Paper introduces a new method for Gaussian Processes that improves prediction and hyper-parameter optimization.
problem Efficiently predicting unknown functions and optimizing hyper-parameters in Gaussian Processes.
method Sequential randomized low-rank matrix factorization for incremental predictions and hyper-parameter optimization.
result The proposed method outperforms existing approaches in terms of accuracy and computational efficiency.
Study multi-curve extension of short rate models with Gaussian factor processes.
problem Derivative pricing in multi-curve financial models.
method Gaussian factor model with short rate and spreads as second order polynomials of Gaussian processes.
result Adjustment factor for pricing linear and optional derivatives in multi-curve setup.
A scalable factorized Gaussian process VAE for faster inference.
problem Inference bottlenecks in Gaussian process VAEs.
method Factorizes latent kernel across auxiliary features, leveraging independence.
result Significant speed-up in inference time (in theory and practice).
Proposes GPLFR for predicting high-dimensional outputs with few data.
problem Predicting high-dimensional outputs from limited data.
method GPLFR combines Gaussian process and linear-Gaussian decoding for high-dimensional prediction.
result GPLFR outperforms existing methods in predicting high-dimensional outputs.
Improves Gaussian process factor models for multi-population recordings.
problem Cubic runtime scaling with trial length and group number limits application to large-scale recordings.
method Two approximate approaches: inducing variables and frequency domain.
result Achieved orders of magnitude speed-up with minimal statistical performance impact.
Paper improves efficiency in matrix computations for Gaussian processes.
problem Efficiency in matrix computations for Gaussian processes.
method Variance reduction via matrix factorization.
result Factorized estimator can be up to 1,000 times more efficient.
Gaussian processes struggle with compositional functions, but deep Gaussian processes can outperform.
problem Gaussian process regression struggles with compositional functions.
method We study information-theoretic lower bounds for posterior contraction rates in Gaussian process regression for a continuous regression model.
result Posterior based on any mean-zero Gaussian process can only recover the truth at a rate strictly slower than the minimax rate for generalized additive functions.
A new method uses Gaussian processes to efficiently model and compute counterparty credit valuation adjustments (CVA).
problem Efficiently modeling and computing CVA for large OTC derivative portfolios.
method Multi-Gaussian process regression approach to learn a metamodel for the mark-to-market cube of a derivative portfolio.
result The method accurately and efficiently computes CVA for interest rate swap portfolios.
A new GP method handles both qualitative and quantitative factors using latent variables.
problem Handling both qualitative and quantitative inputs in simulations.
method Mapping qualitative factors to latent variables and treating them similarly to numerical variables.
result Superior predictive performance across various examples.
GPLVMF improves CARS performance by addressing overfitting and context importance.
problem Overfitting and lack of automatic context importance determination in GP-based CARS.
method GPLVMF applies a non-zero mean function and real-valued latent space to improve GP model performance.
result Significant improvement in performance on real datasets and automatic context importance determination.
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model …
A new method speeds up Bayesian Optimization for hyperparameter tuning.
problem Efficient hyperparameter tuning for machine learning models.
method Lazy Gaussian Processes approximation to reduce cubic complexity to quadratic.
result Significant speedup in Bayesian Optimization, up to 162x in single node.
Proposes a nonparametric tensor factorization for sparse data.
problem Handling sparse tensor data with structural and interpretability benefits.
method Hierarchical Gamma processes and Poisson random measures for tensor-valued process, Dirichlet processes for sampling entry indices, Gaussian processes for values.
result Demonstrates superior performance on benchmark datasets.
IPGP framework improves psychological assessment by integrating shared and unique traits.
problem Tackles the debate on shared vs unique personality traits across individuals.
method Uses Gaussian process coregionalization model for non-Gaussian ordinal data, with stochastic variational inference for scalability.
result Improves prediction and estimation of individualized factor structures compared to existing methods.
Bayesian model improves discriminative factor analysis for non-Gaussian data.
problem Discriminative factor analysis for non-Gaussian data.
method Introduces max-margin rank-likelihood and integrates it with linear Bayesian support vector machines. Extends to nonlinear case using mixtures of local linear classifiers.
result Superior performance demonstrated on benchmark and real data.
