Gaussian-Dirichlet posterior dominance proven for sequential categorical data.
problem Sequential learning from categorical observations bounded in [0,1]
method Establishing an ordering between Dirichlet and Gaussian posteriors under N(0,1) noise
result Posterior mean of categorical distribution stochastically dominates Gaussian distribution
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Study convergence rates of variational posterior distributions for inference.
problem Characterize convergence rates of variational posterior distributions for nonparametric and high-dimensional inference.
method Formulate general conditions on prior, likelihood, and variational class to characterize convergence rates. Propose novel prior mass conditions for specific prior distributions.
result The convergence rate of variational posterior distributions is the sum of the convergence rate of the true posterior and the variational approximation error.
Bayesian neural networks explore rare fluctuations for better feature learning.
problem Understanding rare but dominant fluctuations in Bayesian neural networks.
method Large-deviation theory and joint optimization over predictors and internal kernels.
result Posterior rate function optimization reveals data-dependent kernel selection.
New method improves variational inference for dynamical systems without extra computational cost.
problem Inexact variational inference leading to overconfident posterior and overestimation of process noise.
method Proposes a non-factorised posterior distribution for Gaussian process transition functions.
result Improves accuracy of posterior over transition function and process noise estimation.
Advocates for a new posterior that predicts better than classical and generalised Bayes.
problem Combining parameter inference and density estimation for better predictive models.
method Predictively Oriented (PrO) posterior using mean field Langevin dynamics.
result PrO posteriors converge to the predictively optimal model average, adapting to model misspecification.
VB under misspecified models yields asymptotically normal posterior and predictive distributions.
problem Theoretical guarantees for VB under model misspecification.
method Proved asymptotic normality and KL divergence minimization for VB posterior under misspecified models.
result VB posterior mean centers at the true distribution's minimum KL divergence, explaining predictive accuracy with MCMC.
Neighborhood sampling affects graph neural network training outcomes.
problem Understanding the impact of neighborhood sampling on graph neural network training.
method Theoretical analysis using neural tangent kernels and Gaussian processes.
result Posterior covariance differs for different neighborhood sampling approaches, indicating no dominant approach.
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.
Improved predictive uncertainties in Gaussian Process regression.
problem Substantially underestimated uncertainties in GP predictive distributions.
method Two methods for scalable GP regression: variational inference for FITC and direct posterior predictive distribution.
result Significantly better calibrated uncertainties and higher log likelihoods.
A tutorial on variational inference for high-dimensional models.
problem Approximating marginal likelihood and posterior in Bayesian models.
method Parametric approach to variational inference.
result Variational inference is now preferred for high-dimensional models and large datasets.
New data-dependent priors improve PAC-Bayes bounds.
problem Improving PAC-Bayes bounds for nonconvex learning.
method Using data to learn a conditional expectation of the posterior, given a subset of training data.
result Data-dependent oracle priors lead to stronger PAC-Bayes bounds.
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
New approach to quantify posterior concentration rates using Wasserstein dynamics.
problem Quantifying the speed of posterior distribution concentration in Bayesian statistics.
method Combining local Lipschitz-continuity with dynamic formulation of Wasserstein distance.
result Optimal posterior contraction rates in finite and infinite-dimensional models.
WBCP improves conformal prediction for distribution shifts using weighted Dirichlet posteriors.
problem Handling distribution shifts in conformal prediction.
method Generalizes Bayesian Quadrature Conformal Prediction (BQ-CP) to arbitrary importance-weighted settings.
result WBCP maintains coverage guarantees while providing richer uncertainty information.
Entropy regularization improves interpretability of probabilistic clustering models.
problem Bayesian nonparametric mixture models often produce unbalanced cluster frequencies.
method Interpreting the posterior as penalized likelihood, entropy regularization reduces sparsely-populated clusters.
result The proposed entropy-regularized estimator enhances interpretability without sacrificing computational convenience.
