We extend a recently proposed 1-nearest-neighbor based multiclass learning algorithm and prove that our modification is universally strongly Bayes-consistent in all metric spaces admitting any such learner, making it an "optimistically universal" Bayes-consistent learner. This is the first learning algorithm known to e…
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48 results for “Bayes Consistency”
Adversarial consistency depends on the uniqueness of adversarial Bayes classifiers.
problem Consistency of adversarial surrogate losses is not guaranteed.
method Connected consistency of adversarial surrogate losses to the uniqueness of adversarial Bayes classifiers.
result A convex surrogate loss is statistically consistent for adversarial learning if and only if the adversarial Bayes classifier is unique.
Research on nearest-neighbor methods tends to focus somewhat dichotomously either on the statistical or the computational aspects -- either on, say, Bayes consistency and rates of convergence or on techniques for speeding up the proximity search. This paper aims at bridging these realms: to reap the advantages of fast …
Study of loss functions for learning to defer, proving consistency.
problem Learning to defer in machine learning.
method Introduced a family of surrogate losses parameterized by and proved their consistency.
result Proved realizable -consistency and Bayes-consistency of specific surrogate losses.
We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k growing appropriately with sample size. We will argue that a margin-regularized 1…
This paper establishes the asymptotic consistency of the {\it loss-calibrated variational Bayes} (LCVB) method. LCVB was proposed in~\cite{LaSiGh2011} as a method for approximately computing Bayesian posteriors in a `loss aware' manner. This methodology is also highly relevant in general data-driven decision-making con…
Differentially-private Bayes consistency rule for binary classification and density estimation.
problem Privacy constraints limit private learning in the distribution-free PAC model.
method Constructs a universally Bayes consistent learning rule that satisfies differential privacy.
result Private learning is possible for arbitrary distributions, even with a single algorithm.
New algorithm learns mappings between metric spaces, achieving strong consistency.
problem Learning mappings between metric spaces with unbounded loss.
method Metric medoids and semi-stable compression.
result Strong Bayes-consistency for topologically separable spaces and bounded labels.
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.
Bayes-consistent disagreement discrepancy loss improves model robustness.
problem Distribution shift in real-world neural network deployment.
method Introducing a novel disagreement loss that is Bayes consistent.
result Proves existing surrogates for disagreement discrepancy are not Bayes consistent.
The paper proves statistical consistency and fairness guarantees for a plug-in algorithm.
problem Establishing statistical guarantees for fairness-aware binary classification.
method Proves statistical consistency and derives finite sample guarantees for the plug-in algorithm.
result The plug-in algorithm is statistically consistent and guarantees fairness and differential privacy.
The paper revisits discriminative vs. generative classifiers, showing naive Bayes requires fewer samples.
problem Comparing discriminative and generative classifiers in multiclass settings.
method Theoretical analysis and simulations of naive Bayes vs. logistic regression.
result Multiclass naive Bayes requires fewer samples to approach asymptotic error compared to logistic regression.
A new framework integrates classification and regression tasks in multi-task learning.
problem Jointly solving classification and regression tasks in multi-task scenarios.
method Two-Stage Learning-to-Defer (L2D) framework with a unified deferral mechanism.
result Unified deferral mechanism ensures convergence to the Bayes-optimal rejector.
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…
Separable losses are inconsistent for structured prediction models.
problem Inconsistency of separable losses in structured prediction models.
method Analysis of separable negative log-likelihood losses for structured prediction.
result Separable losses are not Bayes consistent and may not predict the most probable structure.
Neyman-Scott is a classic example of an estimation problem with a partially-consistent posterior, for which standard estimation methods tend to produce inconsistent results. Past attempts to create consistent estimators for Neyman-Scott have led to ad-hoc solutions, to estimators that do not satisfy representation inva…
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.
DCC separates marginal estimation from dependence modeling for improved classification accuracy.
problem Classifying with strong dependence between features.
method Deep Copula Classifier using neural copula densities.
result Achieves excess-risk for -smooth copulas.
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 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.
Unified surrogate loss framework for multi-label learning with strong consistency guarantees.
problem Improving consistency and accounting for label correlations in multi-label learning.
method Introducing multi-label logistic loss and extending it to comprehensive multi-label comp-sum losses, proving strong consistency guarantees for any multi-label loss.
result Unified surrogate loss framework benefiting from strong consistency guarantees for any multi-label loss.
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.
New method for high-dimensional linear regression using empirical Bayes.
problem Estimating prior in high-dimensional linear regression.
method Variational empirical Bayes approach with NPMLE and mean field approximation.
result Established asymptotic consistency and computational efficiency of the method.
Distance weighted discrimination (DWD) is a margin-based classifier with an interesting geometric motivation. DWD was originally proposed as a superior alternative to the support vector machine (SVM), however DWD is yet to be popular compared with the SVM. The main reasons are twofold. First, the state-of-the-art algor…
GES algorithm improves consistency for nonparametric DAG models.
problem Consistent estimation of nonparametric DAG models.
method Greedy equivalence search with new consistency proof for nonparametric families.
result Consistency of GES for general nonparametric DAG models with smooth factorization.
