""" ============================================================= Online Latent Dirichlet Allocation with variational inference ============================================================= This implementation is modified from Matthew D. Hoffman's onlineldavb code Link: http://matthewdhoffman.com/code/onlineldavb.tar """ # Author: Chyi-Kwei Yau # Author: Matthew D. Hoffman (original onlineldavb implementation) import numpy as np import scipy.sparse as sp from scipy.special import gammaln import warnings from ..base import BaseEstimator, TransformerMixin from ..utils import (check_random_state, check_array, gen_batches, gen_even_slices, _get_n_jobs) from ..utils.validation import check_non_negative from ..utils.extmath import logsumexp from ..externals.joblib import Parallel, delayed from ..externals.six.moves import xrange from ..exceptions import NotFittedError from ._online_lda import (mean_change, _dirichlet_expectation_1d, _dirichlet_expectation_2d) EPS = np.finfo(np.float).eps def _update_doc_distribution(X, exp_topic_word_distr, doc_topic_prior, max_iters, mean_change_tol, cal_sstats, random_state): """E-step: update document-topic distribution. Parameters ---------- X : array-like or sparse matrix, shape=(n_samples, n_features) Document word matrix. exp_topic_word_distr : dense matrix, shape=(n_topics, n_features) Exponential value of expection of log topic word distribution. In the literature, this is `exp(E[log(beta)])`. doc_topic_prior : float Prior of document topic distribution `theta`. max_iters : int Max number of iterations for updating document topic distribution in the E-step. mean_change_tol : float Stopping tolerance for updating document topic distribution in E-setp. cal_sstats : boolean Parameter that indicate to calculate sufficient statistics or not. Set `cal_sstats` to `True` when we need to run M-step. random_state : RandomState instance or None Parameter that indicate how to initialize document topic distribution. Set `random_state` to None will initialize document topic distribution to a constant number. Returns ------- (doc_topic_distr, suff_stats) : `doc_topic_distr` is unnormalized topic distribution for each document. In the literature, this is `gamma`. we can calculate `E[log(theta)]` from it. `suff_stats` is expected sufficient statistics for the M-step. When `cal_sstats == False`, this will be None. """ is_sparse_x = sp.issparse(X) n_samples, n_features = X.shape n_topics = exp_topic_word_distr.shape[0] if random_state: doc_topic_distr = random_state.gamma(100., 0.01, (n_samples, n_topics)) else: doc_topic_distr = np.ones((n_samples, n_topics)) # In the literature, this is `exp(E[log(theta)])` exp_doc_topic = np.exp(_dirichlet_expectation_2d(doc_topic_distr)) # diff on `component_` (only calculate it when `cal_diff` is True) suff_stats = np.zeros(exp_topic_word_distr.shape) if cal_sstats else None if is_sparse_x: X_data = X.data X_indices = X.indices X_indptr = X.indptr for idx_d in xrange(n_samples): if is_sparse_x: ids = X_indices[X_indptr[idx_d]:X_indptr[idx_d + 1]] cnts = X_data[X_indptr[idx_d]:X_indptr[idx_d + 1]] else: ids = np.nonzero(X[idx_d, :])[0] cnts = X[idx_d, ids] doc_topic_d = doc_topic_distr[idx_d, :] # The next one is a copy, since the inner loop overwrites it. exp_doc_topic_d = exp_doc_topic[idx_d, :].copy() exp_topic_word_d = exp_topic_word_distr[:, ids] # Iterate between `doc_topic_d` and `norm_phi` until convergence for _ in xrange(0, max_iters): last_d = doc_topic_d # The optimal phi_{dwk} is proportional to # exp(E[log(theta_{dk})]) * exp(E[log(beta_{dw})]). norm_phi = np.dot(exp_doc_topic_d, exp_topic_word_d) + EPS doc_topic_d = (exp_doc_topic_d * np.dot(cnts / norm_phi, exp_topic_word_d.T)) # Note: adds doc_topic_prior to doc_topic_d, in-place. _dirichlet_expectation_1d(doc_topic_d, doc_topic_prior, exp_doc_topic_d) if mean_change(last_d, doc_topic_d) < mean_change_tol: break doc_topic_distr[idx_d, :] = doc_topic_d # Contribution of document d to the expected sufficient # statistics for the M step. if cal_sstats: norm_phi = np.dot(exp_doc_topic_d, exp_topic_word_d) + EPS suff_stats[:, ids] += np.outer(exp_doc_topic_d, cnts / norm_phi) return (doc_topic_distr, suff_stats) class