Minimum Mean Squared Error Time Series Classification Using an Echo State Network Prediction Model
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Minimum Mean Squared Error Time Series Classification Using an Echo State Network Prediction Model Mark Skowronski and John Harris Computational Neuro-Engineering Lab University of Florida
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Minimum Mean Squared Error Time Series Classification Using an Echo State Network Prediction Model. Mark Skowronski and John Harris Computational Neuro-Engineering Lab University of Florida. Automatic Speech Recognition Using an Echo State Network. Mark Skowronski and John Harris - PowerPoint PPT Presentation
Transcript of Minimum Mean Squared Error Time Series Classification Using an Echo State Network Prediction Model
Minimum Mean Squared Error Time Series Classification Using an Echo
State Network Prediction Model
Mark Skowronski and John Harris
Computational Neuro-Engineering Lab
University of Florida
Automatic Speech Recognition Using an Echo State Network
Mark Skowronski and John Harris
Computational Neuro-Engineering Lab
University of Florida
Transformation of a graduate student
20062000
Motivation: Man vs. Machine
Wall Street Journal/Broadcast news readings, 5000 words
Untrained human listeners vs. Cambridge HTK LVCSR system
Overview
• Why is ASR so poor?• Hidden Markov Model (HMM)• Echo state network (ESN)• ESN applied to speech• Conclusions
ASR State of the Art
• Feature extraction: MFCC vs. HFCC*
• Acoustic pattern rec: HMM
• Language models
*Skowronski & Harris. JASA, (3):1774–1780, 2004.
... m1 m2 m3 m4 m5 m6
frequency… coefficients
Hidden Markov ModelPremier stochastic model of non-stationary time series used for decision making.
Assumptions:
1) Speech is piecewise-stationary process.
2) Features are independent.
3) State duration is exponential.
4) State transition prob. function of previous-next state only.
ASR Example• Isolated English digits “zero” - “nine” from TI46:
8 male, 8 female, 26 utterances each, fs=12.5 kHz.
• 10 word models, various #states and #gaussians/state.
• Features: 13 HFCC, 100 fps, Hamming window, pre-emphasis (α=0.95), CMS, Δ+ΔΔ (±4 frames)
• Pre-processing: zero-mean and whitening transform
• M1/F1: testing; M2/F2: validation; M3-M8/F3-F8 training
• Test: corrupted by additive noise from “real” sources (subway, babble, car, exhibition hall, restaurant, street, airport terminal, train station)
HMM Test Results
Overcoming the limitations of HMMs
• HMMs do not take advantage of the dynamics of speech
• Well known HMM limitations include:– Only the present state affects transition
probabilities– Successive observations are independent– Assumes static density models
Need an architecture that better captures the dynamics of speech
Echo State NetworkRecurrent neural network proposed by Jaeger 2001
L MI AN PE PA ER R
W
Win
dx
dy
Recurrent “reservoir” of nonlinear processing elements with random untrained weights.
Linear readout, easily trained weights.
Note similarities to Liquid State Machine
Wout
random untrained input weights.
ESN Diagram & Equations
)()(
))()1(()(
nn
nnfn
out
in
xWy
uWxWx
How to classify with predictors
Build 10 word models that are trained to predict the future of each of the 10 digits
Z-1
0
1
2
8
9
?
The best predictor determines the class
Not a new idea!
ESN Training
• Minimize mean-squared error between y(n) and desired signal d(n).
1
1( ( ) ( ) ) ( ( ) ( ) )
out
T Tout n n n n
W R p
W x x x d
Wiener solution:
Multiple Readout Filters
• Need good predictors for separation of classes
• One linear filter will give mediocre prediction.• Question: how to divide reservoir space and
use multiple readout filters?• Answer: competitive network of filters
• Question: how to train/test competitive network of K filters?
• Answer: mimic HMM.
],1[),()( Kknn kout
k xWy
ASR Example
• Same spoken digit experiment as before.
• ESN: M=60 PEs, r=2.0, rin=0.1, 10 word models, various #states and #filters/state.
• Identical pre-processing and input features• Desired signal: next frame of 39-dimension
features
ESN Results
ESN/HMM Comparison
Conclusions
• ESN classifies by predicting• Multiple filters mimic sequential nature of HMMs• ESN classifier noise robust compared to HMM:
– Ave. over all sources, 0-20 dB SNR: +21 percentage points
– Ave. over all sources: +9 dB SNR
• ESN reservoir provides a dynamical model of the
history of the speech.
Questions?
HMM vs. ESN Classifier
HMM ESN ClassifierOutput Likelihood MSE
Architecture States, left-to-right States, left-to-right
Minimum element
Gaussian kernel Readout filter
Elements combined
GMM Winner-take-all
Transitions State transition matrix Binary switching matrix
Training Segmental K-means (Baum-Welch)
Segmental K-means
Discriminatory No Maybe, depends on desired signal
