New method for Bayesian neural networks with unbounded weights.
problem Posterior inference for Bayesian neural networks with unbounded weights.
method Conditionally Gaussian representation for efficient posterior inference.
result Interpretable and computationally efficient procedure for posterior inference.
WE constructs GP kernels for mixed inputs using weighted EDMs.
problem Limitation of standard GP models in handling categorical variables.
method WEGP constructs kernel function using weighted EDMs for categorical inputs.
result WEGP improves GP model accuracy in both synthetic and real-world optimization problems.
This paper introduces hierarchical Gaussian process priors for neural networks to capture weight correlations and inductive biases.
problem Capturing weight correlations and inductive biases in neural networks.
method Hierarchical Gaussian process priors with unit embeddings and input-dependent kernels.
result Hierarchical Gaussian process priors provide competitive predictive performance and desirable uncertainty estimates.
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the kernel weights is obtained by adopting a hierarchical Bayesian approa…
The paper studies deep neural networks with Gaussian weights and finds their asymptotic behavior.
problem Understanding the behavior of deep neural networks with large width.
method Function-space perspective, Gaussian process analysis, weak convergence in large-width limit.
result Deep neural networks with large width converge to a continuous Gaussian process.
Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables to the model. Previous work on DGP models has introduced noise additively and use…
Wide deep neural networks with Gaussian weights approximate Gaussian processes closely.
problem Understanding the approximation of deep neural networks with Gaussian weights to Gaussian processes.
method Established novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters and Lipschitz activation functions in the wide limit.
result The distance between the network output and the Gaussian approximation scales inversely with the width of the network.
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. Study of deep neural networks with dependent weights leading to new model limits and properties.
problem Characterizing deep neural networks with dependent weights in the infinite-width limit.
method Modeling weights as a mixture of Gaussian distributions and analyzing the infinite-width limit.
result Characterization of neural network layers by scalar parameters and Lévy measures, leading to new model limits.
Study on MC dropout in wide neural networks and its convergence to Gaussian processes.
problem Understanding the behavior of Monte Carlo dropout in wide neural networks.
method Rigorously studied the limiting distribution of wide untrained NNs under dropout, proving convergence to Gaussian processes. Investigated correlations and non-Gaussian behavior in finite width NNs.
result Wide untrained neural networks under dropout converge to Gaussian processes for fixed sets of weights and biases.
Study connects Gaussian processes and regularization for sequence-function mappings.
problem Understanding and interpreting sequence-function maps in biology.
method Relates Gaussian process priors, regularization, and gauge fixing in overparameterized weight space.
result Established the relationship between regularized regression and Gaussian processes in function space.
This paper extends the Gaussian process interpretation of deep networks to more varied weight distributions.
problem Understanding the impact of different weight initialization schemes on deep learning dynamics.
method Extending the Gaussian process interpretation to PSEUDO-IID weight distributions, including sparse and low-rank networks.
result PSEUDO-IID initialized networks are effectively equivalent up to variance, enabling tractable posterior distributions.
A new method for computing image curvature efficiently and accurately.
problem Low performance, low accuracy, and requirement of second order differentiability in conventional computation schemes.
method Proposes a novel discrete computation scheme for weighted Gaussian curvature.
result More accurate, computationally more efficient, and does not require second order differentiability.
The paper integrates multiple Gaussian process predictions using Monte Carlo sampling.
problem Accurate prediction of variables using multiple models.
method Log-linear pooling of Gaussian process predictions, combined with Monte Carlo sampling.
result The log-linear pooling method improves prediction accuracy compared to linear pooling.
Study Gaussian-process limits of neural networks using tensor programs.
problem Understanding the behavior of neural networks as they approach infinite width.
method Quantitative analysis through tensor programs and Wasserstein distance.
result Explicit finite-width error bounds, showing convergence to Gaussian-process limits.
Random neural networks with ReLU activations are non-Gaussian processes.
problem Understanding the behavior of neural networks with random initialization and rectified linear units.
method Proving these networks are non-Gaussian processes and deriving their properties.
result These networks can converge to non-Gaussian processes under certain conditions.
