GPyTorch
stable

Tutorials:

  • GPyTorch Regression Tutorial
    • Introduction
      • Set up training data
    • Setting up the model
      • The GP Model
      • The likelihood
      • Model modes
    • Training the model
    • Make predictions with the model
    • Plot the model fit

Examples:

  • Basic Usage
    • Hyperparameters in GPyTorch
      • Defining an example model
      • Viewing model hyperparameters
        • Raw vs Actual Parameters
        • How do constraints work?
        • Convenience Getters/Setters for Transformed Values
      • Changing Parameter Constraints
      • Priors
      • Putting it Together
      • Initializing hyperparameters in One Call
    • Saving and Loading Models
      • Saving a Simple Model
        • Change Model State
        • Getting Model State
        • Saving Model State
        • Loading Model State
      • A More Complex Example
        • Getting Model State
    • Kernels with Additive or Product Structure
      • Simple Sums and Products
      • Efficient Parallel Implementations of Additive Structure or Product Structure Kernels
        • Example #1: Efficient Summations of Univariate Kernels
        • Full Example
        • Example #2: Efficient Products of Univariate Kernels
      • Summing Higher Order Interactions Between Univariate Kernels (Additive Gaussian Processes)
    • Implementing a custom kernel in GPyTorch
      • A first kernel
      • Adding hyperparameters
    • Metrics in GPyTorch
      • Negative Log Predictive Density (NLPD)
      • Mean Standardized Log Loss (MSLL)
      • Mean Squared Error (MSE)
      • Mean Absolute Error (MAE)
  • Exact GPs (Regression)
    • GPyTorch Regression Tutorial
      • Introduction
        • Set up training data
      • Setting up the model
        • The GP Model
        • The likelihood
        • Model modes
      • Training the model
      • Make predictions with the model
      • Plot the model fit
    • Spectral GP Learning with Deltas
      • Load Data
      • Define a Model
      • Train
      • Plot Results
    • GP Regression with a Spectral Mixture Kernel
      • Introduction
      • Set up the model
    • Fully Bayesian GPs - Sampling Hyperparamters with NUTS
      • Running Sampling
      • Loading Samples
      • Plot Mean Functions
      • Simulate Loading Model from Disk
    • GP Regression with Uncertain Inputs
      • Introduction
        • Using a distributional kernel to deal with uncertain inputs
    • Exact GP Regression on Classification Labels
      • Generate Data
      • Setting Up the Model
      • Model Predictions
  • Exact GPs with Scalable (GPU) Inference
    • BlackBox Matrix-Matrix Inference (BBMM)
    • LancZos Variance Estimates (LOVE)
      • GP Regression with LOVE for Fast Predictive Variances and Sampling
        • Overview
        • The KISS-GP + LOVE GP Model
        • Computing predictive variances (KISS-GP or Exact GPs)
        • Computing posterior samples (KISS-GP only)
    • Exact GPs with GPU Acceleration
      • GPyTorch Regression Tutorial (GPU)
        • Introduction
        • Using the GPU
      • Exact GP Regression with Multiple GPUs
        • Introduction
        • How many GPUs do you want to use?
        • Computing test time caches
      • GPyTorch Regression With KeOps
        • Introduction
        • Using KeOps with a GPyTorch Model
    • Scalable Posterior Sampling with CIQ
      • Scalable Exact GP Posterior Sampling using Contour Integral Quadrature
        • Are we running with KeOps?
        • Define an Exact GP Model and train
        • Define test set
        • Draw a sample with CIQ
    • Scalable Kernel Approximations
      • Sparse Gaussian Process Regression (SGPR)
        • Overview
        • Defining the SGPR Model
      • Structured Kernel Interpollation (SKI/KISS-GP)
        • Overview
        • KISS-GP for 1D Data
        • KISS-GP for 2D-4D Data
        • Scaling to more dimensions
      • Scalable Kernel Interpolation for Product Kernels (SKIP)
        • Overview
        • Defining the SKIP GP Model
    • Structure-Exploiting Kernels
      • GP Regression with Grid Structured Training Data
        • Make the grid and training data
        • Creating the Grid GP Model
  • Multitask/Multioutput GPs with Exact Inference
    • Multi-output (vector valued functions)
      • Multitask GP Regression
        • Introduction
        • Define a multitask model
      • Batch Independent Multioutput GP
        • Introduction
        • Define a batch GP model
      • ModelList (Multi-Output) GP Regression
        • Introduction
        • Set up the sub-models
    • Scalar function with multiple tasks
      • Hadamard Multitask GP Regression
        • Introduction
        • Set up a Hadamard multitask model
  • Gaussian Process Latent Variable Models (GPLVM) with SVI
    • Introduction
      • Set up training data
    • Defining the GPLVM model
    • Training the model
    • Visualising the 2d latent subspace
  • Variational and Approximate GPs
    • Stochastic Variational GP Regression
      • Overview
      • Creating a DataLoader
      • Creating a SVGP Model
        • The GP Model
    • Modifying the Variational Strategy/Variational Distribution
      • Experimental setup
      • Some quick training/testing code
        • The Standard Approach
        • Reducing parameters
      • MeanFieldVariationalDistribution: a diagonal \(\mathbf S\) matrix
      • DeltaVariationalDistribution: no \(\mathbf S\) matrix
        • Reducing computation (through decoupled inducing points)
    • Using Natural Gradient Descent with Variational Models
      • Overview
      • What is natural gradient descent (NGD)?
      • Jointly optimizing variational parameters/hyperparameters
      • SVGP models for NGD
