This post overviews the paper Confident Learning: Estimating Uncertainty in Dataset Labels authored by Curtis G. Northcutt, Lu Jiang, and Isaac L. Chuang.

If you’ve ever used datasets like CIFAR, MNIST, ImageNet, or IMDB, you likely assumed the class labels are correct. Surprise: there are likely at least 100,000 label issues in ImageNet. Why did we not know this sooner? Principled approaches for characterizing and finding label errors in massive datasets is challenging and solutions are limited.

In this post, I discuss an emerging, principled framework to identify label errors, characterize label noise, and learn with noisy labels known as confident learning (CL), open-sourced as the cleanlab Python package.

cleanlab is a framework for machine learning and deep learning with label errors like how PyTorch is a framework for deep learning. Learn more in the cleanlab documentation.
cleanlab + the confidentlearning-reproduce repo reproduce results in the CL paper.

The figure above shows examples of label errors in the 2012 ILSVRC ImageNet training set found using confident learning. For interpretability, we group label issues found in ImageNet using CL into three categories:

1. Multi-label images (blue) have more than one label in the image.
2. Ontological issues (green) comprise is-a (bathtub labeled tub) or has-a (oscilloscope labeled CRT screen) relationships. In these cases, the dataset should include one of the classes.
3. Label errors (red) occur when a class exists in the dataset that is more appropriate for an example than its given class label.

Using confident learning, we can find label errors in any dataset using any appropriate model for that dataset. Here are three other real-world examples in common datasets.

## What is Confident Learning?

Confident learning (CL) has emerged as a subfield within supervised learning and weak-supervision to:

• characterize label noise
• find label errors
• learn with noisy labels
• find ontological issues

CL is based on the principles of pruning noisy data (as opposed to fixing label errors or modifying the loss function), counting to estimate noise (as opposed to jointly learning noise rates during training), and ranking examples to train with confidence (as opposed to weighting by exact probabilities). Here, we generalize CL, building on the assumption of Angluin and Laird’s classification noise process , to directly estimate the joint distribution between noisy (given) labels and uncorrupted (unknown) labels.

From the figure above, we see that CL requires two inputs:

• out-of-sample predicted probabilities (matrix size: # of examples by # of classes)
• noisy labels (vector length: number of examples)

For the purpose of weak supervision, CL consists of three steps:

1. Estimate the joint distribution of given, noisy labels and latent (unknown) uncorrupted labels to fully characterize class-conditional label noise.
2. Find and prune noisy examples with label issues.
3. Train with errors removed, re-weighting examples by the estimated latent prior.

### Benefits of Confident Learning

Unlike most machine learning approaches, confident learning requires no hyperparameters. We use cross-validation to obtain predicted probabilities out-of-sample. Confident learning features a number of other benefits. CL

• directly estimates the joint distribution of noisy and true labels
• works for multi-class datasets
• finds the label errors (errors are ordered from most likely to least likely)
• is non-iterative (finding training label errors in ImageNet takes 3 minutes)
• is theoretically justified (realistic conditions exactly find label errors and consistent estimation of the joint distribution)
• does not assume randomly uniform label noise (often unrealistic in practice)
• only requires predicted probabilities and noisy labels (any model can be used)
• does not require any true (guaranteed uncorrupted) labels
• extends naturally to multi-label datasets
• is free and open-sourced as the cleanlab Python package for characterizing, finding, and learning with label errors.

### The Principles of Confident Learning

CL builds on principles developed across the literature dealing with noisy labels:

## Theoretical Findings in Confident Learning

For full coverage of CL algorithms, theory, and proofs, please read our paper. Here, I summarize the main ideas.

Theoretically, we show realistic conditions where CL (Theorem 2: General Per-Example Robustness) exactly finds label errors and consistently estimates the joint distribution of noisy and true labels. Our conditions allow for error in predicted probabilities for every example and every class.

## How does Confident Learning Work?

To understand how CL works, let’s imagine we have a dataset with images of dogs, foxes, and cows. CL works by estimating the joint distribution of noisy and true labels (the Q matrix on the right in the figure below).

Continuing with our example, CL counts 100 images labeled dog with high probability of belonging to class dog, shown by the C matrix in the left of the figure above. CL also counts 56 images labeled fox with high probability of belonging to class dog and 32 images labeled cow with high probability of belonging to class dog.

