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Modeling of learning curves with applications to pos tagging

Manuel Vilares Ferro, Victor M. Darriba Bilbao, Francisco J. Ribadas Pena

TL;DR

The paper tackles the problem of reducing training and annotation costs by predicting full learning curves from partial training data in NLP. It introduces an iterative functional framework where partial curves are captured as learning trends driven by an accuracy pattern, with a formal limit function $A_\infty$ and a proximity-based stopping criterion. A key contribution is the proof of uniform convergence of the learning traces to the limit curve and an anchoring mechanism that improves robustness against irregular observations, validated on POS tagging across English and Spanish corpora. The method shows potential to generalize to other ML/NLP tasks such as MT, parsing, and text classification, enabling proactive resource planning and configuration choices without waiting for complete training.

Abstract

An algorithm to estimate the evolution of learning curves on the whole of a training data base, based on the results obtained from a portion and using a functional strategy, is introduced. We approximate iteratively the sought value at the desired time, independently of the learning technique used and once a point in the process, called prediction level, has been passed. The proposal proves to be formally correct with respect to our working hypotheses and includes a reliable proximity condition. This allows the user to fix a convergence threshold with respect to the accuracy finally achievable, which extends the concept of stopping criterion and seems to be effective even in the presence of distorting observations. Our aim is to evaluate the training effort, supporting decision making in order to reduce the need for both human and computational resources during the learning process. The proposal is of interest in at least three operational procedures. The first is the anticipation of accuracy gain, with the purpose of measuring how much work is needed to achieve a certain degree of performance. The second relates the comparison of efficiency between systems at training time, with the objective of completing this task only for the one that best suits our requirements. The prediction of accuracy is also a valuable item of information for customizing systems, since we can estimate in advance the impact of settings on both the performance and the development costs. Using the generation of part-of-speech taggers as an example application, the experimental results are consistent with our expectations.

Modeling of learning curves with applications to pos tagging

TL;DR

The paper tackles the problem of reducing training and annotation costs by predicting full learning curves from partial training data in NLP. It introduces an iterative functional framework where partial curves are captured as learning trends driven by an accuracy pattern, with a formal limit function and a proximity-based stopping criterion. A key contribution is the proof of uniform convergence of the learning traces to the limit curve and an anchoring mechanism that improves robustness against irregular observations, validated on POS tagging across English and Spanish corpora. The method shows potential to generalize to other ML/NLP tasks such as MT, parsing, and text classification, enabling proactive resource planning and configuration choices without waiting for complete training.

Abstract

An algorithm to estimate the evolution of learning curves on the whole of a training data base, based on the results obtained from a portion and using a functional strategy, is introduced. We approximate iteratively the sought value at the desired time, independently of the learning technique used and once a point in the process, called prediction level, has been passed. The proposal proves to be formally correct with respect to our working hypotheses and includes a reliable proximity condition. This allows the user to fix a convergence threshold with respect to the accuracy finally achievable, which extends the concept of stopping criterion and seems to be effective even in the presence of distorting observations. Our aim is to evaluate the training effort, supporting decision making in order to reduce the need for both human and computational resources during the learning process. The proposal is of interest in at least three operational procedures. The first is the anticipation of accuracy gain, with the purpose of measuring how much work is needed to achieve a certain degree of performance. The second relates the comparison of efficiency between systems at training time, with the objective of completing this task only for the one that best suits our requirements. The prediction of accuracy is also a valuable item of information for customizing systems, since we can estimate in advance the impact of settings on both the performance and the development costs. Using the generation of part-of-speech taggers as an example application, the experimental results are consistent with our expectations.
Paper Structure (33 sections, 6 theorems, 19 equations, 9 figures, 4 tables)

This paper contains 33 sections, 6 theorems, 19 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The state of the art
  3. Working on correctness
  4. Working on robustness
  5. An overview for the nlp domain
  6. Our contribution
  7. The formal framework
  8. The mathematical support
  9. The working hypotheses
  10. The notational support
  11. The abstract model
  12. Correctness
  13. Robustness
  14. Irregularities before the working level
  15. Irregularities after the working level
  16. ...and 18 more sections

Key Result

Theorem 1

Let ${\mathcal{A}}^\pi[{\mathcal{D}}^{\mathcal{K}}_{\sigma}]$ be a learning trace, with or without anchors. Then its asymptotic backbone is monotonic and ${\mathcal{A}}_{\infty}^\pi[{\mathcal{D}}^{\mathcal{K}}_{\sigma}] := {\lim \limits_{i \rightarrow \infty}}^u {\mathcal{A}}_{i}^\pi[{\mathcal{D}}^{

Figures (9)

  • Figure 1: Learning curve for the training process of fn tbl on frown corpus, and an accuracy pattern fitting it.
  • Figure 2: Learning trace for the training process of fn tbl on frown, with details in zoom.
  • Figure 5: Working and prediction levels for asymptotic backbones built without and with anchors for fn tbl on frown.
  • Figure 6: mapes and rrs for runs without anchors. dmrs when excluding crossing learning curves along the control sequences.
  • Figure 7: Learning trends, without anchors, for the best and worst mapes.
  • ...and 4 more figures

Theorems & Definitions (18)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Theorem 1
  • Theorem 2
  • Definition 7
  • Theorem 3
  • ...and 8 more