LatentDirichletAllocation(BaseEstimator, TransformerMixin): """Latent Dirichlet Allocation with online variational Bayes algorithm .. versionadded:: 0.17 Read more in the :ref:`User Guide `. Parameters ---------- n_topics : int, optional (default=10) Number of topics. doc_topic_prior : float, optional (default=None) Prior of document topic distribution `theta`. If the value is None, defaults to `1 / n_topics`. In the literature, this is called `alpha`. topic_word_prior : float, optional (default=None) Prior of topic word distribution `beta`. If the value is None, defaults to `1 / n_topics`. In the literature, this is called `eta`. learning_method : 'batch' | 'online', default='online' Method used to update `_component`. Only used in `fit` method. In general, if the data size is large, the online update will be much faster than the batch update. The default learning method is going to be changed to 'batch' in the 0.20 release. Valid options:: 'batch': Batch variational Bayes method. Use all training data in each EM update. Old `components_` will be overwritten in each iteration. 'online': Online variational Bayes method. In each EM update, use mini-batch of training data to update the ``components_`` variable incrementally. The learning rate is controlled by the ``learning_decay`` and the ``learning_offset`` parameters. learning_decay : float, optional (default=0.7) It is a parameter that control learning rate in the online learning method. The value should be set between (0.5, 1.0] to guarantee asymptotic convergence. When the value is 0.0 and batch_size is ``n_samples``, the update method is same as batch learning. In the literature, this is called kappa. learning_offset : float, optional (default=10.) A (positive) parameter that downweights early iterations in online learning. It should be greater than 1.0. In the literature, this is called tau_0. max_iter : integer, optional (default=10) The maximum number of iterations. total_samples : int, optional (default=1e6) Total number of documents. Only used in the `partial_fit` method. batch_size : int, optional (default=128) Number of documents to use in each EM iteration. Only used in online learning. evaluate_every : int optional (default=0) How often to evaluate perplexity. Only used in `fit` method. set it to 0 or negative number to not evalute perplexity in training at all. Evaluating perplexity can help you check convergence in training process, but it will also increase total training time. Evaluating perplexity in every iteration might increase training time up to two-fold. perp_tol : float, optional (default=1e-1) Perplexity tolerance in batch learning. Only used when ``evaluate_every`` is greater than 0. mean_change_tol : float, optional (default=1e-3) Stopping tolerance for updating document topic distribution in E-step. max_doc_update_iter : int (default=100) Max number of iterations for updating document topic distribution in the E-step. n_jobs : int, optional (default=1) The number of jobs to use in the E-step. If -1, all CPUs are used. For ``n_jobs`` below -1, (n_cpus + 1 + n_jobs) are used. verbose : int, optional (default=0) Verbosity level. random_state : int or RandomState instance or None, optional (default=None) Pseudo-random number generator seed control. Attributes ---------- components_ : array, [n_topics, n_features] Topic word distribution. ``components_[i, j]`` represents word j in topic `i`. n_batch_iter_ : int Number of iterations of the EM step. n_iter_ : int Number of passes over the dataset. References ---------- [1] "Online Learning for Latent Dirichlet Allocation", Matthew D. Hoffman, David M. Blei, Francis Bach, 2010 [2] "Stochastic Variational Inference", Matthew D. Hoffman, David M. Blei, Chong Wang, John Paisley, 2013 [3] Matthew D. Hoffman's onlineldavb code. Link: http://matthewdhoffman.com//code/onlineldavb.tar """ def __init__(self, n_topics=10, doc_topic_prior=None, topic_word_prior=None, learning_method=None, learning_decay=.7, learning_offset=10., max_iter=10, batch_size=128, evaluate_every=-1, total_samples=1e6, perp_tol=1e-1, mean_change_tol=1e-3, max_doc_update_iter=100, n_jobs=1, verbose=0, random_state=None): self.n_topics = n_topics self.doc_topic_prior = doc_topic_prior self.topic_word_prior = topic_word_prior self.learning_method = learning_method self.learning_decay = learning_decay self.learning_offset = learning_offset self.max_iter = max_iter self.batch_size = batch_size self.evaluate_every = evaluate_every self.total_samples = total_samples self.perp_tol = perp_tol self.mean_change_tol = mean_change_tol self.max_doc_update_iter = max_doc_update_iter self.n_jobs = n_jobs self.verbose = verbose self.random_state = random_state def _check_params(self): """Check model parameters.""" if self.n_topics <= 0: raise ValueError("Invalid 'n_topics' parameter: %r" % self.n_topics) if self.total_samples <= 0: raise ValueError("Invalid 'total_samples' parameter: %r" % self.total_samples) if self.learning_offset < 0: raise ValueError("Invalid 'learning_offset' parameter: %r" % self.learning_offset) if self.learning_method not in ("batch", "online", None): raise ValueError("Invalid 'learning_method' parameter: %r" % self.learning_method) def _init_latent_vars(self, n_features): """Initialize latent variables.""" self.random_state_ = check_random_state(self.random_state) self.n_batch_iter_ = 1 self.n_iter_ = 0 if self.doc_topic_prior is None: self.doc_topic_prior_ = 1. / self.n_topics else: self.doc_topic_prior_ = self.doc_topic_prior if self.topic_word_prior is None: self.topic_word_prior_ = 1. / self.n_topics else: self.topic_word_prior_ = self.topic_word_prior init_gamma = 100. init_var = 1. / init_gamma # In the literature, this is called `lambda` self.components_ = self.random_state_.gamma( init_gamma, init_var, (self.n_topics, n_features)) # In the literature, this is `exp(E[log(beta)])` self.exp_dirichlet_component_ = np.exp( _dirichlet_expectation_2d(self.components_)) def _e_step(self, X, cal_sstats, random_init, parallel=None): """E-step in EM update. Parameters ---------- X : array-like or sparse matrix, shape=(n_samples, n_features) Document word matrix. cal_sstats : boolean Parameter that indicate whether to calculate sufficient statistics or not. Set ``cal_sstats`` to True when we need to run M-step. random_init : boolean Parameter that indicate whether to initialize document topic distribution randomly in the E-step. Set it to True in training steps. parallel : joblib.Parallel (optional) Pre-initialized instance of joblib.Parallel. Returns ------- (doc_topic_distr, suff_stats) : `doc_topic_distr` is unnormailzed topic distribution for each document. In the literature, this is called `gamma`. `suff_stats` is expected sufficient statistics for the M-step. When `cal_sstats == False`, it will be None. """ # Run e-step in parallel random_state = self.random_state_ if random_init else None # TODO: make Parallel._effective_n_jobs public instead? n_jobs = _get_n_jobs(self.n_jobs) if parallel is None: parallel = Parallel(n_jobs=n_jobs, verbose=max(0, self.verbose - 1)) results = parallel( delayed(_update_doc_distribution)(X[idx_slice, :], self.exp_dirichlet_component_, self.doc_topic_prior_, self.max_doc_update_iter, self.mean_change_tol, cal_sstats, random_state) for idx_slice in gen_even_slices(X.shape[0], n_jobs)) # merge result doc_topics, sstats_list = zip(*results) doc_topic_distr = np.vstack(doc_topics) if cal_sstats: # This step finishes computing the sufficient statistics for the # M-step. suff_stats = np.zeros(self.components_.shape) for sstats in sstats_list: suff_stats += sstats suff_stats *= self.exp_dirichlet_component_ else: suff_stats = None return (doc_topic_distr, suff_stats) def _em_step(self, X, total_samples, batch_update, parallel=None): """EM update for 1 iteration. update `_component` by batch VB or online VB. Parameters ---------- X : array-like or sparse matrix, shape=(n_samples, n_features) Document word matrix. total_samples : integer Total umber of documents. It is only used when batch_update is `False`. batch_update : boolean Parameter that controls updating method. `True` for batch learning, `False` for online learning. parallel : joblib.Parallel Pre-initialized instance of joblib.Parallel Returns ------- doc_topic_distr : array, shape=(n_samples, n_topics) Unnormalized document topic distribution. """ # E-step _, suff_stats = self._e_step(X, cal_sstats=True, random_init=True, parallel=parallel) # M-step if batch_update: self.components_ = self.topic_word_prior_ + suff_stats else: # online update # In the literature, the weight is `rho` weight = np.power(self.learning_offset + self.n_batch_iter_, -self.learning_decay) doc_ratio = float(total_samples) / X.shape[0] self.components_ *= (1 - weight) self.components_ += (weight * (self.topic_word_prior_ + doc_ratio * suff_stats)) # update `component_` related variables self.exp_dirichlet_component_ = np.exp( _dirichlet_expectation_2d(self.components_)) self.n_batch_iter_ += 1 return def _check_non_neg_array(self, X, whom): """check X format check X format and make sure no negative value in X. Parameters ---------- X : array-like or sparse matrix """ X = check_array(X, accept_sparse='csr') check_non_negative(X, whom) return X def partial_fit(self, X, y=None): """Online VB with Mini-Batch update. Parameters ---------- X : array-like or sparse matrix, shape=(n_samples, n_features) Document word matrix. Returns ------- self """ self._check_params() X = self._check_non_neg_array(X, "LatentDirichletAllocation.partial_fit") n_samples, n_features = X.shape batch_size = self.batch_size # initialize parameters or check if not hasattr(self, 'components_'): self._init_latent_vars(n_features) if n_features != self.components_.shape[1]: raise ValueError( "The provided data has %d dimensions while " "the model was trained with feature size %d." % (n_features, self.components_.shape[1])) n_jobs = _get_n_jobs(self.n_jobs) with Parallel(n_jobs=n_jobs, verbose=max(0, self.verbose - 1)) as parallel: for idx_slice in gen_batches(n_samples, batch_size): self._em_step(X[idx_slice, :], total_samples=self.total_samples, batch_update=False, parallel=parallel) return self def fit(self, X, y=None): """Learn model for the data X with variational Bayes method. When `learning_method` is 'online', use mini-batch update. Otherwise, use batch update. Parameters ---------- X : array-like or sparse matrix, shape=(n_samples, n_features) Document word matrix. Returns ------- self """ self._check_params() X = self._check_non_neg_array(X, "LatentDirichletAllocation.fit") n_samples, n_features = X.shape max_iter = self.max_iter evaluate_every = self.evaluate_every learning_method = self.learning_method if learning_method == None: warnings.warn("The default value for 'learning_method' will be " "changed from 'online' to 'batch' in the release 0.20. " "This warning was introduced in 0.18.", DeprecationWarning) learning_method = 'online' batch_size = self.batch_size # initialize parameters self._init_latent_vars(n_features) # change to perplexity later last_bound = None n_jobs = _get_n_jobs(self.n_jobs) with Parallel(n_jobs=n_jobs, verbose=max(0, self.verbose - 1)) as parallel: for i in xrange(max_iter): if learning_method == 'online': for idx_slice in gen_batches(n_samples, batch_size): self._em_step(X[idx_slice, :], total_samples=n_samples, batch_update=False, parallel=parallel) else: # batch update self._em_step(X, total_samples=n_samples, batch_update=True, parallel=parallel) # check perplexity if evaluate_every > 0 and (i + 1) % evaluate_every == 0: doc_topics_distr, _ = self._e_step(X, cal_sstats=False, random_init=False, parallel=parallel) bound = self.perplexity(X, doc_topics_distr, sub_sampling=False) if self.verbose: print('iteration: %d, perplexity: %.4f' % (i + 1, bound)) if last_bound and abs(last_bound - bound) < self.perp_tol: break last_bound = bound self.n_iter_ += 1 return self def transform(self, X): """Transform data X according to the fitted model. Parameters ---------- X : array-like or sparse matrix, shape=(n_samples, n_features) Document word matrix. Returns ------- doc_topic_distr : shape=(n_samples, n_topics) Document topic distribution for X. """ if not hasattr(self, 'components_'): raise NotFittedError("no 'components_' attribute in model." " Please fit model first.") # make sure feature size is the same in fitted model and in X X = self._check_non_neg_array(X, "LatentDirichletAllocation.transform") n_samples, n_features = X.shape if n_features != self.components_.shape[1]: raise ValueError( "The provided