TensorFlow
Install Learn
  • Introduction
    New to TensorFlow?
  • TensorFlow
    The core open source ML library
  • For JavaScript
    TensorFlow.js for ML using JavaScript
  • For Mobile & Edge
    TensorFlow Lite for mobile and edge devices
  • For Production
    TensorFlow Extended for end-to-end ML components
API
  • TensorFlow (v2.12.0)
  • Versions…
  • TensorFlow.js
  • TensorFlow Lite
  • TFX
Resources
  • Models & datasets
    Pre-trained models and datasets built by Google and the community
  • Tools
    Ecosystem of tools to help you use TensorFlow
  • Libraries & extensions
    Libraries and extensions built on TensorFlow
  • TensorFlow Certificate program
    Differentiate yourself by demonstrating your ML proficiency
  • Learn ML
    Educational resources to learn the fundamentals of ML with TensorFlow
  • Responsible AI
    Resources and tools to integrate Responsible AI practices into your ML workflow
Community
  • Join
    Explore ways to get involved
  • Blog
    Stay up to date with all things TensorFlow
  • Forum ↗
    Discussion platform for the TensorFlow community
  • Groups
    User groups, interest groups and mailing lists
  • Contribute
    Guide for contributing to code and documentation
Why TensorFlow
  • About
  • Case studies
  • English
  • 中文 – 简体
GitHub Sign in
  • Probability
Overview Guide & Tutorials API
TensorFlow
  • Install
  • Learn
    • More
  • API
    • More
  • Resources
    • More
    • Overview
    • Guide & Tutorials
    • API
  • Community
    • More
  • Why TensorFlow
    • More
  • GitHub
  • tfp
    • Overview
  • tfp.bijectors
    • Overview
    • AbsoluteValue
    • Ascending
    • AutoCompositeTensorBijector
    • AutoregressiveNetwork
    • BatchNormalization
    • Bijector
    • Blockwise
    • Chain
    • CholeskyOuterProduct
    • CholeskyToInvCholesky
    • Composition
    • CorrelationCholesky
    • Cumsum
    • DiscreteCosineTransform
    • Exp
    • Expm1
    • FFJORD
    • FillScaleTriL
    • FillTriangular
    • FrechetCDF
    • GeneralizedExtremeValueCDF
    • GeneralizedPareto
    • Glow
    • GlowDefaultExitNetwork
    • GlowDefaultNetwork
    • GompertzCDF
    • GumbelCDF
    • Householder
    • Identity
    • Inline
    • Invert
    • IteratedSigmoidCentered
    • JointMap
    • KumaraswamyCDF
    • LambertWTail
    • Log
    • Log1p
    • MaskedAutoregressiveFlow
    • MatrixInverseTriL
    • MatvecLU
    • MoyalCDF
    • NormalCDF
    • Pad
    • Permute
    • Power
    • PowerTransform
    • RationalQuadraticSpline
    • RayleighCDF
    • RealNVP
    • Reciprocal
    • Reshape
    • Restructure
    • Scale
    • ScaleMatvecDiag
    • ScaleMatvecLU
    • ScaleMatvecLinearOperator
    • ScaleMatvecLinearOperatorBlock
    • ScaleMatvecTriL
    • Shift
    • ShiftedGompertzCDF
    • Sigmoid
    • Sinh
    • SinhArcsinh
    • SoftClip
    • Softfloor
    • SoftmaxCentered
    • Softplus
    • Softsign
    • Split
    • Square
    • Tanh
    • TransformDiagonal
    • Transpose
    • UnitVector
    • WeibullCDF
    • masked_autoregressive_default_template
    • masked_dense
    • pack_sequence_as
    • real_nvp_default_template
    • tree_flatten
  • tfp.debugging
    • Overview
    • benchmarking
      • Overview
      • BenchmarkTfFunctionConfig
      • benchmark_tf_function
      • default_benchmark_config
  • tfp.distributions
    • Overview
    • AutoCompositeTensorDistribution
    • Autoregressive
    • BatchBroadcast
    • BatchReshape
    • Bates
    • Bernoulli
    • Beta
    • BetaBinomial
    • BetaQuotient
    • Binomial
    • Blockwise
    • Categorical
    • Cauchy
    • Chi
    • Chi2
    • CholeskyLKJ
    • DeterminantalPointProcess
    • Deterministic
    • Dirichlet
    • DirichletMultinomial
    • Distribution
    • DoublesidedMaxwell
    • Empirical
    • ExpGamma
    • ExpInverseGamma
    • ExpRelaxedOneHotCategorical
    • Exponential
    • ExponentiallyModifiedGaussian
    • FiniteDiscrete
    • Gamma
    • GammaGamma
    • GaussianProcess
    • GaussianProcessRegressionModel
    • GeneralizedExtremeValue
    • GeneralizedNormal
    • GeneralizedPareto
    • Geometric
    • Gumbel
    • HalfCauchy
    • HalfNormal
    • HalfStudentT
    • HiddenMarkovModel
    • Horseshoe
    • Independent
    • Inflated
    • InverseGamma
    • InverseGaussian
    • JohnsonSU
    • JointDistribution
    • JointDistribution.Root
    • JointDistributionCoroutine
    • JointDistributionCoroutineAutoBatched
    • JointDistributionNamed
    • JointDistributionNamedAutoBatched
    • JointDistributionSequential
    • JointDistributionSequentialAutoBatched
    • Kumaraswamy
    • LKJ
    • LambertWDistribution
    • LambertWNormal
    • Laplace
    • LinearGaussianStateSpaceModel
    • LogLogistic
    • LogNormal
    • Logistic
    • LogitNormal
    • MarkovChain
    • Masked