A new model combines Gaussian processes with collaborative filtering for uncertainty-aware recommendations.
problem Uncertainty in recommendation systems.
method Combining Gaussian process multi-output models with collaborative filtering.
result Generates uncertainty estimates for predictions.
Flexible multi-view learning through Gaussian process latent variable model.
problem Learning from multiple data views with latent factors.
method Nonparametric Gaussian process latent variable model for multi-view data.
result First published results of learning from dozens of views, even with scarce data.
Scalable multi-task regression via sparse Gaussian process priors.
problem Efficiently modeling and predicting multiple related tasks.
method Direct Cholesky factorization for sparse parameterization of Gaussian process priors.
result Sparse parameterization improves scalability and accuracy in multi-task regression.
In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian P…
We develop a fast inference method for non-conjugate Gaussian process models on spike count data.
problem Non-Gaussian spike count data complicates Gaussian Process Factor Analysis.
method We introduce Polynomial Approximate Log-Likelihood (PAL) estimators for non-conjugate GPFA models.
result PAL estimators achieve fast and accurate extraction of latent structure from spike train data.
This paper explores approximations for fully Bayesian Gaussian Process Regression.
problem Learning in Gaussian Process models through hyperparameter adaptation.
method Two approximation schemes: Hamiltonian Monte Carlo and Variational Inference.
result Predictive performance analysis on various benchmark datasets.
Develops Chained Gaussian Processes for non-linear likelihoods.
problem Handling non-linear combinations of Gaussian process parameters.
method Introduces Chained Gaussian Processes and develops scalable approximate inference.
result Demonstrates scalability and applicability to various likelihood functions.
Hybrid model combines deep learning and Gaussian processes for forecasting.
problem Challenges in classical and neural forecasting for large time series data.
method Data-driven hybrid model with a deep latent component and a local Gaussian Process.
result Obtains higher accuracy than state-of-the-art methods.
New method predicts dynamic relationships in terrorist networks.
problem Dynamic co-evolution of multiplex graphs and nodal attributes in terrorism networks.
method Time-varying stochastic latent factor models with neural network Gaussian processes.
result Superior performance in predicting unobserved dynamic relationships.
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequentl…
This work improves adaptive sampling for multi-fidelity Gaussian processes by considering cost and uncertainty.
problem Adaptive sampling for multi-fidelity Gaussian processes is computationally demanding and complex.
method The authors extend the design of experiment framework by partitioning prediction uncertainty based on fidelity level and cost, and utilize the Believer concept.
result The proposed framework effectively reduces predictive uncertainty in multi-fidelity Gaussian processes.
It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is optimal (up to logarithmic factors) for the smoothness class the true function be…
This paper develops a fast algorithm for solving nonlinear PDEs using sparse Cholesky factorization.
problem Efficiently solving nonlinear PDEs with Gaussian processes and kernel methods.
method Sparse Cholesky factorization for near-linear complexity.
result Near-linear complexity algorithm for working with kernel matrices of nonlinear PDEs.
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.
Scalable GP model tackles big data, categorical factors, and multiple responses.
problem Handling big datasets, categorical inputs, and multiple responses in Gaussian processes.
method Latent variable Gaussian process (LVGP) with variational inference for scalability and interpretability.
result The method scales well for large datasets and outperforms state-of-the-art methods.
New model extracts shared brain activity patterns from fMRI data.
problem Challenges in aggregating multi-subject fMRI data due to variability.
method Shared Gaussian Process Factor Analysis (S-GPFA) incorporating temporal information.
result Model reveals ground truth latent structures and replicates experimental performance.
Efficient sparse GP model improves audio source separation.
problem Sparse Gaussian Process (GP) inference is computationally expensive for long audio frames.
method Used GP regression, spectral mixture kernels, and variational sparse GPs.
result Proposed method outperforms LD-PSDTF, KL-NMF, and IS-NMF.
