Robust Bayesian Classification Using an Optimistic Score Ratio
- URL: http://arxiv.org/abs/2007.04458v1
- Date: Wed, 8 Jul 2020 22:25:29 GMT
- Title: Robust Bayesian Classification Using an Optimistic Score Ratio
- Authors: Viet Anh Nguyen and Nian Si and Jose Blanchet
- Abstract summary: We use an optimistic score ratio for robust binary classification when there is limited information on the class-conditional, or contextual, distribution.
The optimistic score searches for the distribution that is most plausible to explain the observed outcomes in the testing sample.
- Score: 18.047694351309204
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We build a Bayesian contextual classification model using an optimistic score
ratio for robust binary classification when there is limited information on the
class-conditional, or contextual, distribution. The optimistic score searches
for the distribution that is most plausible to explain the observed outcomes in
the testing sample among all distributions belonging to the contextual
ambiguity set which is prescribed using a limited structural constraint on the
mean vector and the covariance matrix of the underlying contextual
distribution. We show that the Bayesian classifier using the optimistic score
ratio is conceptually attractive, delivers solid statistical guarantees and is
computationally tractable. We showcase the power of the proposed optimistic
score ratio classifier on both synthetic and empirical data.
Related papers
- Deep Clustering via Probabilistic Ratio-Cut Optimization [0.7366405857677227]
We propose a novel approach for optimizing the graph ratio-cut by modeling the binary assignments as random variables.
We provide an upper bound on the expected ratio-cut, as well as an unbiased estimate of its gradient, to learn the parameters of the assignment variables in an online setting.
arXiv Detail & Related papers (2025-02-05T17:47:53Z) - Conformal Prediction Sets with Improved Conditional Coverage using Trust Scores [52.92618442300405]
It is impossible to achieve exact, distribution-free conditional coverage in finite samples.
We propose an alternative conformal prediction algorithm that targets coverage where it matters most.
arXiv Detail & Related papers (2025-01-17T12:01:56Z) - Optimal Projections for Classification with Naive Bayes [5.953513005270837]
We study the problem of obtaining an alternative basis for the factorisation of class conditional densities.
We formulate the problem as a projection pursuit to find the optimal linear projection on which to perform classification.
We find that the proposed approach substantially outperforms other popular probabilistic discriminant analysis models.
arXiv Detail & Related papers (2024-09-09T14:05:30Z) - Covariate Assisted Entity Ranking with Sparse Intrinsic Scores [3.2839905453386162]
We introduce novel model identification conditions and examine the regularized penalized Maximum Likelihood Estimator statistical rates.
We also apply our method to the goodness-of-fit test for models with no latent intrinsic scores.
arXiv Detail & Related papers (2024-07-09T19:58:54Z) - SimPro: A Simple Probabilistic Framework Towards Realistic Long-Tailed Semi-Supervised Learning [49.94607673097326]
We propose a highly adaptable framework, designated as SimPro, which does not rely on any predefined assumptions about the distribution of unlabeled data.
Our framework, grounded in a probabilistic model, innovatively refines the expectation-maximization algorithm.
Our method showcases consistent state-of-the-art performance across diverse benchmarks and data distribution scenarios.
arXiv Detail & Related papers (2024-02-21T03:39:04Z) - On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates [5.13323375365494]
We provide theoretical guarantees for the convergence behaviour of diffusion-based generative models under strongly log-concave data.
Our class of functions used for score estimation is made of Lipschitz continuous functions avoiding any Lipschitzness assumption on the score function.
This approach yields the best known convergence rate for our sampling algorithm.
arXiv Detail & Related papers (2023-11-22T18:40:45Z) - Variational Classification [51.2541371924591]
We derive a variational objective to train the model, analogous to the evidence lower bound (ELBO) used to train variational auto-encoders.
Treating inputs to the softmax layer as samples of a latent variable, our abstracted perspective reveals a potential inconsistency.
We induce a chosen latent distribution, instead of the implicit assumption found in a standard softmax layer.
arXiv Detail & Related papers (2023-05-17T17:47:19Z) - Characterizing the Optimal 0-1 Loss for Multi-class Classification with
a Test-time Attacker [57.49330031751386]
We find achievable information-theoretic lower bounds on loss in the presence of a test-time attacker for multi-class classifiers on any discrete dataset.
We provide a general framework for finding the optimal 0-1 loss that revolves around the construction of a conflict hypergraph from the data and adversarial constraints.
arXiv Detail & Related papers (2023-02-21T15:17:13Z) - Taming Adversarial Robustness via Abstaining [7.1975923901054575]
We consider a binary classification problem where the observations can be perturbed by an adversary.
We include an abstaining option, where the classifier abstains from taking a decision when it has low confidence about the prediction.
We show that there exist a tradeoff between the two metrics regardless of what method is used to choose the abstaining region.
arXiv Detail & Related papers (2021-04-06T07:36:48Z) - Nonparametric Score Estimators [49.42469547970041]
Estimating the score from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models.
We provide a unifying view of these estimators under the framework of regularized nonparametric regression.
We propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.
arXiv Detail & Related papers (2020-05-20T15:01:03Z) - Distributionally Robust Bayesian Quadrature Optimization [60.383252534861136]
We study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples.
A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set.
We propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose.
arXiv Detail & Related papers (2020-01-19T12:00:33Z)
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.