A novel Bayesian framework for private linear regression with MCMC.
problem Private linear regression in a distributed setting.
method Generative statistical model, MCMC algorithms, fast Bayesian estimation.
result The proposed methods provide well-rounded estimation and prediction.
Paper proposes a new method for Bayesian linear regression using spike-and-slab priors.
problem Identifying predictors with similar relationships in linear regression models.
method Hierarchical Bayesian models with spike-and-slab priors and a Gibbs sampler.
result The proposed method outperforms previous methods in simulations and real data analysis.
Bayesian optimization (BO) is a model-based approach for gradient-free black-box function optimization. Typically, BO is powered by a Gaussian process (GP), whose algorithmic complexity is cubic in the number of evaluations. Hence, GP-based BO cannot leverage large amounts of past or related function evaluations, for e…
New algorithms improve Bayesian linear regression with spike-and-slab priors.
problem Efficiently sampling from Bayesian linear regression models with sparsity-inducing priors.
method Design of two sampling algorithms: Gibbs sampling and Stochastic Localization.
result Stochastic Localization sampler shows significant advantage for poorly designed data matrices.
Paper develops robust Bayesian models for linear regression under adversarial perturbations.
problem Ensuring reliable machine learning models under data perturbations.
method Formulates adversarial Bregman divergence loss, computes adversarial perturbation, introduces adversarially robust posteriors, derives generalization certificates.
result Derives first rigorous generalization certificates for adversarially robust Bayesian linear regression.
As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption is beyond Gaussian distribution. In this paper, we propose a Bayesian linear reg…
Derives TAP approximation for Bayesian linear regression.
problem Log-normalizing constant of posterior distribution in high-dimensional linear regression.
method Variational representation and Thouless-Anderson-Palmer approximation.
result Proves TAP approximation for spherical prior in proportional asymptotic regime.
The neural linear model is a simple adaptive Bayesian linear regression method that has recently been used in a number of problems ranging from Bayesian optimization to reinforcement learning. Despite its apparent successes in these settings, to the best of our knowledge there has been no systematic exploration of its …
Bayesian Additive Distribution Regression (DistBART) predicts distributions from grouped data.
problem Predicting distributions from grouped data with varying characteristics.
method Bayesian nonparametric approach using BART for modeling the regression function.
result Empirical and theoretical evidence supports DistBART's effectiveness in learning from low-dimensional marginals.
Study high-dimensional Bayesian linear regression using variational inference.
problem High-dimensional Bayesian linear regression with product priors.
method Non-linear large deviations theory and variational inference.
result Unique optimizer in variational problem governs posterior distribution under separation condition.
In this work, we study the use of logistic regression in manufacturing failures detection. As a data set for the analysis, we used the data from Kaggle competition Bosch Production Line Performance. We considered the use of machine learning, linear and Bayesian models. For machine learning approach, we analyzed XGBoost…
The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial for the derivation of variational Bayesian inference for simple models, as well a…
Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case basis; examples include robust linear regression, robust mixture models, and bur…
Bayesian model estimates treatment effects near cutoffs in regression discontinuity designs.
problem Estimating conditional average treatment effects in regression discontinuity designs.
method Develops a Bayesian additive regression tree (BART) model with linear leaf-level regressions.
result Adapts to different slopes on the running variable near the cutoff, providing interpretable inference.
Improved Bayesian regression for large datasets using multilevel Gibbs sampling.
problem Efficiently handling large-scale Bayesian regression with complex posterior distributions.
method Developed a multilevel Gibbs sampler for linear mixed models, incorporating data clustering and correlated samples for variance reduction.
result Significant speed-up achieved for Bayesian regression without sacrificing predictive performance.
Bayesian method improves predictions in overparameterized nonlinear regression.
problem Understanding overparameterization in nonlinear regression models.
method Bayesian framework with adaptive prior considering data spectral structure.
result Posterior contraction established for generalized linear and single-neuron models, demonstrating prediction consistency.
New method for GLMs under DP provides private uncertainty quantification.
problem Private inference for GLMs with uncertainty quantification.
method Noise-aware DP Bayesian inference method for GLMs.
result Posterior uncertainty allows determination of statistically significant coefficients.
A scalable Bayesian linear regression framework for spatial data.
problem Scalable methodologies for analyzing large spatial datasets.
method Conjugate Bayesian linear regression framework.
result Exact sampling from joint posterior distribution without iterative algorithms.
Bayesian MAML outperforms MAML in meta learning tasks with theoretical guarantees.
problem Theoretical understanding of Bayesian MAML's superiority over MAML.
method Comparison of meta test risks between Bayesian MAML and MAML in meta linear regression.
result Bayesian MAML has provably lower meta test risks than MAML in both distribution agnostic and linear centroid cases.
BART and MOTR-BART improve tree-based predictions with local linear models.
problem Non-linearity and high-order interactions in data.
method Bayesian Additive Regression Trees (BART) and Model Trees BART (MOTR-BART) using piecewise linear functions.
result MOTR-BART achieves equal or better performance with fewer trees than BART.
This work explores function-space inference using KL divergence and proposes Bayesian linear regression as a benchmark.
problem Approximating the predictive posterior distribution of Bayesian models without parameter posterior approximation.
method Employing Kullback-Leibler divergence and proposing featurized Bayesian linear regression as a benchmark.
result Minimizing KL divergence leads to an ill-defined objective function, highlighting limitations of this approach.
Bayesian nonparametric machine learning improves instrumental variable inference.
problem Estimating causal effects with nonlinear relationships.
method Bayesian Additive Regression Trees (BART) for estimating functions and Dirichlet Process mixtures for error terms.
result Dramatic improvements in inference with nonlinear data, no manual tuning required.
Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals while still allowing modelers to draw insights from data by estimating regressio…
Work proposes a new framework to improve uncertainty estimation in deep Bayesian models.
problem Traditional training procedures underestimate uncertainty in NLMs, leading to unreliable predictions.
method Introduces a novel training framework that captures useful predictive uncertainties for out-of-distribution inputs.
result Demonstrates that traditional methods for NLMs significantly underestimate uncertainty and propose a new framework to address this issue.
Simple linear models outperform complex BO methods in high dimensions.
problem Overcoming the curse of dimensionality in Bayesian optimization.
method Bayesian linear regression with linear kernels, applied to high-dimensional search spaces.
result Simple linear models match or outperform state-of-the-art BO methods in high-dimensional tasks.
Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the increasing popularity of the linear quantile regression model. This work proposes a…
PROBE algorithm efficiently solves sparse high-dimensional linear regression.
problem Sparse high-dimensional linear regression models with complex parameter spaces.
method Partitioned empirical Bayes ECM algorithm for computationally efficient MAP estimation.
result PROBE algorithm provides robust and efficient coordinate-wise optimization.
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick to inference in a parametric Bayesian model. For example, Gaussian process regre…
Efficient Bayesian variable selection for binomial and negative binomial data.
problem Computational challenges in Bayesian variable selection for complex models.
method Tempered Gibbs Sampling and MCMC scheme.
result Demonstrated effectiveness on cancer data with thousands of covariates.
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coeffici…
Bayesian approach for estimating heterogeneous treatment effects in RDD designs.
problem Heterogeneity in treatment effects in RDD designs can lead to misleading conclusions.
method Direct Bayesian Additive Regression Trees (BART) for modeling heterogeneous treatment effects.
result Flexibly captures complicated structures of heterogeneous treatment effects as a function of covariates.
Flexible Bayesian approach for generalized linear models, especially for sparse logistic regression.
problem Sparse logistic regression challenges in machine learning.
method Empirical Bayes approach with mean-field variational inference, tuning-free and scalable.
result Superior predictive performance in sparse logistic regression compared to existing methods.
In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data t…
The paper analyzes methods for sparse Bayesian regression in nonlinear system identification.
problem Learning sparse models in Bayesian regression with nonlinear applications.
method Two classes of methods: regularization and thresholding based, built on automatic relevance determination (ARD).
result Analytical demonstration of favorable performance with sparse solutions in linear problems.
This paper offers a simple method for Bayesian regression with unknown transformations.
problem Joint inference of unknown transformations and model parameters in Bayesian regression is computationally inefficient and cumbersome.
method The paper introduces a Bayesian nonparametric model via the Bayesian bootstrap to directly target the posterior distribution of the transformation.
result The approach delivers joint posterior consistency and efficient Monte Carlo inference for the transformation and all parameters.
The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-ℓ1-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection and prediction properties, as well as minimax optimality. This paper introduces …
Bayesian econometrics improves nowcasting during pandemics.
problem Improving nowcasting during extreme economic events like pandemics.
method Bayesian econometric methods using non-parametric mixed frequency VARs with additive regression trees.
result Significant improvements in nowcasting performance compared to linear models.
A simple approach to obtaining uncertainty-aware neural networks for regression is to do Bayesian linear regression (BLR) on the representation from the last hidden layer. Recent work [Riquelme et al., 2018, Azizzadenesheli et al., 2018] indicates that the method is promising, though it has been limited to homoscedasti…
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.
A fast MCMC sampler for sparse Bayesian inference.
problem Sparse Bayesian inference problems with high computational cost.
method Asynchronous Gibbs sampler extended with data sub-sampling.
result The Markov chain admits an invariant distribution that recovers the main signal with high probability.
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that takes the hierarchical model formulation of the Bayesian Lasso. The main differenc…
Study compares random and learned features in deep Bayesian linear models.
problem Understanding how feature learning affects generalization in deep learning.
method Comparing deep random feature models to deep networks with trained layers.
result Random feature models can display double-descent behavior, while deep networks do not.
Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size grows. To resolve this difficulty in the case of Bayesian linear regression, we dev…
Bayesian method tackles variable selection in high-dimensional data.
problem Challenges in Bayesian variable selection with large P.
method Efficient MCMC scheme with sublinear cost per iteration, extended to generalized linear models.
result Demonstrated effectiveness on cancer and maize genomic data.
BFTS uses Bayesian Additive Regression Trees for improved personalized mobile health interventions.
problem Adapting to complex, non-linear user behaviors in personalized mobile health interventions.
method Bayesian Forest Thompson Sampling (BFTS) integrates Bayesian Additive Regression Trees (BART) into the exploration loop of contextual bandits.
result BFTS achieves state-of-the-art regret on tabular benchmarks and improves engagement rates by over 30% in a behavioral intervention study.
Bayesian framework for semiparametric regression of discrete data.
problem Complex distributional features of discrete data.
method Semiparametric modeling with nonparametric marginal and latent linear regression.
result Posterior consistency and analytical/posterior predictive distributions.
We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be v…
A new method for efficient BNC parameter estimation outperforms HDP smoothing.
problem Efficiently estimating parameters for Bayesian network classifiers to match or exceed random forest performance.
method Uses log-linear regression to approximate hierarchical Dirichlet process (HDP) smoothing, making the approach simpler and faster.
result Our method outperforms HDP smoothing while being orders of magnitude faster and competitive with random forests.