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// ivector/ivector-extractor.h // Copyright 2013-2014 Daniel Povey // 2015 David Snyder // See ../../COPYING for clarification regarding multiple authors // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED // WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE, // MERCHANTABLITY OR NON-INFRINGEMENT. // See the Apache 2 License for the specific language governing permissions and // limitations under the License. #ifndef KALDI_IVECTOR_IVECTOR_EXTRACTOR_H_ #define KALDI_IVECTOR_IVECTOR_EXTRACTOR_H_ #include <vector> #include <mutex> #include "base/kaldi-common.h" #include "matrix/matrix-lib.h" #include "gmm/model-common.h" #include "gmm/diag-gmm.h" #include "gmm/full-gmm.h" #include "itf/options-itf.h" #include "util/common-utils.h" #include "hmm/posterior.h" namespace kaldi { // Note, throughout this file we use SGMM-type notation because // that's what I'm comfortable with. // Dimensions: // D is the feature dim (e.g. D = 60) // I is the number of Gaussians (e.g. I = 2048) // S is the ivector dim (e.g. S = 400) // Options for estimating iVectors, during both training and test. Note: the // "acoustic_weight" is not read by any class declared in this header; it has to // be applied by calling IvectorExtractorUtteranceStats::Scale() before // obtaining the iVector. // The same is true of max_count: it has to be applied by programs themselves // e.g. see ../ivectorbin/ivector-extract.cc. struct IvectorEstimationOptions { double acoustic_weight; double max_count; IvectorEstimationOptions(): acoustic_weight(1.0), max_count(0.0) {} void Register(OptionsItf *opts) { opts->Register("acoustic-weight", &acoustic_weight, "Weight on part of auxf that involves the data (e.g. 0.2); " "if this weight is small, the prior will have more effect."); opts->Register("max-count", &max_count, "Maximum frame count (affects prior scaling): if >0, the prior " "term will be scaled up after the frame count exceeds this " "value. Note that this count is considered after posterior " "scaling (e.g. --acoustic-weight option, or scale argument to " "scale-post), so you would normally use a cutoff 10 times " "smaller than the corresponding number of frames."); } }; class IvectorExtractor; class IvectorExtractorComputeDerivedVarsClass; /// These are the stats for a particular utterance, i.e. the sufficient stats /// for estimating an iVector (if need_2nd_order_stats == true, we can also /// estimate the variance of the model; these 2nd order stats are not needed if /// we just need the iVector. class IvectorExtractorUtteranceStats { public: IvectorExtractorUtteranceStats(int32 num_gauss, int32 feat_dim, bool need_2nd_order_stats): gamma_(num_gauss), X_(num_gauss, feat_dim) { if (need_2nd_order_stats) { S_.resize(num_gauss); for (int32 i = 0; i < num_gauss; i++) S_[i].Resize(feat_dim); } } void AccStats(const MatrixBase<BaseFloat> &feats, const Posterior &post); void Scale(double scale); // Used to apply acoustic scale. double NumFrames() { return gamma_.Sum(); } protected: friend class IvectorExtractor; friend class IvectorExtractorStats; Vector<double> gamma_; // zeroth-order stats (summed posteriors), dimension [I] Matrix<double> X_; // first-order stats, dimension [I][D] std::vector<SpMatrix<double> > S_; // 2nd-order stats, dimension [I][D][D], if // required. }; struct IvectorExtractorOptions { int ivector_dim; int num_iters; bool use_weights; IvectorExtractorOptions(): ivector_dim(400), num_iters(2), use_weights(true) { } void Register(OptionsItf *opts) { opts->Register("num-iters", &num_iters, "Number of iterations in " "iVector estimation (>1 needed due to weights)"); opts->Register("ivector-dim", &ivector_dim, "Dimension of iVector"); opts->Register("use-weights", &use_weights, "If true, regress the " "log-weights on the iVector"); } }; // Forward declaration. This class is used together with IvectorExtractor to // compute iVectors in an online way, so we can update the estimate efficiently // as we add frames. class OnlineIvectorEstimationStats; // Caution: the IvectorExtractor is not the only thing required to get an // ivector. We also need to get posteriors from a GMM, typically a FullGmm. // Typically these will be obtained in a process that involves using a DiagGmm // for Gaussian selection, followed by getting posteriors from the FullGmm. To // keep track of these, we keep them all in the same directory, // e.g. final.