Distribution Density, Tails, and Outliers in Machine Learning: Metrics and Applications

By Nicholas Carlini, Ú. Erlingsson, Nicolas Papernot. 2019

74 citations recorded by the source corpus.

We develop techniques to quantify the degree to which a given (training or testing) example is an outlier in the underlying distribution. We evaluate five methods to score examples in a dataset by how well-represented the examples are, for different plausible definitions of "well-represented", and apply these to four common datasets: MNIST, Fashion-MNIST, CIFAR-10, and ImageNet. Despite being independent approaches, we find all five are highly correlated, suggesting that the notion of being well-represented can be quantified. Among other uses, we find these methods can be combined to identify (a) prototypical examples (that match human expectations); (b) memorized training examples; and, (c) uncommon submodes of the dataset. Further, we show how we can utilize our metrics to determine an improved ordering for curriculum learning, and impact adversarial robustness. We release all metric values on training and test sets we studied.

Subfields: Artificial Intelligence, Statistics and Probability, Anomaly & Outlier Detection

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

In Anomaly & Outlier Detection

Citations in the corpus

FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence (2020, methodology): “Speciﬁcally, we take the ordering of the CIFAR-10 training set from [4] that sorts examples from those that are most representative to those that are least.”
What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation (2020, background): “[11] consider different ways to measure how “prototypical" each of the data points is according to several metrics and across multiple datasets.”
Interpretable deep learning: interpretation, interpretability, trustworthiness, and beyond (2021, background): “Contributions of Long-Tailed Training Examples Instead of identifying mislabeled samples, easy/difficult-to-learn samples from the training set, more theoretical works on detecting the long-tail examples and outliers [28, 52, 53].”
Unlocking High-Accuracy Differentially Private Image Classification through Scale (2022, background): “…diﬀerentially private training can potentially reduce the accuracy of models on under-represented subgroups in the dataset (Bagdasaryan et al., 2019; Carlini et al., 2019; Suriyakumar et al., 2021; Tran et al., 2021), and therefore deploying any application with DP would require careful…”
Metadata Archaeology: Unearthing Data Subsets by Leveraging Training Dynamics (2022, methodology): “We achieve top-1 accuracies of 93.68% on CIFAR-10, 72.80% on CIFAR-100, and 73.94% on ImageNet.”
Deep Learning Through the Lens of Example Difficulty (2021, background): “There are a number of definitions of example difficulty in the literature (E.g. see Carlini et al. (2019); Hooker et al. (2019); Lalor et al. (2018); Agarwal and Hooker (2020)).”