# Evaluating State-of-the-Art Classification Models Against Bayes Optimality

@inproceedings{Theisen2021EvaluatingSC, title={Evaluating State-of-the-Art Classification Models Against Bayes Optimality}, author={Ryan Theisen and Huan Wang and Lav R. Varshney and Caiming Xiong and Richard Socher}, booktitle={NeurIPS}, year={2021} }

Evaluating the inherent difficulty of a given data-driven classification problem is important for establishing absolute benchmarks and evaluating progress in the field. To this end, a natural quantity to consider is the Bayes error, which measures the optimal classification error theoretically achievable for a given data distribution. While generally an intractable quantity, we show that we can compute the exact Bayes error of generative models learned using normalizing flows. Our technique…

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## References

SHOWING 1-10 OF 40 REFERENCES

### Learning to Benchmark: Determining Best Achievable Misclassification Error from Training Data

- Computer ScienceArXiv
- 2019

This work proposes a benchmark learner based on an ensemble of $\epsilon$-ball estimators and Chebyshev approximation that achieves an optimal (parametric) mean squared error (MSE) rate of $O(N^{-1})$, where $N$ is the number of samples.

### Meta learning of bounds on the Bayes classifier error

- Computer Science2015 IEEE Signal Processing and Signal Processing Education Workshop (SP/SPE)
- 2015

This work estimates multiple bounds on the Bayes error using an estimator that applies meta learning to slowly converging plug-in estimators to obtain the parametric convergence rate.

### Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means

- Computer SciencePattern Recognit. Lett.
- 2014

### Understanding the Limitations of Conditional Generative Models

- Computer ScienceICLR
- 2020

The theoretical result reveals that it is impossible to guarantee detectability of adversarially-perturbed inputs even for near-optimal generative classifiers, and the results indicate that likelihood-based conditional generative models may are surprisingly ineffective for robust classification.

### Sharpness-Aware Minimization for Efficiently Improving Generalization

- Computer ScienceICLR
- 2021

This work introduces a novel, effective procedure for simultaneously minimizing loss value and loss sharpness, Sharpness-Aware Minimization (SAM), which improves model generalization across a variety of benchmark datasets and models, yielding novel state-of-the-art performance for several.

### Multivariate f-divergence Estimation With Confidence

- Computer Science, MathematicsNIPS
- 2014

This work establishes the asymptotic normality of a recently proposed ensemble estimator of f-divergence between two distributions from a finite number of samples, which has MSE convergence rate of O (1/T), is simple to implement, and performs well in high dimensions.

### Ensemble Estimation of Information Divergence †

- Computer Science, MathematicsEntropy
- 2018

An empirical estimator of Rényi-α divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions and is shown to be robust to the choice of tuning parameters.

### DIME: An Information-Theoretic Difficulty Measure for AI Datasets

- Computer Science
- 2019

This work proposes DIME, an information-theoretic DIfficulty MEasure for datasets, based on Fano’s inequality and a neural network estimation of the conditional entropy of the sample-label distribution, which can be decomposed into components attributable to the data distribution and the number of samples.

### Normalizing Flows for Probabilistic Modeling and Inference

- Computer ScienceJ. Mach. Learn. Res.
- 2021

This review places special emphasis on the fundamental principles of flow design, and discusses foundational topics such as expressive power and computational trade-offs, and summarizes the use of flows for tasks such as generative modeling, approximate inference, and supervised learning.

### Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions

- Computer ScienceUAI
- 2011

Estimation algorithms are presented, how to apply them for machine learning tasks on distributions are described, and empirical results on synthetic data, real word images, and astronomical data sets are shown.