{ubm,dubm,ie}. class IvectorExtractor { public: friend class IvectorExtractorStats; friend class OnlineIvectorEstimationStats; IvectorExtractor(): prior_offset_(0.0) { } IvectorExtractor( const IvectorExtractorOptions &opts, const FullGmm &fgmm); /// Gets the distribution over ivectors (or at least, a Gaussian approximation /// to it). The output "var" may be NULL if you don't need it. "mean", and /// "var", if present, must be the correct dimension (this->IvectorDim()). /// If you only need a point estimate of the iVector, get the mean only. void GetIvectorDistribution( const IvectorExtractorUtteranceStats &utt_stats, VectorBase<double> *mean, SpMatrix<double> *var) const; /// The distribution over iVectors, in our formulation, is not centered at /// zero; its first dimension has a nonzero offset. This function returns /// that offset. double PriorOffset() const { return prior_offset_; } /// Returns the log-likelihood objective function, summed over frames, /// for this distribution of iVectors (a point distribution, if var == NULL). double GetAuxf(const IvectorExtractorUtteranceStats &utt_stats, const VectorBase<double> &mean, const SpMatrix<double> *var = NULL) const; /// Returns the data-dependent part of the log-likelihood objective function, /// summed over frames. If variance pointer is NULL, uses point value. double GetAcousticAuxf(const IvectorExtractorUtteranceStats &utt_stats, const VectorBase<double> &mean, const SpMatrix<double> *var = NULL) const; /// Returns the prior-related part of the log-likelihood objective function. /// Note: if var != NULL, this quantity is a *probability*, otherwise it is /// a likelihood (and the corresponding probability is zero). double GetPriorAuxf(const VectorBase<double> &mean, const SpMatrix<double> *var = NULL) const; /// This returns just the part of the acoustic auxf that relates to the /// variance of the utt_stats (i.e. which would be zero if the utt_stats had /// zero variance. This does not depend on the iVector, it's included as an /// aid to debugging. We can only get this if we stored the S statistics. If /// not we assume the variance is generated from the model. double GetAcousticAuxfVariance( const IvectorExtractorUtteranceStats &utt_stats) const; /// This returns just the part of the acoustic auxf that relates to the /// speaker-dependent means (and how they differ from the data means). double GetAcousticAuxfMean( const IvectorExtractorUtteranceStats &utt_stats, const VectorBase<double> &mean, const SpMatrix<double> *var = NULL) const; /// This returns the part of the acoustic auxf that relates to the /// gconsts of the Gaussians. double GetAcousticAuxfGconst( const IvectorExtractorUtteranceStats &utt_stats) const; /// This returns the part of the acoustic auxf that relates to the /// Gaussian-specific weights. (impacted by the iVector only if /// we are using w_). double GetAcousticAuxfWeight( const IvectorExtractorUtteranceStats &utt_stats, const VectorBase<double> &mean, const SpMatrix<double> *var = NULL) const; /// Gets the linear and quadratic terms in the distribution over iVectors, but /// only the terms arising from the Gaussian means (i.e. not the weights /// or the priors). /// Setup is log p(x) \propto x^T linear -0.5 x^T quadratic x. /// This function *adds to* the output rather than setting it. void GetIvectorDistMean( const IvectorExtractorUtteranceStats &utt_stats, VectorBase<double> *linear, SpMatrix<double> *quadratic) const; /// Gets the linear and quadratic terms in the distribution over /// iVectors, that arise from the prior. Adds to the outputs, /// rather than setting them. void GetIvectorDistPrior( const IvectorExtractorUtteranceStats &utt_stats, VectorBase<double> *linear, SpMatrix<double> *quadratic) const; /// Gets the linear and quadratic terms in the distribution over /// iVectors, that arise from the weights (if applicable). The /// "mean" parameter is the iVector point that we compute /// the expansion around (it's a quadratic approximation of a /// nonlinear function, but with a "safety factor" (the "max" stuff). /// Adds to the outputs, rather than setting them. void GetIvectorDistWeight( const