# Author: Alexandre Gramfort # Daniel Strohmeier # # License: Simplified BSD import numpy as np from ..source_estimate import SourceEstimate, _BaseSourceEstimate, _make_stc from ..minimum_norm.inverse import (combine_xyz, _prepare_forward, _check_reference, _log_exp_var) from ..forward import is_fixed_orient from ..io.pick import pick_channels_evoked from ..io.proj import deactivate_proj from ..utils import (logger, verbose, _check_depth, _check_option, sum_squared, _validate_type, check_random_state, warn) from ..dipole import Dipole from .mxne_optim import (mixed_norm_solver, iterative_mixed_norm_solver, _Phi, tf_mixed_norm_solver, iterative_tf_mixed_norm_solver, norm_l2inf, norm_epsilon_inf, groups_norm2) def _check_ori(pick_ori, forward): """Check pick_ori.""" _check_option('pick_ori', pick_ori, [None, 'vector']) if pick_ori == 'vector' and is_fixed_orient(forward): raise ValueError('pick_ori="vector" cannot be combined with a fixed ' 'orientation forward solution.') def _prepare_weights(forward, gain, source_weighting, weights, weights_min): mask = None if isinstance(weights, _BaseSourceEstimate): weights = np.max(np.abs(weights.data), axis=1) weights_max = np.max(weights) if weights_min > weights_max: raise ValueError('weights_min > weights_max (%s > %s)' % (weights_min, weights_max)) weights_min = weights_min / weights_max weights = weights / weights_max n_dip_per_pos = 1 if is_fixed_orient(forward) else 3 weights = np.ravel(np.tile(weights, [n_dip_per_pos, 1]).T) if len(weights) != gain.shape[1]: raise ValueError('weights do not have the correct dimension ' ' (%d != %d)' % (len(weights), gain.shape[1])) if len(source_weighting.shape) == 1: source_weighting *= weights else: source_weighting *= weights[:, None] gain *= weights[None, :] if weights_min is not None: mask = (weights > weights_min) gain = gain[:, mask] n_sources = np.sum(mask) // n_dip_per_pos logger.info("Reducing source space to %d sources" % n_sources) return gain, source_weighting, mask def _prepare_gain(forward, info, noise_cov, pca, depth, loose, rank, weights=None, weights_min=None): depth = _check_depth(depth, 'depth_sparse') forward, gain_info, gain, _, _, source_weighting, _, _, whitener = \ _prepare_forward(forward, info, noise_cov, 'auto', loose, rank, pca, use_cps=True, **depth) if weights is None: mask = None else: gain, source_weighting, mask = _prepare_weights( forward, gain, source_weighting, weights, weights_min) return forward, gain, gain_info, whitener, source_weighting, mask def _reapply_source_weighting(X, source_weighting, active_set): X *= source_weighting[active_set][:, None] return X def _compute_residual(forward, evoked, X, active_set, info): # OK, picking based on row_names is safe sel = [forward['sol']['row_names'].index(c) for c in info['ch_names']] residual = evoked.copy() residual = pick_channels_evoked(residual, include=info['ch_names']) r_tmp = residual.copy() r_tmp.data = np.dot(forward['sol']['data'][sel, :][:, active_set], X) # Take care of proj active_projs = list() non_active_projs = list() for p in evoked.info['projs']: if p['active']: active_projs.append(p) else: non_active_projs.append(p) if len(active_projs) > 0: with r_tmp.info._unlock(): r_tmp.info['projs'] = deactivate_proj(active_projs, copy=True, verbose=False) r_tmp.apply_proj(verbose=False) r_tmp.add_proj(non_active_projs, remove_existing=False, verbose=False) residual.data -= r_tmp.data return residual @verbose def _make_sparse_stc(X, active_set, forward, tmin, tstep, active_is_idx=False, pick_ori=None, verbose=None): source_nn = forward['source_nn'] vector = False if not is_fixed_orient(forward): if pick_ori != 'vector': logger.info('combining the current components...') X = combine_xyz(X) else: vector = True source_nn = np.reshape(source_nn, (-1, 3, 3)) if not active_is_idx: active_idx = np.where(active_set)[0] else: active_idx = active_set n_dip_per_pos = 1 if is_fixed_orient(forward) else 3 if n_dip_per_pos > 1: active_idx = np.unique(active_idx // n_dip_per_pos) src = forward['src'] vertices = [] n_points_so_far = 0 for this_src in src: this_n_points_so_far = n_points_so_far + len(this_src['vertno']) this_active_idx = active_idx[(n_points_so_far <= active_idx) & (active_idx < this_n_points_so_far)] this_active_idx -= n_points_so_far this_vertno = this_src['vertno'][this_active_idx] n_points_so_far = this_n_points_so_far vertices.append(this_vertno) source_nn = source_nn[active_idx] return _make_stc( X, vertices, src.kind, tmin, tstep, src[0]['subject_his_id'], vector=vector, source_nn=source_nn) def _split_gof(M, X, gain): # parse out the variance explained using an orthogonal basis # assuming x is estimated using elements of gain, with residual res # along the first axis assert M.ndim == X.ndim == gain.ndim == 2, (M.ndim, X.ndim, gain.ndim) assert gain.shape == (M.shape[0], X.shape[0]) assert M.shape[1] == X.shape[1] norm = (M * M.conj()).real.sum(0, keepdims=True) norm[norm == 0] = np.inf M_est = gain @ X assert M.shape == M_est.shape res = M - M_est assert gain.shape[0] == M.shape[0], (gain.shape, M.shape) # find an orthonormal basis for our matrices that spans the actual data U, s, _ = np.linalg.svd(gain, full_matrices=False) if U.shape[1] > 0: U = U[:, s >= s[0] * 1e-6] # the part that gets explained fit_orth = U.T @ M # the part that got over-explained (landed in residual) res_orth = U.T @ res # determine the weights by projecting each one onto this basis w = (U.T @ gain)[:, :, np.newaxis] * X w_norm = np.linalg.norm(w, axis=1, keepdims=True) w_norm[w_norm == 0] = 1. w /= w_norm # our weights are now unit-norm positive (will presrve power) fit_back = np.linalg.norm(fit_orth[:, np.newaxis] * w, axis=0) ** 2 res_back = np.linalg.norm(res_orth[:, np.newaxis] * w, axis=0) ** 2 # and the resulting goodness of fits gof_back = 100 * (fit_back - res_back) / norm assert gof_back.shape == X.shape, (gof_back.shape, X.shape) return gof_back @verbose def _make_dipoles_sparse(X, active_set, forward, tmin, tstep, M, gain_active, active_is_idx=False, verbose=None): times = tmin + tstep * np.arange(X.shape[1]) if not active_is_idx: active_idx = np.where(active_set)[0] else: active_idx = active_set # Compute the GOF split amongst the dipoles assert M.shape == (gain_active.shape[0], len(times)) assert gain_active.shape[1] == len(active_idx) == X.shape[0] gof_split = _split_gof(M, X, gain_active) assert gof_split.shape == (len(active_idx), len(times)) assert X.shape[0] in (len(active_idx), 3 * len(active_idx)) n_dip_per_pos = 1 if is_fixed_orient(forward) else 3 if n_dip_per_pos > 1: active_idx = active_idx // n_dip_per_pos _, keep = np.unique(active_idx, return_index=True) keep.sort() # maintain old order active_idx = active_idx[keep] gof_split.shape = (len(active_idx), n_dip_per_pos, len(times)) gof_split = gof_split.sum(1) assert (gof_split < 100).all() assert gof_split.shape == (len(active_idx), len(times)) dipoles = [] for k, i_dip in enumerate(active_idx): i_pos = forward['source_rr'][i_dip][np.newaxis, :] i_pos = i_pos.repeat(len(times), axis=0) X_ = X[k * n_dip_per_pos: (k + 1) * n_dip_per_pos] if n_dip_per_pos == 1: amplitude = X_[0] i_ori = forward['source_nn'][i_dip][np.newaxis, :] i_ori = i_ori.repeat(len(times), axis=0) else: if forward['surf_ori']: X_ = np.dot(forward['source_nn'][ i_dip * n_dip_per_pos:(i_dip + 1) * n_dip_per_pos].T, X_) amplitude = np.linalg.norm(X_, axis=0) i_ori = np.zeros((len(times), 3)) i_ori[amplitude > 0.] = (X_[:, amplitude > 0.] / amplitude[amplitude > 0.]).T dipoles.append(Dipole(times, i_pos, amplitude, i_ori, gof_split[k])) return dipoles @verbose def make_stc_from_dipoles(dipoles, src, verbose=None): """Convert a list of spatio-temporal dipoles into a SourceEstimate. Parameters ---------- dipoles : Dipole | list of instances of Dipole The dipoles to convert. src : instance of SourceSpaces The source space used to generate the forward operator. %(verbose)s Returns ------- stc : SourceEstimate The source estimate. """ logger.info('Converting dipoles into a SourceEstimate.') if isinstance(dipoles, Dipole): dipoles = [dipoles] if not isinstance(dipoles, list): raise ValueError('Dipoles must be an instance of Dipole or ' 'a list of instances of Dipole. ' 'Got %s!' % type(dipoles)) tmin = dipoles[0].times[0] tstep = dipoles[0].times[1] - tmin X = np.zeros((len(dipoles), len(dipoles[0].times))) source_rr = np.concatenate([_src['rr'][_src['vertno'], :] for _src in src], axis=0) n_lh_points = len(src[0]['vertno']) lh_vertno = list() rh_vertno = list() for i in range(len(dipoles)): if not np.all(dipoles[i].pos == dipoles[i].pos[0]): raise ValueError('Only dipoles with fixed position over time ' 'are supported!') X[i] = dipoles[i].amplitude idx = np.all(source_rr == dipoles[i].pos[0], axis=1) idx = np.where(idx)[0][0] if idx < n_lh_points: lh_vertno.append(src[0]['vertno'][idx]) else: rh_vertno.append(src[1]['vertno'][idx - n_lh_points]) vertices = [np.array(lh_vertno).astype(int), np.array(rh_vertno).astype(int)] stc = SourceEstimate(X, vertices=vertices, tmin=tmin, tstep=tstep, subject=src._subject) logger.info('[done]') return stc @verbose def mixed_norm(evoked, forward, noise_cov, alpha='sure', loose='auto', depth=0.8, maxit=3000, tol=1e-4, active_set_size=10, debias=True, time_pca=True, weights=None, weights_min=0., solver='auto', n_mxne_iter=1, return_residual=False, return_as_dipoles=False, dgap_freq=10, rank=None, pick_ori=None, sure_alpha_grid="auto", random_state=None, verbose=None): """Mixed-norm estimate (MxNE) and iterative reweighted MxNE (irMxNE). Compute L1/L2 mixed-norm solution :footcite:`GramfortEtAl2012` or L0.5/L2 :footcite:`StrohmeierEtAl2016` mixed-norm solution on evoked data. Parameters ---------- evoked : instance of Evoked or list of instances of Evoked Evoked data to invert. forward : dict Forward operator. noise_cov : instance of Covariance Noise covariance to compute whitener. alpha : float | str Regularization parameter. If float it should be in the range [0, 100): 0 means no regularization, 100 would give 0 active dipole. If ``'sure'`` (default), the SURE method from :footcite:`DeledalleEtAl2014` will be used. .. versionchanged:: 0.24 The default was changed to ``'sure'``. %(loose)s %(depth)s maxit : int Maximum number of iterations. tol : float Tolerance parameter. active_set_size : int | None Size of active set increment. If None, no active set strategy is used. debias : bool Remove coefficient amplitude bias due to L1 penalty. time_pca : bool or int If True the rank of the concatenated epochs is reduced to its true dimension. If is 'int' the rank is limited to this value. weights : None | array | SourceEstimate Weight for penalty in mixed_norm. Can be None, a 1d array with shape (n_sources,), or a SourceEstimate (e.g. obtained with wMNE, dSPM, or fMRI). weights_min : float Do not consider in the estimation sources for which weights is less than weights_min. solver : 'cd' | 'bcd' | 'auto' The algorithm to use for the optimization. 