A new method for faster prediction in distributed Gaussian processes.
problem Inefficient aggregation of distributed Gaussian processes with correlations.
method Proposes a novel approach for aggregated prediction in distributed GPs that incorporates correlations among experts.
result Results in more stable predictions in less time compared to state-of-the-art methods.
Improved kernel ridge regression for large datasets using weighted random binning.
problem Efficiently approximating kernel matrices for large-scale datasets.
method Introduced weighted random binning features for locality sensitive hashing.
result Weighted random binning features generate Gaussian processes of any desired smoothness.
Hybrid Bayesian neural networks use function uncertainty for probabilistic inference.
problem Uncertainty in neural network weights is hard to specify and interpret.
method Integrates probabilistic layers with standard deterministic layers for function uncertainty.
result Improves probabilistic inference by encoding function uncertainty.
New active learning methods for Gaussian process improve predictive modeling of composite fuselage.
problem Improving predictive modeling of composite fuselage with limited training samples and uncertainties.
method Proposed two new active learning algorithms for Gaussian process considering uncertainties.
result The proposed approach realizes better prediction performance for automatic shape control of composite fuselage.
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.
Develops a Bayesian non-parametric approach for signal separation with varying components.
problem Signal separation with varying components across different input locations.
method Augments Gaussian Process Latent Variable Models with weighted sums of pure component signals and incorporates priors for linear weights.
result Framework allows for non-linear variations in signals and incorporates useful priors for linear weights.
Optimizes sliding window approach for tracking Gaussian densities.
problem Improving tracking performance of Gaussian density estimation.
method Theoretical analysis of sliding window Gaussian Kernel Density Estimators.
result Empirical evidence shows improved tracking performance with optimal weight sequence.
A new ensemble of Gaussian processes improves active learning efficiency.
problem Efficiently labeling data in high-cost domains like medical imaging.
method Adaptive weighted ensemble of Gaussian processes (EGP) for active learning.
result EGP-based approaches outperform single GP-based active learning methods.
This paper improves Gaussian process predictions by integrating prior knowledge.
problem Gaussian processes lack predictive power when prior information is ignored.
method Derive mean and covariance functions from previous data using weighted sums of basis functions.
result Integrating prior knowledge significantly increases look-ahead time and accuracy.
New framework models complex spatial data with basis functions and graphical vectors.
problem Modeling highly-multivariate spatial processes with varying resolutions.
method Extends graphical lasso to multivariate Gaussian processes with independent graphical vectors at different resolutions, using an orthogonal basis and fusion penalty.
result Linear complexity and parsimonious conditional independence structure in multilevel graphical model.
Quantitative CLTs show neural network distributions converge to Gaussian as width increases.
problem Understanding the distribution of fully connected neural networks with random weights and biases.
method Analyzing the distribution of a fully connected neural network with random Gaussian weights and biases, proving quantitative bounds on normal approximations.
result The distance between a random fully connected network and the corresponding infinite width Gaussian process scales like n−γ for γ>0. A new method for efficient Gaussian process regression reduces complexity and improves scalability.
problem Efficient Gaussian process regression for large datasets.
method Learnable coreset-based variational inference for Gaussian processes.
result CVGP reduces the dimensionality of the variational parameter search space to linear complexity.
Finite-width neural networks are approximated by Gaussian processes with finite size corrections.
problem Understanding the behavior of finite-width neural networks as they approach infinite width.
method Analyzing the distribution of outputs at initialization for large, finite neural networks with a single hidden layer.
result The distribution of outputs at initialization is well described by a Gaussian perturbed by the fourth Hermite polynomial, with the perturbation scale inversely proportional to the number of network units.
Researchers develop a new spatial process model for non-Gaussian data.
problem Non-Gaussian spatial data with asymmetry and heavy-tailedness.
method Re-parameterized Unified Skew-Normal (SUN) distribution, GSUN process, neural Bayes inference with GATs.
result GSUN process captures non-Gaussian spatial data properties and outperforms conventional models.
A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds optimal values of function (value-nodes) and the corresponding weights. The Gaussi…
Wide neural networks can be closely approximated by Gaussian processes, with rates depending on the activation function's properties.
problem Approximating the behavior of wide neural networks using Gaussian processes.
method Established convergence rates for the central limit theorem in an infinite-dimensional functional space, using a transportation distance metric.
result Explicit convergence rates for neural networks approximated by Gaussian processes, varying based on the activation function's properties.
