New approach shows AI can adapt like toddlers by correcting old knowledge.
problem Lack of adaptability in AI models compared to humans and animals.
method Casting adaptation as posterior correction and using Bayesian Learning Rule.
result AI can learn to adapt quickly by using posterior correction.
Adaptive variational Bayes framework improves inference adaptively.
problem Lack of general and computationally tractable variational Bayes method for adaptive inference.
method Proposes a novel adaptive variational Bayes framework combining variational posteriors over individual models.
result Adaptive variational Bayes achieves optimal contraction rates adaptively under general conditions.
Bayesian model infers factor dimensionality and sparse loading matrix adaptively.
problem Inference of high-dimensional sparse factor model with varying sparsity and factor dimensions.
method Adaptive Bayesian sparse factor model with posterior concentration.
result Posterior distribution asymptotically concentrates on true factor dimensionality and sparsity.
JADAI optimizes design and inference for parameter estimation.
problem Parameter estimation with active optimization of design variables.
method Jointly trains a policy, history network, and inference network to minimize posterior error.
result Achieves superior or competitive performance across benchmarks.
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.
Bayesian nonparametric LABS model adapts to function smoothness in Besov spaces.
problem Estimating functions with unknown smoothness in Besov spaces.
method Lévy Adaptive B-spline (LABS) regression model with automatic smoothness adaptation.
result LABS posterior contracts around true function in Besov classes at nearly minimax-optimal rates.
Study adaptive sensing of Cox processes using posterior sampling and positive bases.
problem Adaptive sensing of Cox point processes with intensity function modeling.
method Model intensity function as truncated Gaussian process in positive basis, use Langevin dynamics and posterior sampling.
result Demonstrated improved sensing compared to classical Bayesian experimental design.
ABI bypasses likelihood intractability with nonparametric distribution matching.
problem Approximate Bayesian computation's inefficiency in high-dimensional settings and under diffuse priors.
method Adaptive Bayesian Inference (ABI) compares posterior distributions directly using nonparametric distribution matching and MSW distance.
result ABI significantly outperforms other methods in high-dimensional or dependent observation regimes.
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.
The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.
problem Sparse high-dimensional linear regression with random design and unknown error variance.
method Analysis of posterior concentration rates, employing techniques to address model misspecification.
result Adaptiveness and concentration rates of the posterior for sparse high-dimensional linear regression.
Adaptive querying learns user psychometrics with AI personas.
problem Learning user psychometrics within query budgets.
method Persona-induced latent variable model with AI personas and large language model response distributions.
result Persona-based posteriors deliver accurate probabilistic predictions.
cKAM improves adaptive sampling by incorporating a cyclical stepsize scheme.
problem Adaptive Metropolis algorithms can get stuck in local modes.
method cKAM uses a cyclical stepsize scheme to encourage exploration and escape from local modes.
result cKAM successfully escapes local modes and converges to the true posterior distribution.
Bayesian neural networks approximate Gaussian, this method adapts to non-Gaussian posteriors.
problem Bayesian neural networks struggle with non-Gaussian posteriors, leading to poor performance.
method Proposes a Riemannian Laplace approximation to adapt to the shape of the true posterior.
result Consistently improves over conventional Laplace approximation across tasks.
Conformal Bayes under label shift: post-hoc calibration vs. in-training adaptation
problem Bayesian prediction sets under label shift
method Post-hoc calibration vs. In-training adaptation
result Both strategies achieve valid coverage equally in an unbiased training regime
Adaptive stepsizing improves sampling in Bayesian neural networks.
problem Scalable sampling of posterior distributions in Bayesian neural networks.
method SA-SGLD, employing time rescaling to adapt stepsize dynamically.
result SA-SGLD achieves more accurate posterior sampling than SGLD.
A new data-adaptive prior stabilizes kernel learning in operators.
problem Learning kernels in operators from data is ill-posed due to nonlocal dependence.
method Introduces a data-adaptive prior to stabilize the Bayesian posterior mean.
result The data-adaptive prior achieves a stable posterior with small noise limits.
New perspective on federated learning as posterior inference, improving optimization.
problem Optimizing global models in distributed learning settings.
method Formulated as posterior inference problem, using MCMC for approximate inference and federated averaging for refinement.
result Federated posterior averaging (FedPA) outperforms existing methods on benchmarks.
Bayesian posterior contraction rates improve with decreasing tails
problem Bayesian posterior contraction in nonparametric settings
method Using p p p -exponential tails for contraction rates result Improvement in contraction rates with decreasing tails
AMF-VI uses adaptive mixtures of flows for robust VI across diverse distributions.
problem Inconsistent behavior of single-flow models across different distributions.
method Sequential expert training of individual flows and adaptive global weight estimation via likelihood-driven updates.
result AMF-VI achieves lower negative log-likelihood and stable gains in transport metrics across various posterior families.
New BNN model proves optimal posterior concentration and enables practical inference.
problem Improving generalization and uncertainty quantification in deep neural networks.
method Proposes a new node-sparse BNN model with theoretical guarantees and a novel MCMC algorithm for inference.
result Proves near minimax optimal posterior concentration rate and adaptiveness to true model smoothness.
In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: un…
We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates pathologies in existing adaptive methods. ITs adaptively sample from hierarchica…
Transformer pretraining yields strong EB performance without explicit adaptation.
problem Empirical Bayes problems with unknown test distributions.
method Indirect analysis of pretrained transformer's performance under universal priors.
result Near-optimal regret bound of O ~ ( 1 n ) \widetilde{O}(\frac{1}{n}) O ( n 1 ) for arbitrary test distributions. Oracle inequality for sparse neural nets adapts to unknown structure.
problem Sparse deep neural nets in nonparametric regression.
method Gibbs posterior distribution with Metropolis-adjusted Langevin algorithms and mixture of uniform priors.
result Oracle inequality showing adaptation to unknown regularity and structure, achieving minimax-optimal rate of convergence.