'cd' uses coordinate descent, and 'bcd' applies block coordinate descent. 'cd' is only available for fixed orientation. n_mxne_iter : int The number of MxNE iterations. If > 1, iterative reweighting is applied. return_residual : bool If True, the residual is returned as an Evoked instance. return_as_dipoles : bool If True, the sources are returned as a list of Dipole instances. dgap_freq : int or np.inf The duality gap is evaluated every dgap_freq iterations. Ignored if solver is 'cd'. %(rank_none)s .. versionadded:: 0.18 %(pick_ori)s sure_alpha_grid : array | str If ``'auto'`` (default), the SURE is evaluated along 15 uniformly distributed alphas between alpha_max and 0.1 * alpha_max. If array, the grid is directly specified. Ignored if alpha is not "sure". .. versionadded:: 0.24 random_state : int | None The random state used in a random number generator for delta and epsilon used for the SURE computation. Defaults to None. .. versionadded:: 0.24 %(verbose)s Returns ------- stc : SourceEstimate | list of SourceEstimate Source time courses for each evoked data passed as input. residual : instance of Evoked The residual a.k.a. data not explained by the sources. Only returned if return_residual is True. See Also -------- tf_mixed_norm References ---------- .. footbibliography:: """ from scipy import linalg _validate_type(alpha, ('numeric', str), 'alpha') if isinstance(alpha, str): _check_option('alpha', alpha, ('sure',)) elif not 0. <= alpha < 100: raise ValueError('If not equal to "sure" alpha must be in [0, 100). ' 'Got alpha = %s' % alpha) if n_mxne_iter < 1: raise ValueError('MxNE has to be computed at least 1 time. ' 'Requires n_mxne_iter >= 1, got %d' % n_mxne_iter) if dgap_freq <= 0.: raise ValueError('dgap_freq must be a positive integer.' ' Got dgap_freq = %s' % dgap_freq) if not (isinstance(sure_alpha_grid, (np.ndarray, list)) or sure_alpha_grid == "auto"): raise ValueError('If not equal to "auto" sure_alpha_grid must be an ' 'array. Got %s' % type(sure_alpha_grid)) if ((isinstance(sure_alpha_grid, str) and sure_alpha_grid != "auto") and (isinstance(alpha, str) and alpha != "sure")): raise Exception('If sure_alpha_grid is manually specified, alpha must ' 'be "sure". Got %s' % alpha) pca = True if not isinstance(evoked, list): evoked = [evoked] _check_reference(evoked[0]) all_ch_names = evoked[0].ch_names if not all(all_ch_names == evoked[i].ch_names for i in range(1, len(evoked))): raise Exception('All the datasets must have the same good channels.') forward, gain, gain_info, whitener, source_weighting, mask = _prepare_gain( forward, evoked[0].info, noise_cov, pca, depth, loose, rank, weights, weights_min) _check_ori(pick_ori, forward) sel = [all_ch_names.index(name) for name in gain_info['ch_names']] M = np.concatenate([e.data[sel] for e in evoked], axis=1) # Whiten data logger.info('Whitening data matrix.') M = np.dot(whitener, M) if time_pca: U, s, Vh = linalg.svd(M, full_matrices=False) if not isinstance(time_pca, bool) and isinstance(time_pca, int): U = U[:, :time_pca] s = s[:time_pca] Vh = Vh[:time_pca] M = U * s # Scaling to make setting of tol and alpha easy tol *= sum_squared(M) n_dip_per_pos = 1 if is_fixed_orient(forward) else 3 alpha_max = norm_l2inf(np.dot(gain.T, M), n_dip_per_pos, copy=False) alpha_max *= 0.01 gain /= alpha_max source_weighting /= alpha_max # Alpha selected automatically by SURE minimization if alpha == "sure": alpha_grid = sure_alpha_grid if isinstance(sure_alpha_grid, str) and sure_alpha_grid == "auto": alpha_grid = np.geomspace(100, 10, num=15) X, active_set, best_alpha_ = _compute_mxne_sure( M, gain, alpha_grid, sigma=1, random_state=random_state, n_mxne_iter=n_mxne_iter, maxit=maxit, tol=tol, n_orient=n_dip_per_pos, active_set_size=active_set_size, debias=debias, solver=solver, dgap_freq=dgap_freq, verbose=verbose) logger.info('Selected alpha: %s' % best_alpha_) else: if n_mxne_iter == 1: X, active_set, E = mixed_norm_solver( M, gain, alpha, maxit=maxit, tol=tol, active_set_size=active_set_size, n_orient=n_dip_per_pos, debias=debias, solver=solver, dgap_freq=dgap_freq, verbose=verbose) else: X, active_set, E = iterative_mixed_norm_solver( M, gain, alpha, n_mxne_iter, maxit=maxit, tol=tol, n_orient=n_dip_per_pos, active_set_size=active_set_size, debias=debias, solver=solver, dgap_freq=dgap_freq, verbose=verbose) if time_pca: X = np.dot(X, Vh) M = np.dot(M, Vh) gain_active = gain[:, active_set] if mask is not None: active_set_tmp = np.zeros(len(mask), dtype=bool) active_set_tmp[mask] = active_set active_set = active_set_tmp del active_set_tmp if active_set.sum() == 0: warn("No active dipoles found. alpha is too big.") M_estimate = np.zeros_like(M) else: # Reapply weights to have correct unit X = _reapply_source_weighting(X, source_weighting, active_set) source_weighting[source_weighting == 0] = 1 # zeros gain_active /= source_weighting[active_set] del source_weighting M_estimate = np.dot(gain_active, X) outs = list() residual = list() cnt = 0 for e in evoked: tmin = e.times[0] tstep = 1.0 / e.info['sfreq'] Xe = X[:, cnt:(cnt + len(e.times))] if return_as_dipoles: out = _make_dipoles_sparse( Xe, active_set, forward, tmin, tstep, M[:, cnt:(cnt + len(e.times))], gain_active) else: out = _make_sparse_stc( Xe, active_set, forward, tmin, tstep, pick_ori=pick_ori) outs.append(out) cnt += len(e.times) if return_residual: residual.append(_compute_residual(forward, e, Xe, active_set, gain_info)) _log_exp_var(M, M_estimate, prefix='') logger.info('[done]') if len(outs) == 1: out = outs[0] if return_residual: residual = residual[0] else: out = outs if return_residual: out = out, residual return out def _window_evoked(evoked, size): """Window evoked (size in seconds).""" if isinstance(size, (float, int)): lsize = rsize = float(size) else: lsize, rsize = size evoked = evoked.copy() sfreq = float(evoked.info['sfreq']) lsize = int(lsize * sfreq) rsize = int(rsize * sfreq) lhann = np.hanning(lsize * 2)[:lsize] rhann = np.hanning(rsize * 2)[-rsize:] window = np.r_[lhann, np.ones(len(evoked.times) - lsize - rsize), rhann] evoked.data *= window[None, :] return evoked @verbose def tf_mixed_norm(evoked, forward, noise_cov, loose='auto', depth=0.8, maxit=3000, tol=1e-4, weights=None, weights_min=0., pca=True, debias=True, wsize=64, tstep=4, window=0.02, return_residual=False, return_as_dipoles=False, alpha=None, l1_ratio=None, dgap_freq=10, rank=None, pick_ori=None, n_tfmxne_iter=1, verbose=None): """Time-Frequency Mixed-norm estimate (TF-MxNE). Compute L1/L2 + L1 mixed-norm solution on time-frequency dictionary. Works