IvectorExtractorUtteranceStats &utt_stats, const VectorBase<double> &mean, VectorBase<double> *linear, SpMatrix<double> *quadratic) const; // Note: the function GetStats no longer exists due to code refactoring. // Instead of this->GetStats(feats, posterior, &utt_stats), call // utt_stats.AccStats(feats, posterior). int32 FeatDim() const; int32 IvectorDim() const; int32 NumGauss() const; bool IvectorDependentWeights() const { return w_.NumRows() != 0; } void Write(std::ostream &os, bool binary) const; void Read(std::istream &is, bool binary); // Note: we allow the default assignment and copy operators // because they do what we want. protected: void ComputeDerivedVars(); void ComputeDerivedVars(int32 i); friend class IvectorExtractorComputeDerivedVarsClass; // Imagine we'll project the iVectors with transformation T, so apply T^{-1} // where necessary to keep the model equivalent. Used to keep unit variance // (like prior re-estimation). void TransformIvectors(const MatrixBase<double> &T, double new_prior_offset); /// Weight projection vectors, if used. Dimension is [I][S] Matrix<double> w_; /// If we are not using weight-projection vectors, stores the Gaussian mixture /// weights from the UBM. This does not affect the iVector; it is only useful /// as a way of making sure the log-probs are comparable between systems with /// and without weight projection matrices. Vector<double> w_vec_; /// Ivector-subspace projection matrices, dimension is [I][D][S]. /// The I'th matrix projects from ivector-space to Gaussian mean. /// There is no mean offset to add-- we deal with it by having /// a prior with a nonzero mean. std::vector<Matrix<double> > M_; /// Inverse variances of speaker-adapted model, dimension [I][D][D]. std::vector<SpMatrix<double> > Sigma_inv_; /// 1st dim of the prior over the ivector has an offset, so it is not zero. /// This is used to handle the global offset of the speaker-adapted means in a /// simple way. double prior_offset_; // Below are *derived variables* that can be computed from the // variables above. /// The constant term in the log-likelihood of each Gaussian (not /// counting any weight). Vector<double> gconsts_; /// U_i = M_i^T \Sigma_i^{-1} M_i is a quantity that comes up /// in ivector estimation. This is conceptually a /// std::vector<SpMatrix<double> >, but we store the packed-data /// in the rows of a matrix, which gives us an efficiency /// improvement (we can use matrix-multiplies). Matrix<double> U_; /// The product of Sigma_inv_[i] with M_[i]. std::vector<Matrix<double> > Sigma_inv_M_; private: // var <-- quadratic_term^{-1}, but done carefully, first flooring eigenvalues // of quadratic_term to 1.0, which mathematically is the least they can be, // due to the prior term. static void InvertWithFlooring(const SpMatrix<double> &quadratic_term, SpMatrix<double> *var); }; /** This class helps us to efficiently estimate iVectors in situations where the data is coming in frame by frame. */ class OnlineIvectorEstimationStats { public: // Search above for max_count to see an explanation; if nonzero, it will // put a higher weight on the prior (vs. the stats) once the count passes // that value. OnlineIvectorEstimationStats(int32 ivector_dim, BaseFloat prior_offset, BaseFloat max_count); OnlineIvectorEstimationStats(const OnlineIvectorEstimationStats &other); // Accumulate stats for one frame. void AccStats(const IvectorExtractor &extractor, const VectorBase<BaseFloat> &feature, const std::vector<std::pair<int32, BaseFloat> > &gauss_post); // Accumulate stats for a sequence (or collection) of frames. void AccStats(const IvectorExtractor &extractor, const MatrixBase<BaseFloat> &features, const std::vector<std::vector<std::pair<int32, BaseFloat> > > &gauss_post); int32 IvectorDim() const { return linear_term_.Dim(); } /// This function gets the current estimate of the iVector. Internally it /// does some work to compute it (currently matrix inversion, but we are doing /// to use Conjugate Gradient which will increase the speed). At entry, /// "ivector" must be a pointer to a vector dimension IvectorDim(), and free /// of NaN's. For faster estimation, you can set "num_cg_iters" to some value /// > 0, which will limit how many iterations of conjugate gradient we use to /// re-estimate the iVector; in this