Neural Diffusion Intensity Models simplify Cox processes inference.
problem Intractable nonparametric estimation and posterior inference of latent stochastic intensity in Cox processes.
method Variational framework using neural SDEs, with theoretical guarantee of ELBO maximization coinciding with maximum likelihood estimation.
result Accurate recovery of latent intensity dynamics and posterior paths with significant speedup.
Develops variational inference for Neyman-Scott processes for faster sampling.
problem Slow mixing time in MCMC for posterior sampling in Neyman-Scott processes.
method Variational inference algorithm for Neyman-Scott processes, minimizing KL divergence.
result Achieves better prediction performance than MCMC with limited computational time.
New method DDVI improves posterior inference for deep Gaussian processes.
problem Inference of inducing points in DGPs is challenging and biased.
method DDVI uses denoising diffusion SDE and score matching for posterior approximation.
result Empirically shows DDVI outperforms baseline methods in inducing point inference.
VAR-GPs solve continual learning by updating posteriors sequentially.
problem Catastrophic forgetting in sequential learning tasks.
method Sparse inducing point approximations and auto-regressive variational distribution.
result VAR-GPs prevent catastrophic forgetting and outperform baselines.
Global inducing points improve Bayesian neural network performance.
problem Improving Bayesian neural network performance.
method Adapting correlated approximate posterior to all layers in a Bayesian neural network and deep Gaussian processes using learned global inducing points.
result State-of-the-art performance on CIFAR-10 (86.7%) without data augmentation or tempering.
Gaussian process regression helps approximate Bayesian inverse problems efficiently.
problem Computational intractability of Bayesian posterior distributions in inverse problems.
method Gaussian process regression to build a surrogate model for the likelihood.
result Error between true and approximate posterior can be bounded by weighted L2-norm error between true and approximate likelihood. Bayesian approach for inhomogeneous Poisson process intensity estimation.
problem Intractable integral in likelihood of Gaussian Cox process.
method Joint modeling of intensity and cumulative intensity as transformed Gaussian process; exact MCMC sampler.
result Exact posterior inference without approximations.
Bayesian ODEs with Gaussian processes infer unknown dynamics from data.
problem Estimating unknown continuous-time system dynamics from data.
method Bayesian nonparametric model using Gaussian processes, sparse variational inference, probabilistic shooting.
result Posterior predictive uncertainty scores outperform alternative methods on multiple ODE learning tasks.
Paper tightens variational GP approximations for large datasets.
problem Scaling Gaussian processes to large datasets.
method Relaxing the standard assumption about inducing points' posterior matching the prior, leading to a tighter variational approximation.
result The proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining computational cost.
A new algorithm optimizes Gaussian process posterior mean functions efficiently.
problem Optimizing Gaussian process posterior mean functions over hyperrectangles is challenging due to nonlinearity and nonconvexity.
method PALM-Mean, a piecewise-analytic lower-bounding framework embedded in reduced-space spatial branch-and-bound.
result PALM-Mean improves scalability for large datasets compared to general-purpose solvers.
New method optimizes Bayesian optimization for high-dimensional posterior samples.
problem Difficult inner-loop optimization of posterior sample paths in Bayesian optimization.
method Global rootfinding approach with carefully selected starting points.
result The method discovers the global optimum most of the time with just one starting point per set.
Enhanced Gaussian process models accelerate optimization and posterior approximation.
problem Improving the accuracy and speed of Gaussian process models for optimization and inference.
method Introduces a random exploration step to classical GP-UCB algorithms, facilitating faster convergence.
result New algorithms achieve nearly optimal convergence rates and provide bounds for Hellinger distance.
The posterior variance of Gaussian processes is a valuable measure of the learning error which is exploited in various applications such as safe reinforcement learning and control design. However, suitable analysis of the posterior variance which captures its behavior for finite and infinite number of training data is …
Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run independent MCMC algorithms targeting the corresponding subposterior, can spread…
Improved sparse Gaussian processes using structured scaling matrices and Power-EP framework.
problem Scaling Gaussian processes for large datasets.
method Structured diagonal scaling matrix and Power-EP framework.
result Structured approximations improve performance without increasing computational cost.
Study adaptive sensing of Cox processes using posterior sampling and positive bases.
problem Adaptive sensing of Cox point processes with intensity function modeling.
method Model intensity function as truncated Gaussian process in positive basis, use Langevin dynamics and posterior sampling.
result Demonstrated improved sensing compared to classical Bayesian experimental design.
Improves Bayesian optimization using Gaussian process Thompson sampling.
problem Global optimization of Gaussian process posterior samples.
method Carefully selects starting points for gradient-based multi-start optimizers, identifies all local optima via univariate global rootfinding, and optimizes the posterior sample.
result Dramatic improvements in overall performance of Bayesian optimization.
One of the most compelling features of Gaussian process (GP) regression is its ability to provide well-calibrated posterior distributions. Recent advances in inducing point methods have sped up GP marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining …
Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called \textit{Type II maximum likelihood} or ML-II). An alternative learning proced…
Bayesian method with Gaussian process priors achieves optimal convergence rates for regression function and its derivatives.
problem Estimating the regression function and its derivatives in nonparametric regression.
method Bayesian approach with Gaussian process priors, focusing on convergence rates and plug-in property.
result Equivalence of convergence rates of posterior distributions and Bayes estimators for regression function and its derivatives.
KL annealing helps VAEs avoid posterior collapse and overfitting.
problem Posterior collapse and overfitting in VAEs.
method Theoretical analysis of learning dynamics with KL annealing.
result Posterior collapse is inevitable when β exceeds a threshold. Kernel interpolation speeds up online Gaussian process updates.
problem Efficiently updating Gaussian process posteriors with new data.
method Structured kernel interpolation for constant-time updates.
result Exact inference maintained with constant-time updates.
