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.
This paper improves Bayesian neural nets by using local linearization.
problem Underfitting in Bayesian neural networks.
method Local linearization of Bayesian neural networks to create a generalized linear model (GLM) for predictions.
result The GLM predictive resolves common underfitting problems of the Laplace approximation.
Solla discusses neural processing using statistical physics and Bayesian methods.
problem Understanding neural information processing through statistical physics.
method Bayesian inference, Gibbs description, Generalized Linear Models, dimensionality reduction.
result Connection between neural processing and statistical physics.
New method uses diffusion models for Bayesian inverse problems.
problem Solving Bayesian inverse problems with linear-Gaussian models.
method Decoupled Diffusion Sequential Monte Carlo (DDSMC) method.
result Asymptotically exact solution demonstrated on various data types.
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization, which predicts unobserved entries as linear combinations of latent variables. We g…
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.
FBMS R package simplifies Bayesian model selection and averaging.
problem Complex regression settings with multi-modal posterior landscapes.
method Efficient MJMCMC and GMJMCMC algorithms for Bayesian model exploration.
result FBMS effectively handles Bayesian generalized linear and nonlinear models.
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…
Study clarifies Bayesian generalization error in CBM for 3-layered linear neural networks.
problem Understanding the generalization error in concept bottleneck models.
method Mathematical analysis of Bayesian generalization error and free energy in CBM for 3-layered linear neural networks.
result CBM significantly alters the parameter region and Bayesian generalization error compared to standard models.
Develops generic spike-and-slab priors for high-dimensional linear regression.
problem Bayesian high-dimensional linear regression challenges.
method Proposes a class of generic spike-and-slab priors and a unified framework for theoretical assessment.
result Achieves nearly-optimal posterior contraction rate and model selection consistency under general conditions.
Neural linear model performs well on simple regression tasks but requires tuning.
problem Characterizing the neural linear model's performance on simple regression tasks.
method Characterized the neural linear model on UCI and gap datasets.
result The neural linear model shows good performance but requires good hyperparameter tuning.
Automates model selection for GLMs using optimization.
problem Automating model selection for generalized linear models.
method Mixed-integer conic optimization for feature subset selection and model constraints.
result Optimization of AIC and BIC criteria with multicollinearity constraints.
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…
Bayesian optimization improved for biased data.
problem Adversarial bias in observations, especially hidden confounders.
method Reduction to dueling bandits, information-directed sampling (IDS).
result First efficient kernelized algorithm with regret guarantees.
Bayesian framework for encoding uncertainty and inducing sparsity.
problem Handling uncertainty and inducing sparsity in statistical models.
method General Bayesian framework with explicit encoding of uncertainty and sparsity-inducing approach.
result Effective in linear and logistic regression, and Bayesian neural networks.
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…
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.
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…
Bayesian deep learning faces posterior collapse due to likelihood vs. prior competition.
problem Posterior collapse in Bayesian deep learning models.
method Identified competition between likelihood and prior regularization in a linear latent variable model.
result Posterior collapse is related to neural and dimensional collapse, suggesting a broader learning issue.
New methods combine model predictions to avoid linear mixtures' limitations.
problem Combining predictions from different models to avoid linear mixtures' limitations.
method Log-linear pooling (locking) and quantum superposition (quacking) to optimise model weights.
result Demonstrated locking method with illustrative example and practical application.
MCGDiff uses SGM to guide SMC for solving ill-posed linear inverse problems.
problem Solving ill-posed linear inverse problems in Bayesian settings.
method Exploiting SGM structure, defining a sequence of intermediate problems, and using SMC methods.
result MCGDiff outperforms competing methods in Bayesian ill-posed inverse problems.
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.
Deep networks become equivalent to linear models in large data regimes.
problem Understanding the behavior of deep neural networks in large data regimes.
method Information-theoretic analysis of fully-trained neural networks in proportional scaling regime.
result Proves deep Gaussian equivalence principle, showing deep networks can be simplified to linear models.
This dissertation uses ILP to learn Bayesian network structures efficiently.
problem Learning the structure of Bayesian networks from data.
method Integer Linear Programming formulation with cluster constraints and cutting planes.
result The approach finds feasible solutions for Bayesian network structures efficiently.
