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Q&A Label Learning

Kota Kawamoto, Masato Uchida

TL;DR

This work introduces Q&A labeling, a practical annotation paradigm where a question generator selects a subset of classes and an annotator answers to assign labels, enabling labeling even when ordinary class labels are hard to identify. It formalizes two procedures, which-one-type and is-in-type, and derives explicit label-generative models that link to existing candidate/complementary-label frameworks, ensuring theoretical compatibility. A corresponding loss function and an upper bound on classification error demonstrate statistical consistency for learning from QA-labeled data, with generalization guarantees via Rademacher complexity. Empirical validation on MNIST-family datasets confirms that increasing the number of QA items improves discriminative performance in line with the theory, supporting the method’s practical viability for challenging annotation tasks.

Abstract

Assigning labels to instances is crucial for supervised machine learning. In this paper, we proposed a novel annotation method called Q&A labeling, which involves a question generator that asks questions about the labels of the instances to be assigned, and an annotator who answers the questions and assigns the corresponding labels to the instances. We derived a generative model of labels assigned according to two different Q&A labeling procedures that differ in the way questions are asked and answered. We showed that, in both procedures, the derived model is partially consistent with that assumed in previous studies. The main distinction of this study from previous studies lies in the fact that the label generative model was not assumed, but rather derived based on the definition of a specific annotation method, Q&A labeling. We also derived a loss function to evaluate the classification risk of ordinary supervised machine learning using instances assigned Q&A labels and evaluated the upper bound of the classification error. The results indicate statistical consistency in learning with Q&A labels.

Q&A Label Learning

TL;DR

This work introduces Q&A labeling, a practical annotation paradigm where a question generator selects a subset of classes and an annotator answers to assign labels, enabling labeling even when ordinary class labels are hard to identify. It formalizes two procedures, which-one-type and is-in-type, and derives explicit label-generative models that link to existing candidate/complementary-label frameworks, ensuring theoretical compatibility. A corresponding loss function and an upper bound on classification error demonstrate statistical consistency for learning from QA-labeled data, with generalization guarantees via Rademacher complexity. Empirical validation on MNIST-family datasets confirms that increasing the number of QA items improves discriminative performance in line with the theory, supporting the method’s practical viability for challenging annotation tasks.

Abstract

Assigning labels to instances is crucial for supervised machine learning. In this paper, we proposed a novel annotation method called Q&A labeling, which involves a question generator that asks questions about the labels of the instances to be assigned, and an annotator who answers the questions and assigns the corresponding labels to the instances. We derived a generative model of labels assigned according to two different Q&A labeling procedures that differ in the way questions are asked and answered. We showed that, in both procedures, the derived model is partially consistent with that assumed in previous studies. The main distinction of this study from previous studies lies in the fact that the label generative model was not assumed, but rather derived based on the definition of a specific annotation method, Q&A labeling. We also derived a loss function to evaluate the classification risk of ordinary supervised machine learning using instances assigned Q&A labels and evaluated the upper bound of the classification error. The results indicate statistical consistency in learning with Q&A labels.
Paper Structure (18 sections, 14 theorems, 75 equations, 2 figures, 1 table)

This paper contains 18 sections, 14 theorems, 75 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary
  4. Multiclass Classification with Ordinary Labels
  5. Generative Model of Candidate Labels
  6. Receiver's Perspective of Candidate Labels
  7. Formulation of Q&A Labeling
  8. Procedure of Q$\&$A Labeling
  9. Which-one-type Q&A Labeling
  10. Is-in-type Q$\&$A Labeling
  11. Analysis
  12. Which-one-type Q&A Labeling
  13. Is-in-type Q&A Labeling
  14. Experiment
  15. Generation of Datasets
  16. ...and 3 more sections

Key Result

Theorem 1

When assigning a label to an instance $x$ using the which-one-type Q$\&$A labeling, the probability that the assigned label is $\tilde{y}$ is given as follows:

Figures (2)

  • Figure 1: Process of executing the Q$\&$A labeling.
  • Figure 2: The average and standard deviation of the classification accuracy on the test data for a 10-class classifier trained on instances labeled with different types of Q&A labeling and a varying number of question items $I$. The colors indicate the number of question items in the Q&A labeling used to label each instance in the training data. The vertical axis is shown on a logarithmic scale.

Theorems & Definitions (18)

  • Theorem 1
  • Corollary 1
  • Theorem 2
  • Corollary 2
  • Theorem 3
  • Lemma 1
  • Theorem 4
  • Theorem 5
  • Lemma 2
  • Theorem 6
  • ...and 8 more