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

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, m 1 m 2 m 3 m 4 m 5 m 6 frequency … coefficients

Hidden Markov Model Premier 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 Network Recurrent neural network proposed by Jaeger 2001 L M I A N P E P A E R W W in dxdx dydy Recurrent “reservoir” of nonlinear processing elements with random untrained weights. Linear readout, easily trained weights. Note similarities to Liquid State Machine W out random untrained input weights.

ESN Diagram & Equations

How to classify with predictors Build 10 word models that are trained to predict the future of each of the 10 digits Z ? The best predictor determines the class Not a new idea!

ESN Training Minimize mean-squared error between y(n) and desired signal d(n). 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.

ASR Example Same spoken digit experiment as before. ESN: M=60 PEs, r=2.0, r in =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 HMMESN Classifier OutputLikelihoodMSE ArchitectureStates, left-to-right Minimum element Gaussian kernelReadout filter Elements combined GMMWinner-take-all TransitionsState transition matrixBinary switching matrix TrainingSegmental K-means (Baum-Welch) Segmental K-means DiscriminatoryNoMaybe, depends on desired signal