The paper introduces a method to probabilistically select inducing points in sparse Gaussian processes.
problem The challenge is selecting the optimal number of inducing points in sparse Gaussian processes.
method A point process prior is applied to the inducing points, and the posterior is approximated using stochastic variational inference.
result The model learns which and how many inducing points to use, leading to fewer inducing points being preferred as they become less informative.
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate co…
FastMuyGPs speeds up GP predictions for large datasets.
problem High cost of Gaussian process predictions for large data.
method Combines cross-validation, batching, nearest neighbors sparsification, and precomputation.
result Superior accuracy and competitive runtime compared to other methods.
New algorithm for continuous-time switching systems using variational inference.
problem Inference in time-series data with continuous-time switching systems.
method Developed a variational inference algorithm combining Gaussian process approximation and posterior inference for Markov jump processes.
result Bayesian latent state estimates and point estimates of unknown parameters for arbitrary points on the real axis.
Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and simultaneous Bayesian credible sets in GP regression. As an intermediate result, we develop…
Stochastic gradient descent approximates Gaussian process posteriors efficiently.
problem Efficiently sampling from Gaussian process posteriors with limited computational resources.
method Developed stochastic gradient optimization objectives for sampling from Gaussian process posteriors.
result Stochastic gradient descent produces accurate predictive distributions, even in non-convergent cases.
Efficiently optimize GPs by reusing candidate solutions multiple times.
problem High computational cost of Gaussian process optimization due to unique historical points.
method Sticking to a candidate solution for multiple evaluation steps and limiting switches.
result Improved efficiency and practicality of Gaussian process optimization algorithms.
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
problem Efficient inference in complex hierarchical point processes.
method Developed an efficient posterior sampling via Markov chain Monte Carlo for likelihood-based inference.
result More hidden Poisson processes improve likelihood fitting and event prediction.
New GP methods account for both data and computational uncertainty.
problem Approximation error in Gaussian process models.
method Develops a new class of methods to estimate combined uncertainty.
result Proves convergence and decomposability of combined posterior covariance.
Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and can be difficult to tune. This work provides a method for numerical marginalizat…
Improves GP models with known bounds for sampling and optimization.
problem Functions with known upper and lower bounds.
method Transforms GP models with bounds for posterior sampling and BO.
result Bounded entropy search (BES) selects points satisfying constraints.
Optimizes functions on manifolds using Gaussian processes and graph models.
problem Optimizing functions on unknown manifolds with limited data.
method Graph Gaussian process surrogate model for sequential optimization.
result Established regret bounds for the proposed algorithm.
DSPPs improve predictive distributions in scalable regression tasks.
problem Improving predictive distributions in scalable regression tasks.
method Inspired by DGPs, DSPPs use mini-batch training and kernel basis functions for uncertainty control.
result DSPPs provide significantly better calibrated predictive distributions than other methods.
Rényi Neural Processes replace KL divergence with Rényi divergence to improve NP performance.
problem Parameterization coupling in Neural Processes leads to prior misspecification.
method Propose Rényi Neural Processes (RNP) by replacing KL divergence with Rényi divergence.
result Significant performance improvements in real-world problems, including better log-likelihoods.
Develops an online Gaussian process method that maintains convergence guarantees without sample complexity issues.
problem The computational intractability of Gaussian processes with streaming data.
method Parsimonious Online Gaussian Processes (POG) that maintains asymptotic consistency with bounded memory.
result POG preserves convergence guarantees to the population posterior with finite memory, even for constant error radius.
New method for fast inference in diffusion models.
problem Intractable probabilistic inference in diffusion models.
method Variational Gaussian Process, exponential family description, convex optimization.
result Improved fast algorithm for learning model parameters.
Differential privacy of Gaussian process posterior sampling
problem Privacy of posterior sample paths from Gaussian process
method Intrinsic randomness yields DP guarantees
result Intrinsic randomness yields DP guarantees
A new method for efficient inference in sequential latent-variable models.
problem Computational challenges in integrating subject-specific random effects.
method Anchored variational inference framework to approximate posterior distributions.
result The method achieves accurate estimation with significant computational gains.
Sparse Gaussian Processes improve scalability by learning inducing points from data.
problem Scaling issues in Gaussian Processes due to cubic computational cost.
method Amortized learning of inducing points and variational posterior parameters using neural networks.
result Significant reduction in the number of inducing points, improving scalability.
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
Bayesian method classifies actin cytoskeleton networks using topological data.
problem Classifying the structure of biological networks, especially actin cytoskeleton networks.
method Transform actin cytoskeleton networks into persistence diagrams, quantify variability with Bayesian framework, estimate posterior distributions.
result Bayesian framework successfully classifies actin filament networks, outperforming state-of-the-art methods.
A new method for efficient Gaussian process inference using sparse approximations.
problem Scalable and accurate inference for latent Gaussian processes.
method Variational approximation with sparse inverse Cholesky factors and double Kullback-Leibler minimization.
result The proposed method can achieve highly accurate approximations with polylogarithmic time complexity.
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of inducing points. The inference is accurate only when data points have strong corre…
A new shrinkage-based construction is developed for a compressible vector x∈Rn, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$ corresponds to the coefficients of a wavelet or block-DCT representation of data. The me…
Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier feat…
Develops a new method for functional regression that works with non-Gaussian data.
problem Limited models for regression in function spaces with Gaussian process priors.
method Introduces Neural Operator Flows (OpFlow) for non-Gaussian function spaces.
result OpFlow enables robust and accurate uncertainty quantification for functional regression.