Paper proposes a QUBO formulation that reduces binary variables in Bayesian network learning.
problem Reducing the number of binary variables in QUBO formulations for Bayesian network learning.
method Proposes a new QUBO formulation that minimizes binary variables.
result Significantly reduces the number of binary variables required for Bayesian network structure learning.
Bayesian optimization identifies optimal alloy formulations.
problem Accelerated discovery in materials science with autonomous systems.
method Bayesian optimization over problem formulation space.
result Framework converges on optimal alloy formulations.
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.
This article provides a unifying Bayesian network view on various approaches for acoustic model adaptation, missing feature, and uncertainty decoding that are well-known in the literature of robust automatic speech recognition. The representatives of these classes can often be deduced from a Bayesian network that exten…
New method reduces over-pessimism in Bayesian control under parameter uncertainty.
problem Over-pessimism in Bayesian control due to misspecified priors.
method Distributionally robust Bayesian control (DRBC) with strong duality and optimization.
result Validated algorithm on synthetic and real data, reducing over-pessimism.
This paper simplifies MTGP derivations for Gaussian processes.
problem Understanding the derivations of Multi-task Gaussian Process formulations and their gradients.
method Friendly derivations of Multi-task Gaussian Process formulations and their gradients.
result Simplified derivations of Multi-task Gaussian Process formulations and gradients.
Bayesian rLASSO improves model selection and prediction.
problem Improving model selection and prediction in linear regression.
method A Bayesian formulation of the rLASSO problem using inverse Laplace priors and scale mixture distributions.
result Bayesian rLASSO outperforms classical rLASSO in estimation, prediction, and variable selection.
Anomaly Detection has several important applications. In this paper, our focus is on detecting anomalies in seller-reviewer data using tensor decomposition. While tensor-decomposition is mostly unsupervised, we formulate Bayesian semi-supervised tensor decomposition to take advantage of sparse labeled data. In addition…
Bayesian approach for handling incomplete clinical data.
problem Challenges in machine learning with multimodal, incomplete clinical data.
method Generative and discriminative learning, semi-supervised strategy, imputation of missing views.
result Automatic imputation of missing views and robust inference across different data sources.
Study evaluates posterior covariance matrix W for frequentist evaluation of Bayesian estimators.
problem Evaluating variability of posterior estimates in Bayesian models.
method Use of Bayesian Infinitesimal Jackknife approximation and W-kernel.
result Principal space of W is central to frequentist evaluation of Bayesian models.
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.
We begin by reiterating that common neural network activation functions have simple Bayesian origins. In this spirit, we go on to show that Bayes's theorem also implies a simple recurrence relation; this leads to a Bayesian recurrent unit with a prescribed feedback formulation. We show that introduction of a context in…
WNVI solves inverse problems without forward models using neural networks.
problem Solving high-dimensional Bayesian inverse problems based on PDEs.
method WNVI uses weighted residuals and SVI with neural networks to infer state variables and unknowns.
result WNVI is more accurate and efficient than traditional methods and handles ill-posed problems.
Improves DRO with Bayesian Ambiguity Sets for model misspecification.
problem Overly conservative decisions due to misspecified models in DRO.
method Introduces DRO-RoBAS with robust posterior predictive distribution.
result Outperforms other Bayesian and empirical DRO approaches in out-of-sample performance.
PAC-Bayesian bounds for MLPs with cross entropy loss validated.
problem Generalization bounds for MLPs with cross entropy loss.
method Introduced probabilistic explanations and proved PAC-Bayesian bounds using ELBO.
result MLPs with cross entropy loss inherently guarantee PAC-Bayesian generalization bounds.
Bayesian approach uses deep learning for seismic imaging and uncertainty quantification.
problem Uncertainty in seismic imaging due to nonuniqueness and noise.
method Implicit structured prior from randomly initialized convolutional neural network, combined with Bayesian model averaging and stochastic gradient Langevin dynamics.
result Deep priors reduce imaging artifacts and overfitting in noisy conditions.
A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is proved to be optimum in the Neyman-Pearson sense. The algorithm is defined by a …
Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.
problem Efficiently solving ordinary differential equations (ODEs) with reduced computational cost.
method Formulated a parallel-in-time probabilistic numerical ODE solver using time-parallel formulation of iterated extended Kalman smoothers.
result Reduces span cost from linear to logarithmic in the number of time steps.
Stochastic VB improves nonlinear model inference speed and accuracy.
problem Bayesian inference of nonlinear models from noisy data.
method Stochastic Variational Bayesian (VB) inference for nonlinear models.
result Stochastic VB achieves comparable parameter recovery to analytical solution but is faster.
In this work, we introduce a novel probabilistic representation of deep learning, which provides an explicit explanation for the Deep Neural Networks (DNNs) in three aspects: (i) neurons define the energy of a Gibbs distribution; (ii) the hidden layers of DNNs formulate Gibbs distributions; and (iii) the whole architec…
New method uses constrained transport metric for robust Bayesian inference.
problem Flexible Bayesian models with many uninterpretable parameters.
method Exponentially tilted empirical likelihood with a novel Wasserstein metric, combined with a prior.
result Superior performance compared to state-of-the-art robust Bayesian inference methods.
Bayesian tensor train method recovers streaming data with high accuracy.
problem Recovering high-order, incomplete, and noisy streaming data.
method Bayesian tensor train decomposition using streaming variational Bayes method.
result The proposed SPTT algorithm excels in recovering streaming data compared to state-of-the-art methods.
R package abn fits Bayesian models to observational data.
problem Analyzing complex observational datasets with Bayesian networks.
method Bayesian and information theoretic scoring, exact and greedy search algorithms.
result Effective modeling of mixed data types and prior knowledge integration.