New GP-VAE model improves scalability and performance.
problem Inability of conventional VAEs to model correlations between data points.
method Principled sparse inference approaches to improve scalability of GP-VAEs.
result New model outperforms existing approaches in runtime and memory usage.
New method efficiently samples Gaussian process posteriors without cubic scaling.
problem Intractable posterior distributions in Gaussian processes.
method Decomposes Gaussian processes into prior and data components for scalable sampling.
result Fast posterior sampling at a fraction of the usual cost.
Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the non…
TPLVM models portfolio construction for non-Gaussian financial data.
problem Optimal asset allocation in finance with non-Gaussian fluctuations.
method Student's t-process latent variable model (TPLVM) for portfolio optimization.
result TPLVM outperforms Gaussian process latent variable model in minimum-variance portfolio construction.
Polynomial networks converge to Gaussian processes at a rate of O(n^(-1/2)).
problem Understanding the convergence rate of polynomial networks to Gaussian processes.
method Examined one-hidden-layer neural networks with random weights, focusing on polynomial activations and their convergence rate in the 2-Wasserstein metric.
result The rate of convergence for polynomial networks to Gaussian processes is $O(n^{- rac{1}{2}})$.
Deep-HGP uses Bayesian nonparametric approach for complex data regression.
problem Complex data regression with compositional structures.
method Deep Gaussian processes with a squared-exponential kernel, data-driven lengthscale parameters.
result Posterior distribution optimally recovers unknown true regression curve in terms of quadratic loss.
Paper proposes Walsh-Hadamard Variational Inference for efficient approximate inference in large models.
problem Over-regularization in variational inference for large models.
method Walsh-Hadamard factorization strategies to reduce parameterization, accelerate computations, and increase posterior expressiveness.
result Efficient approximate inference achieved in over-parameterized models.
We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation crucially depends on a set of points, called knots, at which the original proces…
A new model detects anomalies in time series data efficiently.
problem Detect anomalies in high-dimensional time series data.
method r-ssGPFA, an unsupervised online anomaly detection model using state space Gaussian processes.
result The model detects anomalies efficiently and is computationally cheaper.
Bayesian method filters unevenly-sampled time series.
problem Bayesian nonparametric low-pass filtering for unevenly-sampled time series.
method Latent-factor model with Gaussian processes for time series, Bayesian inference.
result The proposed model identifies low-pass filtering as low-frequency latent component via Bayesian inference.
Modeling disease progression in brain images using monotonic Gaussian Processes.
problem Disentangling spatio-temporal disease trajectories from brain imaging data.
method Spatio-temporal matrix factorization with anatomically plausible priors, monotonic Gaussian Processes, and sparse codes.
result Monotonic Gaussian Processes model realistic disease trajectories in brain imaging data.
Study uses a bivariate model to price crude oil futures.
problem Pricing crude oil futures using latent factors and state-space models.
method Modelled short and long term factors as OU processes, estimated using Kalman Filter and maximised Gaussian likelihood.
result Successfully estimated model parameters and factors from WTI Crude Oil NYMEX futures data.
New method for nonlinear filtering and smoothing using factor graphs.
problem Handling deterministic nonlinear transformations in factor graphs.
method Approximate Gaussian message passing rules for factor graphs with Markov property.
result Proposed nonlinear modified Bryson-Frazier smoother.
New model scales GP regression for large datasets with consistent predictions.
problem Scaling Gaussian process regression to large datasets with inconsistent predictions.
method Generalized Robust Bayesian Committee Machine, combining predictions from distributed experts in a consistent manner.
result The new model provides consistent predictions that converge to the true underlying function as training size increases.
Efficient deep learning with matrix Gaussian posteriors.
problem Efficiently modeling correlations in deep neural networks.
method Employing matrix variate Gaussian posterior distribution with approximate covariance matrices and incorporating pseudo-data.
result Achieved more efficient representation of correlations and connections with Gaussian Processes.
VNNGP uses nearest neighbors to approximate GPs, improving scalability and performance.
problem Scalability issues in Gaussian process approximations.
method Sparse precision structure via nearest neighbors, variational framework.
result VNNGP outperforms low-rank methods and is less prone to overfitting.