Deep Transformed Gaussian Processes extend TGPs with variational inference for scalable multi-layer modeling.
problem Flexible modeling of complex data distributions.
method DTGPs are a multi-layer model of TGPs using variational inference for scalability.
result DTGPs achieve good scalability and performance in multiple regression datasets.
DGPFM uses deep Gaussian processes to map functions accurately and quantify uncertainty.
problem Learning mappings between functional spaces, especially when data are noisy, sparse, or irregularly sampled.
method Constructs a sequence of GP-based linear and nonlinear transformations directly in function space, leveraging kernel integral transforms, GP conditional means, and nonlinear activations sampled from Gaussian processes.
result Empirical results show DGPFM outperforms existing methods in predictive accuracy and uncertainty calibration.
We propose a novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function. The key property of differential Gaussian processes is the warping of inputs through infinitely deep, but infinitesimal, diff…
A new method for training deep Gaussian processes using stochastic imputation.
problem Efficiently training deep Gaussian processes with varying regimes or sharp changes.
method Stochastic imputation to transform DGPs into linked GPs for efficient training.
result The method produces fast and analytically tractable predictions from DGP emulators.
New theory explains deep learning's success in transforming inputs.
problem Standard theoretical approaches eliminate representation learning.
method Developed a new infinite width limit for representation learning.
result Deep Gaussian processes (DGPs) have multivariate Gaussian posteriors.
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
problem Efficient regression and state estimation for deep Gaussian processes.
method Hierarchical transformed Gaussian process priors, state-space representation, linear stochastic differential equations, sequential methods.
result The state-space approach enables efficient state estimation and regression for deep Gaussian processes.
New approach learns image transformations directly for clustering.
problem Learning better deep representations for image clustering.
method Directly learns transformations and clusters in image space without abstract features.
result Jointly learns prototypes and transformations using deep learning modules.
Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by tr…
The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This transformation is a special form of the reparametrization trick, flattens the hierarchy a…
Transformers can solve complex filtering problems for non-Gaussian signals.
problem Non-linear and non-Markovian filtering problems for conditionally Gaussian signals.
method Continuous-time transformer models called filterformers.
result Filterformers can approximate the conditional law of non-Markovian and conditionally Gaussian signal processes.
Graph transformers outperform graph convolutions by preserving community information.
problem Understanding why graph transformers perform well in node-level prediction tasks.
method Analyzing the Gaussian process limits of graph transformers with infinite width and infinite heads.
result Graph transformers maintain discriminative node representations even in deep layers, preventing oversmoothing.
Choosing appropriate architectures and regularization strategies for deep networks is crucial to good predictive performance. To shed light on this problem, we analyze the analogous problem of constructing useful priors on compositions of functions. Specifically, we study the deep Gaussian process, a type of infinitely…
KITT uses transformers to quickly recommend kernels for GP models.
problem Kernel selection for high-dimensional GP regression models.
method Transformer-based architecture for generating kernel recommendations.
result KITT selects kernels that perform well on various regression benchmarks.
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
Novel CMG framework improves financial sentiment forecasting.
problem Challenges in short-term sentiment forecasting of financial OHLC data.
method Integrates chaos theory, Markov chains, and Gaussian processes with transformer models.
result Consistently outperforms traditional models in accuracy and efficiency.
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a posterior distribution of compositions of multiple functions giving rise to the…
SGPA calibrates transformer uncertainty for safety-critical tasks.
problem Uncertainty estimation in transformer models for safety-critical domains.
method Bayesian inference in transformer's output space using sparse Gaussian processes.
result SGPA-based Transformers improve in-distribution calibration and out-of-distribution robustness.
ETGP improves multi-class classification efficiency.
problem Efficiently handling non-stationary, dependent multi-class classification problems.
method ETGP uses transformed Gaussian processes with efficient sparse variational inference.
result ETGPs outperform state-of-the-art methods in multi-class classification tasks.
Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.
problem Capturing complex non-stationary patterns in non-linear dynamical systems.
method Integrates ODE-based RKHS Fourier features into DGPs using convolution operations for adaptive amplitude and phase modulation. Uses a doubly stochastic variational inference framework.
result Improved predictive performance across various regression tasks.
Meta-learning improves Gaussian process uncertainty estimation.
problem Poor uncertainty estimation in Gaussian processes with deep kernels.
method Meta-learning to calibrate deep kernel GPs using task-specific uncalibrated and calibrated distributions.
result Improves uncertainty estimation performance with high regression performance.
We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the non-parametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a deep architecture, using local kernel interpolation, inducing points, and struc…
Improved variational approximation for deep Wishart process models.
problem Improving predictive performance of deep Wishart process models.
method Generalizing the Bartlett decomposition of the Wishart distribution to allow linear combinations of rows and columns.
result Better predictive performance achieved with minimal additional computation cost.
This work extends Gaussian process priors to neural operators for function space mappings.
problem Improving uncertainty quantification in deep neural networks.
method Extending Gaussian process priors to neural operators with conditions for convergence and computation of covariance functions.
result Arbitrary-depth neural operators with Gaussian kernels converge to function-valued GPs, enabling posterior computation in regression scenarios.
