arXiv research

Optimizes seismic monitoring networks using Bayesian OED.

GO-OED maximizes predictive information gain on nonlinear QoIs.

A new method for experimental design focuses on predicting downstream quantities of interest.

New bounds for Bayesian bandits show prior improves performance.

Scalable Bayesian LASSO using variational inference for large p and n.

New algorithm learns LQR with $O(\sqrt{T})$ regret using Langevin dynamics and excitation.

Sparse matrices simplify computation of GP variances and likelihoods.

New method speeds up Bayesian optimization in high dimensions.

We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009). Given a causal Bayesian network $\mathcal{M}$ on a graph with $n$ discrete variables and bounded in-degree and bounded `confounded components', we show that $O(\log n)$ interventions on an unknown causal Bayesian ne…

Bayesian hyperbolic MDS improves tree-like data representation.

New algorithm robust to outliers in Bayesian Optimization.

We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n 2^n) time, where n is the number of attributes; the number of parents per attribute is bound…

Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.

Bayesian bandit algorithms with approximate inference improve regret bounds in stochastic linear bandits.

vOED-NFs uses normalizing flows to improve Bayesian OED without likelihood evaluations.

We study the problem of learning Bayesian network structures from data. Koivisto and Sood (2004) and Koivisto (2006) presented algorithms that can compute the exact marginal posterior probability of a subnetwork, e.g., a single edge, in O(n2n) time and the posterior probabilities for all n(n-1) potential edges in O(n2n…

New analysis shows scores learn data manifolds better than distributions.

Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discret…

Enhances RL with function approximation, improving regret bounds.

A new method reduces Volterra kernel complexity and uncertainty quantification.

New method for sampling on constrained domains using orthogonal-space gradient flow.

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

A new sampler speeds up Bayesian mixture models.

Bayesian optimisation (BO) is a well-known efficient algorithm for finding the global optimum of expensive, black-box functions. The current practical BO algorithms have regret bounds ranging from $\mathcal{O}(\frac{logN}{\sqrt{N}})$ to $\mathcal O(e^{-\sqrt{N}})$, where $N$ is the number of evaluations. This paper exp…

We show that the square Hellinger distance between two Bayesian networks on the same directed graph, $G$, is subadditive with respect to the neighborhoods of $G$. Namely, if $P$ and $Q$ are the probability distributions defined by two Bayesian networks on the same DAG, our inequality states that the square Hellinger di…

Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$ dimensions requires linear solves and log determinants with an ${n(d+1) \times n(d…

Bayesian optimization with Gaussian process as surrogate model has been successfully applied to analog circuit synthesis. In the traditional Gaussian process regression model, the kernel functions are defined explicitly. The computational complexity of training is O(N 3 ), and the computation complexity of prediction i…

EBUCB framework achieves optimal regret with bounded approximate inference error.

Proposes TAGI for efficient Gaussian inference in Bayesian neural networks.

New method reduces SBL complexity from cubic to linear, improving scalability.

Paper introduces IO-NPF for efficient Bayesian experimental design.

Efficiently discovers Bayesian network structure with reduced memory usage.

WBCP improves conformal prediction for distribution shifts using weighted Dirichlet posteriors.

Discovering interaction effects on a response of interest is a fundamental problem faced in biology, medicine, economics, and many other scientific disciplines. In theory, Bayesian methods for discovering pairwise interactions enjoy many benefits such as coherent uncertainty quantification, the ability to incorporate b…

In this paper, we consider Bayesian image denoising based on a Gaussian Markov random field (GMRF) model, for which we propose an new algorithm. Our method can solve Bayesian image denoising problems, including hyperparameter estimation, in $O(n)$-time, where $n$ is the number of pixels in a given image. From the persp…

We extend the herding algorithm to continuous spaces by using the kernel trick. The resulting "kernel herding" algorithm is an infinite memory deterministic process that learns to approximate a PDF with a collection of samples. We show that kernel herding decreases the error of expectations of functions in the Hilbert …

The paper addresses frequentist regret of Linear Thompson Sampling in stochastic linear bandits.

DeltaBO accelerates Bayesian optimization with theoretical guarantees.

Influence maximization, adaptive routing, and dynamic spectrum allocation all require choosing the right action from a large set of alternatives. Thanks to the advances in combinatorial optimization, these and many similar problems can be efficiently solved given an environment with known stochasticity. In this paper, …

Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great computational burden in big data applications. In contrast to MCMC methods, Stochastic Gra…

A new method reduces the time needed for Bayesian optimization by a factor of 10-100.

Bayesian framework calibrates imperfect models using physics-informed priors and Hamiltonian Monte Carlo.

New meta-learning framework for minimizing simple regret in bandits.

Kernel interpolation speeds up online Gaussian process updates.

We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. To address the challenges posed by this noise, we analyze Bayesian oracles given the observed noisy features. Our Bayesian analysis reveals that the optimal hypothesis can significantly deviate f…

The paper tightens the regret rate for linear bandit problems.

CEI achieves convergence rates for constrained Bayesian optimization.