Misspecification-Aware Simulation-Based Inference via Side-Channel Guidance
problem Simulation-based inference (SBI) of latent parameters is hindered by simulator misspecification.
method Misspecification-Aware Simulation-Based Inference (MA-SBI) turns side-channel text into a posterior correction.
result MA-SBI matches the oracle posterior across 10 seeds and two backbones.
RVRAE combines deep learning and dynamic factor models for better stock returns prediction.
problem Improving stock returns prediction in volatile markets.
method Combines dynamic factor modeling with variational recurrent autoencoder (VRAE). Uses prior-posterior learning for optimal factor model.
result RVRAE outperforms traditional methods in predicting stock returns and estimating variances.
The paper optimizes LLM accuracy by stopping early based on consistent answers.
problem Improving LLM accuracy in math and reasoning problems.
method Bayesian stopping policy to save on sampling costs, tracking only the L-1 most frequent answer counts.
result The L=3 stopping policy is sufficient for asymptotic optimality and significantly reduces inference costs.
Improves state space models' resistance to noise.
problem State space models' initialization assumes noise-free data, which is often violated.
method Uncertainty-aware initialization for state space models, reformulating HiPPO with measurement noise.
result Improves model resistance to noise at training and inference time.
Study on limits of LLM-based multi-agent planning reliability.
problem Reliability limits of LLM-based multi-agent planning.
method Modeling LLM-based multi-agent architecture as a decision network, showing dominance by centralized Bayes decision maker.
result Optimizing multi-agent directed acyclic graphs under communication budget is equivalent to choosing a constrained experiment.
Differentiable relaxation for inferring partial orders from noisy linear data.
problem Inference of partial orders from linear data with noisy observations.
method Introducing a differentiable relaxation to model noisy linear extensions, replacing discontinuous precedence and feasibility with smooth surrogates.
result Smooth posterior that preserves partial-order semantics, supports gradient-based inference, and converges to hard likelihood.
This paper presents a fast Bayesian filtering technique for state estimation.
problem Bottleneck in Bayesian inference for state estimation from noisy sensor data.
method Processor-native uncertainty tracking for uncertainty propagation and inference.
result Deterministic approximate filtering with up to 805x speedup and competitive accuracy.
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.
Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.
problem Boundary-induced acquisition bias in Gaussian processes.
method Traced root cause to geometric mechanism of kernel truncation at domain boundaries.
result Boundary effects create distortion that worsens with dimensionality, affecting acquisition behavior.
Develops a Bayesian framework for symbolic regression of scientific expressions.
problem Lack of principled uncertainty quantification and interpretability in existing symbolic regression methods.
method Hierarchical Bayesian framework with tree-structured symbolic expressions and Markov chain Monte Carlo inference.
result Robust performance on various datasets, including single-atom catalysis.
Deep clustering models are shown to be equivalent to K-means under certain conditions.
problem The challenge of unsupervised deep learning and clustering.
method The study proves the equivalence of recent discriminative models and K-means under specific conditions and parameters.
result Maximizing the L2 regularized mutual information is equivalent to a soft and regularized K-means loss.
Bayesian neural networks improve performance at finite temperature.
problem Improving generalization in neural network classifiers.
method Sampling from finite temperature distributions derived from the posterior.
result Optimal performance achieved at non-zero temperature values.
Connected domination numbers found for plane triangulations up to 13 vertices.
problem Finding connected domination numbers for plane triangulations.
method Analyzing triangulations of up to 13 vertices and proving the difference between connected and regular domination numbers can be arbitrarily large.
result Connected domination numbers for triangulations up to 13 vertices and upper bound for larger triangulations.
BBVI relies on adaptive stochastic optimization algorithms for posterior approximation, but these require extensive tuning.
problem BBVI posterior approximation
method Adaptive stochastic optimization algorithms
result No single method dominates, but a selection of 5 suffices.
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.
New algorithm identifies dominant arm with high probability.
problem Identifying the arm with the highest realized reward in multi-armed bandits.
method Dominance score criterion and joint mixing and recycling mechanism.
result Identifies the best dominant arm with nearly optimal sample complexity.
