Kernel Bayes' rule has been proposed as a nonparametric kernel-based method to realize Bayesian inference in reproducing kernel Hilbert spaces. However, we demonstrate both theoretically and experimentally that the prediction result by kernel Bayes' rule is in some cases unnatural. We consider that this phenomenon is i…
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48 results for “kernel Bayes' rule”
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…
A novel Bayesian computation method using importance weighting improves numerical stability and performance.
problem Bayesian computation stability and performance issues.
method Nonparametric approach via feature means, importance weighting, and kernel Bayes' rule.
result Importance weighted kernel Bayes' rule yields superior numerical stability and performance.
RoPAWS improves semi-supervised learning on uncurated data.
problem Efficiency of semi-supervised learning with real-world unlabeled data.
method Reinterprets PAWS as a generative classifier and calibrates predictions using densities of labeled and unlabeled data.
result Significant improvement in performance for uncurated data.
Kernel Bayesian inference is a principled approach to nonparametric inference in probabilistic graphical models, where probabilistic relationships between variables are learned from data in a nonparametric manner. Various algorithms of kernel Bayesian inference have been developed by combining kernelized basic probabil…
Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian …
Test-time training adapts a pretrained model to each prompt via parameter updates, improving accuracy under pretraining-to-test distribution shifts.
problem Improving accuracy of pretrained models under distribution shifts.
method Explaining TTT behavior through a decision-theoretic lens.
result TTT reduces prediction error when updates are spectrally matched to the prompt's signal-to-noise ratio and aligned with query-relevant eigen-directions.
Bayes classifier cannot be learned from noisy labels without knowing noise distribution.
problem Learning a Bayes classifier from noisy labels when the noise distribution is unknown.
method Demonstrates the identifiability issues and proposes a simple algorithm for learning the Bayes decision rule.
result The Bayes decision rule is generally unidentified and cannot be learned without knowing the noise distribution.
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.
Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying function of interest whose conditional mean was observed is a challenging inferenc…
When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updatingstat.ME
New decision-theoretic characterization separates belief and decision posteriors.
problem Understanding the conditions under which loss-based updating coincides with Bayesian updating.
method Decision-theoretic approach to distinguish belief and decision posteriors.
result Generalized Bayes coincides with ordinary Bayesian updating only if the loss is proportional to negative log-likelihood.
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.
A nonparametric approach for policy learning for POMDPs is proposed. The approach represents distributions over the states, observations, and actions as embeddings in feature spaces, which are reproducing kernel Hilbert spaces. Distributions over states given the observations are obtained by applying the kernel Bayes' …
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.
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the …
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.
We propose a novel approach to model selection for simulator-based statistical models. The proposed approach defines a mixture of candidate models, and then iteratively updates the weight coefficients for those models as well as the parameters in each model simultaneously; this is done by recursively applying Bayes' ru…
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributi…
We propose a new method for blind system identification. Resorting to a Gaussian regression framework, we model the impulse response of the unknown linear system as a realization of a Gaussian process. The structure of the covariance matrix (or kernel) of such a process is given by the stable spline kernel, which has b…
Propose an XMSE-aware mixed estimator for EB that interpolates between ML and EB shrinkage.
problem Kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter.
method An XMSE-aware mixed estimator that interpolates between ML and EB shrinkage.
result Fixed-weight XMSE is a scalar quadratic, yielding a closed-form oracle mixing weight that is no worse than both ML and the base EB estimator at the XMSE scale.
New bounds prevent degradation in high-dimensional signal estimation.
problem Statistical learning bounds degradation with increasing dimensionality.
method Investigates linear prediction rules under structural assumptions.
result Derives upper and lower bounds on generalization error.
We present a particle flow realization of Bayes' rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists. Its neural parameterization can be trained in a meta-learning framework, allowing this operator to re…
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.
Paper explores Bayes rule for Gaussian mixtures with missing data, outperforming supervised classifiers.
problem Improving classification accuracy in partially classified samples with missing data.
method Generative model framework with missing-data mechanism, Bayes rule allocation.
result Bayes rule classifier with missing-data mechanism outperforms fully supervised classifiers in various conditions.
