The computational costs of inference and planning have confined Bayesian model-based reinforcement learning to one of two dismal fates: powerful Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian non-parametric models but using simple, myopic planning strategies such as Thompson sampling. We …
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48 results for “Bayes' Power”
New inequality for ternary variables improves on existing measures.
problem Analyzing excess losses and weighted majority votes with ternary random variables.
method Developed a split-kl inequality and its PAC-Bayes extension.
result Outperforms existing inequalities in certain regimes.
We presented Bayesian portfolio selection strategy, via the factor asset pricing model. If the market is information efficient, the proposed strategy will mimic the market; otherwise, the strategy will outperform the market. The strategy depends on the selection of a portfolio via Bayesian multiple testing methodol…
FAB-PPI uses prior knowledge to improve prediction-powered inference.
problem Improving statistical inference with machine learning predictions.
method Informing PPI with prior knowledge on prediction quality.
result FAB-PPI improves inference accuracy and confidence intervals.
We present a growing dimension asymptotic formalism. The perspective in this paper is classification theory and we show that it can accommodate probabilistic networks classifiers, including naive Bayes model and its augmented version. When represented as a Bayesian network these classifiers have an important advantage:…
PAS improves estimation of multiple means using ML predictions and shrinkage.
problem Improving statistical estimates with limited gold-standard data and noisy ML predictions.
method Prediction-Powered Adaptive Shrinkage (PAS) that combines PPI with empirical Bayes shrinkage.
result PAS adapts to the reliability of ML predictions and outperforms traditional methods in large-scale applications.
Empirical Bayes Rebiasingstat.ME
We rebias estimates to improve interval calibration and prediction accuracy.
problem Constructing accurate intervals for noisy and biased estimates.
method Empirical Bayes rebiasing strategy that learns bias distribution from data.
result Substantial precision gains in prediction-powered inference.
PROBE algorithm efficiently solves sparse high-dimensional linear regression.
problem Sparse high-dimensional linear regression models with complex parameter spaces.
method Partitioned empirical Bayes ECM algorithm for computationally efficient MAP estimation.
result PROBE algorithm provides robust and efficient coordinate-wise optimization.
Evidence Networks simplify Bayesian model comparison for complex models.
problem Bayesian model comparison challenges with intractable likelihoods or priors.
method Loss functions and neural networks for fast, amortized estimation of Bayes factors.
result Evidence Networks provide accurate and scalable Bayes factor estimation.
Optimal projections enhance Naive Bayes classification.
problem Improving Naive Bayes classification accuracy.
method Projection pursuit to find optimal linear projections.
result The approach substantially outperforms other models.
AdaPT-GMM improves multiple testing power with covariates.
problem Powerful and robust multiple testing with covariates.
method Covariate-assisted Gaussian mixture model with adaptive thresholding.
result AdaPT-GMM delivers high power in various scenarios.
A method for selecting pseudo-labeled data in semi-supervised learning using generalized Bayes and soft revision.
problem Selecting pseudo-labeled data for semi-supervised learning with robustness to uncertainty.
method Using credal sets and the Gamma-Maximin method with soft revision to update priors and select pseudo-labeled data.
result The Gamma-Maximin method with soft revision can achieve promising results, especially in scenarios with low labeled data proportions.
Robust VB framework handles contamination using min-max median aggregation.
problem Handling contamination and outliers in datasets.
method Partition data into subsets, formulate robust optimization problem, use min-max median KL divergence.
result Min-max median formulation improves robustness and statistical rates.
Active Reinforcement Learning (ARL) is a twist on RL where the agent observes reward information only if it pays a cost. This subtle change makes exploration substantially more challenging. Powerful principles in RL like optimism, Thompson sampling, and random exploration do not help with ARL. We relate ARL in tabular …
The paper argues for interpreting neural networks as approximating the true posterior, enhancing in-context learning.
problem The limitations of traditional MLE interpretation in large-scale, single-epoch training setups.
method Demonstrates the power of interpreting neural networks as approximations of the true posterior, using experiments to predict generalizations.
result Models become robust in-context learners by effectively composing knowledge from their training data, revealing surprising generalizations.
