Testing for Typicality with Respect to an Ensemble of Learned Distributions

• URL: http://arxiv.org/abs/2011.06041v1
• Date: Wed, 11 Nov 2020 19:47:46 GMT
• Title: Testing for Typicality with Respect to an Ensemble of Learned Distributions
• Authors: Forrest Laine and Claire Tomlin
• Abstract summary: One-sample approaches to the goodness-of-fit problem offer significant computational advantages for online testing. The ability to correctly reject anomalous data in this setting hinges on the accuracy of the model of the base distribution. Existing methods for the one-sample goodness-of-fit problem do not account for the fact that a model of the base distribution is learned. We propose training an ensemble of density models, considering data to be anomalous if the data is anomalous with respect to any member of the ensemble.
• Score: 5.850572971372637
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Methods of performing anomaly detection on high-dimensional data sets are needed, since algorithms which are trained on data are only expected to perform well on data that is similar to the training data. There are theoretical results on the ability to detect if a population of data is likely to come from a known base distribution, which is known as the goodness-of-fit problem. One-sample approaches to this problem offer significant computational advantages for online testing, but require knowing a model of the base distribution. The ability to correctly reject anomalous data in this setting hinges on the accuracy of the model of the base distribution. For high dimensional data, learning an accurate-enough model of the base distribution such that anomaly detection works reliably is very challenging, as many researchers have noted in recent years. Existing methods for the one-sample goodness-of-fit problem do not account for the fact that a model of the base distribution is learned. To address that gap, we offer a theoretically motivated approach to account for the density learning procedure. In particular, we propose training an ensemble of density models, considering data to be anomalous if the data is anomalous with respect to any member of the ensemble. We provide a theoretical justification for this approach, proving first that a test on typicality is a valid approach to the goodness-of-fit problem, and then proving that for a correctly constructed ensemble of models, the intersection of typical sets of the models lies in the interior of the typical set of the base distribution. We present our method in the context of an example on synthetic data in which the effects we consider can easily be seen.

Related papers

• Demystifying amortized causal discovery with transformers [21.058343547918053]
  Supervised learning approaches for causal discovery from observational data often achieve competitive performance. In this work, we investigate CSIvA, a transformer-based model promising to train on synthetic data and transfer to real data. We bridge the gap with existing identifiability theory and show that constraints on the training data distribution implicitly define a prior on the test observations.
  arXiv  Detail & Related papers  (2024-05-27T08:17:49Z)
• Testing for Overfitting [0.0]
  We discuss the overfitting problem and explain why standard and concentration results do not hold for evaluation with training data. We introduce and argue for a hypothesis test by means of which both model performance may be evaluated using training data.
  arXiv  Detail & Related papers  (2023-05-09T22:49:55Z)
• Conformal prediction for the design problem [72.14982816083297]
  In many real-world deployments of machine learning, we use a prediction algorithm to choose what data to test next. In such settings, there is a distinct type of distribution shift between the training and test data. We introduce a method to quantify predictive uncertainty in such settings.
  arXiv  Detail & Related papers  (2022-02-08T02:59:12Z)
• Leveraging Unlabeled Data to Predict Out-of-Distribution Performance [63.740181251997306]
  Real-world machine learning deployments are characterized by mismatches between the source (training) and target (test) distributions. In this work, we investigate methods for predicting the target domain accuracy using only labeled source data and unlabeled target data. We propose Average Thresholded Confidence (ATC), a practical method that learns a threshold on the model's confidence, predicting accuracy as the fraction of unlabeled examples.
  arXiv  Detail & Related papers  (2022-01-11T23:01:12Z)
• Composite Goodness-of-fit Tests with Kernels [19.744607024807188]
  We propose a kernel-based hypothesis tests for the challenging composite testing problem. Our tests make use of minimum distance estimators based on the maximum mean discrepancy and the kernel Stein discrepancy. As our main result, we show that we are able to estimate the parameter and conduct our test on the same data, while maintaining a correct test level.
  arXiv  Detail & Related papers  (2021-11-19T15:25:06Z)
• Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms [2.266704469122763]
  This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. We establish the existence and well-posedness of the associated posterior moments under easily verifiable conditions. A model accuracy analysis suggests that the Bayesian probability probabilities reported by the data-driven models are also remarkably accurate under a frequentist definition.
  arXiv  Detail & Related papers  (2021-03-18T11:34:08Z)
• Improving Uncertainty Calibration via Prior Augmented Data [56.88185136509654]
  Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. They are often overconfident in their predictions, which leads to inaccurate and miscalibrated probabilistic predictions. We propose a solution by seeking out regions of feature space where the model is unjustifiably overconfident, and conditionally raising the entropy of those predictions towards that of the prior distribution of the labels.
  arXiv  Detail & Related papers  (2021-02-22T07:02:37Z)
• Graph Embedding with Data Uncertainty [113.39838145450007]
  spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. Most subspace learning methods do not take into consideration possible measurement inaccuracies or artifacts that can lead to data with high uncertainty.
  arXiv  Detail & Related papers  (2020-09-01T15:08:23Z)
• Learning while Respecting Privacy and Robustness to Distributional Uncertainties and Adversarial Data [66.78671826743884]
  The distributionally robust optimization framework is considered for training a parametric model. The objective is to endow the trained model with robustness against adversarially manipulated input data. Proposed algorithms offer robustness with little overhead.
  arXiv  Detail & Related papers  (2020-07-07T18:25:25Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.