We consider using an ensemble of binary classifiers for transductive prediction, when unlabeled test data are known in advance. We derive minimax optimal rules for confidence-rated prediction in this setting. By using PAC-Bayes analysis on these rules, we obtain data-dependent performance guarantees without distributio…
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.
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.
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…
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…
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.
A tutorial on VAEs explaining its derivation and applications.
problem Understanding the VAE model and its limitations.
method Explains VAE through probabilistic and information theoretic perspectives.
result Identifies two common misconceptions and their practical consequences.
This research improves binary classification by balancing overfitting and generalization with a novel Bayesian approach.
problem Improving binary classification models to avoid overfitting and generalize well.
method Introduces a PAC-Bayes type learning rule with a balancing parameter λ to balance training error and KL divergence to a prior.
result A choice of λ ensures uniformly vanishing excess loss, even in the agnostic case, by under-regularizing or over-regularizing appropriately.
Unified quadrature framework for large-scale kernel machines.
problem Efficiently approximating kernel functions for large-scale machine learning.
method Deterministic and randomized interpolatory rules for numerical integration of kernel functions.
result The proposed method reduces the number of nodes needed for accurate kernel approximation.
This paper introduces Bayes Hilbert spaces for efficient posterior approximation.
problem Efficient posterior approximation in Bayesian models for large datasets.
method Develops Bayes Hilbert spaces for posterior approximation and connects them to Bayesian coresets and kernel-based distances.
result Bayes Hilbert spaces provide a novel framework for posterior approximation that is computationally efficient.
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.
New priors can update posteriors without re-estimating likelihoods.
problem Degradation of classification approaches when class priors change.
method Recompute posteriors using recovered likelihoods from original posteriors and new priors.
result Dynamic update of original posteriors is possible without re-estimating likelihoods.
We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of sparsity across precision matrices. It gives sparse estimates of interactions and pro…
We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then demonstrate that the Kernel Score includes the Maximum Mean Discrepancy as a special …
Bayesian framework for policy learning in decision problems.
problem Maximizing expected welfare in decision-making problems.
method Loss-based Bayesian updating and squared-loss surrogate for welfare maximization.
result General Bayes posterior over decision rules with Gaussian pseudo-likelihood interpretation.
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.
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.
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.
A short note on extension theorems and their connection to universal consistency in machine learningstat.ML
Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or in some stronger sense to the Bayes risk or to the Bayes decision function. Kerne…
Estimates classification rules from partially classified data.
problem Estimating Bayes' rule for unclassified observations in partially classified data.
method Fitting a g-component mixture model by maximum likelihood (ML) via the EM algorithm.
result Asymptotic relative efficiency (ARE) of Bayes' rule estimated from partially classified samples.
A new method for accurately reconstructing signals without knowing the kernel or signal regularity.
problem Recovering signals from noisy measurements without prior knowledge of the convolution kernel or signal regularity.
method Parametrizing the convolution kernel and prior length-scales, jointly estimated in the inversion procedure.
result Accurate reconstructions of signals with varying regularity and unknown kernel size.
Signature Kernel Scoring Rule: A Spatio-Temporal Diagnostic for Probabilistic Weather Forecastingstat.ML
Signature kernel scoring rule improves weather forecasting by capturing temporal and spatial dependencies.
problem Lack of suitable scoring rules for probabilistic weather forecasting.
method Reframe weather variables as continuous paths using iterated integrals (signature kernels) to capture temporal and spatial dependencies.
result Signature kernel scoring rule outperforms conventional methods in weather forecasting, especially for long-term forecasts.
Proposes a method to reconcile count time series forecasts.
problem No formal framework for probabilistic reconciliation of count time series.
method Generalizes Bayes' rule for reconciling real-valued and count variables.
result Improves forecast accuracy for count variables compared to Gaussian reconciliation.
In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function , provided that the latent positions are i.i.d. from some distribution F. We then consider the exploitation task of vertex classi…