Meta-learning framework improves model performance on few-shot classification tasks.
problem Improving model performance on few-shot classification tasks.
method Empirical Bayes formulation with synthetic gradients for transductive meta-learning.
result Meta-learning framework outperforms previous state-of-the-art methods on benchmarks.
Recursive PAC-Bayes: A Frequentist Approach to Sequential Prior Updates with No Information Losscs.LG
New PAC-Bayes method updates priors without losing confidence information.
problem Lack of sequential prior updates in PAC-Bayes without losing confidence information.
method Recursive PAC-Bayes decomposition of expected loss.
result Sequential prior updates with no information loss.
New method improves Bayesian inference for parametric models, robust to misspecification.
problem Inference can be untrustworthy when parametric models are wrong.
method Adaptive nonparametric corrections for parametric Bayesian models using generalized Bayes.
result The method achieves robustness and efficiency, converging fast when the parametric model is close to true.
The CAP slope is Bayes' theorem in cumulative coordinates, unlocking the weight of evidence, Somers' D, and Gini coefficient.
problem Calibration and weight of evidence
method Identifying the CAP slope as Bayes' theorem
result Revealing the CAP slope as Bayes' theorem
Higher-Order Generalization Bounds: Learning Deep Probabilistic Programs via PAC-Bayes Objectivescs.LG
Unified framework for learning flexible probabilistic programs using DPP and PAC-Bayes bounds.
problem Learning and generalizing from complex probabilistic models.
method Unified DPP representation and PAC-Bayes bounds for stochastic programs.
result Improved performance and generalization prediction using flexible DPP model representations and learned complexity measures.
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.
We study methods for simultaneous analysis of many noisy experiments in the presence of rich covariate information. The goal of the analyst is to optimally estimate the true effect underlying each experiment. Both the noisy experimental results and the auxiliary covariates are useful for this purpose, but neither data …
Extends PPI to sequential setting, improving inference over time.
problem Sequential data growth with unlabelled data.
method Prediction-powered confidence sequence procedures using Ville's inequality and the method of mixtures.
result Asymptotically valid uniformly over time, accommodating prior knowledge.
Bayesian entity resolution merges together multiple, noisy databases and returns the minimal collection of unique individuals represented, together with their true, latent record values. Bayesian methods allow flexible generative models that share power across databases as well as principled quantification of uncertain…
Improves model accuracy for neural nets in stochastic dynamics with partial prior knowledge.
problem Stability and accuracy in neural nets modeling stochastic dynamics with many parameters.
method Three steps: probabilistic weights, partial knowledge incorporation, and PAC-Bayesian training.
result Improved model fit with partial and noisy prior knowledge.
Paper analyzes consistency of Bayesian and machine learning methods for hierarchical parameter estimation.
problem Learning hierarchical parameters in complex and real-world problems.
method Empirical Bayes and Kernel Flow approaches.
result Consistency results for Matérn-like model on the torus, and comparison of algorithms.
Naive Bayes spam filters are highly susceptible to data poisoning attacks. Here, known spam sources/blacklisted IPs exploit the fact that their received emails will be treated as (ground truth) labeled spam examples, and used for classifier training (or re-training). The attacking source thus generates emails that will…
A new model combines deep learning and Gaussian Processes with hyperdata learning.
problem Combining deep learning and Gaussian Processes for expressive and robust learning.
method Conditional Deep Gaussian Process (DGP) with hyperdata learning and approximate inference.
result Conditional DGP offers better expressiveness and robustness compared to existing methods.
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.
New uniqueness concept for adversarial Bayes classifier.
problem Understanding adversarial Bayes classifiers in binary classification.
method Developed a new notion of uniqueness and analyzed it for a family of one-dimensional data distributions.
result Improved regularity of adversarial Bayes classifiers as perturbation radius increases.
Empirical Bayes rates via variational approximations and prior decomposition.
problem Nonparametric and high-dimensional inference convergence rates.
method Variational perspective and prior decomposition.
result Empirical Bayes posterior rates derived from variational Bayes.
