Focal loss improves classification but not class-posterior probability estimation.
problem Improving class-posterior probability estimation from focal loss.
method Proved classification-calibration and derived a transformation to recover true class-posterior probabilities.
result A transformation of the confidence score from focal loss minimization allows recovery of true class-posterior probabilities.
One of the central themes in the classification task is the estimation of class posterior probability at a new point x. The vast majority of classifiers output a score for x, which is monotonically related to the posterior probability via an unknown relationship. There are many attempts in the literature …
Implied posterior probability of a given model (say, Support Vector Machines (SVM)) at a point x is an estimate of the class posterior probability pertaining to the class of functions of the model applied to a given dataset. It can be regarded as a score (or estimate) for the true posterior probability, which ca…
PosCal training improves classification models by calibrating posterior probabilities.
problem Poorly calibrated posterior probabilities in classification models.
method End-to-end training procedure that directly optimizes the objective while minimizing the difference between predicted and empirical posterior probabilities.
result PosCal training achieves about 2.5% task performance gain and 16.1% calibration error reduction.
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.
New method corrects skewed confidence for PbN classification.
problem Weakly supervised binary classification with biased negative data.
method Corrects skewed confidence in negative data to improve classifier.
result Reduces distortion in posterior probability for PbN classification.
SJS model predicts label shifts in multinomial datasets.
problem Predicting label shifts in multinomial datasets.
method Sparse joint shift model for dataset shift.
result Valid predictions and class prior probabilities estimates.
This paper argues against using calibration metrics for assessing posterior probabilities and proposes expected proper scoring rules instead.
problem The assessment of posterior probabilities generated by machine learning classifiers using calibration metrics is flawed and should be replaced with expected proper scoring rules.
method The paper reviews proper scoring rules from a practical perspective, explains why expected PSRs are a principled measure of posterior quality, and introduces a new calibration metric called calibration loss.
result Calibration loss is superior to expected calibration error and expected score divergence calibration metrics for assessing posterior probabilities.
Theoretical framework for M-posteriors connects Bayesian and frequentist statistics.
problem Connecting Bayesian and frequentist approaches in statistical inference.
method Developed a theoretical framework for M-posteriors, showing asymptotic normality and frequentist consistency.
result M-posteriors are robust and contract around M-estimators under mild conditions.
FJS method improves multinomial classification accuracy.
problem Improving multinomial classification accuracy under dataset shift.
method Derive FJS representation and propose alternative methods.
result Factorizable joint shift is not fully identifiable without additional assumptions.
We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. To that end, the training posteriors are used for dictionary learning and sparse coding. Sparse representation of the test posteriors using this dictionary enables proje…
We extend Bayes' theorem for upper probabilities considering likelihood uncertainty.
problem Addressing uncertainty in likelihood for upper probability bounds.
method Generalization of Wasserman and Kadane's result, considering both prior and likelihood uncertainty.
result A sufficient condition for the upper bound to become an equality.
The paper compares one-hot encoding to Naïve Bayes for categorical variables.
problem Incorrect one-hot encoding affects Naïve Bayes performance.
method Mathematical and experimental analysis of PoB vs. categorical Naïve Bayes.
result Posterior probabilities are usually greater in the PoB case, but agree on the maximum a posteriori class label.
In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emp…
Bayesian DWD improves classification of high-dimensional data.
problem Classifying high-dimensional data with uncertainty.
method Bayesian approach to DWD using MCMC for inference.
result Bayesian DWD yields well-calibrated class probabilities and penalized coefficients.
Bayesian histograms achieve optimal distribution estimation with minimal memory usage.
problem Efficiently estimating distributions with minimal memory footprint.
method Bayesian histograms for distribution estimation under Wasserstein distance.
result Bayesian histograms require fewer bins to achieve minimax optimality, reducing memory usage by a polynomial factor.