        • Difference #1: NaturalVariationalDistribution
        • Difference #2: Two optimizers - one for the variational parameters; one for the hyperparameters
        • Difference #3: The updated training loop
        • Evaluation
    • Stochastic Variational GP Regression with Contour Integral Quadrature
      • Overview
      • DataLoaders with CIQ-SVGP
      • Number of inducing points
      • CIQ - SVGP models
    • VNNGP: Variational Nearest Neighbor Gaussian Procceses
      • Overview
      • Creating a VNNGP model
      • Training the Model (mode 1, recommended)
      • Making predictions
      • Training the Model (mode 2)
      • Making predictions
    • Different objective functions for Approximate GPs
      • Overview
        • Experimental setup
      • Objective Funtion 1) The Variational ELBO
        • How to use the variational ELBO in GPyTorch
      • Objective Funtion 2) The Predictive Log Likelihood
        • How to use the predictive log likelihood in GPyTorch
    • Non-Gaussian Likelihoods
      • Introduction
        • Set up training data
      • Setting up the classification model
        • Model modes
      • Learn the variational parameters (and other hyperparameters)
      • Make predictions with the model
      • Notes on other Non-Gaussian Likeihoods
    • Using Pòlya-Gamma Auxiliary Variables for Binary Classification
      • Overview
      • Pòlya-Gamma Augmentation
      • Setup
      • Variational Inference with PG Auxiliaries
        • Setup optimizers
        • Define training loop
        • Visualization and Evaluation
    • Variational GPs w/ Multiple Outputs
      • Introduction
        • Set up training data
      • Define a multitask model
        • Types of Variational Multitask Models
        • Output modes
        • Train the model
        • Make predictions with the model
    • GP Regression with Uncertain Inputs
      • Introduction
      • Using stochastic variational inference to deal with uncertain inputs
        • Set up training data
      • Setting up the model
      • Training the model with uncertain features
  • Deep GP and Deep Sigma Point Processes
    • Deep GP
    • Deep Sigma Point Processes (DSPP)
      • Deep Gaussian Processes
        • Introduction
        • Defining GP layers
        • Building the deep GP
        • Objective function (approximate marginal log likelihood/ELBO)
        • Training/Testing
      • Deep Sigma Point Processes
        • Basic settings
        • Create PyTorch DataLoader objects
        • Initialize Hidden Layer Inducing Points
        • Create The DSPPHiddenLayer Class
        • Create the DSPP Class
        • Train the Model
        • Make Predictions, compute RMSE and Test NLL
      • Deep GPs and DSPPs w/ Multiple Outputs
        • Introduction
        • Structure of a multitask deep GP
  • PyTorch NN Integration (Deep Kernel Learning)
    • Exact DKL (Deep Kernel Learning) Regression w/ KISS-GP
      • Overview
      • Loading Data
      • Defining the DKL Feature Extractor
      • Defining the DKL-GP Model
        • The forward method
        • Training the model
        • Making Predictions
    • SVDKL (Stochastic Variational Deep Kernel Learning) on CIFAR10/100
      • Set up data augmentation
      • Create DataLoaders
      • Creating the DenseNet Model
      • Creating the GP Layer
      • Creating the full SVDKL Model
      • Defining Training and Testing Code
  • Pyro Integration
    • High-level Pyro Interface (for predictive models)
      • Predictions with Pyro + GPyTorch (High-Level Interface)
        • Overview
        • The PyroGP model
        • Performing inference with Pyro
        • Making predictions
        • Next steps
      • Clustered Multitask GP (w/ Pyro/GPyTorch High-Level Interface)
        • Introduction
        • Adding additional latent variables to the likelihood
        • Constructing the PyroGP model
    • Low-level Pyro Interface (for latent function inference)
      • Latent Function Inference with Pyro + GPyTorch (Low-Level Interface)
        • Overview
        • Using the low-level Pyro/GPyTorch interface
        • Performing inference with Pyro
        • Making predictions
        • Next steps
      • Cox Processes (w/ Pyro/GPyTorch Low-Level Interface)
        • Introduction
        • Parameterizing the intensity function using a GP
        • The Cox process likelihood
        • Using the low-level Pyro/GPyTorch interface
        • Performing inference
        • Evaluate the inferred intensity function
  • Advanced Usage
    • Batch GPs
      • Batch Independent Multioutput GP
        • Introduction
        • Define a batch GP model
      • Batch GP Regression
        • Introduction
        • Set up training data
        • Setting up the model
        • Training the model
        • Make predictions with the model
    • GPs with Derivatives
      • GPyTorch regression with derivative information
        • Introduction
        • Setting up the training data
        • Setting up the model
      • GPyTorch regression with derivative information in 2d
        • Introduction
        • Franke function
        • Setting up the training data
        • Setting up the model
    • Variational Fantasization
      • SVGP Model Updating
        • Training Data
        • Model definition
        • Model Training
        • Model Evaluation
        • Model Updating
    • Converting Models to TorchScript
      • Converting Exact GP Models to TorchScript
        • Define and train an exact GP
        • Trace the Model
        • Compare Predictions from TorchScript model and Torch model
      • Converting Variational Models to TorchScript
        • Download Data and Define Model
        • Load a Trained Model
        • Define a Wrapper
        • Trace the Model

