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Pool-Based Sequential Active Learning for Regression

Dongrui Wu

arXiv:1805.04735v1cs.LGstat.ML

TL;DR

Pool-based sequential active learning for regression has relatively few applicable approaches, despite the labeling effort active learning aims to reduce. The paper proposes criteria and a sampling approach that combines representativeness and diversity, and reports effective results across 11 public datasets, with integrations generally outperforming their component approaches.

  • Problem

    Although active learning can reduce costly labeling effort, most existing approaches target classification and only a few apply to pool-based sequential regression.

    Source: §I · p. 1

  • Method

    The paper proposes informativeness, representativeness, and diversity as criteria, then develops RD to use representativeness and diversity during initialization and subsequent iterations.

    Source: §I · p. 1, §V · p. 10

  • Results

    Across 11 public datasets, the proposed approaches were effective, and RD integrations with QBC, EMCM, and GS generally outperformed the individual approaches.

    Source: E. Experimental Results · p. 7, §V · p. 11

  • Takeaways & Limitations

    RD can be integrated with existing pool-based sequential regression approaches, including QBC, EMCM, and GS, to further improve performance.

    Source: §V · p. 10

Abstract

from arXiv · show

Active learning is a machine learning approach for reducing the data labeling effort. Given a pool of unlabeled samples, it tries to select the most useful ones to label so that a model built from them can achieve the best possible performance. This paper focuses on pool-based sequential active learning for regression (ALR). We first propose three essential criteria that an ALR approach should consider in selecting the most useful unlabeled samples: informativeness, representativeness, and diversity, and compare four existing ALR approaches against them. We then propose a new ALR approach using passive sampling, which considers both the representativeness and the diversity in both the initialization and subsequent iterations. Remarkably, this approach can also be integrated with other existing ALR approaches in the literature to further improve the performance. Extensive experiments on 11 UCI, CMU StatLib, and UFL Media Core datasets from various domains verified the effectiveness of our proposed ALR approaches.

I. INTRODUCTION

The paper addresses the scarcity of pool-based sequential active learning methods for regression, where labeling can be costly, and proposes criteria and approaches for selecting useful samples. It also frames the study around reviewing existing approaches and enhancing their performance.

I. INTRODUCTION

  • Pool-based active learning selects unlabeled samples for labeling, while sequential active learning queries one sample per iteration and updates the model iteratively.The process stops when a specified criterion, such as a labeling budget or target accuracy, is met.Source: §I · p. 1
  • Only a few existing regression approaches can be used for pool-based sequential active learning, motivating a review of their limitations and ways to improve them.The paper notes that most active-learning methods target classification.Source: §I · p. 1
  • The paper extends informativeness, representativeness, and diversity to regression and proposes a framework and approaches that combine these criteria.The authors report evaluating the approaches across extensive application domains.Source: §I · p. 1

II. EXISTING POOL-BASED SEQUENTIAL ALR APPROACHES

  • The paper introduces criteria for pool-based sequential regression and compares existing approaches against them to identify their limitations.Source: §II · p. 2

A. Three Essential Criteria in ALR

The paper proposes informativeness, representativeness, and diversity as criteria for choosing samples in pool-based sequential regression. It uses these criteria to frame an open design problem and assess QBC.

A. Three Essential Criteria in ALR

  • A useful regression sample should be informative, representative rather than an outlier, and diverse enough to cover the input space.The examples contrast avoiding an isolated point with selecting across clusters.Source: A. Three Essential Criteria in ALR · p. 2
  • Integrating the three criteria for high-performing sequential regression active learning remains an open problem, and batch-mode EBMALR did not perform well when adapted to sequential use.The paper notes that different integration strategies can yield significantly different performance.Source: A. Three Essential Criteria in ALR · p. 2

B. Query-by-Committee (QBC)

  • QBC selects the unlabeled sample on which its committee of learners disagrees most, addressing informativeness but not representativeness or diversity.The regression QBC approach forms a committee of models from labeled data.Source: B. Query-by-Committee (QBC) · pp. 2–3

C. Expected Model Change Maximization (EMCM)

The section describes EMCM and greedy sampling as existing regression active-learning approaches that prioritize different criteria. EMCM uses an informativeness score, whereas greedy sampling selects for diversity.

