.Series)): model_null = np.squeeze(model_null.values) self.fnull = np.sum((model_null.T * self.data.weights).T, 0) self.expected_value = self.linkfv(self.fnull) # see if we have a vector output self.vector_out = True if len(self.fnull.shape) == 0: self.vector_out = False self.fnull = np.array([self.fnull]) self.D = 1 else: self.D = self.fnull.shape[0] def shap_values(self, X, **kwargs): """ Estimate the SHAP values for a set of samples. Parameters ---------- X : numpy.array or pandas.DataFrame or any scipy.sparse matrix A matrix of samples (# samples x # features) on which to explain the model's output. nsamples : "auto" or int Number of times to re-evaluate the model when explaining each prediction. More samples lead to lower variance estimates of the SHAP values. The "auto" setting uses `nsamples = 2 * X.shape[1] + 2048`. l1_reg : "num_features(int)", "auto" (default for now, but deprecated), "aic", "bic", or float The l1 regularization to use for feature selection (the estimation procedure is based on a debiased lasso). The auto option currently uses "aic" when less that 20% of the possible sample space is enumerated, otherwise it uses no regularization. THE BEHAVIOR OF "auto" WILL CHANGE in a future version to be based on num_features instead of AIC. The "aic" and "bic" options use the AIC and BIC rules for regularization. Using "num_features(int)" selects a fix number of top features. Passing a float directly sets the "alpha" parameter of the sklearn.linear_model.Lasso model used for feature selection. Returns ------- For models with a single output this returns a matrix of SHAP values (# samples x # features). Each row sums to the difference between the model output for that sample and the expected value of the model output (which is stored as expected_value attribute of the explainer). For models with vector outputs this returns a list of such matrices, one for each output. """ # convert dataframes if str(type(X)).endswith("pandas.core.series.Series'>"): X = X.values elif str(type(X)).endswith("'pandas.core.frame.DataFrame'>"): if self.keep_index: index_value = X.index.values index_name = X.index.name column_name = list(X.columns) X = X.values x_type = str(type(X)) arr_type = "'numpy.ndarray'>" # if sparse, convert to lil for performance if sp.sparse.issparse(X) and not sp.sparse.isspmatrix_lil(X): X = X.tolil() assert x_type.endswith(arr_type) or sp.sparse.isspmatrix_lil(X), "Unknown instance type: " + x_type assert len(X.shape) == 1 or len(X.shape) == 2, "Instance must have 1 or 2 dimensions!" # single instance if len(X.shape) == 1: data = X.reshape((1, X.shape[0])) if self.keep_index: data = convert_to_instance_with_index(data, column_name, index_name, index_value) explanation = self.explain(data, **kwargs) # vector-output s = explanation.shape if len(s) == 2: outs = [np.zeros(s[0]) for j in range(s[1])] for j in range(s[1]): outs[j] = explanation[:, j] return outs # single-output else: out = np.zeros(s[0]) out[:] = explanation return out # explain the whole dataset elif len(X.shape) == 2: explanations = [] for i in tqdm(range(X.shape[0]), disable=kwargs.get("silent", False)): data = X[i:i + 1, :] if self.keep_index: data = convert_to_instance_with_index(data, column_name, index_value[i:i + 1], index_name) explanations.append(self.explain(data, **kwargs)) # vector-output s = explanations[0].shape if len(s) == 2: outs = [np.zeros((X.shape[0], s[0])) for j in range(s[1])] for i in range(X.shape[0]): for j in range(s[1]): outs[j][i] = explanations[i][:, j] return outs # single-output else: out = np.zeros((X.shape[0], s[0])) for i in range(X.shape[0]): out[i] = explanations[i] return out def explain(self, incoming_instance, **kwargs): # convert incoming input to a standardized iml object instance = convert_to_instance(incoming_instance) match_instance_to_data(instance, self.data) # find the feature groups we will test. If a feature does not change from its # current value then we know it doesn't impact the model self.varyingInds = self.varying_groups(instance.x) if self.data.groups is None: self.varyingFeatureGroups = np.array([i for i in self.varyingInds]) self.M = self.varyingFeatureGroups.shape[0] else: self.varyingFeatureGroups = [self.data.groups[i] for i in self.varyingInds] self.M = len(self.varyingFeatureGroups) groups = self.data.groups # convert to numpy array as it is much faster if not jagged array (all groups of same length) if self.varyingFeatureGroups and all(len(groups[i]) == len(groups[0]) for i in self.varyingInds): self.varyingFeatureGroups = np.array(self.varyingFeatureGroups) # further performance optimization in case each group has a single value if self.varyingFeatureGroups.shape[1] == 1: self.varyingFeatureGroups = self.varyingFeatureGroups.flatten() # find f(x) if self.keep_index: model_out = self.model.f(instance.convert_to_df()) else: model_out = self.model.f(instance.x) if isinstance(model_out, (pd.DataFrame, pd.Series)): model_out = model_out.values self.fx = model_out[0] if not self.vector_out: self.fx = np.array([self.fx]) # if no features vary then no feature has an effect if self.M == 0: phi = np.zeros((self.data.groups_size, self.D)) phi_var = np.zeros((self.data.groups_size, self.D)) # if only one feature varies then it has all the effect elif self.M == 1: phi = np.zeros((self.data.groups_size, self.D)) phi_var = np.zeros((self.data.groups_size, self.D)) diff = self.link.f(self.fx) - self.link.f(self.fnull) for d in range(self.D): phi[self.varyingInds[0],d] = diff[d] # if more than one feature varies then we have to do real work else: self.l1_reg = kwargs.get("l1_reg", "auto") # pick a reasonable number of samples if the user didn't specify how many they wanted self.nsamples = kwargs.get("nsamples", "auto") if self.nsamples == "auto": self.nsamples = 2 * self.M + 2**11 # if we have enough samples to enumerate all subsets then ignore the unneeded samples self.max_samples = 2 ** 30 if self.M <= 30: self.max_samples = 2 ** self.M - 2 if self.nsamples > self.max_samples: self.nsamples = self.max_samples # reserve space for some of our computations self.allocate() # weight the different subset sizes num_subset_sizes = np.int(np.ceil((self.M - 1) / 2.0)) num_paired_subset_sizes = np.int(np.floor((self.M - 1) / 2.0)) weight_vector = np.array([(self.M - 1.0) / (i * (self.M - i)) for i in range(1, num_subset_sizes + 1)]) weight_vector[:num_paired_subset_sizes] *= 2 weight_vector /= np.sum(weight_vector) log.debug("weight_vector = {0}".format(weight_vector)) log.debug("num_subset_sizes = {0}".format(num_subset_sizes)) log.debug("num_paired_subset_sizes = {0}".format(num_paired_subset_sizes)) log.debug("M = {0}".format(self.M)) # fill out all the subset sizes we can completely enumerate # given nsamples*remaining_weight_vector[subset_size] num_full_subsets = 0 num_samples_left = self.nsamples group_inds = np.arange(self.M, dtype='int64') mask = np.zeros(self.M) remaining_weight_vector = copy.copy(weight_vector) for subset_size in range(1, num_subset_sizes + 1): # determine how many subsets (and their complements) are of the current size nsubsets = binom(self.M, subset_size) if subset_size <= num_paired_subset_sizes: nsubsets *= 2 log.debug("subset_size = {0}".format(subset_size)) log.debug("nsubsets = {0}".format(nsubsets)) log.debug("self.nsamples*weight_vector[subset_size-1] = {0}".format( num_samples_left * remaining_weight_vector[subset_size - 1])) log.debug("self.nsamples*weight_vector[subset_size-1]/nsubsets = {0}".format( num_samples_left * remaining_weight_vector[subset_size - 1] / nsubsets)) # see if we have enough