We consider effort allocation in crowdsourcing, where we wish to assign labeling tasks to imperfect homogeneous crowd workers to maximize overall accuracy in a continuous-time Bayesian setting, subject to budget and time constraints. The Bayes-optimal policy for this problem is the solution to a partially observable Ma…
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48 results for “Bayes' Optimal Solution”
A new optimization algorithm for Gaussian Variational Inference on precision matrices.
problem Complex models with positive definite constraints on covariance matrices.
method Manifold Gaussian Variational Bayes (MGVBP) with natural gradient updates.
result Empirically validated as a feasible and efficient solution for VI in complex models.
Meta-learning method improves PU classification performance.
problem Improving binary classifiers from PU data in unseen tasks.
method Adapts model to PU data using related tasks and neural networks.
result Proposed method outperforms existing methods on synthetic and real-world datasets.
Sparsity via Hyperpriors: A Theoretical and Algorithmic Study under Empirical Bayes Frameworkstat.ML
The paper studies sparsity in EBF with hyperpriors and proposes a PALM algorithm.
problem Promoting sparsity in sparse learning problems.
method Empirical Bayes framework, hyperpriors, proximal alternating linearized minimization (PALM) algorithm.
result Appropriate hyperpriors can significantly enhance sparsity and restoration accuracy.
This work analyzes two methods for combining multiple binary labels in bipartite ranking.
problem Combining multiple binary labels for optimal bipartite ranking.
method Loss aggregation vs. label aggregation approaches.
result Label aggregation is preferable to loss aggregation due to label dictatorship issues.
Quantum annealing improves VB inference, avoiding local minima.
problem Variational Bayes inference stuck in local minima.
method Quantum annealing approach to VB inference.
result Quantum annealing variational Bayes (QAVB) outperforms classical VB.
Paper tackles regression with cost-based rejection, balancing prediction and rejection costs.
problem Regression with cost-based rejection, balancing prediction and rejection costs in a continuous target space.
method Formulated expected risk, derived Bayes optimal solution, proposed surrogate loss function.
result Bayes optimal solution can be recovered by the proposed surrogate loss function.
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
problem Bayesian filtering for nonlinear systems with non-Gaussian observations.
method Optimal transport theory applied to Bayes' law, constructing Brenier maps.
result New variational formulations of EnKF and FPF for non-Gaussian settings.
We investigate the problem of multiclass classification with rejection, where a classifier can choose not to make a prediction to avoid critical misclassification. First, we consider an approach based on simultaneous training of a classifier and a rejector, which achieves the state-of-the-art performance in the binary …
This paper explores minimax-Bayes solutions for reinforcement learning problems.
problem How to select appropriate priors for decision making under uncertainty in sequential decision making.
method Study of minimax-Bayes solutions for various reinforcement learning problems.
result Minimax policies are more robust than standard priors.
New method handles unknown task boundaries in continual learning.
problem Catastrophic forgetting in neural networks.
method Fixed-point equations for online variational Bayes optimization.
result Approximates online Bayes update for non-stationary data.
Solution to sparse PCA tuning problem using Empirical Bayes.
problem Sparse PCA multiple tuning problem (MTP).
method Empirical Bayes covariance decomposition for penalized PCA.
result Empirical Bayes approach efficiently solves MTP in sparse PCA.
Researchers estimate optimal PAC-Bayes bounds using Hamiltonian Monte Carlo.
problem Estimating tight PAC-Bayes bounds with restricted posterior families.
method Sampling from optimal Gibbs posterior using Hamiltonian Monte Carlo, estimating KL divergence, and proposing high-probability bounds.
result Significant tightness gaps in PAC-Bayes bounds, up to 5-6% in some cases.
The study compares clustering risk in Hidden Markov and i.i.d. models, showing the Bayes classifier is nearly optimal.
problem Comparing clustering risk in Hidden Markov and i.i.d. models.
method Analysis of Bayes risk, theoretical bounds, and simulations.
result The Bayes classifier is nearly optimal for clustering in both Hidden Markov and i.i.d. models.