Logistic regression can handle noisy labels effectively when labels are imperfectly assigned by multiple experts.
problem Label noise in supervised classification due to manual labelling by multiple experts.
method Using approximate posterior probabilities of class membership from multiple experts to train logistic regression models.
result Logistic regression can be robust to label noise when classification difficulty is the only source of errors.
The semantic map calibrates uncertainty from language model probabilities.
problem Uncertainty in language model probabilities for professional decisions.
method Prespecified semantic map linking probabilities of verbal responses to probabilities of declared states.
result Language-derived probabilities outperform printed numerical probabilities and recover valid uncertainty coverage.
Method trains emulators to estimate posterior probabilities safely.
problem Uncertainty in slow forward model calculations.
method Trains emulators while estimating posterior probabilities with MCMC, propagating error.
result Demonstrates robust posterior inference for ΛCDM cosmology model. We study the problem of learning Bayesian network structures from data. Koivisto and Sood (2004) and Koivisto (2006) presented algorithms that can compute the exact marginal posterior probability of a subnetwork, e.g., a single edge, in O(n2n) time and the posterior probabilities for all n(n-1) potential edges in O(n2n…
Method estimates noise transition matrix from noisy labels without relying on unreliable class-posterior estimation.
problem Estimating noise transition matrix from noisy data.
method Total variation regularization to encourage distinguishable predicted probabilities.
result Consistent estimator of the noise transition matrix under mild assumptions.
We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of to…
New MCMC method for complex models with large variables.
problem Inference on posterior model probabilities in large model spaces.
method Reversible genetically modified mode jumping Markov chain Monte Carlo (GMJMCMC).
result Introduced a proper MCMC with correct limiting distribution.
The study quantifies decision-making risks from suboptimal classifiers and proposes methods to reduce these risks.
problem Excess risk in decision-making from suboptimal probabilistic classifiers.
method Analytical expressions and upper/lower bounds for excess risk, calibration curve estimation, grouping loss estimator.
result Identifies regimes where recalibration alone or post-training is more effective.
New tools connect CP to GF inference for better probabilistic prediction.
problem Lack of versatility in conformal prediction for quantifying evidence.
method Imprecise probability theory and generalized fiducial inference.
result Establishes a formal connection between CP and GF inference.
A new method infers graph structure and parameters using a single generative flow network.
problem Bayesian Network structure and parameter inference from data.
method Single GFlowNet with two-phase sampling: DAG generation followed by parameter assignment.
result Accurate approximation of joint posterior distribution over graph structure and parameters.
The paper reinterprets Bayesian priors and posteriors using Riemannian manifolds.
problem The dependence of maximum a posteriori estimates on parametrization.
method Assuming a Riemannian manifold with Fisher metric, the paper reinterprets priors and posteriors as distributions over probability distributions, making estimates independent of parametrization.
result A maximum a posteriori estimate independent of parametrization is defined.
DPPS uses DP priors for Bayesian non-parametric multi-arm bandits.
problem Optimizing multi-arm bandit environments with prior beliefs.
method Bayesian non-parametric algorithm based on Dirichlet Process priors.
result DPPS provides principled incorporation of prior beliefs and is optimal in Bayesian regret setup.
Improves reliability of medical diagnosis uncertainty estimates.
problem Label uncertainty in medical diagnosis.
method Post-hoc alpha-calibration method for neural network classifiers. result Significantly enhances reliability of uncertainty estimates.
Geometry-aware KDE model improves multiclass quantification.
problem Accurately estimating class prevalence for label shift adaptation.
method Log-ratio representations and Aitchison geometry for compositional data, shrinkage regularization.
result Competitive with state-of-the-art quantifiers, often improving over standard KDE-based baselines.
Bayesian method learns network structure from Gaussian process priors.
problem Computational infeasibility of Bayesian structure learning in GPNs.
method Monte Carlo and MCMC methods for sampling network structures.
result Method outperforms state-of-the-art algorithms in recovering network structure.
