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Analysis of the Maximum Prediction Gain of Short-Term Prediction on Sustained Speech

Reemt Hinrichs, Muhamad Fadli Damara, Stephan Preihs, Jörn Ostermann

TL;DR

This work addresses the question of how large the prediction gain can be for short-term prediction of sustained speech, independent of a particular predictor. It combines an information-theoretic upper bound with Nadaraya-Watson kernel regression to bound and estimate the maximum PG, comparing linear and nonlinear predictors on a newly recorded sustained-phoneme dataset. The findings show unvoiced speech is nearly optimally predicted by linear predictors (within ~0.3 dB), while voiced speech can achieve median improvements of 2–3 dB, with some segments exceeding 6 dB under NWKR-based estimation. These results have practical implications for low-latency speech coding and predictor design, and the authors provide the dataset and code for research use to enable further exploration and model development. Future work includes collecting longer stationary phoneme data, exploring long-term prediction, and using the NWKR-derived conditional expectation to guide symbolic regression toward explicit optimal predictors.

Abstract

Signal prediction is widely used in, e.g., economic forecasting, echo cancellation and in data compression, particularly in predictive coding of speech and music. Predictive coding algorithms reduce the bit-rate required for data transmission or storage by signal prediction. The prediction gain is a classic measure in applied signal coding of the quality of a predictor, as it links the mean-squared prediction error to the signal-to-quantization-noise of predictive coders. To evaluate predictor models, knowledge about the maximum achievable prediction gain independent of a predictor model is desirable. In this manuscript, Nadaraya-Watson kernel-regression (NWKR) and an information theoretic upper bound are applied to analyze the upper bound of the prediction gain on a newly recorded dataset of sustained speech/phonemes. It was found that for unvoiced speech a linear predictor always achieves the maximum prediction gain within at most 0.3 dB. On voiced speech, the optimum one-tap predictor was found to be linear but starting with two taps, the maximum achievable prediction gain was found to be about 2 dB to 6 dB above the prediction gain of the linear predictor. Significant differences between speakers/subjects were observed. The created dataset as well as the code can be obtained for research purpose upon request.

Analysis of the Maximum Prediction Gain of Short-Term Prediction on Sustained Speech

TL;DR

This work addresses the question of how large the prediction gain can be for short-term prediction of sustained speech, independent of a particular predictor. It combines an information-theoretic upper bound with Nadaraya-Watson kernel regression to bound and estimate the maximum PG, comparing linear and nonlinear predictors on a newly recorded sustained-phoneme dataset. The findings show unvoiced speech is nearly optimally predicted by linear predictors (within ~0.3 dB), while voiced speech can achieve median improvements of 2–3 dB, with some segments exceeding 6 dB under NWKR-based estimation. These results have practical implications for low-latency speech coding and predictor design, and the authors provide the dataset and code for research use to enable further exploration and model development. Future work includes collecting longer stationary phoneme data, exploring long-term prediction, and using the NWKR-derived conditional expectation to guide symbolic regression toward explicit optimal predictors.

Abstract

Signal prediction is widely used in, e.g., economic forecasting, echo cancellation and in data compression, particularly in predictive coding of speech and music. Predictive coding algorithms reduce the bit-rate required for data transmission or storage by signal prediction. The prediction gain is a classic measure in applied signal coding of the quality of a predictor, as it links the mean-squared prediction error to the signal-to-quantization-noise of predictive coders. To evaluate predictor models, knowledge about the maximum achievable prediction gain independent of a predictor model is desirable. In this manuscript, Nadaraya-Watson kernel-regression (NWKR) and an information theoretic upper bound are applied to analyze the upper bound of the prediction gain on a newly recorded dataset of sustained speech/phonemes. It was found that for unvoiced speech a linear predictor always achieves the maximum prediction gain within at most 0.3 dB. On voiced speech, the optimum one-tap predictor was found to be linear but starting with two taps, the maximum achievable prediction gain was found to be about 2 dB to 6 dB above the prediction gain of the linear predictor. Significant differences between speakers/subjects were observed. The created dataset as well as the code can be obtained for research purpose upon request.
Paper Structure (21 sections, 11 equations, 9 figures)

This paper contains 21 sections, 11 equations, 9 figures.

Table of Contents

  1. Introduction
  2. The Prediction Problem
  3. Background
  4. Contribution
  5. Overview
  6. Methods and Materials
  7. An Upper Bound of the Prediction Gain:
  8. Mutual Information Estimation:
  9. Evaluation of the Mutual Information Estimators:
  10. Estimation of the Conditional Expectation:
  11. Speech Material
  12. Measuring Stationarity
  13. Predictor Models:
  14. Results
  15. Estimator Evaluation:
  16. ...and 6 more sections

Figures (9)

  • Figure 1: Setup inside the anechoic chamber. A chair was positioned right infront of a microphone. Unlike depicted, for recording, the microphone was positioned closer to the mouth of the subjects.
  • Figure 2: Example waveforms from the 10,000 samples long audio snippets. The samples were taken from two different subjects, each producing a sustained /e:/ vowel. (a) shows the entire sequence and (b) a smaller segment to highlight the finer structure. The waveform deemed stationary exhibited a difference of at most 0.13 dB in prediction gain between the static and the adaptive linear predictor, where this maximum was achieved for the two step predictor. The waveform deemed instationary exhibited a difference of at most 1.17 dB in prediction gain. This maximum was achieved for the one step predictor. Some minor variations can still be observed in both waveforms.
  • Figure 3: Estimation bias and standard deviation for the (a) KSG and (b) FMI estimator on AR(N) processes. Process parameters were extracted from the recording of an /a:/ (voiced) and /s/ (unvoiced) phoneme. Error bars indicate $0.25\cdot \sigma$.
  • Figure 4: Prediction gain of linear and nonlinear predictors for the phonemes /a:/ (left) and /s/ (right), each corresponding to one segment of a male subject.
  • Figure 5: (a) Difference $\Delta PG = PG_{NL} - PG_{Lin}$ of the $PG_{NL}$ of the investigated nonlinear methods and the static linear predictor $PG_{Lin}$ assessed for the /e:/ phoneme for one tap (1T) to three taps (3T), (b) $\Delta PG = PG_{NL} - PG_{Lin}$ for NWKR 1T to NWKR 3T assessed for the /e:/ phoneme across subjects, (c) $\Delta PG = PG_{NWKR} - PG_{RBF}$ between the PG of the NWKR and the RBF and (d) number of taps required by a static linear predictor (LP) to obtain the same PG as achieved by the NWKR 2T and NWKR 3T, respectively. The search was limited to a maximum of 100 taps.
  • ...and 4 more figures