import copy import gc import itertools import logging import time import warnings import numpy as np import pandas as pd import scipy.sparse import sklearn from _kernel_lib import _exp_val from packaging import version from scipy.special import binom from sklearn.linear_model import Lasso, LassoLarsIC, lars_path from sklearn.pipeline import make_pipeline from sklearn.preprocessing import StandardScaler from tqdm.auto import tqdm from .._explanation import Explanation from ..utils import safe_isinstance from ..utils._exceptions import DimensionError from ..utils._legacy import ( DenseData, SparseData, convert_to_data, convert_to_instance, convert_to_instance_with_index, convert_to_link, convert_to_model, match_instance_to_data, match_model_to_data, ) from ._explainer import Explainer log = logging.getLogger("shap") 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 coefficients 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 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 the sparse case, we accept any sparse matrix but convert to lil format for performance. feature_names : list The names of the features in the background dataset. If the background dataset is supplied as a pandas.DataFrame, then ``feature_names`` can be set to ``None`` (default), and the feature names will be taken as the column names of the dataframe. 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 output with a link function where link(output) = sum(phi). Default is "identity" (a no-op). If the model output is a probability, then "logit" can be used to transform the SHAP values into log-odds units. Examples -------- See :ref:`Kernel Explainer Examples `. """ def __init__(self, model, data, feature_names=None, link="identity", **kwargs): if feature_names is not None: self.data_feature_names = feature_names elif isinstance(data, pd.DataFrame): self.data_feature_names = list(data.columns) # convert incoming inputs to standardized iml objects self.link = convert_to_link(link) self.keep_index = kwargs.get("keep_index", False) self.keep_index_ordered = kwargs.get("keep_index_ordered", False) self.model = convert_to_model(model, keep_index=self.keep_index) 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 if not isinstance(self.data, (DenseData, SparseData)): emsg = "Shap explainer only supports the DenseData and SparseData input currently." raise TypeError(emsg) if self.data.transposed: emsg = "Shap explainer does not support transposed DenseData or SparseData currently." raise DimensionError(emsg) # 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.sample(data, K) or shap.kmeans(data, K) to " + "summarize the background as K 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) if safe_isinstance(model_null, "tensorflow.python.framework.ops.EagerTensor"): model_null = model_null.numpy() elif safe_isinstance(model_null, "tensorflow.python.framework.ops.SymbolicTensor"): model_null = self._convert_symbolic_tensor(model_null) 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 self.expected_value = float(self.expected_value) else: self.D = self.fnull.shape[0] @staticmethod def _convert_symbolic_tensor(symbolic_tensor) -> np.ndarray: import tensorflow as tf if tf.__version__ >= "2.0.0": with tf.compat.v1.Session() as sess: sess.run(tf.compat.v1.global_variables_initializer()) tensor_as_np_array = sess.run(symbolic_tensor) else: # this is untested with tf.Session() as sess: sess.run(tf.global_variables_initializer()) tensor_as_np_array = sess.run(symbolic_tensor) return tensor_as_np_array def __call__(self, X, l1_reg="num_features(10)", silent=False): start_time = time.time() if isinstance(X, pd.DataFrame): feature_names = list(X.columns) else: feature_names = getattr(self, "data_feature_names", None) v = self.shap_values(X, l1_reg=l1_reg, silent=silent) if isinstance(v, list): v = np.stack(v, axis=-1) # put outputs at the end # the explanation object expects an expected value for each row if hasattr(self.expected_value, "__len__"): ev_tiled = np.tile(self.expected_value, (v.shape[0], 1)) else: ev_tiled = np.tile(self.expected_value, v.shape[0]) return Explanation( v, base_values=ev_tiled, data=X.to_numpy() if isinstance(X, pd.DataFrame) else X, feature_names=feature_names, compute_time=time.time() - start_time, ) 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)", "aic", "bic", or float The l1 regularization to use for feature selection. The estimation procedure is based on a debiased lasso. * "num_features(int)" selects a fixed number of top features. * "aic" and "bic" options use the AIC and BIC rules for regularization. * Passing a float directly sets the "alpha" parameter of the ``sklearn.linear_model.Lasso`` model used for feature selection. * "auto" (deprecated): uses "aic" when less than 20% of the possible sample space is enumerated, otherwise it uses no regularization. .. versionchanged:: 0.47.0 The default value changed from ``"auto"`` to ``"num_features(10)"``. silent: bool If True, hide tqdm progress bar. Default False. gc_collect : bool Run garbage collection after each explanation round. Sometime needed for memory intensive explanations (default False). Returns ------- np.array or list Estimated SHAP values, usually of shape ``(# 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 the ``expected_value`` attribute of the explainer). The type and shape of the return value depends on the number of model inputs and outputs: * one input, one output: array of shape ``(#num_samples, *X.shape[1:])``. * one input, multiple outputs: array of shape ``(#num_samples, *X.shape[1:], #num_outputs)`` * multiple inputs: list of arrays of corresponding shape above. .. versionchanged:: 0.45.0 Return type for models with multiple outputs and one input changed from list to np.ndarray. """ # convert dataframes if isinstance(X, pd.Series): X = X.values elif isinstance(X, pd.