case, you should make sure *ivector is /// set at entry to a recently estimated iVector from the same utterance, /// which will give the CG a better starting point. /// If num_cg_iters is set to -1, it will compute the iVector exactly; if it's /// set to a positive number, the number of conjugate gradient iterations will /// be limited to that number. Note: the iVectors output still have a nonzero /// mean (first dim offset by PriorOffset()). void GetIvector(int32 num_cg_iters, VectorBase<double> *ivector) const; double NumFrames() const { return num_frames_; } double PriorOffset() const { return prior_offset_; } /// ObjfChange returns the change in objective function *per frame* from /// using the default value [ prior_offset_, 0, 0, ... ] to /// using the provided value; should be >= 0, if "ivector" is /// a value we estimated. This is for diagnostics. double ObjfChange(const VectorBase<double> &ivector) const; double Count() const { return num_frames_; } /// Scales the number of frames of stats by 0 <= scale <= 1, to make it /// as if we had fewer frames of adaptation data. Note: it does not /// apply the scaling to the prior term. void Scale(double scale); void Write(std::ostream &os, bool binary) const; void Read(std::istream &is, bool binary); // Override the default assignment operator inline OnlineIvectorEstimationStats &operator=(const OnlineIvectorEstimationStats &other) { this->prior_offset_ = other.prior_offset_; this->max_count_ = other.max_count_; this->num_frames_ = other.num_frames_; this->quadratic_term_=other.quadratic_term_; this->linear_term_=other.linear_term_; return *this; } protected: /// Returns objective function per frame, at this iVector value. double Objf(const VectorBase<double> &ivector) const; /// Returns objective function evaluated at the point /// [ prior_offset_, 0, 0, 0, ... ]... this is used in diagnostics. double DefaultObjf() const; friend class IvectorExtractor; double prior_offset_; double max_count_; double num_frames_; // num frames (weighted, if applicable). SpMatrix<double> quadratic_term_; Vector<double> linear_term_; }; // This code obtains periodically (for each "ivector_period" frames, e.g. 10 // frames), an estimate of the iVector including all frames up to that point. // This emulates what you could do in an online/streaming algorithm; its use is // for neural network training in a way that's matched to online decoding. // [note: I don't believe we are currently using the program, // ivector-extract-online.cc, that calls this function, in any of the scripts.]. // Caution: this program outputs the raw iVectors, where the first component // will generally be very positive. You probably want to subtract PriorOffset() // from the first element of each row of the output before writing it out. // For num_cg_iters, we suggest 15. It can be a positive number (more -> more // exact, less -> faster), or if it's negative it will do the optimization // exactly each time which is slower. // It returns the objective function improvement per frame from the "default" iVector to // the last iVector estimated. double EstimateIvectorsOnline( const Matrix<BaseFloat> &feats, const Posterior &post, const IvectorExtractor &extractor, int32 ivector_period, int32 num_cg_iters, BaseFloat max_count, Matrix<BaseFloat> *ivectors); /// Options for IvectorExtractorStats, which is used to update the parameters of /// IvectorExtractor. struct IvectorExtractorStatsOptions { bool update_variances; bool compute_auxf; int32 num_samples_for_weights; int cache_size; IvectorExtractorStatsOptions(): update_variances(true), compute_auxf(true), num_samples_for_weights(10), cache_size(100) { } void Register(OptionsItf *opts) { opts->Register("update-variances", &update_variances, "If true, update the " "Gaussian variances"); opts->Register("compute-auxf", &compute_auxf, "If true, compute the " "auxiliary functions on training data; can be used to " "debug and check convergence."); opts->Register("num-samples-for-weights", &num_samples_for_weights, "Number of samples from iVector distribution to use " "for accumulating stats for weight update. Must be >1"); opts->Register("cache-size", &cache_size, "Size of an internal " "cache (not critical, only affects speed/memory)"); } }; /// Options for training the