Since the discovery of adversarial examples - the ability to fool modern CNN classifiers with tiny perturbations of the input, there has been much discussion whether they are a "bug" that is specific to current neural architectures and training methods or an inevitable "feature" of high dimensional geometry. In this pa…
A new framework for consistent segmentation evaluation reduces operating losses.
problem Inconsistent thresholding-based segmentation methods lead to suboptimal solutions.
method Developed a consistent ranking-based framework (RankDice/RankIoU) using Bayes rules and Dice-/IoU-calibration.
result The proposed framework is Dice-/IoU-calibrated and provides excess risk bounds and convergence rates.
Kernel Bayes' rulestat.ML
A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functio…
In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli which caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the pr…
Optimizes portfolio construction using Bayesian methods and variational techniques.
problem Balancing reward and risk in portfolio construction.
method Bayesian decision-theoretic formulation, saddle-point problem, variational Bayes relaxation, efficient algorithm, provable convergence.
result Proves statistical consistency of proposed decision with optimal Bayesian decision.
Unified approach for fair classification with overlapping groups.
problem Ensuring fairness across multiple overlapping groups in prediction problems.
method Probabilistic population analysis leading to Bayes-optimal classifier, unifying existing methods.
result Outperforms baselines in fairness-performance tradeoff on real datasets.
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.
Study on top- classification with new loss functions and algorithms.
problem Improving multi-class classification accuracy and cardinality trade-off.
method Introducing cardinality-aware loss functions and deriving their consistency bounds.
result New cardinality-aware algorithms for top- classification.
This paper tackles deferral learning with multiple experts, providing strong theoretical guarantees.
problem Optimizing input assignment to experts balancing accuracy and computational cost.
method Introducing new surrogate loss functions and efficient algorithms with strong theoretical learning guarantees.
result Realizable -consistency, -consistency bounds, and Bayes-consistency for deferral learning.
Improved model-based estimation through tempered Bayes filter.
problem Improving predictive accuracy in partially-observable stochastic systems.
method Developed tempered Bayes filter combining likelihood and full posterior tempering.
result Tempered Bayes filter achieves improved predictive performance over the Bayes filter baseline.
High-Throughput Asset Pricingq-fin.GN
EB improves asset pricing by mining large strategies without lookahead bias.
problem Lack of unbiased asset pricing models with out-of-sample performance.
method Empirical Bayes applied to 136,000 long-short strategies.
result EB provides unbiased predictions with transparent intuition.
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.
Given a vertex of interest in a network , the vertex nomination problem seeks to find the corresponding vertex of interest (if it exists) in a second network . A vertex nomination scheme produces a list of the vertices in , ranked according to how likely they are judged to be the corresponding vertex of …
Bayes-CPACE: PAC Optimal Exploration in Continuous Space Bayes-Adaptive Markov Decision Processescs.LG
We present the first PAC optimal algorithm for Bayes-Adaptive Markov Decision Processes (BAMDPs) in continuous state and action spaces, to the best of our knowledge. The BAMDP framework elegantly addresses model uncertainty by incorporating Bayesian belief updates into long-term expected return. However, computing an e…
Paper establishes statistical validity for variational Bayes in neural networks.
problem Lack of theoretical validity for Variational Bayes in Bayesian Neural Networks.
method Establishes posterior consistency for mean-field variational posterior in feed-forward neural networks.
result Proves VP concentrates around Hellinger neighborhoods of true density function under certain conditions.
Data-Driven Estimation of the False Positive Rate of the Bayes Binary Classifier via Soft Labelscs.LG
Paper estimates FPR of Bayes classifier using soft labels.
problem Determining optimal classifier performance.
method Uses soft labels and denoising technique.
result Consistent and unbiased FPR estimator developed.
Bayes predictor remains robust to ignorable missingness shifts.
problem Challenges in prediction with missing covariates and shifts in missingness reasons.
method Bayesian approach and different prediction methods.
result Bayes predictor remains unchanged by ignorable shifts, but robust prediction requires disregarding missingness for non-ignorable shifts.
Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list. Previous work has yielded several approaches to this problem, with theoretical re…
Paper extends transfer learning for decision rules, improving treatment rule estimation.
problem Estimating optimal individualized treatment rules under changing conditions.
method Bayes decision rules and low-dimensional empirical risk minimization.
result Consistent estimators and risk bounds established under mild conditions.
New work shows limits of certifying neural network robustness.
problem Certified training improves robustness but decreases accuracy.
method Bayes error analysis to investigate robustness limits.
result Upper bound for certified robust accuracy established.
Solves open problem on universally consistent online learning with unbounded losses.
problem Open problem on universally consistent online learning with unbounded losses.
method Constructs random measurable partitions of the instance space.
result Simple memorization rule is optimistically universal for any unbounded loss.
CT compares two distributions using Bayes' theorem and chain rule.
problem Measuring the difference between two probability distributions.
method Conditional transport (CT) using chain rule and Bayes' theorem.
result CT strikes a good balance between mode-covering and mode-seeking behaviors.
Efficiently selects important variables in high-dimensional logistic regression.
problem Variable selection in high-dimensional logistic regression with binary responses.
method Developed a variational empirical Bayes approach for efficient model space marginal distribution.
result The variational approximation inherits strong selection consistency from the posterior distribution.