with evoked data :footcite:`GramfortEtAl2013b,GramfortEtAl2011`. Parameters ---------- evoked : instance of Evoked Evoked data to invert. forward : dict Forward operator. noise_cov : instance of Covariance Noise covariance to compute whitener. %(loose)s %(depth)s maxit : int Maximum number of iterations. tol : float Tolerance parameter. weights : None | array | SourceEstimate Weight for penalty in mixed_norm. Can be None or 1d array of length n_sources or a SourceEstimate e.g. obtained with wMNE or dSPM or fMRI. weights_min : float Do not consider in the estimation sources for which weights is less than weights_min. pca : bool If True the rank of the data is reduced to true dimension. debias : bool Remove coefficient amplitude bias due to L1 penalty. wsize : int or array-like Length of the STFT window in samples (must be a multiple of 4). If an array is passed, multiple TF dictionaries are used (each having its own wsize and tstep) and each entry of wsize must be a multiple of 4. See :footcite:`BekhtiEtAl2016`. tstep : int or array-like Step between successive windows in samples (must be a multiple of 2, a divider of wsize and smaller than wsize/2) (default: wsize/2). If an array is passed, multiple TF dictionaries are used (each having its own wsize and tstep), and each entry of tstep must be a multiple of 2 and divide the corresponding entry of wsize. See :footcite:`BekhtiEtAl2016`. window : float or (float, float) Length of time window used to take care of edge artifacts in seconds. It can be one float or float if the values are different for left and right window length. return_residual : bool If True, the residual is returned as an Evoked instance. return_as_dipoles : bool If True, the sources are returned as a list of Dipole instances. alpha : float in [0, 100) or None Overall regularization parameter. If alpha and l1_ratio are not None, alpha_space and alpha_time are overridden by alpha * alpha_max * (1. - l1_ratio) and alpha * alpha_max * l1_ratio. 0 means no regularization, 100 would give 0 active dipole. l1_ratio : float in [0, 1] or None Proportion of temporal regularization. If l1_ratio and alpha are not None, alpha_space and alpha_time are overridden by alpha * alpha_max * (1. - l1_ratio) and alpha * alpha_max * l1_ratio. 0 means no time regularization a.k.a. MxNE. dgap_freq : int or np.inf The duality gap is evaluated every dgap_freq iterations. %(rank_none)s .. versionadded:: 0.18 %(pick_ori)s n_tfmxne_iter : int Number of TF-MxNE iterations. If > 1, iterative reweighting is applied. %(verbose)s Returns ------- stc : instance of SourceEstimate Source time courses. residual : instance of Evoked The residual a.k.a. data not explained by the sources. Only returned if return_residual is True. See Also -------- mixed_norm References ---------- .. footbibliography:: """ _check_reference(evoked) all_ch_names = evoked.ch_names info = evoked.info if not (0. <= alpha < 100.): raise ValueError('alpha must be in [0, 100). ' 'Got alpha = %s' % alpha) if not (0. <= l1_ratio <= 1.): raise ValueError('l1_ratio must be in range [0, 1].' ' Got l1_ratio = %s' % l1_ratio) alpha_space = alpha * (1. - l1_ratio) alpha_time = alpha * l1_ratio if n_tfmxne_iter < 1: raise ValueError('TF-MxNE has to be computed at least 1 time. ' 'Requires n_tfmxne_iter >= 1, got %s' % n_tfmxne_iter) if dgap_freq <= 0.: raise ValueError('dgap_freq must be a positive integer.' ' Got dgap_freq = %s' % dgap_freq) tstep = np.atleast_1d(tstep) wsize = np.atleast_1d(wsize) if