The paper discusses the impact of prior densities on Bayesian model selection.
problem The sensitivity of marginal likelihood to prior choice in Bayesian model selection.
method Analyzes the role of prior densities in model selection, discusses improper priors, and proposes solutions.
result Marginal likelihood can be sensitive to prior choice, but improper priors can still be used with caution.
Two algorithms improve GP bandits by selecting priors and minimizing regret.
problem Selecting appropriate GP priors for unknown functions.
method Developed two algorithms: Prior-Elimination GP-TS and HyperPrior GP-TS.
result Established sublinear regret bound for HyperPrior GP-TS.
In this paper, we derive a Bayesian model order selection rule by using the exponentially embedded family method, termed Bayesian EEF. Unlike many other Bayesian model selection methods, the Bayesian EEF can use vague proper priors and improper noninformative priors to be objective in the elicitation of parameter prior…
Bayesian evidence computation revisited for model selection with improper priors.
problem Model selection with improper priors and their impact on Bayesian evidence computation.
method Employing improper priors in model selection problems, distinguishing between Bayesian evidence and fake evidences.
result Diffuse priors asymptotically to infinity do not recover the area under the likelihood.
Bayesian method corrects for model selection multiplicity in regression.
problem Model selection multiplicity in regression analysis.
method Developed a Bayesian prior distribution based on Holm procedure analogy.
result Adequate multiplicity correction requires sparsity not provided by recommended priors.
Bayesian approach to portfolio selection reduces pessimism in frequent trading.
problem Tackling the challenge of estimating drift in Merton's portfolio selection model.
method Bayesian distributionally robust control with nonlinear Wasserstein projections.
result Reduced pessimism and improved performance in frequent rebalancing compared to existing methods.
Bayesian Cox model identifies biomarkers from multi-omics data.
problem Produce interpretable survival prognosis from multi-omics data.
method Penalized semiparametric Bayesian Cox model with graph-structured selection priors.
result Model identifies new biomarkers and improves survival prediction.
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This requires repeated, costly, posterior inference. We provide an alternative for selecting…
Proposes a Bayesian approach for automatic node selection in sparse neural networks.
problem Reduces structural complexity and computational speedup in large-scale predictive models.
method Uses spike-and-slab Gaussian priors and variational Bayes approach for node selection.
result Establishes variational posterior consistency and optimal contraction rates for sparse networks.
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by …
Proposes I-prior extension for additive interaction models.
problem Challenges in estimating and selecting models with interactions.
method Extends I-prior methodology to multiple covariates, introducing a parsimonious model specification.
result Improves estimation and model selection for additive interaction models.
This paper explores minimax-Bayes solutions for reinforcement learning problems.
problem How to select appropriate priors for decision making under uncertainty in sequential decision making.
method Study of minimax-Bayes solutions for various reinforcement learning problems.
result Minimax policies are more robust than standard priors.
Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. In this work, we apply a horseshoe prior over node pre-activations of a Bayesian neur…
Factorized Information Criterion (FIC) is a recently developed information criterion, based on which a novel model selection methodology, namely Factorized Asymptotic Bayesian (FAB) Inference, has been developed and successfully applied to various hierarchical Bayesian models. The Dirichlet Process (DP) prior, and one …
Enhances Bayesian model selection for high-dimensional problems.
problem Bayesian model selection for high-dimensional problems.
method Proximal nested sampling with data-driven priors.
result Improves model selection for log-convex likelihood models.
Identifying small subsets of features that are relevant for prediction and/or classification tasks is a central problem in machine learning and statistics. The feature selection task is especially important, and computationally difficult, for modern datasets where the number of features can be comparable to, or even ex…
Improves feature selection in high-dimensional data using LLM-generated weights.
problem Inaccurate LLM-generated weights degrade feature selection performance.
method Integrates LLM-generated weights into prior inclusion probabilities using LLM Sparsity Prior (LSP).
result Improves prediction accuracy and identifies clinically relevant features.
A new criterion selects models in overparameterized settings.
problem Model selection for overparameterized models with more parameters than data.
method Establishes Bayesian duality and introduces the Interpolating Information Criterion.
result The Interpolating Information Criterion selects models in overparameterized settings.