For the mathematically curious, this counting process takes the following form.

While we encourage reading our paper for an explanation of notation, the central idea is that when the predicted probability of an example is greater than a per-class-threshold, we confidently count that example as actually belonging to that threshold’s class. The thresholds for each class are the average predicted probability of examples in that class. This form of thresholding generalizes well-known robustness results in PU Learning (Elkan & Noto, 2008) to multi-class weak supervision.

### Find label issues using the joint distribution of label noise

From the matrix on the right in the figure above, to estimate label issues:

1. Multiply the joint distribution matrix by the number of examples. Let’s assume 100 examples in our dataset. So, by the figure above (Q matrix on the right), there are 10 images labeled dog that are actually images of foxes.
2. Mark the 10 images labeled dog with largest probability of belonging to class fox as label issues.
3. Repeat for all non-diagonal entries in the matrix.

Note: this simplifies the methods used in our paper, but captures the essence.

## Practical Applications of Confident Learning

#### CL Improves State-of-the-Art in Learning with Noisy Labels by over 10% on average and by over 30% in high noise and high sparsity regimes

The table above shows a comparison of CL versus recent state-of-the-art approaches for multiclass learning with noisy labels on CIFAR-10. At high sparsity (see next paragraph) and 40% and 70% label noise, CL outperforms Google’s top-performing MentorNet, Co-Teaching, and Facebook Research’s Mix-up by over 30%. Prior to confident learning, improvements on this benchmark were significantly smaller (on the order of a few percentage points).

Sparsity (the fraction of zeros in Q) encapsulates the notion that real-world datasets like ImageNet have classes that are unlikely to be mislabeled as other classes, e.g. p(tiger,oscilloscope) ~ 0 in Q. Shown by the highlighted cells in the table above, CL exhibits significantly increased robustness to sparsity compared to state-of-the-art methods like Mixup, MentorNet, SCE-loss, and Co-Teaching. This robustness comes from directly modeling Q, the joint distribution of noisy and true labels.

#### Training on ImageNet cleaned with CL Improves ResNet Test Accuracy

In the figure above, each point on the line for each method, from left to right, depicts the accuracy of training with 20%, 40%…, 100% of estimated label errors removed. The black dotted line depicts accuracy when training with all examples. Observe increased ResNet validation accuracy using CL to train on a cleaned ImageNet train set (no synthetic noise added) when less than 100k training examples are removed. When over 100k training examples are removed, observe the relative improvement using CL versus random removal, shown by the red dash-dotted line.

#### Good Characterization of Label Noise in CIFAR with Added Label Noise

The figure above shows CL estimation of the joint distribution of label noise for CIFAR with 40% added label noise. Observe how close the CL estimate in (b) is to the true distribution in (a) and the low error of the absolute difference of every entry in the matrix in (c). Probabilities are scaled up by 100.

#### Automatic Discovery of Onotological (Class-Naming) Issues in ImageNet

CL automatically discovers ontological issues of classes in a dataset by estimating the joint distribution of label noise directly. In the table above, we show the largest off diagonals in our estimate of the joint distribution of label noise for ImageNet, a single-class dataset. Each row lists the noisy label, true label, image id, counts, and joint probability. Because these are off-diagonals, the noisy class and true class must be different, but in row 7, we see ImageNet actually has two different classes that are both called maillot. Also observe the existence of misnomers: projectile and missile in row 1, is-a relationships: bathtub is a tub in row 2, and issues caused by words with multiple definitions: corn and ear in row 9.

## Final Thoughts

Our theoretical and experimental results emphasize the practical nature of confident learning, e.g. identifying numerous label issues in ImageNet and CIFAR and improving standard ResNet performance by training on a cleaned dataset. Confident learning motivates the need for further understanding of uncertainty estimation in dataset labels, methods to clean training and test sets, and approaches to identify ontological and label issues in datasets.

## Thanks!

A number of researchers, friends, and colleagues contributed to the development of confident learning. To highlight, Anish Athalye (MIT) and Tailin Wu (MIT) helped with theoretical contributions, Niranjan Subrahmanya (Google) helped with feedback, and Jonas Mueller (Amazon) helped with notation.