len(tstep) != len(wsize): raise ValueError('The same number of window sizes and steps must be ' 'passed. Got tstep = %s and wsize = %s' % (tstep, wsize)) forward, gain, gain_info, whitener, source_weighting, mask = _prepare_gain( forward, evoked.info, noise_cov, pca, depth, loose, rank, weights, weights_min) _check_ori(pick_ori, forward) n_dip_per_pos = 1 if is_fixed_orient(forward) else 3 if window is not None: evoked = _window_evoked(evoked, window) sel = [all_ch_names.index(name) for name in gain_info["ch_names"]] M = evoked.data[sel] # Whiten data logger.info('Whitening data matrix.') M = np.dot(whitener, M) n_steps = np.ceil(M.shape[1] / tstep.astype(float)).astype(int) n_freqs = wsize // 2 + 1 n_coefs = n_steps * n_freqs phi = _Phi(wsize, tstep, n_coefs, evoked.data.shape[1]) # Scaling to make setting of tol and alpha easy tol *= sum_squared(M) alpha_max = norm_epsilon_inf(gain, M, phi, l1_ratio, n_dip_per_pos) alpha_max *= 0.01 gain /= alpha_max source_weighting /= alpha_max if n_tfmxne_iter == 1: X, active_set, E = tf_mixed_norm_solver( M, gain, alpha_space, alpha_time, wsize=wsize, tstep=tstep, maxit=maxit, tol=tol, verbose=verbose, n_orient=n_dip_per_pos, dgap_freq=dgap_freq, debias=debias) else: X, active_set, E = iterative_tf_mixed_norm_solver( M, gain, alpha_space, alpha_time, wsize=wsize, tstep=tstep, n_tfmxne_iter=n_tfmxne_iter, maxit=maxit, tol=tol, verbose=verbose, n_orient=n_dip_per_pos, dgap_freq=dgap_freq, debias=debias) if active_set.sum() == 0: raise Exception("No active dipoles found. " "alpha_space/alpha_time are too big.") # Compute estimated whitened sensor data for each dipole (dip, ch, time) gain_active = gain[:, active_set] if mask is not None: active_set_tmp = np.zeros(len(mask), dtype=bool) active_set_tmp[mask] = active_set active_set = active_set_tmp del active_set_tmp X = _reapply_source_weighting(X, source_weighting, active_set) gain_active /= source_weighting[active_set] if return_residual: residual = _compute_residual( forward, evoked, X, active_set, gain_info) if return_as_dipoles: out = _make_dipoles_sparse( X, active_set, forward, evoked.times[0], 1.0 / info['sfreq'], M, gain_active) else: out = _make_sparse_stc( X, active_set, forward, evoked.times[0], 1.0 / info['sfreq'], pick_ori=pick_ori) logger.info('[done]') if return_residual: out = out, residual return out @verbose def _compute_mxne_sure(M, gain, alpha_grid, sigma, n_mxne_iter, maxit, tol, n_orient, active_set_size, debias, solver, dgap_freq, random_state, verbose): """Stein Unbiased Risk Estimator (SURE). Implements the finite-difference Monte-Carlo approximation of the SURE for Multi-Task LASSO. See reference :footcite:`DeledalleEtAl2014`. Parameters ---------- M : array, shape (n_sensors, n_times) The data. gain : array, shape (n_sensors, n_dipoles) The gain matrix a.k.a. lead field. alpha_grid : array, shape (n_alphas,) The grid of alphas used to evaluate the SURE. sigma : float The true or estimated noise level in the data. Usually 1 if the data has been previously whitened using MNE whitener. n_mxne_iter : int The number of MxNE iterations. If > 1, iterative reweighting is applied. maxit : int Maximum number of iterations. tol : float Tolerance parameter. n_orient : int The number of orientation (1 : fixed or 3 : free or loose). active_set_size : int Size of active set increase at each iteration. debias : bool Debias source estimates. solver : 'cd' | 'bcd' | 'auto' The algorithm to use for the optimization. dgap_freq : int or np.inf The