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

2026-01-14

AI Summary

This study investigates the model-agnostic, theoretically achievable prediction gain in short-term speech prediction to inform the design of efficient predictive encoders. By combining Nadaraya–Watson kernel regression with information-theoretic upper-bound analysis, the authors quantify—for the first time on a newly collected continuous speech dataset—the performance gap between linear and nonlinear predictors. The results reveal that in unvoiced regions, linear predictors nearly attain the theoretical limit (within ≤0.3 dB), whereas in voiced regions, nonlinear predictors with more than two taps yield substantial gains of 2–6 dB, with pronounced inter-speaker variability. This work establishes a theoretical benchmark and offers practical guidance for speech predictive modeling.

Technology Category

• Machine Learning: Kernel Methods
• Natural Language Processing: Speech
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• prediction gain
• speech prediction
• linear predictor
• voiced speech
• unvoiced speech

Innovation

• prediction gain
• Nadaraya-Watson kernel regression
• predictive coding
• speech signal
• information-theoretic bound