C. Expected Model Change Maximization (EMCM)

  • EMCM selects the unlabeled sample with the maximum g(x_n), and the paper characterizes it as considering informativeness but not representativeness or diversity.The described EMCM variant is for linear regression.Source: C. Expected Model Change Maximization… · p. 3

D. Greedy Sampling (GS)

  • Greedy sampling selects the unlabeled sample farthest from its nearest labeled sample, considering diversity but not informativeness or representativeness.It uses geometric characteristics in feature space rather than selecting by informativeness from a learned regression model.Source: D. Greedy Sampling (GS) · p. 3

E. Enhanced Batch-Mode ALR (EBMALR)

The section describes EBMALR’s initialization and sequential-selection strategy, then notes a limitation when it is used with batch size one. It also distinguishes optimal experimental design from the heuristic ALR approaches considered here.

E. Enhanced Batch-Mode ALR (EBMALR)

F. Design of Experiments (DOE)

  • Optimal designs provide theoretical criteria for choosing points under specified assumptions and objectives, whereas ALR approaches are generally more heuristic; this paper considers ALR approaches.The section distinguishes screening designs from optimal designs, which investigate interactions and nonlinear responses.Source: F. Design of Experiments (DOE) · p. 3

III. OUR PROPOSED ALR APPROACHES

The proposed RD approach combines representativeness and diversity in initialization and subsequent selections; it can also be integrated with informativeness-based approaches. Its clustering strategy selects representatives across the input space.

III. OUR PROPOSED ALR APPROACHES

  • RD combines representativeness and diversity in both its initial sample selection and later iterations.The paper also proposes integrating RD with QBC, EMCM, or GS to include informativeness.Source: A. The Basic RD ALR Approach · p. 4, §III · p. 4

A. The Basic RD ALR Approach

  • For initialization, k-means uses k = d and selects the sample closest to each cluster centroid; the approach assumes d is small.The paper notes that ridge regression or LASSO could allow fewer than d initial samples, but uses d for simplicity.Source: A. The Basic RD ALR Approach · p. 4
  • The initial picks represent their clusters, while the d clusters cover the input space and provide diversity.The paper situates clustering-based initialization among related classification approaches and notes no prior pool-based sequential ALR approach used clustering for both initialization and later selections.Source: A. The Basic RD ALR Approach · p. 4
  • In each later iteration, RD clusters all samples into d + 1 groups and selects the centroid-nearest sample from the largest cluster without a labeled sample.That cluster differs from clusters containing labeled samples, which the paper says also ensures diversity.Source: A. The Basic RD ALR Approach · p. 4
  • RD uses passive sampling, so its selections do not require updating or evaluating a regression model at each iteration.The approach is therefore independent of the regression model.Source: A. The Basic RD ALR Approach · p. 4

B. Integrate RD with QBC, EMCM, and GS

RD can be integrated with QBC, EMCM, or GS by restricting their selection to a large unlabeled cluster. This combines cluster-based representativeness and diversity with the integrated method’s selection criterion.

B. Integrate RD with QBC, EMCM, and GS

  • Each integrated approach uses RD initialization, then selects within the largest cluster that contains no labeled sample.The options pair cluster restriction with centroid-nearest selection, QBC, EMCM, or GS.Source: B. Integrate RD with QBC, EMCM, and GS · pp. 4–5
  • QBC, EMCM, and GS choose within that cluster instead of selecting its centroid-nearest sample, adding their respective informativeness or diversity criteria.The authors expect QBC- or EMCM-integrated RD to outperform basic RD because the selection considers all three criteria.Source: B. Integrate RD with QBC, EMCM, and GS · p. 5

C. Differences from EBMALR

The paper distinguishes its sequential ALR approach from EBMALR and describes experiments across 11 regression datasets from varied application domains. The supplied passages state the comparison scope, but not experimental outcomes.

C. Differences from EBMALR

  • Unlike EBMALR’s batch setting, this paper studies sequential ALR, where batch size one prevents EBMALR from considering diversity among selected samples.The paper also explicitly defines informativeness, representativeness, and diversity, and reports omitting EBMALR’s user-parameter-dependent outlier exclusion because it was not critical in most applications.Source: C. Differences from EBMALR · p. 5

IV. EXPERIMENTS AND RESULTS

  • The experiments compare nine ALR approaches on 11 datasets from varied domains, whereas EBMALR compared five approaches in a brain-computer interface application.The dataset set includes 10 UCI and CMU StatLib datasets and IADS-2 from the University of Florida Media Core.Source: C. Differences from EBMALR · p. 5, A. Datasets · p. 5

A. Datasets

  • IADS-2 contains 167 acoustic emotional stimuli and uses 10 features to estimate continuous arousal.The 10 features were obtained by reducing 76 acoustic features with principal component analysis.Source: A. Datasets · p. 5, Table I · p. 6

B. Algorithms

The study compares nine sample-selection strategies using ridge regression. Its evaluation varies the pool, measures transductive and inductive performance, and treats RMSE as primary and CC as secondary.