    • MatrixNormalLinearOperator
    • MatrixTLinearOperator
    • Mixture
    • MixtureSameFamily
    • Moyal
    • Multinomial
    • MultivariateNormalDiag
    • MultivariateNormalDiagPlusLowRank
    • MultivariateNormalDiagPlusLowRankCovariance
    • MultivariateNormalFullCovariance
    • MultivariateNormalLinearOperator
    • MultivariateNormalTriL
    • MultivariateStudentTLinearOperator
    • NegativeBinomial
    • NoncentralChi2
    • Normal
    • NormalInverseGaussian
    • OneHotCategorical
    • OrderedLogistic
    • PERT
    • Pareto
    • PixelCNN
    • PlackettLuce
    • Poisson
    • PoissonLogNormalQuadratureCompound
    • PowerSpherical
    • ProbitBernoulli
    • QuantizedDistribution
    • RegisterKL
    • RelaxedBernoulli
    • RelaxedOneHotCategorical
    • ReparameterizationType
    • Sample
    • SigmoidBeta
    • SinhArcsinh
    • Skellam
    • SphericalUniform
    • StoppingRatioLogistic
    • StudentT
    • StudentTProcess
    • StudentTProcessRegressionModel
    • TransformedDistribution
    • Triangular
    • TruncatedCauchy
    • TruncatedNormal
    • TwoPieceNormal
    • TwoPieceStudentT
    • Uniform
    • VariationalGaussianProcess
    • VectorDeterministic
    • VonMises
    • VonMisesFisher
    • Weibull
    • WishartLinearOperator
    • WishartTriL
    • ZeroInflatedNegativeBinomial
    • Zipf
    • independent_joint_distribution_from_structure
    • kl_divergence
    • mvn_conjugate_linear_update
    • normal_conjugates_known_scale_posterior
    • normal_conjugates_known_scale_predictive
    • quadrature_scheme_lognormal_gauss_hermite
    • quadrature_scheme_lognormal_quantiles
  • tfp.experimental
    • Overview
    • AutoCompositeTensor
    • as_composite
    • auto_composite_tensor
    • register_composite
    • auto_batching
      • Overview
      • Context
      • NumpyBackend
      • TensorFlowBackend
      • TensorType
      • Type
      • truthy
      • allocation_strategy
        • Overview
        • optimize
      • dsl
        • Overview
        • ProgramBuilder
      • frontend
        • Overview
        • gast_util
          • Overview
          • Module
          • Name
          • Str
          • is_constant
          • is_ellipsis
          • is_literal
      • instructions
        • Overview
        • Block
        • BranchOp
        • ControlFlowGraph
        • Function
        • FunctionCallOp
        • GotoOp
        • IndirectGotoOp
        • PopOp
        • PrimOp
        • Program
        • PushGotoOp
        • VariableAllocation
        • extract_referenced_variables
        • halt_op
        • interpret
        • push_op
      • liveness
        • Overview
        • liveness_analysis
      • lowering
        • Overview
        • lower_function_calls
      • numpy_backend
        • Overview
      • stack_optimization
        • Overview
        • fuse_pop_push
      • stackless
        • Overview
        • ExecutionQueue
        • execute
        • is_running
      • tf_backend
        • Overview
      • type_inference
        • Overview
        • infer_types
        • infer_types_from_signature
        • is_inferring
        • signature
        • type_of_pattern
      • virtual_machine
        • Overview
        • execute
        • is_staging
      • xla
        • Overview
        • compile_nested_output
    • bayesopt
      • Overview
      • acquisition
        • Overview
        • AcquisitionFunction
        • GaussianProcessExpectedImprovement
        • GaussianProcessMaxValueEntropySearch
        • GaussianProcessProbabilityOfImprovement
        • GaussianProcessUpperConfidenceBound
        • MCMCReducer
        • ParallelExpectedImprovement
        • ParallelUpperConfidenceBound
        • StudentTProcessExpectedImprovement
        • WeightedPowerScalarization
    • bijectors
      • Overview
      • HighwayFlow
      • ScalarFunctionWithInferredInverse
      • Sharded
      • build_trainable_highway_flow
      • forward_log_det_jacobian_ratio
      • inverse_log_det_jacobian_ratio
      • make_distribution_bijector
    • distribute
      • Overview
      • JointDistributionCoroutine
      • JointDistributionNamed
      • JointDistributionSequential
      • Sharded
      • make_pbroadcast_function
      • make_psum_function
      • make_sharded_log_prob_parts
    • distributions
      • Overview
      • ImportanceResample
      • IncrementLogProb
      • JointDistributionPinned
      • MultiTaskGaussianProcess
      • MultiTaskGaussianProcessRegressionModel
      • MultivariateNormalPrecisionFactorLinearOperator
      • inflated_factory
      • log_prob_ratio
      • marginal_fns
        • Overview
        • make_backoff_cholesky
        • make_cholesky_like_marginal_fn
        • make_eigh_marginal_fn
        • retrying_cholesky
        • mvn_linear_operator
          • Overview
