Finding label errors in an image dataset

Confident learning#

Northcutt, Jiang and Chuang (2021), Confident Learning: Estimating Uncertainty in Dataset Labels (JAIR), formalise this. Let $\tilde{y}$ be the observed (noisy) label and $y^$ the latent true label. Assume class-conditional noise, so $p(\tilde{y} = i \mid y^ = j, \mathbf{x}) = p(\tilde{y} = i \mid y^* = j)$: the corruption depends on the true class, not on the image.

Define a per-class threshold as the average self-confidence of the examples carrying that label:

$$ t_j = \frac{1}{|\mathbf{X}{\tilde{y}=j}|} \sum{\mathbf{x} \in \mathbf{X}_{\tilde{y}=j}} \hat{p}(\tilde{y} = j; \mathbf{x}, \boldsymbol{\theta}) $$

Then build the confident joint $C_{\tilde{y}, y^*}$. It counts examples labelled $i$ whose predicted probability for class $j$ exceeds $t_j$:

$$ C_{\tilde{y}=i,\, y^*=j} = \left| \left{ \mathbf{x} \in \mathbf{X}_{\tilde{y}=i} : \hat{p}(\tilde{y}=j; \mathbf{x}, \boldsymbol{\theta}) \ge t_j,\; j = \arg\max_{k:\, \hat{p}(\tilde{y}=k) \ge t_k} \hat{p}(\tilde{y}=k; \mathbf{x}, \boldsymbol{\theta}) \right} \right| $$

Normalising gives an estimate of the joint distribution $\hat{Q}_{\tilde{y}, y^*}$. The off-diagonal mass estimates the number of errors in each direction.

Two properties make this useful in practice. The per-class thresholds handle class-conditional calibration error. A model underconfident on a hard class does not have that whole class flagged. And the paper proves exact estimation of the joint under perfect model calibration. It adds consistency results under bounded calibration error. The method degrades gracefully rather than failing.

The prevalence of the problem#

Northcutt, Athalye and Mueller (2021) applied this to the test sets of ten widely used benchmarks. They validated the flagged items with Mechanical Turk. Their paper is Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks. They estimate an average of 3.3 percent errors. ImageNet validation sits at about 5.8 percent, and QuickDraw at about 10.1 percent.

The consequential finding is not the error rate but its effect on ranking. On ImageNet and QuickDraw, correcting the test labels reverses the ordering of model families. Higher-capacity models that scored better on the original labels score worse on the corrected ones. Their extra capacity fit the systematic noise. Their conclusion is uncomfortable and well supported. Practitioners may be better served by lower-capacity models, on real-world datasets with noisy labels.

The implication for benchmark reading is direct. Take a reported gap of one to two percentage points. On a test set with three percent label error, it measures nothing.

Alternative signals#

Confident learning uses predicted probabilities. Several other signals identify mislabelled data, with different cost and different failure modes.

• Loss-based filtering. Small-loss examples are likely clean, since networks fit clean data first. Co-teaching (Han et al., 2018) trains two networks that select small-loss batches for each other. That prevents the self-confirmation single-network filtering suffers.
• Training dynamics. Swayamdipta et al. (2020), Dataset Cartography, plot per-example mean confidence against its variability across epochs. Low-confidence low-variability items are the mislabelled candidates; high-variability items are the genuinely ambiguous ones. This separates two categories that confident learning merges.
• Influence functions. Koh and Liang (2017) estimate each training example's effect on a specific test loss. Principled and expensive, and unstable in deep non-convex models (Basu et al., 2021).
• Area under the margin. Pleiss et al. (2020) rank by the accumulated margin between the assigned logit and the largest other logit. They calibrate the threshold using deliberately mislabelled inserted examples.
• Nearest-neighbour disagreement in embedding space. Cheap, model-agnostic, and it also surfaces near-duplicates carrying different labels.

Dataset Cartography deserves particular attention, because it is the cheapest to add. The data is already being produced during training. And it distinguishes hard-but-correct from mislabelled, exactly the distinction a reviewer needs.

Learning with noisy labels, as an alternative to cleaning#

Where relabelling is impossible, robust training methods exist:

• Robust losses. Mean absolute error is noise-robust but optimises poorly; generalised cross entropy (Zhang and Sabuncu, 2018) interpolates between the two.
• Loss correction. Estimate the noise transition matrix and adjust the loss (Patrini et al., 2017). The confident joint provides such an estimate directly.
• Sample reweighting. Learn per-example weights from a small clean validation set (Ren et al., 2018).
• Early stopping. Deep networks fit clean structure before memorising noise (Arpit et al., 2017). Stopping early is therefore a genuine, if crude, noise-robustness mechanism.

Cleaning and robust training are complementary. Cleaning improves the dataset permanently and for every future model; robust training only helps the current run.

Reporting standard#

Any claim that a dataset was cleaned should state five things. The model and cross-validation scheme used to produce out-of-sample probabilities. The flagging rule and its parameters. How many flagged items were reviewed by a human, and by how many reviewers. The outcome breakdown into corrected, deleted and confirmed-correct. And the evaluation protocol: whether the test set was cleaned, and whether historical numbers were recomputed.

Without the last item, before-and-after accuracy comparisons are not interpretable.

References#

• Arpit et al., A Closer Look at Memorization in Deep Networks, 2017 — arxiv.org/abs/1706.05394
• Koh and Liang, Understanding Black-box Predictions via Influence Functions, 2017 — arxiv.org/abs/1703.04730
• Patrini et al., Making Deep Neural Networks Robust to Label Noise, 2017 — arxiv.org/abs/1609.03683
• Han et al., Co-teaching, 2018 — arxiv.org/abs/1804.06872
• Pleiss et al., Identifying Mislabeled Data using the Area Under the Margin Ranking, 2020 — arxiv.org/abs/2001.10528
• Swayamdipta et al., Dataset Cartography, 2020 — arxiv.org/abs/2009.10795
• Northcutt et al., Confident Learning: Estimating Uncertainty in Dataset Labels, JAIR 2021 — arxiv.org/abs/1911.00068
• Northcutt et al., Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks, 2021 — arxiv.org/abs/2103.14749

What to learn next#

• Active learning for labelling — choosing which images to label next, with the same machinery.
• Data leakage in image splits — the other way a test set stops measuring anything.
• Model evaluation — what a corrupted answer key does to every metric.