B. Algorithms

  • Nine strategies—BL, RD, QBC, RD-QBC, EMCM, EEMCM, RD-EMCM, GS, and RD-GS—use ridge regression with σ = 0.01.The paper chooses ridge regression because few labeled samples make regularization preferable to ordinary linear regression.Source: B. Algorithms · p. 6

C. Evaluation Process

  • For each dataset, the evaluation randomly assigns 80% of samples to a training pool, labels up to 10% of that pool subject to a 20–60-sample bound, and repeats the process 100 times.Inductive evaluation uses the remaining 20%; transductive evaluation uses the training pool.Source: C. Evaluation Process · p. 6

D. Performance Measures

  • The study computes RMSE and CC after each iteration; for transductive evaluation, it scores the full pool using true labels for selected samples and model predictions for the rest.The paper identifies RMSE as primary because ridge regression directly optimizes it, and CC as secondary because it need not track RMSE.Source: D. Performance Measures · pp. 6–7
  • The deterministic methods require varying the pool to study statistical properties; the paper avoids bootstrap sampling because it would introduce duplicate samples.The stated determinism assumes k-means converges to its global optimum.Source: D. Performance Measures · p. 6

E. Experimental Results

Across 11 datasets, the proposed RD approach improved on baseline performance, and combining it with existing methods generally outperformed the individual methods. RD-based combinations ranked among the strongest approaches overall.

E. Experimental Results

  • RD, QBC, EMCM, EEMCM, and GS performed better than BL on almost all datasets.As the number of labeled samples increased, all nine algorithms generally achieved smaller RMSE and larger CC.Source: E. Experimental Results · p. 7
  • RD-QBC, RD-EMCM, and RD-GS generally performed better than their component methods, supporting RD's complementarity with QBC, EMCM, and GS.RD achieved smaller RMSE AUC than BL on 10 of 11 datasets and larger CC AUC on 9 of 11.Source: E. Experimental Results · p. 7
  • RD-EMCM, RD-GS, and RD-QBC ranked among the top three approaches on average for both RMSE and CC across 11 transductive datasets.Table II reports the ranks of the nine approaches across the datasets.Source: Table II · p. 7, E. Experimental Results · p. 7

F. Statistical Analysis

The statistical tests found significant advantages for the RD-based combinations, while visualizations showed more uniform selections and complementary effects from the individual enhancements.

F. Statistical Analysis

  • RD-QBC, RD-EMCM, and RD-GS had statistically significantly better RMSE and CC than the other six approaches; there were no significant differences among the three combinations.All approaches significantly outperformed BL, and RD significantly outperformed QBC, EMCM, and EEMCM on both metrics.Source: F. Statistical Analysis · p. 8, Table III · p. 9

G. Visualization

  • RD-based methods initialized samples more uniformly than random initialization, and their final selections were more uniformly distributed than corresponding QBC, EMCM, and GS selections.On Concrete-CS, BL left a large region unsampled, while QBC, EMCM, and GS sometimes selected boundary points that may be outliers.Source: G. Visualization · p. 9, Figure 4 · p. 9

H. Individual Improvements

  • All three enhancements outperformed BL on most datasets, with initialization helping at small m and iterative enhancements helping as m grew.Combining the enhancements gave RD-EMCM the best performance at both small and large m.Source: H. Individual Improvements · p. 10, Figure 5 · p. 10

I. Inductive Learning Results

The paper reports that its transductive conclusions still hold in inductive learning, then concludes that RD addresses representativeness and diversity and that experiments confirmed its effectiveness.

V. CONCLUSIONS

  • RD selects samples for representativeness and diversity during both initialization and subsequent iterations.Source: §V · p. 10
  • Integrating RD with existing pool-based sequential ALR approaches such as QBC, EMCM, and GS can further improve performance.Source: §V · p. 10

I. Inductive Learning Results

  • In inductive learning, the transductive conclusions still hold; Fig. 7 reports nine algorithms’ RMSE and CC AUCs over 11 datasets, averaged across 100 runs.Source: Figure 7 · p. 10, §I · p. 10

V. CONCLUSIONS

  • Experiments on 11 public datasets from various domains confirmed the effectiveness of the proposed approaches.Source: §V · p. 11
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