Paper examines stability of Bayesian posterior measures using integral probability metrics.
problem Stability of Bayesian inference in large-scale inverse problems.
method New families of integral probability metrics for likelihood and prior perturbations.
result Constructs new stability results for Bayesian posterior measures.
Improved Bayesian inference using power priors with historical data.
problem Improving Bayesian inference with historical data.
method Generalized power priors that adapt to the α parameter of Amari's α-divergence. result Improved performance through appropriate choices of the α parameter. Bayesian neural networks are compressed using feature and weight pruning based on posterior inclusion probabilities.
problem Efficiently compressing Bayesian neural networks to reduce computation cost and improve generalizability.
method Bayesian model selection principles are applied to obtain posterior inclusion probabilities for pruning and feature selection.
result Pruned models show better generalizability on simulated and real-world data.
For information retrieval and binary classification, we show that precision at the top (or precision at k) and recall at the top (or recall at k) are maximised by thresholding the posterior probability of the positive class. This finding is a consequence of a result on constrained minimisation of the cost-sensitive exp…
We develop a new method for regularising neural networks. We learn a probability distribution over the activations of all layers of the model and then insert imputed values into the network during training. We obtain a posterior for an arbitrary subset of activations conditioned on the remainder. This is a generalisati…
This document is an invited chapter covering the specificities of ABC model choice, intended for the incoming Handbook of ABC by Sisson, Fan, and Beaumont (2017). Beyond exposing the potential pitfalls of ABC based posterior probabilities, the review emphasizes mostly the solution proposed by Pudlo et al. (2016) on the…
We consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The `normal' observations are coming from a known distribution whereas the distributio…
New method improves ABC for Bayesian model comparison.
problem Comparing complex models with observed data.
method Approximate Bayesian Computation with posterior density estimation.
result Efficiently assigns high posterior probabilities to ground-truth models.
Brain uses synaptic failure to sample from posterior distributions.
problem Bayesian inference in the brain's probabilistic computations.
method Adapting synaptic failure to sample posterior predictive distributions.
result Synaptic failure enables sampling of complete posterior predictive distributions.
Efficient classifier error estimation without re-training.
problem Estimating classifier error without re-training.
method Generalized resubstitution based on empirical measures.
result Consistent and asymptotically unbiased error estimation.
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled partial order, the conditional probabilities of interest are computed exactly. We…
New conjugate priors improve Bayesian inference for multinomial probit models.
problem Lack of tractable conjugate priors for efficient Bayesian inference in multinomial probit models.
method Unified skew-normal (SUN) distributions as conjugate priors, leading to improved posterior inference and classification.
result Improved computational methods for posterior inference and classification, especially in high dimensions.
BayesBag improves reproducibility of Bayesian inference under model misspecification.
problem Bayesian posteriors can be unreliable and inconsistent under model misspecification.
method Apply bagging to the Bayesian posterior to improve reproducibility.
result Bagged posteriors typically satisfy reproducibility criteria under misspecification.
New method calibrates neural SBI to avoid overconfident posteriors.
problem Overconfident posteriors in SBI due to inaccurate uncertainty quantification.
method Introduces a calibration term into neural model training objective, enabling end-to-end backpropagation.
result Achieves competitive or better coverage and posterior density than existing methods.
This work explores how overparametrization and priors affect Bayesian neural network posteriors.
problem Symmetries, non-identifiabilities, and weight-space priors fragment and inflate BNN posteriors.
method We study the interplay between overparametrization and priors in BNN posteriors, deriving key phenomena and validating through experiments.
result Overparametrization induces structured, prior-aligned weight posterior distributions.
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…
Proposes robust ITRs integrating multiple datasets to handle posterior shift.
problem Posterior shift in conditional outcome distributions between source and target populations.
method Distributionally robust approach with closed-form solution and adaptive uncertainty tuning.
result Achieves superior performance compared to existing methods in simulations and real-data applications.