Bayes-assisted confidence sequences improve efficiency for bounded means.
problem Efficient uncertainty quantification for bounded IID means without parametric assumptions.
method Bayesian working predictive model selects adaptive martingale updates maximizing predictive log-growth.
result Asymptotically log-optimal performance with informative priors reducing width and sampling effort.
When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the high-dimensional setting. We prove two results that hold for all classifiers in any dimensi…
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.
Despite its simplicity, the naive Bayes classifier has surprised machine learning researchers by exhibiting good performance on a variety of learning problems. Encouraged by these results, researchers have looked to overcome naive Bayes primary weakness - attribute independence - and improve the performance of the algo…
Hotelling's -test for the mean of a multivariate normal distribution is one of the triumphs of classical multivariate analysis. It is uniformly most powerful among invariant tests, and admissible, proper Bayes, and locally and asymptotically minimax among all tests. Nonetheless, investigators often prefer non-inva…
Researchers prove NP-hardness of learning parameter-bounded Bayes nets.
problem Learning parameter-bounded Bayes nets is computationally hard.
method Proved NP-hardness of learning parameter-bounded Bayes nets and a promise search variant.
result Proved NP-hardness of a promise search variant of LEARN.
Sharp feature-learning transitions and Bayes-optimal neural scaling laws in extensive-width networksstat.ML
Sharp feature transitions revealed in extensive-width networks.
problem Learning hierarchical features from noisy queries in large networks.
method Information-theoretic analysis and heuristic decoupling argument.
result Sequential phase transitions in feature learnability and effective width.
Deep Bayes Factorsstat.ME
Deep learning improves Bayes factor computation for likelihood-free models.
problem Computing Bayes factors for likelihood-free models is challenging.
method Proposes a deep learning estimator of Bayes factors using simulated data.
result Establishes consistency of the Deep Bayes Factor estimator.
Meta-learning bounds derived using PAC-Bayes theory for improved generalization.
problem Uncertainty in generalization performance for meta-learning with new tasks.
method PAC-Bayes relative entropy bounds and empirical risk minimization (ERM) method.
result Competitive generalization performance and rapid convergence with data-dependent prior.
PAC-Bayes framework fails on simple 1D linear classification task.
problem Proving the learnability of simple 1D linear classification tasks using PAC-Bayes bounds.
method Demonstrated a specific 1D linear classification task that PAC-Bayes cannot analyze.
result PAC-Bayes framework cannot prove learnability of simple 1D linear classification tasks.
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.
New estimators outperform maximum likelihood without hyper-parameter estimation.
problem Improving system identification performance without hyper-parameter estimation.
method Developed generalized Bayes and closed-form biased estimators using excess MSE.
result New estimators have comparable performance to empirical-Bayes-based regularized estimator.
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.
Discriminative classification with generative features: bridging Naive Bayes and logistic regressionstat.ML
Smart Bayes integrates generative and discriminative features for improved classification.
problem Improving classification performance by combining generative and discriminative modeling.
method Integrates generative likelihood-ratio features into a logistic-regression-style classifier.
result Often outperforms logistic regression and Naive Bayes in simulations and real data.
New method reduces computational cost for estimating PAC-Bayes bounds.
problem High computational cost in estimating PAC-Bayes bounds.
method General alternative method that makes computational savings.
result Reduces computational cost on the order of the dataset size.
This work bounds classification error in machine learning for low Bayes error conditions.
problem Understanding the error mismatch between Bayes error and model-based classification error.
method Applying classification error bounds to study the relationship with Kullback-Leibler divergence and proposing a linear approximation for low Bayes error conditions.
result A linear approximation of the classification error bound for low Bayes error conditions is proposed.
Improved Naive Bayes classifier with neural network models.
problem Limited complexity handling and independence assumption in Naive Bayes.
method Introducing Neural Naive Bayes and Neural Pooled Markov Chain models.
result Error rate reduced by 4.5 on IMDB dataset.