Source-linked AI summary
Decoupling "when to update" from "how to update"
Eran Malach, Shai Shalev-Shwartz
TL;DR
Noisy labels often arise when usable training data are mined from sources created for other purposes, making robust supervised learning difficult. The paper introduces a simple two-classifier meta-algorithm that decouples when to update from how to update, and reports state-of-the-art results with favorable theoretical convergence properties under restricted settings.
Problem
Mining or crowdsourcing labels makes data collection easier but can produce abundant corrupted labels that increasingly misdirect neural-network updates.
Method
The method maintains two predictors and updates them with a base learning rule only on examples where they disagree, making update timing independent of the label.
Results
The method achieves state-of-the-art results and outperforms competing approaches; a perceptron version handles label-noise rates up to 40%.
Takeaways & Limitations
Decoupling update selection from the update rule provides a simple approach for supervised learning with noisy labels.
Takeaways & Limitations
The theoretical analysis is restricted to linearly separable data with random label noise and a perceptron base algorithm, and optimal convergence requires distributional assumptions.
Abstract
from arXiv · showhide
Deep learning requires data. A useful approach to obtain data is to be creative and mine data from various sources, that were created for different purposes. Unfortunately, this approach often leads to noisy labels. In this paper, we propose a meta algorithm for tackling the noisy labels problem. The key idea is to decouple "when to update" from "how to update". We demonstrate the effectiveness of our algorithm by mining data for gender classification by combining the Labeled Faces in the Wild (LFW) face recognition dataset with a textual genderizing service, which leads to a noisy dataset. While our approach is very simple to implement, it leads to state-of-the-art results. We analyze some convergence properties of the proposed algorithm.
1 Introduction
Mining labels from readily available data can make supervised learning scalable, but the resulting noisy labels increasingly misdirect optimization as classifiers improve. The paper proposes separating the decision of when to update from how to update and evaluates the approach on noisy gender-classification data.
- Web-mined and crowdsourced labels make data collection easier but often introduce corruption that can deteriorate performance.
- As classifiers improve, wrongly labeled examples can dominate updates and prevent further improvement.
- The proposed approach decides whether to update using a criterion separate from disagreement with the available label.
- The method is evaluated by assigning gender labels to LFW images through an online name-based genderizing service.
- Better results than similar approaches are obtained on a clean subset, while a perceptron version tolerates label-noise rates up to 40%.
- For the perceptron with constant-probability label flips, expected iterations match the noise-free perceptron up to a constant factor, but solution quality can remain bounded away from zero under some distributions.
2 Related Work
Prior noisy-label methods modify losses, model label corruption, group examples, or preprocess data. The paper positions its disagreement-based method as simpler and distinct in purpose, and reports that it outperforms the selected competitors.
- Existing noisy-label approaches include statistical queries, boosting, bagging, and methods specifically targeting deep-learning resilience.
- Modified-loss methods regularize cross-entropy using current predictions, sometimes increasing the regularization weight during training.
- Probabilistic methods model wrong-label probabilities with the correct label latent, but some require known flip rates, extra layers, or complicated two-phase training.
- Group-based classification reduces the impact of noisy labels by combining correctly and incorrectly labeled examples in an input group.
- Preprocessing methods remove suspected mislabeled instances, whereas this method disregards contaminated instances without a separate preprocessing phase.
- The experiment compares against vanilla training, two bootstrapped cross-entropy variants, and a noise-modeling layer method.
- The proposed method outperformed all selected competing methods while remaining extremely simple to implement.
- Although related to query-by-committee and ensemble methods, the method targets noisy labels rather than reducing label queries and was not previously used for this purpose.
3 Method
The method uses two classifiers and separates update selection from the base learning rule: both classifiers update only on examples where they disagree. Initialization and final classifier selection are left flexible.
- The meta-algorithm uses two base classifiers, a base update rule, and a mini-batch size.
- Update selection is label-independent and depends on disagreement between the two classifiers.
- The paper does not specify a single initialization procedure; random initialization or an earlier conventional-training stage are possible options.
- After optimization, either classifier can be returned, or a clean test set can select the one with better accuracy.
- Each training iteration forms a subset of examples on which the classifiers disagree and applies the base update rule to both classifiers.
4 Theoretical analysis
The theoretical analysis establishes fast convergence for the proposed algorithm under perceptron-based, linearly separable random-label-noise assumptions, while showing that convergence to a good solution requires additional distributional assumptions.
- Scope and assumptions: The analysis restricts attention to linearly separable data corrupted by random label noise, using the perceptron as the base algorithm.The paper states that a full convergence analysis for deep learning is beyond reach even in the noise-free setting.
- Scope and assumptions: The theoretical questions are whether the algorithm converges, how quickly it converges, and whether its limit is optimal.These are presented as the two central questions of the analysis: convergence rate and convergence quality.
- Convergence rate: Theorem 1 shows that the algorithm’s update count exceeds the noise-free vanilla perceptron bound by only a constant factor depending on initialization and noise.The theorem bounds the expected number of updates E[T] using the initial-vector norm and noise-dependent terms.
- Convergence rate: The method’s convergence rate is proved by analyzing noisy-label updates as random label flips and bounding progress through the perceptron update dynamics.The proof rewrites noisy labels as ỹ_t = θ_t y_t and uses the update rule together with upper and lower bounds on alignment with w*.