Improved uncertainty estimation in neural networks with VBLL.
problem Improving uncertainty estimation in neural networks.
method Deterministic variational formulation for training Bayesian last layer neural networks.
result Improves predictive accuracy, calibration, and out-of-distribution detection.
We consider the problem of recovering a function input of a differential equation formulated on an unknown domain M. We assume to have access to a discrete domain Mn={x1,…,xn}⊂M, and to noisy measurements of the output solution at p≤n of those points. We introduce a graph-based Bayesian inve…
Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' rule, imposing posterior regularization is arguably more direct and in s…
Bayesian inference using stochastic neural networks ensembles.
problem Approximating Bayesian posterior distributions.
method Formulate stochastic ensembles of neural networks, train with variational inference, and evaluate using Monte Carlo dropout.
result Stochastic ensembles provide more accurate posterior estimates than other methods.
We present a formulation of the transaction cost analysis (TCA) in the Bayesian framework for the primary purpose of comparing broker algorithms using standardized benchmarks. Our formulation allows effective calculation of the expected value of trading benchmarks with only a finite sample of data relevant to practical…
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative …
Bayesian PINNs optimize loss weights for PDEs and data.
problem Optimizing loss weights in physics-informed neural networks.
method Laplace approximation for efficient model evidence computation.
result Unified Bayesian setting for PDEs and noisy measurements.
Decision tree learning is a popular approach for classification and regression in machine learning and statistics, and Bayesian formulations---which introduce a prior distribution over decision trees, and formulate learning as posterior inference given data---have been shown to produce competitive performance. Unlike c…
Bayesian optimization tackles non-convex, two-stage stochastic problems efficiently.
problem Solving non-convex, two-stage stochastic optimization problems with expensive, black-box evaluations.
method Knowledge-gradient-based acquisition function for joint optimization of first- and second-stage variables.
result Comparable and superior empirical results compared to alternatives.
Bayesian adaptive PCE method improves surrogate modeling and sensitivity analysis.
problem Lack of fully Bayesian PCE methods in statistics.
method Developed a novel fully Bayesian adaptive PCE method with R implementation.
result Bayesian adaptive PCE provides competitive performance for various UQ tasks.
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian regularizations in a specific category of DNNs, i.e., Convolutional Neural Networks (C…
New research connects evolutionary dynamics to Bayesian learning.
problem Connecting evolutionary biology and Bayesian learning.
method Rigorous mathematical proof using Kushner-Stratonovich equation and gradient flows.
result Discrete time filtering equations converge to Stratonovich interpretation of Kushner-Stratonovich equation.
We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph cluste…
Bayesian neural network (BNN) priors are defined in parameter space, making it hard to encode prior knowledge expressed in function space. We formulate a prior that incorporates functional constraints about what the output can or cannot be in regions of the input space. Output-Constrained BNNs (OC-BNN) represent an int…
The paper identifies network bottlenecks using minimax paths in stochastic networks.
problem Identifying bottlenecks in networks with stochastic weights.
method Modeling as combinatorial semi-bandit problem, applying combinatorial Thompson Sampling, and approximating the original objective due to computational intractability.
result Established an upper bound on Bayesian regret and evaluated Thompson Sampling performance on real-world networks.
Scalings in which the graph Laplacian approaches a differential operator in the large graph limit are used to develop understanding of a number of algorithms for semi-supervised learning; in particular the extension, to this graph setting, of the probit algorithm, level set and kriging methods, are studied. Both optimi…
Novel connections between Neyman-Scott processes and Bayesian nonparametric mixture models enable scalable inference.
problem Efficiently modeling and detecting clusters in spatiotemporal data.
method Adapting collapsed Gibbs sampling for Neyman-Scott processes via connections to mixture of finite mixture models.
result Demonstrated scalability and effectiveness on neural spike trains and document streams.
Bayesian optimization tackles expensive cascade processes.
problem Optimizing multistage decision-making processes with expensive costs.
method Formulated as Bayesian optimization framework with two types of acquisition functions.
result Demonstrated effectiveness through numerical experiments and a solar cell simulator application.
Time series of counts arise in a variety of forecasting applications, for which traditional models are generally inappropriate. This paper introduces a hierarchical Bayesian formulation applicable to count time series that can easily account for explanatory variables and share statistical strength across groups of rela…
We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. By minimizing a hinge-loss using the linear expectation operat…
Qualitative analysis of MC dropout for NN model uncertainty.
problem Measuring uncertainty in neural network models.
method Mathematical formulation of Monte Carlo dropout and its benefits/costs in NN models.
result Potential benefits and associated costs of using MC dropout in NN models.
Bayesian Neural Networks improve uncertainty estimation in deep learning.
problem Lack of robustness and sensitivity to out-of-distribution samples in DNNs.
method Empirical evaluation of Bayesian Neural Networks against point estimate DNNs.
result Bayesian Neural Networks provide better uncertainty quantification and performance.
Unified Bayesian PINN framework for solving inverse problems in infrared image processing.
problem Solving inverse problems in high-dimensional settings with complex physics.
method Bayesian Physics-Informed Neural Networks (BPINN-IP) framework, incorporating physical laws and uncertainties.
result Unified framework for physical constraints, prior knowledge, and data-driven inference with uncertainty quantification.
Bayesian optimization reduces CVaR portfolio risk.
problem Minimizing CVaR under minimum expected return constraints.
method New Bayesian Optimization algorithms with a two-stage procedure.
result Significant reduction in objective function evaluations.
Action-BED: Task-Driven Bayesian Experimental Design
problem Bayesian experimental design with doubly intractable objectives
method Formulating BED in terms of expected future loss (EFL) and optimising it with stochastic gradients
result Simplified and task-driven framework for BED