Package Reference

  • gpytorch.models
    • Models for Exact GP Inference
      • ExactGP
        • ExactGP
    • Models for Approximate GP Inference
      • ApproximateGP
        • ApproximateGP
    • Models for Deep GPs
      • deep_gps.DeepGP
        • DeepGP
      • deep_gps.DeepGPLayer
        • DeepGPLayer
    • Gaussian Process Latent Variable Models (GPLVM)
      • gplvm.BayesianGPLVM
        • BayesianGPLVM
      • gplvm.PointLatentVariable
        • PointLatentVariable
      • gplvm.MAPLatentVariable
        • MAPLatentVariable
      • gplvm.VariationalLatentVariable
        • VariationalLatentVariable
    • Models for integrating with Pyro
      • PyroGP
        • PyroGP
  • gpytorch.likelihoods
    • Likelihood
      • Likelihood
        • Likelihood.__call__()
        • Likelihood.expected_log_prob()
        • Likelihood.forward()
        • Likelihood.log_marginal()
        • Likelihood.marginal()
        • Likelihood.pyro_guide()
        • Likelihood.pyro_model()
    • One-Dimensional Likelihoods
      • GaussianLikelihood
        • GaussianLikelihood
      • GaussianLikelihoodWithMissingObs
        • GaussianLikelihoodWithMissingObs
      • FixedNoiseGaussianLikelihood
        • FixedNoiseGaussianLikelihood
      • DirichletClassificationLikelihood
        • DirichletClassificationLikelihood
      • BernoulliLikelihood
        • BernoulliLikelihood
      • BetaLikelihood
        • BetaLikelihood
      • LaplaceLikelihood
        • LaplaceLikelihood
      • StudentTLikelihood
        • StudentTLikelihood
    • Multi-Dimensional Likelihoods
      • MultitaskGaussianLikelihood
        • MultitaskGaussianLikelihood
      • SoftmaxLikelihood
        • SoftmaxLikelihood
  • gpytorch.kernels
    • Kernel
      • Kernel
        • Kernel.__call__()
        • Kernel.__getitem__()
        • Kernel.covar_dist()
        • Kernel.expand_batch()
        • Kernel.forward()
        • Kernel.named_sub_kernels()
        • Kernel.num_outputs_per_input()
        • Kernel.sub_kernels()
    • Standard Kernels
      • ConstantKernel
        • ConstantKernel
      • CosineKernel
        • CosineKernel
      • CylindricalKernel
        • CylindricalKernel
      • LinearKernel
        • LinearKernel
      • MaternKernel
        • MaternKernel
      • PeriodicKernel
        • PeriodicKernel
      • PiecewisePolynomialKernel
        • PiecewisePolynomialKernel
      • PolynomialKernel
        • PolynomialKernel
      • PolynomialKernelGrad
        • PolynomialKernelGrad
      • RBFKernel
        • RBFKernel
      • RQKernel
        • RQKernel
      • SpectralDeltaKernel
        • SpectralDeltaKernel
      • SpectralMixtureKernel
        • SpectralMixtureKernel
    • Composition/Decoration Kernels
      • AdditiveKernel
        • AdditiveKernel
      • MultiDeviceKernel
        • MultiDeviceKernel
      • AdditiveStructureKernel
        • AdditiveStructureKernel
      • ProductKernel
        • ProductKernel
      • ProductStructureKernel
        • ProductStructureKernel
      • ScaleKernel
        • ScaleKernel
    • Specialty Kernels
      • ArcKernel
        • ArcKernel
      • IndexKernel
        • IndexKernel
      • LCMKernel
        • LCMKernel
      • MultitaskKernel
        • MultitaskKernel
      • RBFKernelGrad
        • RBFKernelGrad
      • RBFKernelGradGrad
        • RBFKernelGradGrad
    • Kernels for Scalable GP Regression Methods
      • GridKernel
        • GridKernel
      • GridInterpolationKernel
        • GridInterpolationKernel
      • InducingPointKernel
        • InducingPointKernel
      • RFFKernel
        • RFFKernel
  • gpytorch.kernels.keops
    • RBFKernel
      • RBFKernel
    • MaternKernel
      • MaternKernel
    • PeriodicKernel
      • PeriodicKernel
  • gpytorch.means
    • Mean
      • Mean
    • Standard Means
      • ZeroMean
        • ZeroMean
      • ConstantMean
        • ConstantMean
      • LinearMean
        • LinearMean
    • Specialty Means
      • MultitaskMean
        • MultitaskMean
      • ConstantMeanGrad
        • ConstantMeanGrad
      • ConstantMeanGradGrad
        • ConstantMeanGradGrad