- Solution quality: Without additional assumptions on the data distribution, convergence to a good solution is impossible to prove, and initialization can determine the outcome.The paper gives examples where the algorithm makes no updates or reaches solutions with error likely to be Ω(µ^3).
- Solution quality: The analysis concludes that fast convergence is established for the perceptron, whereas optimal-solution guarantees require distributional assumptions and extensions beyond linear predictors remain open.The paper identifies practical distributional assumptions and convergence beyond linear predictors as future directions.
5 Experiments
The experiments evaluate the method on noisy gender labels derived from LFW names and compare it with several approaches under two dataset and evaluation scenarios. The method outperforms alternatives in both situations, while combining it with the s-model yields further gains.
- 5.1 Deep Learning: The main experiment applies SGD with momentum to gender classification on LFW images labeled through an external name-based gender service.LFW provides names but not gender labels, so the external service supplies labels with confidence levels.
- 5.1 Deep Learning: The data construction separates 100%-confidence individuals into three equal subsets and groups lower-confidence individuals into N4 and N5.N4 contains confidence in [90%, 100%), while N5 contains confidence below 90%; the sets are disjoint.
- 5.1 Deep Learning: Experiments use each of N1, N2, and N3 as a test set in turn, with training configurations that include lower-confidence data or exclude N5.This produces repeated evaluations across alternative noisy training datasets.
- 5.1 Deep Learning: The evaluation compares vanilla training, soft and hard bootstrapping, the s-model, and the proposed method using the same network architecture.Balanced accuracy is used because the male and female subjects are not equally represented.
- 5.1 Deep Learning: The method outperforms the other methods in both evaluation situations and on both datasets, although gains are smaller on the cleaner dataset.The two situations select either the best iteration using clean test data or the last iteration without clean test data.
- 5.1 Deep Learning: Applying the method on top of the s-model produces even better performance, especially when the data is less noisy.The paper identifies the s-model as the second-best standalone algorithm.
6 Discussion
The paper presents a simple noisy-label approach that separates update timing from the update rule and reports state-of-the-art results. Its theoretical guarantees include fast perceptron convergence, while optimality requires distributional assumptions and remains open beyond linear predictors.
- 6 Discussion: The approach maintains two predictors and updates based on their disagreement, decoupling when to update from how to update.The paper describes this as an extremely simple approach for supervised learning with noisy labels.
- 6 Discussion: The authors report that the simple approach leads to state-of-the-art results.
- 6 Discussion: Theoretical analysis gives a fast convergence rate when the underlying update rule is the perceptron.
- 6 Discussion: Proving convergence to an optimal solution requires distributional assumptions, and extending the convergence proof beyond linear predictors remains open.The paper also identifies practical distributional assumptions and oracle-based convergence guarantees as future directions.
A Proofs
The proofs analyze disagreement-based learning through perceptron coordinates and controlled experiments under random label flips. They derive a coordinate-wise failure mechanism and study its probability using stationary behavior and concentration arguments.
- A Proofs: A proof construction distributes instances uniformly over standard basis vectors and compares two initial predictors against a target vector.For a coordinate where both predictors agree incorrectly, that coordinate is never updated and remains wrong.
- A Proofs: The resulting error is lower bounded by a sum of independent Bernoulli variables with success probability 1/4.Chernoff’s inequality is then used to obtain a high-probability error bound.
- A Proofs: For a perceptron coordinate, the value remains in {−1, 0, 1} and evolves as a Markov chain with a stationary distribution.The proof uses this stationary behavior to analyze failure under label noise.
- A Proofs: When both predictors have a zero coordinate and observe a flipped label, the algorithm can fail on that coordinate with probability of order µ^3 for small µ.
- A Proofs: Controlled experiments test the perceptron-based algorithm on synthetic unit-ball data and MNIST with different random label-flip probabilities.Both setups are designed to evaluate behavior across noise levels.
B.1 Linear Classification on Synthetic Data
The synthetic-data experiment evaluates the proposed perceptron-like algorithm under controlled label noise and finds substantially improved noise resilience over the vanilla perceptron.
- Data generation: Synthetic examples are generated from a separating vector in varying dimensions, with labels assigned by the vector’s sign.Vectors are sampled uniformly from the unit ball until |⟨w*, x⟩| ≥ 1.
- Noise model: Labels are corrupted by independently flipping their sign with probability µ < 0.5.
- Results: Five repetitions are averaged for each noise setting, and the proposed algorithm greatly improves the vanilla perceptron’s noise resilience.
B.2 Linear Classification on MNIST Data Noisy Labels
The MNIST experiment compares the proposed algorithm with a regular perceptron on binary digit classification under varying noise rates.
- Experimental setup: The task discriminates between digits 4 and 7 from the MNIST dataset.
- Experimental setup: Performance is tested against the regular perceptron algorithm across various noise levels.
- Evaluation: Both algorithms are trained for 1M iterations, with accuracy evaluated on the MNIST test set every 1000 iterations.
B.3 Deep Learning Detailed Results
The detailed results report best- and last-iteration accuracy for the LFW experiment and compare methods for handling noisy labels.
- Results: The LFW results table reports balanced accuracy at both the best and last training iterations for each noisy-label method.
- Results: The proposed method outperforms alternative methods, while combining it with the s-model produces an even greater improvement.