samples to enumerate all subsets of this size if num_samples_left * remaining_weight_vector[subset_size - 1] / nsubsets >= 1.0 - 1e-8: num_full_subsets += 1 num_samples_left -= nsubsets # rescale what's left of the remaining weight vector to sum to 1 if remaining_weight_vector[subset_size - 1] < 1.0: remaining_weight_vector /= (1 - remaining_weight_vector[subset_size - 1]) # add all the samples of the current subset size w = weight_vector[subset_size - 1] / binom(self.M, subset_size) if subset_size <= num_paired_subset_sizes: w /= 2.0 for inds in itertools.combinations(group_inds, subset_size): mask[:] = 0.0 mask[np.array(inds, dtype='int64')] = 1.0 self.addsample(instance.x, mask, w) if subset_size <= num_paired_subset_sizes: mask[:] = np.abs(mask - 1) self.addsample(instance.x, mask, w) else: break log.info("num_full_subsets = {0}".format(num_full_subsets)) # add random samples from what is left of the subset space nfixed_samples = self.nsamplesAdded samples_left = self.nsamples - self.nsamplesAdded log.debug("samples_left = {0}".format(samples_left)) if num_full_subsets != num_subset_sizes: remaining_weight_vector = copy.copy(weight_vector) remaining_weight_vector[:num_paired_subset_sizes] /= 2 # because we draw two samples each below remaining_weight_vector = remaining_weight_vector[num_full_subsets:] remaining_weight_vector /= np.sum(remaining_weight_vector) log.info("remaining_weight_vector = {0}".format(remaining_weight_vector)) log.info("num_paired_subset_sizes = {0}".format(num_paired_subset_sizes)) ind_set = np.random.choice(len(remaining_weight_vector), 4 * samples_left, p=remaining_weight_vector) ind_set_pos = 0 used_masks = {} while samples_left > 0 and ind_set_pos < len(ind_set): mask.fill(0.0) ind = ind_set[ind_set_pos] # we call np.random.choice once to save time and then just read it here ind_set_pos += 1 subset_size = ind + num_full_subsets + 1 mask[np.random.permutation(self.M)[:subset_size]] = 1.0 # only add the sample if we have not seen it before, otherwise just # increment a previous sample's weight mask_tuple = tuple(mask) new_sample = False if mask_tuple not in used_masks: new_sample = True used_masks[mask_tuple] = self.nsamplesAdded samples_left -= 1 self.addsample(instance.x, mask, 1.0) else: self.kernelWeights[used_masks[mask_tuple]] += 1.0 # add the compliment sample if samples_left > 0 and subset_size <= num_paired_subset_sizes: mask[:] = np.abs(mask - 1) # only add the sample if we have not seen it before, otherwise just # increment a previous sample's weight if new_sample: samples_left -= 1 self.addsample(instance.x, mask, 1.0) else: # we know the compliment sample is the next one after the original sample, so + 1 self.kernelWeights[used_masks[mask_tuple] + 1] += 1.0 # normalize the kernel weights for the random samples to equal the weight left after # the fixed enumerated samples have been already counted weight_left = np.sum(weight_vector[num_full_subsets:]) log.info("weight_left = {0}".format(weight_left)) self.kernelWeights[nfixed_samples:] *= weight_left / self.kernelWeights[nfixed_samples:].sum() # execute the model on the synthetic samples we have created self.run() # solve then expand the feature importance (Shapley value) vector to contain the non-varying features phi = np.zeros((self.data.groups_size, self.D)) phi_var = np.zeros((self.data.groups_size, self.D)) for d in range(self.D): vphi, vphi_var = self.solve(self.nsamples / self.max_samples, d) phi[self.varyingInds, d] = vphi phi_var[self.varyingInds, d] = vphi_var if not self.vector_out: phi = np.squeeze(phi, axis=1) phi_var = np.squeeze(phi_var, axis=1) return phi def varying_groups(self, x): if not sp.sparse.issparse(x): varying = np.zeros(self.data.groups_size) for i in range(0, self.data.groups_size): inds = self.data.groups[i] x_group = x[0, inds] if sp.sparse.issparse(x_group): if all(j not in x.nonzero()[1] for j in inds): varying[i] = False continue x_group = x_group.todense() num_mismatches = np.sum(np.invert(np.isclose(x_group, self.data.data[:, inds], equal_nan=True))) varying[i] = num_mismatches > 0 varying_indices = np.nonzero(varying)[0] return varying_indices else: varying_indices = [] # go over all nonzero columns in background and evaluation data # if both background and evaluation are zero, the column does not vary varying_indices = np.unique(np.union1d(self.data.data.nonzero()[1], x.nonzero()[1])) remove_unvarying_indices = [] for i in range(0, len(varying_indices)): varying_index = varying_indices[i] # now verify the nonzero values do vary data_rows = self.data.data[:, [varying_index]] nonzero_rows = data_rows.nonzero()[0] if nonzero_rows.size > 0: num_mismatches = np.sum(np.abs(data_rows[nonzero_rows].toarray() - x[0, varying_index]) > 1e-7) # Note: If feature column non-zero but some background zero, can't remove index if num_mismatches == 0 and not \ (np.abs(x[0, [varying_index]][0, 0]) > 1e-7 and len(nonzero_rows) < data_rows.shape[0]): remove_unvarying_indices.append(i) mask = np.ones(len(varying_indices), dtype=bool) mask[remove_unvarying_indices] = False varying_indices = varying_indices[mask] return varying_indices def allocate(self): if sp.sparse.issparse(self.data.data): # We tile the sparse matrix in csr format but convert it to lil # for performance when adding samples shape = self.data.data.shape nnz = self.data.data.nnz data_rows, data_cols = shape rows = data_rows * self.nsamples shape = rows, data_cols if nnz == 0: self.synth_data = sp.sparse.csr_matrix(shape, dtype=self.data.data.dtype).tolil() else: data = self.data.data.data indices = self.data.data.indices indptr = self.data.data.indptr last_indptr_idx = indptr[len(indptr) - 1] indptr_wo_last = indptr[:-1] new_indptrs = [] for i in range(0, self.nsamples - 1): new_indptrs.append(indptr_wo_last + (i * last_indptr_idx)) new_indptrs.append(indptr + ((self.nsamples - 1) * last_indptr_idx)) new_indptr = np.concatenate(new_indptrs) new_data = np.tile(data, self.nsamples) new_indices = np.tile(indices, self.nsamples) self.synth_data = sp.sparse.csr_matrix((new_data, new_indices, new_indptr), shape=shape).tolil() else: self.synth_data = np.tile(self.data.data, (self.nsamples, 1)) self.maskMatrix = np.zeros((self.nsamples, self.M)) self.kernelWeights = np.zeros(self.nsamples) self.y = np.zeros((self.nsamples * self.N, self.D)) self.ey = np.zeros((self.nsamples, self.D)) self.lastMask = np.zeros(self.nsamples) self.nsamplesAdded = 0 self.nsamplesRun = 0 if self.keep_index: self.synth_data_index = np.tile(self.data.index_value, self.nsamples) def addsample(self, x, m, w): offset = self.nsamplesAdded * self.N if isinstance(self.varyingFeatureGroups, (list,)): for j in range(self.M): for k in self.varyingFeatureGroups[j]: if m[j] == 1.0: self.synth_data[offset:offset+self.N, k] = x[0, k] else: # for non-jagged numpy array we can significantly boost performance mask = m == 1.0 groups = self.varyingFeatureGroups[mask] if len(groups.shape) == 2: for group in groups: self.synth_data[offset:offset+self.N, group] = x[0, group] else: # further performance optimization in case each group has a single feature self.synth_data[offset:offset+self.N, groups] = x[0, groups] self.maskMatrix[self.nsamplesAdded, :] = m self.kernelWeights[self.nsamplesAdded] = w self.nsamplesAdded += 1 def run(self): num_to_run = self.nsamplesAdded * self.N - self.nsamplesRun * self.N data = self.synth_data[self.nsamplesRun*self.N:self.nsamplesAdded*self.N,:] if self.keep_index: index = self.synth_data_index[self.nsamplesRun*self.N:self.nsamplesAdded*self.N] index = pd.DataFrame(index, columns=[self.data.index_name]) data = pd.DataFrame(data, columns=self.data.group_names) data = pd.concat([index, data], axis=1).set_index(self.data.index_name) if self.keep_index_ordered: data = data.sort_index() modelOut = self.model.f(data) if isinstance(modelOut, (pd.DataFrame, pd.Series)): modelOut = modelOut.values self.y[self.nsamplesRun * self.N:self.nsamplesAdded * self.N, :] = np.reshape(modelOut, (num_to_run, self.D)) # find the expected value of each output for i in range(self.nsamplesRun, self.nsamplesAdded): eyVal = np.zeros(self.D) for j in range(0, self.N): eyVal += self.y[i * self.N + j, :] * self.data.weights[j] self.ey[i, :] = eyVal self.nsamplesRun += 1 def solve(self, fraction_evaluated, dim): eyAdj = self.linkfv(self.ey[:, dim]) - self.link.f(self.fnull[dim]) s = np.sum(self.maskMatrix, 1) # do feature selection if we have not well enumerated the space nonzero_inds = np.arange(self.M) log.debug("fraction_evaluated = {0}".format(fraction_evaluated)) if self.l1_reg == "auto": warnings.warn( "l1_reg=\"auto\" is deprecated and in the next version (v0.29) the behavior will change from a " \ "conditional use of AIC to simply \"num_features(10)\"!" ) if (self.l1_reg not in ["auto", False, 0]) or (fraction_evaluated < 0.2 and self.l1_reg == "auto"): w_aug = np.hstack((self.kernelWeights * (self.M - s), self.kernelWeights * s)) log.info("np.sum(w_aug) = {0}".format(np.sum(w_aug))) log.info("np.sum(self.kernelWeights) = {0}".format(np.sum(self.kernelWeights))) w_sqrt_aug = np.sqrt(w_aug) eyAdj_aug = np.hstack((eyAdj, eyAdj - (self.link.f(self.fx[dim]) - self.link.f(self.fnull[dim])))) eyAdj_aug *= w_sqrt_aug mask_aug = np.transpose(w_sqrt_aug * np.transpose(np.vstack((self.maskMatrix, self.maskMatrix - 1)))) #var_norms = np.array([np.linalg.norm(mask_aug[:, i]) for i in range(mask_aug.shape[1])]) # select a fixed number of top features if isinstance(self.l1_reg, str) and self.l1_reg.startswith("num_features("): r = int(self.l1_reg[len("num_features("):-1]) nonzero_inds = lars_path(mask_aug, eyAdj_aug, max_iter=r)[1] # use an adaptive regularization method elif self.l1_reg == "auto" or self.l1_reg == "bic" or self.l1_reg == "aic": c = "aic" if self.l1_reg == "auto" else self.l1_reg nonzero_inds = np.nonzero(LassoLarsIC(criterion=c).fit(mask_aug, eyAdj_aug).coef_)[0] # use a fixed regularization coeffcient else: nonzero_inds = np.nonzero(Lasso(alpha=self.l1_reg).fit(mask_aug, eyAdj_aug).coef_)[0] if len(nonzero_inds) == 0: return np.zeros(self.M), np.ones(self.M) # eliminate one variable with the constraint that all features sum to the output eyAdj2 = eyAdj - self.maskMatrix[:, nonzero_inds[-1]] * ( self.link.f(self.fx[dim]) - self.link.f(self.fnull[dim])) etmp = np.transpose(np.transpose(self.maskMatrix[:, nonzero_inds[:-1]]) - self.maskMatrix[:, nonzero_inds[-1]]) log.debug("etmp[:4,:] {0}".format(etmp[:4, :])) # solve a weighted least squares equation to estimate phi tmp = np.transpose(np.transpose(etmp) * np.transpose(self.kernelWeights)) tmp2 = np.linalg.inv(np.dot(np.transpose(tmp), etmp)) w = np.dot(tmp2, np.dot(np.transpose(tmp), eyAdj2)) log.debug("np.sum(w) = {0}".format(np.sum(w))) log.debug("self.link(self.fx) - self.link(self.fnull) = {0}".format( self.link.f(self.fx[dim]) - self.link.f(self.fnull[dim]))) log.debug("self.fx = {0}".format(self.fx[dim])) log.debug("self.link(self.fx) = {0}".format(self.link.f(self.fx[dim]))) log.debug("self.fnull = {0}".format(self.fnull[dim])) log.debug("self.link(self.fnull) = {0}".format(self.link.f(self.fnull[dim]))) phi = np.zeros(self.M) phi[nonzero_inds[:-1]] = w phi[nonzero_inds[-1]] = (self.link.f(self.fx[dim]) - self.link.f(self.fnull[dim])) - sum(w) log.info("phi = {0}".format(phi)) # clean up any rounding errors for i in range(self.M): if np.abs(phi[i]) < 1e-10: phi[i] = 0 return phi, np.ones(len(phi))