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.
RNN-HAR model improves VaR forecasting with long-memory and non-linear dynamics.
problem Efficiently forecasting Value at Risk (VaR) with long-memory and non-linear realized volatility.
method Loss-based generalized Bayesian inference with Sequential Monte Carlo for model estimation and prediction.
result RNN-HAR model consistently outperforms other VaR forecasting models.
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 Bayesian inference on large datasets.
problem Scalable sampling for Bayesian generalized linear mixed models on large datasets.
method Mirror Langevin dynamics with data subsampling, post-processing for variance estimation.
result Asymptotic, order-wise correct estimation of posterior variance.
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…
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.
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…
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.
Develops CLDS models to model neural activity with nonlinear dynamics.
problem Complex, nonlinear dynamics in neural population activity.
method Conditionally Linear Dynamical System (CLDS) models using Gaussian Process (GP) priors.
result CLDS models can perform well even in data-limited conditions.
Paper introduces VBG for Bayesian causal structure and mechanism learning.
problem Bayesian causal structure learning with uncertainty over models.
method Variational Bayes-DAG-GFlowNet (VBG) method.
result VBG outperforms existing methods in modeling posterior over DAGs and mechanisms.
Bayesian bandit algorithms with approximate inference improve regret bounds in stochastic linear bandits.
problem Theoretical justification for Bayesian bandit algorithms with approximate inference in stochastic linear bandits.
method Proposed a theoretical framework to analyze approximate inference impact and conducted frequentist regret analysis on LinTS and LinBUCB.
result LinTS and LinBUCB preserve their original regret upper bounds with larger constant terms in approximate inference settings.
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.
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.
Bayesian analysis reveals epistemic uncertainty as a key diagnostic for delayed generalization in in-context learning.
problem Delayed generalization in in-context learning from few examples.
method Bayesian perspective, modular arithmetic tasks, approximate Bayesian techniques, spectral mechanism analysis.
result Epistemic uncertainty collapses sharply when the model groks, indicating a practical diagnostic of generalization.
Bayesian Federated Inference improves survival model analysis without merging data.
problem Accurately estimating survival model parameters requires sufficient data and events, which is often lacking in practice.
method Bayesian Federated Inference (BFI) for survival models, where local centers perform analyses and combine results.
result Results from BFI are similar to those from merged data analyses, demonstrating excellent performance.
New method improves uncertainty estimation in Bayesian deep learning models.
problem Underestimation of predictive uncertainty in Neural Linear Models (NLMs).
method Proposes a novel training method to capture useful predictive uncertainties and incorporate domain knowledge.
result Traditional training procedures for NLMs can drastically underestimate uncertainty in data-scarce regions.
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.
PCBM improves neural network generalization by partially observing concepts.
problem Decreased generalization performance due to observing all concepts in CBM.
method Developed a theoretical analysis of PCBM's Bayesian generalization error.
result PCBM's generalization error is lower than CBM's due to partial concept observation.
BayesBoost combines boosting and Bayesian methods for linear mixed models, improving uncertainty estimation and variable selection.
problem Lack of straightforward uncertainty estimation for parameters in high-dimensional linear mixed models.
method BayesBoost: Combines boosting and Bayesian inference for linear mixed models.
result Improves uncertainty estimation and variable selection in linear mixed models.
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.
We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with β-divergences. The resulting inference procedure is doubly robust for both the parameter and the changepoint (CP) posterior, with linear time and constant space complexity. We provide a const…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
A scalable method for Bayesian inference in large linear models.
problem High computational cost in Bayesian linear models for large networks.
method Sample-based inference and g-prior for hyperparameter selection.
result Linearised neural network inference on large datasets (ResNet-18, ResNet-50, U-Net).
New method reduces SBL complexity from cubic to linear, improving scalability.
problem Sparse Bayesian Learning's high computational complexity for large feature spaces.
method DQN-SBL, a diagonal Quasi-Newton method for SBL.
result DQN-SBL achieves competitive generalization with sparse models, scaling well to large-scale problems.