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.
New algorithm improves Bayesian neural networks using adaptive importance sampling.
problem High computational cost in training Bayesian neural networks.
method Adaptive Importance Sampling (AIS) integrated into a novel algorithm (PMCnet).
result Improved performance and exploration capabilities for both shallow and deep neural networks.
Improves posterior approximation speed for Dirichlet process mixture models.
problem Inefficiency of stochastic variational inference in large datasets.
method Uses stochastic gradient ascent with adaptive stepsize optimization.
result Adaptive stepsize improves speed and performance of posterior approximation.
Calibrated probabilistic solvers improve accuracy of ODE estimates.
problem Uncertainty in probabilistic ODE solutions is not well-calibrated for adaptive step sizes.
method Introduce and assess several calibration methods for probabilistic ODE solvers.
result Calibration methods interact efficiently with adaptive step-size selection, improving posteriors.
This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated efficient alternative, based on the Adaptive Metropolis algorith…
This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters. Specifically, the filter is designed for the situation where the subsequent data in on…
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.
AdOBEst-LDP improves privacy-preserving frequency estimation for categorical data.
problem Estimating categorical distributions online while preserving privacy.
method AdOBEst-LDP uses adaptive randomized response mechanism to enhance future data utility.
result AdOBEst-LDP selects optimal subset for LDP mechanism with high probability.
Two approaches improve conformal Bayes for label shift, one post-hoc and one in-training.
problem Improving prediction sets for target domain under label shift.
method Two complementary approaches: post-hoc calibration and in-training adaptation.
result In-training adaptation achieves up to 43% width reduction at unchanged coverage.
ABI adapts to graph data for fast, scalable inference.
problem Challenges in inference on graph-structured data.
method Amortized Bayesian Inference (ABI) framework for graph data.
result ABI successfully addresses challenges in graph data inference.
The paper proposes a method to improve Bayesian inference for periodic data using data-driven priors.
problem Efficiency in approximating posterior distribution in models with periodicity.
method Construct a prior distribution from data using a Gaussian process with a periodic kernel, approximated using adaptive importance sampling.
result The proposed method improves the marginal posterior distribution of the period parameter.
PDTS improves robustness in sequential decision-making.
problem Robust active task sampling for efficient and reliable decision-making.
method Characterizes robust active task sampling as a Markov decision process, proposes PDTS method.
result Significantly improves zero-shot and few-shot adaptation robustness.
New methods for scalable inference in modular models with misspecified sub-models.
problem Model misspecification in multi-modular models complicates evidence combination.
method Variational methods for approximating Cut and SMI posteriors, and Variational Meta-Posterior.
result Feasibility of analysis with multiple cuts using a single set of variational parameters.
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 \alpha α parameter of Amari's α \alpha α -divergence. result Improved performance through appropriate choices of the α \alpha α parameter. How can one perform Bayesian inference on stochastic simulators with intractable likelihoods? A recent approach is to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators. However, existing methods are limited to a narrow range of proposal distributions or r…
Bayesian inference for Levy density with Gibbs posterior in discrete sampling.
problem Inference on Levy density for financial models with jumps.
method Gibbs posterior framework using a loss function for intractable likelihood.
result Gibbs posterior achieves nearly optimal rate of convergence under certain conditions.
Fast Bayesian inference with adaptable priors for real-time applications.
problem Intractable exact posterior computation limits Bayesian inference's adoption.
method Distribution Transformer architecture that learns mappings between priors and posteriors.
result Significant reduction in computation time from minutes to milliseconds.
New method quantifies uncertainty in fine-tuned LLMs using LoRA ensembles.
problem Uncertainty in fine-tuned LLMs and how to trust their predictions.
method Posterior approximations using low-rank adaptation ensembles.
result Unexpected retention of acquired knowledge during fine-tuning in overfitting regime.
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.
DABS uses a policy network to select experiments in high-dimensional design spaces.
problem Adaptive factorial screening in high-dimensional discrete design spaces.
method DABS learns a policy network offline to sequentially select experiments, incorporating sparsity and interactions via a spike-and-slab prior.
result DABS achieves superior accuracy and scalability over classical and Bayesian baselines under tight experimental budgets.
Boosting Variational Inference improves posterior approximations with adaptive step-sizes.
problem Limited resources hinder the widespread adoption of Boosting Variational Inference.
method Characterized global curvature impact, introduced local curvature, and developed an approximate backtracking algorithm.
result New theoretical convergence rates and experimental validation demonstrate improved performance.
The paper analyzes how Gaussian kernel parameters affect posterior covariance in Gaussian processes.
problem Understanding the influence of Gaussian kernel parameters on posterior covariance in Gaussian processes.
method Geometric analysis and a posteriori error estimation techniques from adaptive finite element methods.
result The bandwidth parameter and spatial distribution of observations significantly influence posterior covariance and its matrix.
Adaptive quadrature improves Bayesian inference through active learning.
problem Efficiently estimating posterior densities in Bayesian inference.
method Sequential node selection using acquisition functions, combining interpolative surrogate models and quadrature rules.
result Positive estimation of marginal likelihood with improved accuracy.
UDN adapts depth to data complexity, outperforming standard neural networks.
problem Adapting neural network depth to data complexity.
method Variational inference for infinitely deep neural networks with a novel algorithm.
result UDN outperforms standard neural networks and other infinite-depth approaches.