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.
Efficiently trains deep Gaussian processes with sparse approximations.
problem High computational complexity in training and inference for DGP models.
method Tensor Markov Gaussian Processes (TMGP) and hierarchical expansion to create DTMGP model.
result DTMGP model achieves superior computational efficiency compared to existing DGP models.
A robust Gaussian process model using Huber likelihood for outlier resistance.
problem Outliers in observational data sets affect Gaussian process regression's robustness.
method Proposes a Gaussian process model with Huber likelihood and weights based on projection statistics.
result Demonstrates improved statistical efficiency and robustness to outliers.
A-BLINK speeds up Gaussian process covariance estimation.
problem Slow covariance matrix inversion in Gaussian processes.
method Two pre-trained neural networks learn Kriging weights and spatial variance.
result Significant computational speedups and posterior inference.
Proposes FMS for more efficient neural network hyperparameter optimization.
problem Efficient hyperparameter optimization for deep learning models.
method Uses logged checkpoints of trained weights to guide hyperparameter selections.
result Proposes Forecasting Model Search (FMS) method.
Stable processes emerge as limits of deep neural networks with symmetric stable distributions.
problem Understanding the behavior of deep neural networks as they become infinitely wide.
method Analyzing fully connected feed-forward deep neural networks with symmetric stable distributions and showing the limit as a stable process.
result The infinite wide limit of the network is a stable process with multivariate stable distributions.
Gaussian Processes improve data interpolation from diverse experiments.
problem Interpolation of sparse and inconsistent datasets from various experiments.
method Used Gaussian Processes (GP) for data interpolation, including uncertainty quantification.
result GPs successfully interpolate data and quantify uncertainties, demonstrating consistency across different sources.
Bayesian inference for wide neural networks using Edgeworth expansion.
problem Analyzing the non-Gaussian behavior of wide neural networks in Bayesian inference.
method Proposed a non-Gaussian distribution using multivariate Edgeworth expansion for finite-width neural networks.
result Derived non-Gaussian posterior distribution in Bayesian regression tasks.
We introduce a novel personalized Gaussian Process Experts (pGPE) model for predicting per-subject ADAS-Cog13 cognitive scores -- a significant predictor of Alzheimer's Disease (AD) in the cognitive domain -- over the future 6, 12, 18, and 24 months. We start by training a population-level model using multi-modal data …
Paper speeds up Gaussian process inference using Matérn kernels.
problem Efficiently performing Gaussian process inference for large datasets.
method Exact Matérn kernel decomposition into empirical cumulative distribution functions, combined with divide-and-conquer approach.
result The proposed algorithm significantly speeds up Gaussian process inference for low-dimensional problems with hundreds of thousands of data points.
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 $O(n^{- rac{1}{2}})$.
Functional input neural networks approximate continuous functions on weighted spaces.
problem Approximating continuous functions on infinite-dimensional weighted spaces.
method Additive family mapping, non-linear activation, linear readouts, Stone-Weierstrass theorem.
result Global universal approximation of continuous functions on weighted spaces.
Proposes a new complex Gaussian distribution for better modeling of complex-valued signals.
problem Limited ability of Gaussian distribution to represent diverse amplitude characteristics.
method Introduces a power-weighted noncentral complex Gaussian distribution on the complex plane.
result Consistently outperforms conventional distributions in log-likelihood for speech power spectra.
Proposes GPR with local explanation for feature interpretation.
problem Lack of feature interpretation in Gaussian process regression.
method Introduces a locally linear model to explain feature contributions in GPR predictions.
result Achieves comparable predictive performance to GPR and superior interpretability.
A new memory-efficient sign language translation model reduces weight usage.
problem Memory constraints in real-time sign language translation.
method Variational Bayesian sequence-to-sequence network with Gaussian posterior and Indian Buffet Process prior.
result The proposed model achieves substantial weight compression without compromising performance.
Paper optimizes industrial refrigeration using adaptive exploration.
problem Challenges in optimizing real-time industrial processes with unknown characteristics and safety constraints.
method Adaptive and explorative real-time optimization framework with Gaussian process uncertainty quantification.
result Approach increases energy efficiency of refrigeration process, approximating complete information solutions.