We present an Automatic Relevance Determination prior Bayesian Neural Network(BNN-ARD) weight l2-norm measure as a feature importance statistic for the model-x knockoff filter. We show on both simulated data and the Norwegian wind farm dataset that the proposed feature importance statistic yields statistically signific…
Informative Bayesian priors are often difficult to elicit, and when this is the case, modelers usually turn to noninformative or objective priors. However, objective priors such as the Jeffreys and reference priors are not tractable to derive for many models of interest. We address this issue by proposing techniques fo…
New method improves Robbins-Monro algorithm convergence with prior information.
problem Improving convergence speed of Robbins-Monro algorithm.
method Integrates prior information into Robbins-Monro iteration without regression model.
result Prior-information Robbins-Monro sequence converges faster than standard.
Study finds economic data may not be as sparse as previously thought.
problem Modeling economic relations with many variables and prior sensitivity issues.
method Bayesian approach with Spike-and-Slab prior to evaluate variable selection and shrinkage.
result Prior distribution affects detection of sparsity patterns in economic data.
LMs perform poorly in true few-shot learning without held-out examples.
problem Evaluating few-shot performance of language models without access to held-out examples.
method Evaluated two model selection criteria (cross-validation and minimum description length) for choosing LM prompts and hyperparameters in true few-shot learning.
result Selection criteria often prefer models that perform worse than random selection, suggesting overestimation of few-shot ability.
Bayesian framework optimizes 3D view selection for specific tasks.
problem Optimizing 3D view selection for specific tasks in reconstruction.
method Bayesian decision theory, prior and posterior distributions, stochastic surface reconstruction.
result Framework achieves superior performance with fewer views.
Model selection is crucial to high-dimensional learning and inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work assumes implicitly that the models are correctly specified or have fixed dimensionality. Yet both …
A novel Bayesian method for dynamic sparsity in Gaussian dynamic linear regression.
problem Variable selection and shrinkage in time-varying regression models.
method Time-varying sparsity via Markov switching priors for coefficients' variances, extending spike-and-slab priors.
result Induces smoothness or shrinkage towards zero at each time point, leading to improved model performance.
Study uses healthcare claims data to identify Covid-19 risk factors without prior selection.
problem Identify risk factors for severe Covid-19 cases.
method Fine-grained hierarchical information from medical classification systems used to analyze over 33,000 covariates.
result Method has better predictive ability than pre-specified morbidity groups.
Proposes a non-conjugate model selection method for chain event graphs.
problem Existing model selection algorithms for chain event graphs rely on conjugate priors, which is unrealistic for many real-world applications.
method Proposes a mixture modelling approach to model selection in chain event graphs that does not rely on conjugacy.
result The proposed method is more scalable and robust than existing algorithms.
The class of chain event graph models is a generalisation of the class of discrete Bayesian networks, retaining most of the structural advantages of the Bayesian network for model interrogation, propagation and learning, while more naturally encoding asymmetric state spaces and the order in which events happen. In this…
Novel method for model selection in Bayesian autoencoders.
problem Model selection for Bayesian autoencoders.
method Prior hyper-parameter optimization using distributional sliced-Wasserstein distance.
result State-of-the-art results in small-data regimes.
Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous theoretical studies on spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and analyses, and thus can not be generalized directly. In this paper, we propose a class o…
HS-MoE selects sparse experts using adaptive priors and data-adaptive gating.
problem Sparse expert selection in mixture-of-experts architectures.
method Combines horseshoe prior with input-dependent gating for data-adaptive sparsity.
result Data-adaptive sparsity in expert usage.
FEM improves attention mechanisms by applying value-driven log-linear tilts.
problem Standard attention mechanisms read via convex average, limiting channel-wise selection.
method Free Energy Mixer (FEM) applies a value-driven, per-channel log-linear tilt to a fast prior over indices.
result FEM outperforms strong baselines on NLP, vision, and time-series tasks.