Deep kernel processes unify various models using Gram matrices and kernel functions.
problem Unified representation of various deep learning models.
method Defining deep kernel processes with progressively transformed Gram matrices and sampling from inverse Wishart distributions.
result Deep Gaussian processes, BNNs, infinite BNNs, and infinite BNNs with bottlenecks can all be written as deep kernel processes.
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric variational family, which adapts its shape to match complex posterior distributions. T…
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.
Deep Gaussian Processes with polynomial kernels can collapse rapidly without proper hyperparameter tuning.
problem The collapse of Deep Gaussian Processes with polynomial kernels without careful hyperparameter tuning.
method Analysis using the Berry-Esseen Theorem and observation of prior behavior.
result The prior of a Deep Gaussian Process collapses rapidly towards zero or places negligible mass on low norm functions without proper hyperparameter tuning.
Extends Gaussian process regression for non-Gaussian data.
problem Inadequate modeling of uncertainty and over-smoothing in non-Gaussian datasets.
method Time-changed Gaussian processes with Lévy processes.
result Improved modeling of heavy-tailed non-Gaussian behaviors.
Hybrid model improves geopolitical conflict forecasting.
problem Forecasting geopolitical events from sparse, bursty data.
method Sparse Temporal Fusion Transformer (TFT) + Variational Nearest Neighbor Gaussian Process (VNNGP).
result Consistently outperforms standalone TFT in long-range horizons.
This thesis improves deep sequence models by integrating probabilistic methods for uncertainty quantification.
problem Lack of uncertainty awareness in deep sequence models limits their deployment.
method Develops approximate Bayesian inference methods for Transformers and HiPPOs, leveraging inductive biases.
result Improves predictive and generative performance of deep sequence models by incorporating probabilistic structures.
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …
Transformers can approximate Bayesian inference efficiently.
problem Bayesian methods struggle with deep learning due to prior knowledge and uncertainty capture.
method Prior-Data Fitted Networks (PFNs) approximate posteriors using in-context learning.
result PFNs achieve near-perfect mimicry of Gaussian processes and significant speedups.
We propose deep convolutional Gaussian processes, a deep Gaussian process architecture with convolutional structure. The model is a principled Bayesian framework for detecting hierarchical combinations of local features for image classification. We demonstrate greatly improved image classification performance compared …
The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model Gaussian marginal distributions. To model non-Gaussian data, a GP can be warped by a no…
A new method for deep Wishart processes improves kernel-based models.
problem Inference in deep Wishart processes is challenging due to the need for flexible distributions over positive semi-definite matrices.
method Developed a novel approach to flexible distributions over positive semi-definite matrices using the Bartlett decomposition of the Wishart probability density. Used this to create an approximate posterior for the DWP.
result Improved performance of inference in the DWP compared to DGP with equivalent prior.
New analysis explains pathology of deep Gaussian processes.
problem Pathology of deep Gaussian processes reduces learning capacities with increased layers.
method Study nonlinear dynamic systems corresponding to DGPs, derive recurrence relations.
result Provide tighter bounds and rate of convergence for dynamic systems.
Deep neural networks and Gaussian processes are shown to be equivalent through activation functions.
problem Understanding the relationship between neural networks and Gaussian processes.
method Developing an equivalence theory based on activation functions and kernels.
result Models can be seen as neural networks with improved uncertainty prediction or deep Gaussian processes with increased accuracy.
Paper derives a simplified formula for Expected Improvement using log-transformed data.
problem Challenges in enhancing Bayesian optimization with Expected Improvement.
method Derives a closed form of Expected Improvement for Gaussian process trained on log-transformed objective.
result Provides a simplified formula for Expected Improvement.
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.
Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential applicatio…
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.
Time series analysis is a key component of machine learning, with applications in various fields.
problem Time series analysis in machine learning
method Basic concepts, classical statistical models, modern machine learning approaches
result Machine learning techniques for time series analysis
A novel GP architecture, Thin and Deep GP, learns lower-dimensional representations without losing interpretability.
problem Challenges in selecting appropriate kernel for Gaussian processes.
method Proposes a novel synthesis of deep and shallow GP approaches, parameterizing lengthscale in a way that maintains interpretability and learns lower-dimensional embeddings.
result TDGP discovers lower-dimensional manifolds in input data, performs well in benchmark datasets, and behaves well with increasing layers.
Diffusion Transformer captures spatial-temporal dependencies in sequential data.
problem Capturing rich spatial and temporal dependencies in sequential data.
method Established theoretical guarantees for diffusion transformers learning Gaussian process data.
result Spatial-temporal dependencies are captured within attention layers of diffusion transformers.
Survey on Gaussian processes and their deep variants.
problem Limitations of Gaussian processes and their derivatives.
method Comprehensive review of existing methods and research themes.
result Advancements in Deep Gaussian Processes over the past decade.
Inter-domain Deep Gaussian Processes improve inference for non-stationary data.
problem Inference limitations in Gaussian processes for non-stationary data.
method Combines inter-domain and deep Gaussian processes for scalable approximate inference.
result Outperforms inter-domain shallow GPs and conventional DGPs on non-stationary data.
A new model improves uncertainty estimation in deep learning.
problem Deep Kernel Learning (DKL) produces unreliable uncertainty estimates.
method Proposed a bi-Lipschitz constraint to preserve distances in feature space.
result DUE model outperforms previous DKL and other methods in uncertainty quality.
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.