data has %d dimensions while " "the model was trained with feature size %d." % (n_features, self.components_.shape[1])) doc_topic_distr, _ = self._e_step(X, cal_sstats=False, random_init=False) # normalize doc_topic_distr doc_topic_distr /= doc_topic_distr.sum(axis=1)[:, np.newaxis] return doc_topic_distr def _approx_bound(self, X, doc_topic_distr, sub_sampling): """Estimate the variational bound. Estimate the variational bound over "all documents" using only the documents passed in as X. Since log-likelihood of each word cannot be computed directly, we use this bound to estimate it. Parameters ---------- X : array-like or sparse matrix, shape=(n_samples, n_features) Document word matrix. doc_topic_distr : array, shape=(n_samples, n_topics) Document topic distribution. In the literature, this is called gamma. sub_sampling : boolean, optional, (default=False) Compensate for subsampling of documents. It is used in calculate bound in online learning. Returns ------- score : float """ def _loglikelihood(prior, distr, dirichlet_distr, size): # calculate log-likelihood score = np.sum((prior - distr) * dirichlet_distr) score += np.sum(gammaln(distr) - gammaln(prior)) score += np.sum(gammaln(prior * size) - gammaln(np.sum(distr, 1))) return score is_sparse_x = sp.issparse(X) n_samples, n_topics = doc_topic_distr.shape n_features = self.components_.shape[1] score = 0 dirichlet_doc_topic = _dirichlet_expectation_2d(doc_topic_distr) dirichlet_component_ = _dirichlet_expectation_2d(self.components_) doc_topic_prior = self.doc_topic_prior_ topic_word_prior = self.topic_word_prior_ if is_sparse_x: X_data = X.data X_indices = X.indices X_indptr = X.indptr # E[log p(docs | theta, beta)] for idx_d in xrange(0, n_samples): if is_sparse_x: ids = X_indices[X_indptr[idx_d]:X_indptr[idx_d + 1]] cnts = X_data[X_indptr[idx_d]:X_indptr[idx_d + 1]] else: ids = np.nonzero(X[idx_d, :])[0] cnts = X[idx_d, ids] temp = (dirichlet_doc_topic[idx_d, :, np.newaxis] + dirichlet_component_[:, ids]) norm_phi = logsumexp(temp) score += np.dot(cnts, norm_phi) # compute E[log p(theta | alpha) - log q(theta | gamma)] score += _loglikelihood(doc_topic_prior, doc_topic_distr, dirichlet_doc_topic, self.n_topics) # Compensate for the subsampling of the population of documents if sub_sampling: doc_ratio = float(self.total_samples) / n_samples score *= doc_ratio # E[log p(beta | eta) - log q (beta | lambda)] score += _loglikelihood(topic_word_prior, self.components_, dirichlet_component_, n_features) return score def score(self, X, y=None): """Calculate approximate log-likelihood as score. Parameters ---------- X : array-like or sparse matrix, shape=(n_samples, n_features) Document word matrix. Returns ------- score : float Use approximate bound as score. """ X = self._check_non_neg_array(X, "LatentDirichletAllocation.score") doc_topic_distr = self.transform(X) score = self._approx_bound(X, doc_topic_distr, sub_sampling=False) return score def perplexity(self, X, doc_topic_distr=None, sub_sampling=False): """Calculate approximate perplexity for data X. Perplexity is defined as exp(-1. * log-likelihood per word) Parameters ---------- X : array-like or sparse matrix, [n_samples, n_features] Document word matrix. doc_topic_distr : None or array, shape=(n_samples, n_topics) Document topic distribution. If it is None, it will be generated by applying transform on X. Returns ------- score : float Perplexity score. """ if not hasattr(self, 'components_'): raise NotFittedError("no 'components_' attribute in model." " Please fit model first.") X = self._check_non_neg_array(X, "LatentDirichletAllocation.perplexity") if doc_topic_distr is None: doc_topic_distr = self.transform(X) else: n_samples, n_topics = doc_topic_distr.shape if n_samples != X.shape[0]: raise ValueError("Number of samples in X and doc_topic_distr" " do not match.") if n_topics != self.n_topics: raise ValueError("Number of topics does not match.") current_samples = X.shape[0] bound = self._approx_bound(X, doc_topic_distr, sub_sampling) if sub_sampling: word_cnt = X.sum() * (float(self.total_samples) / current_samples) else: word_cnt = X.sum() perword_bound = bound / word_cnt return np.exp(-1.0 * perword_bound)