      • LinearMeanGrad
        • LinearMeanGrad
      • LinearMeanGradGrad
        • LinearMeanGradGrad
  • gpytorch.mlls
    • Exact GP Inference
      • ExactMarginalLogLikelihood
        • ExactMarginalLogLikelihood
      • LeaveOneOutPseudoLikelihood
        • LeaveOneOutPseudoLikelihood
    • Approximate GP Inference
      • VariationalELBO
        • VariationalELBO
      • PredictiveLogLikelihood
        • PredictiveLogLikelihood
      • GammaRobustVariationalELBO
        • GammaRobustVariationalELBO
      • DeepApproximateMLL
        • DeepApproximateMLL
    • Modifications to Objective Functions
      • AddedLossTerm
        • AddedLossTerm.loss()
      • InducingPointKernelAddedLossTerm
        • InducingPointKernelAddedLossTerm
      • KLGaussianAddedLossTerm
        • KLGaussianAddedLossTerm
  • gpytorch.metrics
    • metrics.mean_absolute_error()
    • metrics.mean_squared_error()
    • metrics.mean_standardized_log_loss()
    • metrics.negative_log_predictive_density()
    • metrics.quantile_coverage_error()
  • gpytorch.constraints
    • Parameter Constraints
      • Interval
        • Interval
      • GreaterThan
        • GreaterThan
      • Positive
        • Positive
      • LessThan
        • LessThan
  • gpytorch.distributions
    • Distribution
      • Distribution
    • MultivariateNormal
      • MultivariateNormal
        • MultivariateNormal.__getitem__()
        • MultivariateNormal.add_jitter()
        • MultivariateNormal.confidence_region()
        • MultivariateNormal.expand()
        • MultivariateNormal.get_base_samples()
        • MultivariateNormal.log_prob()
        • MultivariateNormal.rsample()
        • MultivariateNormal.sample()
        • MultivariateNormal.to_data_independent_dist()
    • MultitaskMultivariateNormal
      • MultitaskMultivariateNormal
        • MultitaskMultivariateNormal.__getitem__()
        • MultitaskMultivariateNormal.base_sample_shape
        • MultitaskMultivariateNormal.from_batch_mvn()
        • MultitaskMultivariateNormal.from_independent_mvns()
        • MultitaskMultivariateNormal.from_repeated_mvn()
        • MultitaskMultivariateNormal.to_data_independent_dist()
    • Delta
      • Delta
  • gpytorch.priors
    • Prior
      • Prior
        • Prior.log_prob()
    • Standard Priors
      • GammaPrior
        • GammaPrior
      • HalfCauchyPrior
        • HalfCauchyPrior
      • LKJCovariancePrior
        • LKJCovariancePrior
      • MultivariateNormalPrior
        • MultivariateNormalPrior
      • NormalPrior
        • NormalPrior
      • SmoothedBoxPrior
        • SmoothedBoxPrior
  • gpytorch.variational
    • Variational Strategies
      • _VariationalStrategy
        • _VariationalStrategy
      • VariationalStrategy
        • VariationalStrategy
      • BatchDecoupledVariationalStrategy
        • BatchDecoupledVariationalStrategy
      • CiqVariationalStrategy
        • CiqVariationalStrategy
      • NNVariationalStrategy
        • NNVariationalStrategy
      • OrthogonallyDecoupledVariationalStrategy
        • OrthogonallyDecoupledVariationalStrategy
      • UnwhitenedVariationalStrategy
        • UnwhitenedVariationalStrategy
      • GridInterpolationVariationalStrategy
        • GridInterpolationVariationalStrategy
    • Variational Strategies for Multi-Output Functions
      • LMCVariationalStrategy
        • LMCVariationalStrategy
      • IndependentMultitaskVariationalStrategy
        • IndependentMultitaskVariationalStrategy
    • Variational Distributions
      • _VariationalDistribution
        • _VariationalDistribution
      • CholeskyVariationalDistribution
        • CholeskyVariationalDistribution
      • DeltaVariationalDistribution
        • DeltaVariationalDistribution
      • MeanFieldVariationalDistribution
        • MeanFieldVariationalDistribution
    • Variational Distributions for Natural Gradient Descent
      • NaturalVariationalDistribution
        • NaturalVariationalDistribution
      • TrilNaturalVariationalDistribution
        • TrilNaturalVariationalDistribution
  • gpytorch.optim
    • NGD
      • NGD
        • NGD.step()