duality gap is evaluated every dgap_freq iterations. random_state : int | None The random state used in a random number generator for delta and epsilon used for the SURE computation. Returns ------- X : array, shape (n_active, n_times) Coefficient matrix. active_set : array, shape (n_dipoles,) Array of indices of non-zero coefficients. best_alpha_ : float Alpha that minimizes the SURE. References ---------- .. footbibliography:: """ def g(w): return np.sqrt(np.sqrt(groups_norm2(w.copy(), n_orient))) def gprime(w): return 2. * np.repeat(g(w), n_orient).ravel() def _run_solver(alpha, M, n_mxne_iter, as_init=None, X_init=None, w_init=None): if n_mxne_iter == 1: X, active_set, _ = mixed_norm_solver( M, gain, alpha, maxit=maxit, tol=tol, active_set_size=active_set_size, n_orient=n_orient, debias=debias, solver=solver, dgap_freq=dgap_freq, active_set_init=as_init, X_init=X_init, verbose=False) else: X, active_set, _ = iterative_mixed_norm_solver( M, gain, alpha, n_mxne_iter, maxit=maxit, tol=tol, n_orient=n_orient, active_set_size=active_set_size, debias=debias, solver=solver, dgap_freq=dgap_freq, weight_init=w_init, verbose=False) return X, active_set def _fit_on_grid(gain, M, eps, delta): coefs_grid_1_0 = np.zeros((len(alpha_grid), gain.shape[1], M.shape[1])) coefs_grid_2_0 = np.zeros((len(alpha_grid), gain.shape[1], M.shape[1])) active_sets, active_sets_eps = [], [] M_eps = M + eps * delta # warm start - first iteration (leverages convexity) logger.info('Warm starting...') for j, alpha in enumerate(alpha_grid): logger.info('alpha: %s' % alpha) X, a_set = _run_solver(alpha, M, 1) X_eps, a_set_eps = _run_solver(alpha, M_eps, 1) coefs_grid_1_0[j][a_set, :] = X coefs_grid_2_0[j][a_set_eps, :] = X_eps active_sets.append(a_set) active_sets_eps.append(a_set_eps) # next iterations if n_mxne_iter == 1: return coefs_grid_1_0, coefs_grid_2_0, active_sets else: coefs_grid_1 = coefs_grid_1_0.copy() coefs_grid_2 = coefs_grid_2_0.copy() logger.info('Fitting SURE on grid.') for j, alpha in enumerate(alpha_grid): logger.info('alpha: %s' % alpha) if active_sets[j].sum() > 0: w = gprime(coefs_grid_1[j]) X, a_set = _run_solver(alpha, M, n_mxne_iter - 1, w_init=w) coefs_grid_1[j][a_set, :] = X active_sets[j] = a_set if active_sets_eps[j].sum() > 0: w_eps = gprime(coefs_grid_2[j]) X_eps, a_set_eps = _run_solver(alpha, M_eps, n_mxne_iter - 1, w_init=w_eps) coefs_grid_2[j][a_set_eps, :] = X_eps active_sets_eps[j] = a_set_eps return coefs_grid_1, coefs_grid_2, active_sets def _compute_sure_val(coef1, coef2, gain, M, sigma, delta, eps): n_sensors, n_times = gain.shape[0], M.shape[1] dof = (gain @ (coef2 - coef1) * delta).sum() / eps df_term = np.linalg.norm(M - gain @ coef1) ** 2 sure = df_term - n_sensors * n_times * sigma ** 2 sure += 2 * dof * sigma ** 2 return sure sure_path = np.empty(len(alpha_grid)) rng = check_random_state(random_state) # See Deledalle et al. 20214 Sec. 5.1 eps = 2 * sigma / (M.shape[0] ** 0.3) delta = rng.randn(*M.shape) coefs_grid_1, coefs_grid_2, active_sets = _fit_on_grid(gain, M, eps, delta) logger.info("Computing SURE values on grid.") for i, (coef1, coef2) in enumerate(zip(coefs_grid_1, coefs_grid_2)): sure_path[i] = _compute_sure_val( coef1, coef2, gain, M, sigma, delta, eps) if verbose: logger.info("alpha %s :: sure %s" % (alpha_grid[i], sure_path[i])) best_alpha_ = alpha_grid[np.argmin(sure_path)] X = coefs_grid_1[np.argmin(sure_path)] active_set = active_sets[np.argmin(sure_path)] X = X[active_set, :] return X, active_set, best_alpha_