We study the rates of convergence from empirical surrogate risk minimizers to the Bayes optimal classifier. Specifically, we introduce the notion of \emph{consistency intensity} to characterize a surrogate loss function and exploit this notion to obtain the rate of convergence from an empirical surrogate risk minimizer…
LGD algorithm learns optimal hyperparameters for regression tasks.
problem Learning to learn hyperparameters for regression problems.
method Langevin Gradient Descent (LGD) approximates posterior distribution.
result Meta-learning optimal hyperparameters achieves Bayes' optimal solution.
The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, s…
Proposes a non-convex optimization method for a parsimonious weighted naive Bayes classifier.
problem Improving naïve Bayes classifier performance with a large number of input variables.
method Sparse regularization of model log-likelihood for direct estimation of variable weights.
result Optimization-based weighted naïve Bayes classifiers achieve equivalent performance to averaging-based classifiers.
Unified framework for Bayes-optimal classifiers under group fairness.
problem Mitigating disparate impacts from algorithmic predictions in high-stakes decision-making.
method Unified framework based on Neyman-Pearson argument for deriving Bayes-optimal classifiers under group fairness constraints.
result Proposes FairBayes method that directly controls disparity and achieves optimal fairness-accuracy tradeoff.
Adaptive variational Bayes framework improves inference adaptively.
problem Lack of general and computationally tractable variational Bayes method for adaptive inference.
method Proposes a novel adaptive variational Bayes framework combining variational posteriors over individual models.
result Adaptive variational Bayes achieves optimal contraction rates adaptively under general conditions.
Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This leads to a combinatorial maximum-likelihood problem, for which we provide an exact…
The paper tackles fair classification with multiple sensitive features.
problem Existing fair classification methods often consider a single sensitive feature, but in practice, individuals are defined by multiple sensitive features.
method Characterizes Bayes-optimal fair classifiers for multiple sensitive features under various fairness measures, proposing in-processing and post-processing algorithms.
result Bayes-optimal fair classifiers for multiple sensitive features are instance-dependent thresholding rules that rely on a weighted sum of group membership probabilities.
ContraBAR uses contrastive learning to learn Bayes-optimal policies in RL.
problem Learning optimal policies for unknown tasks sampled from a known distribution.
method Proposes ContraBAR, a meta RL algorithm using contrastive predictive coding (CPC) for belief inference.
result ContraBAR achieves comparable performance to state-of-the-art methods and is computationally efficient.
Study shows how classifiers can approach Bayes error in high-dimensional settings.
problem Generalization error in high-dimensional perceptrons.
method Proved a formula for generalization error using convex optimization and observed that logistic and hinge regression can approach Bayes error closely.
result Logistic and hinge regression can approach Bayes-optimal generalization error closely in high-dimensional settings.
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
Generalized Naive Bayesstat.ML
Paper introduces Generalized Naive Bayes for better data fitting.
problem Improving Naive Bayes for better data fitting.
method Developed new greedy and optimal algorithms for GNB.
result Proves GNB fits data at least as well as classical NB.
We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower …
A new sequential method estimates Poisson means in streaming data, achieving optimality and efficiency.
problem Estimating Poisson means in a streaming, or online, framework.
method A quasi-Bayesian approach based on Newton's algorithm for a sequential estimate.
result Established frequentist guarantees including consistency and asymptotic optimality.
Bayes-optimal classifiers are robust to adversarial attacks, unlike CNNs trained on the same data.
problem The vulnerability of modern CNN classifiers to adversarial examples.
method Constructing realistic image datasets and deriving analytic conditions for Bayes-optimal classifiers.
result Bayes-optimal classifiers are robust to adversarial attacks, unlike CNNs trained on the same data.
Bayes-optimal learning of a neural network with quadratic activations is achieved with GAMP-RIE.
problem Learning a neural network with quadratic activations from quadratic samples.
method Combining approximate message passing with rotationally invariant matrix denoising.
result Derives a closed-form expression for Bayes-optimal test error.
This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for conf…
Researchers compute Bayes error for classification models using normalizing flows.
problem Evaluating the inherent difficulty of classification problems.
method Invertible transformations and Gaussian base distributions to compute Bayes error.
result State-of-the-art models can achieve near-optimal accuracy but not always.