Manifolds can be dominated by hypersurfaces in a sphere.
problem Dominating manifolds with hypersurfaces.
method Proving any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.
result Any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.
3-manifolds virtually 1-dominated by hyperbolic ones.
problem Domination of 3-manifolds by hyperbolic ones.
method Enhanced connection principle in good pants constructions.
result Every 3-manifold is virtually 1-dominated by a hyperbolic one.
SLT reveals how grokking occurs via basin selection in training.
problem Understanding grokking in machine learning models.
method Singular Learning Theory (SLT) to analyze the loss landscape and local learning coefficient (LLC).
result LLC ranks basins by statistical preference, leading to grokking.
New method ranks multivariate distributions in SMOOP using q-dominance.
problem Lack of reliable methods to rank multivariate distributions in SMOOP.
method Introduces center-outward q-dominance and develops empirical test procedures.
result Proves q-dominance implies FSD and establishes a sample size threshold.
New framework for ranking distributions using variable fractional parameters.
problem Ordering distributions with varying steepness and local non-concavities.
method Introducing a function γ:Ro[0,1] to replace the fixed parameter in fractional SD. result Enables ranking of a broader range of distributions and incorporates dynamic greediness.
This paper models default data to capture dynamic dependence across sectors.
problem Static models fail to explain monthly default dependence.
method Dynamic low-rank state-space model for monthly multi-sector default-count data.
result Effective correlation matrices and copulas are induced from monthly data.
We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.
A new family of stochastic dominance orders based on distortion functions.
problem Determining a continuum of dominance relations for risk assessment.
method Introducing H-distorted stochastic dominance, a generalized family of stochastic orders.
result Power-distorted stochastic dominance is particularly appealing due to its simplicity and statistical interpretations.
Research examines when 4-manifolds are dominated by geometric ones.
problem When is an orientable closed 4-manifold dominated by another?
method Focuses on geometric or fibred cases.
result Characterizes conditions for domination.
The study determines dominations between manifold products and semi-norm finiteness.
problem Understanding dominations between different products of manifolds.
method Analyzing the finiteness of product-associated semi-norms on fundamental classes.
result Partial answers to M. Gromov's questions on manifold product dominations and semi-norms.
3-manifolds can virtually dominate others with positive simplicial volume.
problem Domination of 3-manifolds with positive simplicial volume.
method Proving existence of finite covers with degree-1 maps.
result Virtual domination of 3-manifolds with positive simplicial volume.
Temporal coarse-graining of multi-sector default count data generates effective correlation matrices and rank copulas.
problem Explaining the difference in default dependence between monthly and annual aggregation.
method Dynamic low-rank state-space model with AR(1) latent credit-state factors.
result Effective correlation matrices and rank copulas are generated from monthly default count data.
This paper proposes an EM approach to reduce inference latency in NAR sequence generation.
problem High inference latency in NAR models due to multi-modality in sequence generation.
method A unified EM framework that jointly optimizes AR and NAR models, with iterative refinement.
result The proposed approach achieves competitive performance with existing NAR models and significantly reduces inference latency.
Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.
problem Domination problem between non-Fuchsian representations of closed surface groups.
method Analysis of branched harmonic immersions and construction of anti-de Sitter 3-manifolds.
result Found that representations admitting branched harmonic immersions dominate other representations, and constructed large families of branched anti-de Sitter 3-manifolds.
Develops Bayesian approach for end-to-end learning in stochastic optimization.
problem Stochastic optimization problems under uncertainty.
method Bayesian interpretation and new end-to-end learning algorithms.
result Improved decision maps for empirical risk minimization and distributionally robust optimization.
Dominant knots have isomorphic Seifert and Tait graphs.
problem Understanding knot dominance through graph isomorphism.
method Examined alternating knots and their Seifert and Tait graphs.
result Isomorphic Seifert and Tait graphs indicate dominant knots.