Settings and Beta Features

  • gpytorch.settings
    • cg_tolerance
    • cholesky_jitter
    • cholesky_max_tries
    • ciq_samples
    • debug
    • detach_test_caches
    • deterministic_probes
    • eval_cg_tolerance
    • fast_computations
      • fast_computations.covar_root_decomposition
      • fast_computations.log_prob
      • fast_computations.solves
    • fast_pred_samples
    • fast_pred_var
    • lazily_evaluate_kernels
    • linalg_dtypes
    • max_cg_iterations
    • max_cholesky_size
    • max_eager_kernel_size
    • max_lanczos_quadrature_iterations
    • max_preconditioner_size
    • max_root_decomposition_size
    • memory_efficient
    • min_preconditioning_size
    • min_variance
    • minres_tolerance
    • num_contour_quadrature
    • num_gauss_hermite_locs
    • num_likelihood_samples
    • num_trace_samples
    • observation_nan_policy
    • preconditioner_tolerance
    • prior_mode
    • sgpr_diagonal_correction
    • skip_logdet_forward
    • skip_posterior_variances
    • terminate_cg_by_size
    • trace_mode
    • tridiagonal_jitter
    • use_keops
    • use_toeplitz
    • variational_cholesky_jitter
    • verbose_linalg
  • gpytorch.beta_features
    • checkpoint_kernel
    • default_preconditioner

Advanced Package Reference

  • gpytorch.Module
    • Module
      • Module.initialize()
      • Module.local_load_samples()
      • Module.named_added_loss_terms()
      • Module.named_priors()
      • Module.pyro_load_from_samples()
      • Module.pyro_sample_from_prior()
      • Module.register_parameter()
      • Module.register_prior()
      • Module.sample_from_prior()
  • gpytorch.functions
    • Functions
      • add_diagonal()
      • add_jitter()
      • dsmm()
      • diagonalization()
      • inv_quad()
      • inv_quad_logdet()
      • pivoted_cholesky()
      • root_decomposition()
      • root_inv_decomposition()
      • solve()
      • sqrt_inv_matmul()
  • gpytorch.utils
    • NNUtil
      • NNUtil.build_sequential_nn_idx()
      • NNUtil.find_nn_idx()
      • NNUtil.set_nn_idx()
      • NNUtil.to()
    • cached()
    • sum_interaction_terms()
    • Grid Utilities
      • ScaleToBounds
      • choose_grid_size()
      • create_data_from_grid()
      • create_grid()
      • scale_to_bounds()
    • Interpolation Utilities
    • Nearest Neighbors Utilities
      • NNUtil
        • NNUtil.build_sequential_nn_idx()
        • NNUtil.find_nn_idx()
        • NNUtil.set_nn_idx()
        • NNUtil.to()
    • Quadrature Utilities
      • GaussHermiteQuadrature1D
        • GaussHermiteQuadrature1D.forward()
    • Transform Utilities
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