On Prediction Using Variable Order Markov Models (1107.0051v1)

Abstract: This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We focus on six prominent prediction algorithms, including Context Tree Weighting (CTW), Prediction by Partial Match (PPM) and Probabilistic Suffix Trees (PSTs). We discuss the properties of these algorithms and compare their performance using real life sequences from three domains: proteins, English text and music pieces. The comparison is made with respect to prediction quality as measured by the average log-loss. We also compare classification algorithms based on these predictors with respect to a number of large protein classification tasks. Our results indicate that a "decomposed" CTW (a variant of the CTW algorithm) and PPM outperform all other algorithms in sequence prediction tasks. Somewhat surprisingly, a different algorithm, which is a modification of the Lempel-Ziv compression algorithm, significantly outperforms all algorithms on the protein classification problems.

• The paper evaluates various VMM algorithms using the average log-loss metric to assess sequence prediction performance over diverse data types.
• It demonstrates that decomposed CTW and PPM excel in text and music prediction while a modified Lempel-Ziv algorithm significantly improves protein classification accuracy.
• Rigorous experiments with training-test splits and cross-validation provide actionable insights for refining VMM approaches in real-world applications.

Insights into Variable Order Markov Models for Sequence Prediction

The paper "On Prediction Using Variable Order Markov Models" by Begleiter, El-Yaniv, and Yona provides an extensive evaluation of prediction algorithms based on Variable Order Markov Models (VMMs), emphasizing their utility for predicting discrete sequences over finite alphabets. The investigation spans across classic sequence domains such as proteins, English text, and musical pieces.

The researchers evaluate six prominent prediction algorithms including Context Tree Weighting (CTW), Prediction by Partial Match (PPM), and Probabilistic Suffix Trees (PSTs). The analysis is based on the average log-loss criterion, a metric that quantifies the quality of probabilistic predictions, directly relating to compression efficiency.

Key Findings and Numerical Results

1. Algorithm Performance: The decomposed CTW and PPM algorithms demonstrated superior performance in sequence prediction across the studied domains. In sequence prediction tasks, these algorithms consistently showed the lowest average log-loss, indicating their robustness and ability to generalize across various sequence types.
2. Protein Classification: Surprisingly, a modified version of the Lempel-Ziv compression algorithm outperformed the other algorithms in protein classification. This modified algorithm achieved significant accuracy in classifying protein sequences into predefined groups, highlighting its potential effectiveness for applications in computational biology.
3. Experimental Setup and Data: The authors employed a rigorous experimental setup, utilizing a training-test split and multiple datasets to evaluate each algorithm’s prediction quality. Training data comprised half of the sequence, with predictions made on the remaining half. A cross-validation technique was utilized to fine-tune algorithm parameters, ensuring robust results.
4. Domain-Specific Insights: The paper revealed domain-specific behavior among algorithms. For example, while decomposed CTW and PPM excelled in text and music prediction, protein sequence prediction proved challenging for all algorithms. Intriguingly, protein sequence prediction using trivial background models showed comparable or better performance, suggesting a possible lack of structured information in typical protein sequences.

Implications and Theoretical Insights

The findings underscore the importance of selecting appropriate models based on the sequence domain, highlighting that no single algorithm universally outperforms others across all types of data. The unexpected success of a modified Lempel-Ziv algorithm in protein classification suggests potential in reevaluating traditional compression-based approaches for biological data.

Theoretically, the results emphasize the need for further refinement of VMMs, particularly regarding adaptive escape mechanisms and efficient handling of large alphabets. The contrast between prediction accuracy and compression efficiency for certain sequences provides insights into challenges faced when dealing with real-world, non-stationary data sources.

Future Developments and Speculations

Future research could explore combining these prediction techniques with modern ensemble methods, potentially optimizing prediction weights dynamically to leverage the strengths of each algorithm in specific contexts. Additionally, the integration of domain-specific knowledge or hybrid models, drawing inspiration from machine learning advancements, could further enhance prediction accuracy for intricate biological and linguistic sequences.

Furthermore, developing theoretical bounds for algorithms like the PPM scheme could provide deeper insights into their optimal configurations and potential performance enhancements.

In conclusion, this comprehensive evaluation of VMM-based prediction algorithms reinforces their significance in sequence prediction and compression while highlighting areas for continued research and potential application, especially within computational biology and text analysis.