IvectorExtractor, e.g. variance flooring. struct IvectorExtractorEstimationOptions { double variance_floor_factor; double gaussian_min_count; int32 num_threads; bool diagonalize; IvectorExtractorEstimationOptions(): variance_floor_factor(0.1), gaussian_min_count(100.0), diagonalize(true) { } void Register(OptionsItf *opts) { opts->Register("variance-floor-factor", &variance_floor_factor, "Factor that determines variance flooring (we floor each covar " "to this times global average covariance"); opts->Register("gaussian-min-count", &gaussian_min_count, "Minimum total count per Gaussian, below which we refuse to " "update any associated parameters."); opts->Register("diagonalize", &diagonalize, "If true, diagonalize the quadratic term in the " "objective function. This reorders the ivector dimensions" "from most to least important."); } }; class IvectorExtractorUpdateProjectionClass; class IvectorExtractorUpdateWeightClass; /// IvectorExtractorStats is a class used to update the parameters of the /// ivector extractor class IvectorExtractorStats { public: friend class IvectorExtractor; IvectorExtractorStats(): tot_auxf_(0.0), R_num_cached_(0), num_ivectors_(0) { } IvectorExtractorStats(const IvectorExtractor &extractor, const IvectorExtractorStatsOptions &stats_opts); void Add(const IvectorExtractorStats &other); void AccStatsForUtterance(const IvectorExtractor &extractor, const MatrixBase<BaseFloat> &feats, const Posterior &post); // This version (intended mainly for testing) works out the Gaussian // posteriors from the model. Returns total log-like for feats, given // unadapted fgmm. You'd want to add Gaussian pruning and preselection using // the diagonal, GMM, for speed, if you used this outside testing code. double AccStatsForUtterance(const IvectorExtractor &extractor, const MatrixBase<BaseFloat> &feats, const FullGmm &fgmm); void Read(std::istream &is, bool binary, bool add = false); void Write(std::ostream &os, bool binary); // non-const version; relates to cache. // const version of Write; may use extra memory if we have stuff cached void Write(std::ostream &os, bool binary) const; /// Returns the objf improvement per frame. double Update(const IvectorExtractorEstimationOptions &opts, IvectorExtractor *extractor) const; double AuxfPerFrame() { return tot_auxf_ / gamma_.Sum(); } /// Prints the proportion of the variance explained by /// the Ivector model versus the Gaussians. void IvectorVarianceDiagnostic(const IvectorExtractor &extractor); // Copy constructor. explicit IvectorExtractorStats (const IvectorExtractorStats &other); protected: friend class IvectorExtractorUpdateProjectionClass; friend class IvectorExtractorUpdateWeightClass; // This is called by AccStatsForUtterance void CommitStatsForUtterance(const IvectorExtractor &extractor, const IvectorExtractorUtteranceStats &utt_stats); /// This is called by CommitStatsForUtterance. We commit the stats /// used to update the M matrix. void CommitStatsForM(const IvectorExtractor &extractor, const IvectorExtractorUtteranceStats &utt_stats, const VectorBase<double> &ivec_mean, const SpMatrix<double> &ivec_var); /// Flushes the cache for the R_ stats. void FlushCache(); /// Commit the stats used to update the variance. void CommitStatsForSigma(const IvectorExtractor &extractor, const IvectorExtractorUtteranceStats &utt_stats); /// Commit the stats used to update the weight-projection w_-- this one /// takes a point sample, it's called from CommitStatsForW(). void CommitStatsForWPoint(const IvectorExtractor &extractor, const IvectorExtractorUtteranceStats &utt_stats, const VectorBase<double> &ivector, double weight); /// Commit the stats used to update the weight-projection w_. void CommitStatsForW(const IvectorExtractor &extractor, const IvectorExtractorUtteranceStats &utt_stats, const VectorBase<double> &ivec_mean, const SpMatrix<double> &ivec_var); /// Commit the stats used to update the prior distribution. void CommitStatsForPrior(const VectorBase<double> &ivec_mean, const SpMatrix<double> &ivec_var); // Updates M. Returns the objf improvement per frame. double UpdateProjections(const IvectorExtractorEstimationOptions &opts, IvectorExtractor *extractor) const; // This internally called function returns the objf improvement // for this Gaussian index. Updates one M. double