Source-linked AI summary
Learning with Bounded Instance- and Label-dependent Label Noise
Jiacheng Cheng, Tongliang Liu, Kotagiri Ramamohanarao, Dacheng Tao
TL;DR
The paper addresses the limited theoretical treatment of realistic instance- and label-dependent noise by focusing on BILN. It introduces distilled examples, builds a learning algorithm with consistency and performance guarantees, and reports effectiveness on synthetic and real-world datasets. The analysis assumes a bounded-noise condition, while importance reweighting is presented as a practical correction whose computational cost may matter.
Problem
Instance- and label-dependent noise is realistic but has received limited study, and prior work on realistic label noise lacked theoretical robustness guarantees.
Method
The paper introduces distilled examples and uses them to construct a learning algorithm for BILN with theoretical guarantees.
Results
The algorithm is statistically consistent, has a performance bound, and is effective on synthetic and real-world datasets.
Takeaways & Limitations
Under the paper’s conditions, classifiers learned from distilled examples converge to the Bayes-optimal classifier, supporting robust learning under BILN.
Takeaways & Limitations
The analysis uses a bounded-noise assumption, and the importance-reweighting procedure may have concerning time complexity.
Abstract
from arXiv · showhide
Instance- and Label-dependent label Noise (ILN) widely exists in real-world datasets but has been rarely studied. In this paper, we focus on Bounded Instance- and Label-dependent label Noise (BILN), a particular case of ILN where the label noise rates -- the probabilities that the true labels of examples flip into the corrupted ones -- have upper bound less than $1$. Specifically, we introduce the concept of distilled examples, i.e. examples whose labels are identical with the labels assigned for them by the Bayes optimal classifier, and prove that under certain conditions classifiers learnt on distilled examples will converge to the Bayes optimal classifier. Inspired by the idea of learning with distilled examples, we then propose a learning algorithm with theoretical guarantees for its robustness to BILN. At last, empirical evaluations on both synthetic and real-world datasets show effectiveness of our algorithm in learning with BILN.
1. Introduction
Real-world datasets commonly contain label noise, while instance- and label-dependent noise remains relatively understudied. The paper defines BILN, develops a theoretically supported learning algorithm, and evaluates it on synthetic and real-world data.
- Motivation: Label noise arises from inexpensive data collection and human perceptual errors, and can undermine machine-learning performance.The paper motivates robust learning because noisy labels are widespread in real-world datasets.
- Noise models: ILN allows each flip rate ρ_y(x) to depend on both the instance and its true label, making it more realistic than RCN or CCN.The paper notes that lower-quality or less informative instances may be more prone to incorrect labels.
- Contribution: BILN bounds instance- and label-dependent noise rates by values smaller than 1.The paper focuses on this bounded case of ILN and proposes a dedicated learning algorithm.
- Contribution: The proposed algorithm has statistical consistency and a performance bound, with effectiveness demonstrated on synthetic and real-world datasets.The paper also identifies possible relevance to instance-dependent complementary label learning.
- Research gap: Prior work studied realistic label noise empirically, but did not provide theoretical guarantees for noise robustness.Existing theoretical results mainly addressed more restricted noise settings or specialized assumptions.
2. Problem Setup
The problem setup distinguishes clean and noisy binary-classification distributions and measures prediction through risks and surrogate losses. BILN imposes a bounded-noise condition requiring the combined class-specific rates to remain below one.
- Distributions: The setup uses X for observations, Y for uncorrupted labels, and eY for observed noisy labels sampled from the noisy distribution.D denotes the clean distribution P(X,Y), while Dρ denotes the noisy distribution P(X,eY).
- Learning objective: The goal is to learn f so that g(x)=sgn(f(x)) accurately predicts labels from noisy training pairs.The classifier is evaluated through its 0-1 risk and the Bayes-optimal classifier under the clean distribution.
- Risk minimization: Because minimizing 0-1 risk is NP-hard and its objective is neither convex nor smooth, the setup uses surrogate loss functions.A classification-calibrated loss has a minimizer whose induced classifier also minimizes 0-1 risk.
- Noise models: The noise rate ρ_y(x)=P(eY=−y|X=x,Y=y) captures the probability that a true label y flips at instance x.RCN uses a constant rate, CCN uses label-dependent rates independent of x, and ILN depends on both x and y.
- BILN assumption: BILN assumes 0≤ρ_+1(x)+ρ_−1(x)<1, so noisy and clean labels agree on average for each example.The paper treats this bounded-rate condition as its standing assumption and distinguishes it from the Massart noise model.
3. Learning with BILN
The paper learns under BILN by identifying distilled examples and establishing when learning from them recovers the clean-data Bayes classifier. It then constructs such examples from noisy data, addresses selection bias through active labeling and importance reweighting, and reports empirical effectiveness.
- Learning with Distilled Examples: Distilled examples have labels matching the Bayes optimal classifier under the clean distribution.
- Learning with Distilled Examples: When the distilled and target distributions share the same X-support, their Bayes optimal classifiers coincide.
- Learning with Distilled Examples: Under the stated conditions, empirical-risk minimization on distilled examples is statistically consistent and converges to the clean-data Bayes classifier.
- Collecting Distilled Examples: Using upper bounds on instance-dependent noise rates, the algorithm automatically identifies noisy examples suitable for assigning distilled labels.
- Active Labeling: Automatic collection can exclude regions of the input space, so active labeling is used to restore support coverage and consistency.
- Covariate Shift Correction: Importance reweighting treats the resulting sample-selection problem as covariate shift, while the paper notes that its simplified analysis requires Assumption 2.
- Overall Algorithm: The complete framework is summarized in Algorithm 1, extends to multiclass classification, and performs well with or without known noise-rate bounds.
4. Empirical Evaluations
Experiments on synthetic and real-world datasets compare clean, noisy, automatically distilled, actively labeled, and Algorithm 1 training strategies. The proposed method outperforms baselines, remains effective without known noise-rate bounds, and is robust to the hyperparameter k.
- Synthetic datasets: The procedure combines automatically collected distilled examples with actively labeled examples, assigning greater importance to the actively labeled examples.The figure uses (ρ+1max, ρ-1max, nact)=(0.25, 0.49, 10) and visualizes importance β.
- Synthetic datasets: On synthetic datasets, auto+act significantly outperforms the baseline in average classification accuracy and has smaller standard deviations than noisy and noisy+act.The baseline comparisons use varying bounded noise rates and numbers of actively labeled examples.
- Unknown noise-rate bounds: Figure 2 shows that the algorithm is robust to selecting k across three datasets when the noise-rate bounds are unknown.Each curve is averaged over 1000 trials.
- Unknown noise-rate bounds: Without knowledge of ρ+1max and ρ-1max, Algorithm 1 still outperforms the baseline and is comparable with, or sometimes better than, the known-bound version.The unknown-bound evaluations use k=10 without dataset-specific tuning.
5. Conclusion
The paper addresses BILN with a learning algorithm supported by statistical consistency and a performance bound. Experiments on synthetic and real-world datasets demonstrate effectiveness, while future work considers combining the algorithm with more complicated models such as deep neural networks.
- Conclusion: The paper focuses on BILN and establishes statistical consistency and a performance bound for its proposed learning algorithm.BILN is presented as a more general label-noise setting than those previously well studied.
- Conclusion: Empirical evaluations on synthetic and real-world datasets show the effectiveness of the proposed algorithm.The conclusion summarizes the experimental evidence without specifying a single dataset or metric.
- Conclusion: Future work will combine the algorithm with more complicated models, including deep neural networks, for real-world label-noise tasks.The paper identifies this as a direction for future research.