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 scipy.sparse.issparse(X) and not scipy.sparse.isspmatrix_lil(X): X = X.tolil() assert x_type.endswith(arr_type) or scipy.sparse.isspmatrix_lil(X), "Unknown instance type: " + x_type # 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 out = np.zeros(s) 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)) if kwargs.get("gc_collect", False): gc.collect() # 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] outs = np.stack(outs, axis=-1) 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 else: emsg = "Instance must have 1 or 2 dimensions!" raise DimensionError(emsg) 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 elif safe_isinstance(model_out, "tensorflow.python.framework.ops.SymbolicTensor"): model_out = self._convert_symbolic_tensor(model_out) 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", "num_features(10)") # 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 = int(np.ceil((self.M - 1) / 2.0)) num_paired_subset_sizes = 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(f"{weight_vector = }") log.debug(f"{num_subset_sizes = }") log.debug(f"{num_paired_subset_sizes = }") log.debug(f"{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(f"{subset_size = }") log.debug(f"{nsubsets = }") log.debug( "self.nsamples*weight_vector[subset_size-1] = " f"{num_samples_left * remaining_weight_vector[subset_size - 1]}" ) log.debug( "self.nsamples*weight_vector[subset_size-1]/nsubsets = " f"{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(f"{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(f"{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(f"{remaining_weight_vector = }") log.info(f"{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(f"{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 @staticmethod def not_equal(i, j): number_types = (int, float, np.number) if isinstance(i, number_types) and isinstance(j, number_types): return 0 if np.allclose(i, j, equal_nan=True) else 1 elif hasattr(i, "dtype") and hasattr(j, "dtype"): if np.issubdtype(i.dtype, np.number) and np.issubdtype(j.dtype, np.number): return 0 if np.allclose(i, j, equal_nan=True) else 1 if np.issubdtype(i.dtype, np.bool_) and np.issubdtype(j.dtype, np.bool_): return 0 if np.allclose(i, j, equal_nan=True) else 1 return 0 if all(i == j) else 1 else: return 0 if i == j else 1 def varying_groups(self, x): if not scipy.sparse.issparse(x): varying = np.zeros(self.data.groups_size) for i in range(self.data.groups_size): inds = self.data.groups[i] x_group = x[0, inds] if scipy.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() varying[i] = self.not_equal(x_group, self.data.data[:, inds]) 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(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: background_data_rows = data_rows[nonzero_rows] if scipy.sparse.issparse(background_data_rows): background_data_rows = background_data_rows.toarray() num_mismatches = np.sum(np.abs(background_data_rows - 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 scipy.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 = scipy.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(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 = scipy.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 evaluation_data = x[0, groups] # In edge case where background is all dense but evaluation data # is all sparse, make evaluation data dense if scipy.sparse.issparse(x) and not scipy.sparse.issparse(self.synth_data): evaluation_data = evaluation_data.toarray() self.synth_data[offset : offset + self.N, groups] = evaluation_data 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 elif safe_isinstance(modelOut, "tensorflow.python.framework.ops.SymbolicTensor"): modelOut = self._convert_symbolic_tensor(modelOut) 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 self.ey, self.nsamplesRun = _exp_val( self.nsamplesRun, self.nsamplesAdded, self.D, self.N, self.data.weights, self.y, self.ey ) 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(f"{fraction_evaluated = }") if self.l1_reg == "auto": warnings.warn("l1_reg='auto' is deprecated and will be removed in a future version.", DeprecationWarning) 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(f"{np.sum(w_aug) = }") log.info(f"{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 in ("auto", "bic", "aic"): c = "aic" if self.l1_reg == "auto" else self.l1_reg # "Normalize" parameter of LassoLarsIC was deprecated in sklearn version 1.2 if version.parse(sklearn.__version__) < version.parse("1.2.0"): kwg = dict(normalize=False) else: kwg = {} model = make_pipeline(StandardScaler(with_mean=False), LassoLarsIC(criterion=c, **kwg)) nonzero_inds = np.nonzero(model.fit(mask_aug, eyAdj_aug)[1].coef_)[0] # use a fixed regularization coefficient 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(f"{etmp[:4, :] = }") # solve a weighted least squares equation to estimate phi # least squares: # phi = min_w ||W^(1/2) (y - X w)||^2 # the corresponding normal equation: # (X' W X) phi = X' W y # with # X = etmp # W = np.diag(self.kernelWeights) # y = eyAdj2 # # We could just rely on sciki-learn # from sklearn.linear_model import LinearRegression # lm = LinearRegression(fit_intercept=False).fit(etmp, eyAdj2, sample_weight=self.kernelWeights) # Under the hood, as of scikit-learn version 1.3, LinearRegression still uses np.linalg.lstsq and # there are more performant options. See https://github.com/scikit-learn/scikit-learn/issues/22855. y = np.asarray(eyAdj2) X = etmp WX = self.kernelWeights[:, None] * X try: w = np.linalg.solve(X.T @ WX, WX.T @ y) except np.linalg.LinAlgError: warnings.warn( "Linear regression equation is singular, a least squares solutions is used instead.\n" "To avoid this situation and get a regular matrix do one of the following:\n" "1) turn up the number of samples,\n" "2) turn up the L1 regularization with num_features(N) where N is less than the number of samples,\n" "3) group features together to reduce the number of inputs that need to be explained." ) # XWX = np.linalg.pinv(X.T @ WX) # w = np.dot(XWX, np.dot(np.transpose(WX), y)) sqrt_W = np.sqrt(self.kernelWeights) w = np.linalg.lstsq(sqrt_W[:, None] * X, sqrt_W * y, rcond=None)[0] log.debug(f"{np.sum(w) = }") log.debug( f"self.link(self.fx) - self.link(self.fnull) = {self.link.f(self.fx[dim]) - self.link.f(self.fnull[dim])}" ) log.debug(f"self.fx = {self.fx[dim]}") log.debug(f"self.link(self.fx) = {self.link.f(self.fx[dim])}") log.debug(f"self.fnull = {self.fnull[dim]}") log.debug(f"self.link(self.fnull) = {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(f"{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))