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iVector approach to Phonotactic LRE Mehdi Soufifar 2 nd May 2011

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Phonotactic LRE Train Classifier LR, SVM, LM GLC,.. Language-dependant Utterance L Recognizer (Hvite,BUTPR,...) AM Phoneme sequence Extract n-gram statistics N-gram counts Train : Classifier Test Utterance L Recognizer (Hvite,BUTPR,...) AM Phoneme sequence Extract n-gram statistics N-gram counts Test : Language dependant Score

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N-gram Counts N^3= for RU phoneme set 1 Problem : Huge vector of n-gram counts Solutions: ▫Choose the most frequent n-grams ▫Choosing top N n-grams discriminatively(LL) ▫Compress the n-gram counts Singular Value Decomposition (SVD) Decompose the document matrix D Using the the transformation matrix U to reduce the n- gram vector dimensionality PCA-based dimensionality reduction ▫iVector feature selection

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Sub-space multinomial modeling Every vector of n-gram counts consist of E events (#n-grams) Log probability of n th utterance in MN distribution is: can be defined as : Model parameter to be estimated in ML estimation are t and w No analytical solution! We use Newton Raphson update as a Numerical solution N^3= for RU phoneme set

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Sub-space multinomial modeling 1 st solution : ▫consider all 3-grams to be components of a Bernoulli trial ▫Model the entire vector of 3-gram counts with one multinomial distribution ▫N-gram events are not independent (not consistent with Bernoulli trial presumption!) 2 nd solution ▫Cluster 3-grams based on their histories ▫Model each history with a separate MN distribution Data sparsity problem! Clustering 3-grams based on binary-decision tree

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Training of iVector extractor Number of iterations : 5-7 (depends on sub- space dimension) Sub-space dimension : seconds10 seconds30 seconds

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Classifiers Configuration : L one-to-all linear classifier ▫L: number of targeted languages Classifiers: ▫SVM ▫LR ▫Linear Generative Classifier ▫MLR (to be done!)

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Results on different classifiers Task : NIST LRE 2009 Dev-3sDev-10sDev-30sEval-3sEval-10sEval- 30s PCA- SVM PCA-LR PCA-GLC iVec-SVM iVec-LR iVec-GLC

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Results of different systems LRE09 Dev-3sDev-10sDev-30sEvl-3sEvl-10sEvl-30s BASE-HU-SVM PCA-HU-LR iVect-HU-LR iVec+PCA-HU-LR iVec-RU-LR iVec-LR HU+RU iVec-LR HURU

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N-gram clustering Remove all the 3-gram with repetition < 10 over all training utterances Model each history with a separate MN distribution 1084 histories, up to 33 3-grams each Dev-3sDev-10sDev-30sEval-3sEval-10sEval- 30s >10 3-gram

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Merging histories using BDT In case of 3-gram P i P j P k Merging histories which do not increase the entropy more than a certain value P i P 22 P k P i P 33 P k P i P P k E1=Entropy(Model1) Models 1Models 2 E2=Entropy(Model2) D= E1 – E2

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Results on DT Hist. merging More iterations on training T => T matrix is moving toward zero matrix! IterationDev-3sDev-10sDev-30sEval-3sEval-10sEval- 30s DT >10 3-gram

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Deeper insight to the iVector Extrac.

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Strange results 3-grams with no repetition through out the whole training set should not affect system performance! Remove all the 3-grams with no repetition through the whole training set >35406 (567 reduction) Even worse result if we prune more!!!! Dev-30sDev-10sDev-3sEval- 30s Eval-10sEval-3s

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DT clustering of n-gram histories The overall likelihood is an order of magnitude higher than the 1 st solution Change of the model-likelihood is quite notable in each iteration! The T Matrix is mainly zero after some iterations!

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1 st iteration

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2 nd iteration

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3 rd iteration

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4 th iteration

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5 th iteration

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6 th iteration

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Closer look at TRAIN set amhaamha boSnboSn cantcant creocreo croacroa daridari engiengi englengl farsfars frenfren georgeor haushaus hindhind korekore mandmand pashpash portport russruss spanspan turkturk ukraukra urduurdu vietviet TRAIN voa ✔✔✔✔✔✔✗✔✗✔✔✔✔✔✔✔✔✔✔✔✔✔✔ TRAIN cts ✗✗✔✗✗✗✔✔✔✔✗✗✔✔✔✗✔✔✔✗✗✔✔ DEV voa ✔✔✗✔✗✔✗✗✗✔✔✔✗✗✗✔✔✗✗✔✔✗✗ DEV cts ✗✗✔✗✔✗✔✔✔✔✗✗✔✔✔✗✗✔✔✗✗✔✔ EVAL voa ✔✔✔✔✔✔✗✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔✔ EVAL cts ✗✗✔✗✗✗✔✔✔✗✗✗✔✔✔✗✗✔✗✗✗✔✔

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Ivector inspection Cant Engl

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iVect inspection Multiple data source causes bimodality We also see this effect in some single source languages Amha

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