Paper proves fair classification can be done via simple thresholding.
problem Achieving fair binary classification subject to group fairness constraints.
method Proves Bayes optimal fair learning rule is a group-wise thresholding rule over the Bayes regressor with randomization.
result Proposes an efficient unconstrained optimization algorithm for post-processing fair classification.
Study on conditions for Bayes optimal classifier in adversarial robustness.
problem Existence of Bayes optimal classifier for adversarial robustness.
method General sufficient conditions for existence of Bayes optimal classifier.
result Guaranteed existence of Bayes optimal classifier under certain conditions.
Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point…
New PAC-Bayes training method improves model generalization for unbounded loss.
problem Improving generalization of complex models under unbounded loss.
method Established new PAC-Bayes bound for unbounded loss, jointly training prior and posterior.
result Outperforms existing PAC-Bayes training algorithms and matches ERM accuracy.
The study analyzes multi-class teacher-student perceptron performance and generalization errors.
problem Analyzing multi-class classification with the teacher-student perceptron.
method Deriving asymptotic expressions for Bayes-optimal and empirical risk minimization (ERM) generalization errors.
result Regularised cross-entropy minimization yields close-to-optimal accuracy for multi-class classification.
New online GP algorithm offers performance guarantees for streaming data.
problem Training and inference of GPs require all historic data, limiting online decision-making.
method Developed a new theoretical framework based on PAC-Bayes theory, optimizing empirical risk and parameter divergence.
result Offers both a guarantee of generalized performance and good accuracy.
PAC-Bayes bound requires prior to place mass on high-performing predictors.
problem Explaining generalization in machine learning.
method Analyzing necessary conditions for PAC-Bayes bounds to provide meaningful generalization guarantees.
result Achieving a target generalisation level requires the prior to place sufficient mass on high-performing predictors.
Learning to Benchmark: Determining Best Achievable Misclassification Error from Training Datastat.ML
We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previ…
Paper refines PAC-Bayes bounds for bandit problems.
problem Improving probabilistic bounds for off-policy learning.
method Optimizes PAC-Bayesian bounds using a new parameter optimization approach.
result Provides two parameter-free PAC-Bayes bounds that nearly match optimal rates.
SAM improves deep learning by relaxing Bayes objective.
problem Improving generalization in deep learning models.
method SAM as a relaxation of Bayes objective using Fenchel biconjugate.
result SAM connects adversarial and Bayesian methods for robustness.
Bayes optimal algorithm under certain conditions doesn't achieve exponential simple regret.
problem Best arm identification with normal rewards over time.
method Fixed-budget best arm identification problem with rewards from normal distributions. Evaluates performance via simple regret.
result Bayes optimal algorithm does not yield exponential decrease in simple regret.
A new hyperparameter optimization method reduces overfitting.
problem Overfitting in hyperparameter optimization.
method PAC-Bayes bound minimization using gradient-based algorithm.
result Significant reduction in out-of-sample error.
Study optimizes best-arm identification with minimax and Bayes strategies.
problem Efficiently identifying the best arm in fixed-budget scenarios.
method Adaptive procedure with two stages: pilot phase and minimax game.
result Single strategy is asymptotically minimax and Bayes optimal.
Bayes factors and relative belief ratios are compared as measures of statistical evidence.
problem Which measure of evidence is more appropriate: Bayes factors or relative belief ratios?
method Comparison of Bayes factors and relative belief ratios, considering properties and restrictions.
result Relative belief ratio has better properties as a measure of evidence.
VB uses natural gradients in information geometry.
problem Estimating or computing natural gradients in VB.
method Natural-gradient descent algorithm and Bayesian Learning Rule.
result Simplification of Bayes' rule and generalization of quadratic surrogates.
SDF-Bayes finds safe drug combinations safely, balancing optimism and caution.
problem Finding safe drug combinations in clinical trials with multiple drugs and patient heterogeneity.
method SDF-Bayes uses Bayesian statistics to choose the most likely MTD while ensuring safety constraints.
result SDF-Bayes outperforms existing methods in both accuracy and safety for drug combination trials.