Model selection is indispensable to high-dimensional sparse modeling in selecting the best set of covariates among a sequence of candidate models. Most existing work assumes implicitly that the model is correctly specified or of fixed dimensions. Yet model misspecification and high dimensionality are common in real app…
Novel Bayesian model improves EEG-based BCI character selection.
problem Accurately identifying target-related responses in EEG-based BCIs.
method Probit-link Split-and-merge Gaussian Process (P-SMGP) prior for feature selection.
result Reduces computational complexity and provides interpretable statistical interpretations.
The paper decouples shrinkage and selection in Bayesian Quantile Regression.
problem Improving prediction accuracy in high-dimensional Bayesian Quantile Regression.
method Two-step procedure: shrinkage through continuous priors, sparsification through SAVS.
result The method reduces bias and provides interpretable variable selection.
Study membership inference under skewed priors and adaptive thresholds, improving attack accuracy.
problem Membership inference in imbalanced settings with selective thresholding.
method Developed PPV metric for skewed priors, threshold selection procedure, and a new inference attack.
result Improved inference attack accuracy in imbalanced settings.
R2D2-Net improves Bayesian neural networks by preventing over-shrinkage of important weights.
problem Bayesian neural networks struggle with choosing appropriate priors, leading to over-shrinkage or poor predictive performance.
method Proposes R2D2-Net with an R^2-induced Dirichlet Decomposition prior and variational Gibbs inference algorithm.
result R2D2-Net effectively shrinks irrelevant coefficients while preventing key features from over-shrinkage.
Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a single final model via a model selection procedure to account for this model's uncert…
Bayesian framework selects features and lags for time series forecasting.
problem Variable selection and lagged error term identification in time series models.
method Hierarchical Bayesian models with spike-and-slab priors, two-stage MCMC algorithm.
result Posterior selection consistency under mild conditions, improved predictive performance.
PliableBVS extends Bayesian lasso for modeling interactions with modifying variables.
problem Modeling interactions between large and small sets of variables, especially in omics studies.
method Bayesian variable selection with spike-and-slab priors and hierarchical structure.
result PliableBVS outperforms pliable lasso in identifying active main and interaction effects.
CONCERT improves transfer learning by borrowing partial information from auxiliary datasets.
problem Inefficiency of global similarity measures in transfer learning for high-dimensional data.
method Conditional spike-and-slab prior with covariate-specific priors for robust partial information transfer.
result CONCERT achieves variable selection and information transfer simultaneously, improving performance on the target.
Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost and it is difficult to design nonstationary GP priors in practice. In this paper, we propose a sparse Gaussian process model, EigenGP, based on the Karhunen-Loeve (KL) expan…
Develops probabilistic models for gene regulatory network inference.
problem Challenges in reconstructing gene regulatory networks from genome-wide data.
method Two complementary frameworks: PMF-GRN and GLM-Prior.
result Probabilistic inference refines regulatory estimates with quantified uncertainty.
Most deep latent factor models choose simple priors for simplicity, tractability or not knowing what prior to use. Recent studies show that the choice of the prior may have a profound effect on the expressiveness of the model,especially when its generative network has limited capacity. In this paper, we propose to lear…
This paper tackles federated learning for automatic latent variable selection in multi-output Gaussian processes.
problem Challenges in determining the adequate number of latent processes and relying on centralized learning for privacy and computational issues.
method Proposes a hierarchical model with spike-and-slab priors for automatic latent process selection and variational inference-based federated learning algorithm.
result Demonstrates the advantageous features of the proposed federated approach through simulations and real-world data.
This paper proposes a framework for certifying neural network defenses against data poisoning attacks.
problem Vulnerability of neural networks to data poisoning attacks.
method Random selection based defenses that average predictions on sub-datasets sampled from the training set.
result The certified radius of bagging derived by the framework is tighter than previous work.
Regression Prior Networks improve ensemble performance on regression tasks.
problem Improving ensemble performance on regression tasks.
method Extending Prior Networks and Ensemble Distribution Distillation (EnD2) to regression tasks using the Normal-Wishart distribution. result Regression Prior Networks yield performance competitive with ensemble approaches on regression tasks.