UpdateProjection(const IvectorExtractorEstimationOptions &opts, int32 gaussian, IvectorExtractor *extractor) const; // Updates the weight projections. Returns the objf improvement per // frame. double UpdateWeights(const IvectorExtractorEstimationOptions &opts, IvectorExtractor *extractor) const; // Updates the weight projection for one Gaussian index. Returns the objf // improvement for this index. double UpdateWeight(const IvectorExtractorEstimationOptions &opts, int32 gaussian, IvectorExtractor *extractor) const; // Returns the objf improvement per frame. double UpdateVariances(const IvectorExtractorEstimationOptions &opts, IvectorExtractor *extractor) const; // Updates the prior; returns obj improvement per frame. double UpdatePrior(const IvectorExtractorEstimationOptions &opts, IvectorExtractor *extractor) const; // Called from UpdatePrior, separating out some code that // computes likelihood changes. double PriorDiagnostics(double old_prior_offset) const; void CheckDims(const IvectorExtractor &extractor) const; IvectorExtractorStatsOptions config_; /// Caution: if we read from disk, this /// is not recovered. Options will not be /// used during the update phase anyway, /// so this should not matter. /// Total auxiliary function over the training data-- can be /// used to check convergence, etc. double tot_auxf_; /// This mutex guards gamma_ and Y_ (for multi-threaded update) std::mutex gamma_Y_lock_; /// Total occupation count for each Gaussian index (zeroth-order stats) Vector<double> gamma_; /// Stats Y_i for estimating projections M. Dimension is [I][D][S]. The /// linear term in M. std::vector<Matrix<double> > Y_; /// This mutex guards R_ (for multi-threaded update) std::mutex R_lock_; /// R_i, quadratic term for ivector subspace (M matrix)estimation. This is a /// kind of scatter of ivectors of training speakers, weighted by count for /// each Gaussian. Conceptually vector<SpMatrix<double> >, but we store each /// SpMatrix as a row of R_. Conceptually, the dim is [I][S][S]; the actual /// dim is [I][S*(S+1)/2]. Matrix<double> R_; /// This mutex guards R_num_cached_, R_gamma_cache_, R_ivec_cache_ (for /// multi-threaded update) std::mutex R_cache_lock_; /// To avoid too-frequent rank-1 update of R, which is slow, we cache some /// quantities here. int32 R_num_cached_; /// dimension: [num-to-cache][I] Matrix<double> R_gamma_cache_; /// dimension: [num-to-cache][S*(S+1)/2] Matrix<double> R_ivec_scatter_cache_; /// This mutex guards Q_ and G_ (for multi-threaded update) std::mutex weight_stats_lock_; /// Q_ is like R_ (with same dimensions), except used for weight estimation; /// the scatter of ivectors is weighted by the coefficient of the quadratic /// term in the expansion for w (the "safe" one, with the max expression). Matrix<double> Q_; /// G_ is the linear term in the weight projection matrix w_. It has the same /// dim as w_, i.e. [I][S] Matrix<double> G_; /// This mutex guards S_ (for multi-threaded update) std::mutex variance_stats_lock_; /// S_{i}, raw second-order stats per Gaussian which we will use to update the /// variances Sigma_inv_. std::vector< SpMatrix<double> > S_; /// This mutex guards num_ivectors_, ivector_sum_ and ivector_scatter_ (for multi-threaded /// update) std::mutex prior_stats_lock_; /// Count of the number of iVectors we trained on. Need for prior re-estimation. /// (make it double not int64 to more easily support weighting later.) double num_ivectors_; /// Sum of all the iVector means. Needed for prior re-estimation. Vector<double> ivector_sum_; /// Second-order stats for the iVectors. Needed for prior re-estimation. SpMatrix<double> ivector_scatter_; private: /// Computes an orthogonal matrix A from the iVector transform /// T such that T' = A*T is an alternative transform which diagonalizes the /// quadratic_term_ in the iVector estimation objective function. This /// reorders the dimensions of the iVector from most to least important, /// which may be more convenient to view. The transform should not /// affect the performance of systems which use iVectors. void GetOrthogonalIvectorTransform(const SubMatrix<double> &T, IvectorExtractor *extractor, Matrix<double> *A) const; IvectorExtractorStats &operator = (const IvectorExtractorStats &other); // Disallow. }; } // namespace kaldi #endif |