        • ps
          • Overview
          • abs
          • add
          • argmax
          • argmin
          • argsort
          • broadcast_shape
          • broadcast_to
          • case
          • cast
          • ceil
          • concat
          • cond
          • constant
          • convert_to_shape_tensor
          • cumprod
          • cumsum
          • dimension_size
          • equal
          • expm1
          • fill
          • floor
          • gather
          • greater
          • identity
          • invert_permutation
          • is_finite
          • is_inf
          • is_nan
          • is_numpy
          • less
          • linspace
          • log
          • log1p
          • logical_and
          • logical_not
          • logical_or
          • maximum
          • minimum
          • nextafter
          • non_negative_axis
          • not_equal
          • one_hot
          • ones
          • ones_like
          • pad
          • pow
          • range
          • rank
          • rank_from_shape
          • reduce_all
          • reduce_any
          • reduce_max
          • reduce_min
          • reduce_prod
          • reduce_sum
          • repeat
          • reshape
          • reverse
          • round
          • rsqrt
          • setdiff1d
          • shape
          • shape_slice
          • size
          • size0
          • slice
          • smart_where
          • sort
          • split
          • sqrt
          • stack
          • tensor_scatter_nd_add
          • tensor_scatter_nd_sub
          • tensor_scatter_nd_update
          • tile
          • top_k
          • unique
          • unstack
          • where
          • zeros
          • zeros_like
          • dtype_util
            • Overview
            • as_numpy_dtype
            • assert_same_float_dtype
            • base_dtype
            • base_equal
            • common_dtype
            • eps
            • is_bool
            • is_complex
            • is_floating
            • is_integer
            • is_numpy_compatible
            • max
            • min
            • name
            • real_dtype
            • size
          • tensorshape_util
            • Overview
            • as_list
            • assert_has_rank
            • assert_is_compatible_with
            • concatenate
            • constant_value_as_shape
            • dims
            • is_compatible_with
            • is_fully_defined
            • merge_with
            • num_elements
            • rank
            • set_shape
            • with_rank
            • with_rank_at_least
        • tfp_custom_gradient
          • Overview
          • custom_gradient
          • is_valid_gradient
          • prevent_gradient
    • joint_distribution_layers
      • Overview
      • Affine
      • AffineLayer
      • Conv2D
      • Lambda
      • Sequential
      • SequentialLayer
      • make_conv2d_layer_class
      • make_lambda_layer_class
    • linalg
      • Overview
      • LinearOperatorInterpolatedPSDKernel
      • LinearOperatorPSDKernel
      • LinearOperatorRowBlock
      • LinearOperatorUnitary
      • no_pivot_ldl
      • simple_robustified_cholesky
      • linear_operator_row_block
        • Overview
        • LinearOperatorRowBlock
    • marginalize
      • Overview
      • MarginalizableJointDistributionCoroutine
      • logeinsumexp
    • math
      • Overview
      • exp_pade_4_4
      • expm1_pade_4_4
      • log1p_pade_4_4
      • log_pade_4_4
      • patch_manual_special_functions
      • reduce_logsumexp
      • softplus
    • mcmc
      • Overview
      • CovarianceReducer
      • DiagonalMassMatrixAdaptation
      • EllipticalSliceSampler
      • ExpectationsReducer
      • GradientBasedTrajectoryLengthAdaptation
      • GradientBasedTrajectoryLengthAdaptationResults
      • KernelBuilder
      • KernelOutputs
      • NoUTurnSampler
      • PotentialScaleReductionReducer
      • PreconditionedHamiltonianMonteCarlo
      • PreconditionedNoUTurnSampler
      • ProgressBarReducer
      • Reducer
      • SNAPERHamiltonianMonteCarlo
      • SNAPERHamiltonianMonteCarloResults
      • SampleDiscardingKernel
      • SampleSNAPERHamiltonianMonteCarloResults
      • SequentialMonteCarlo
      • SequentialMonteCarloResults
      • Sharded
      • StateWithHistory
      • ThinningKernel
      • TracingReducer
      • VarianceReducer
      • WeightedParticles
      • WithReductions
      • WithReductionsKernelResults
      • augment_prior_with_state_history
      • augment_with_observation_history
      • augment_with_state_history
      • chees_criterion
      • chees_rate_criterion
      • default_make_hmc_kernel_fn
      • ess_below_threshold
      • gen_make_hmc_kernel_fn
      • gen_make_transform_hmc_kernel_fn
      • infer_trajectories
      • init_near_unconstrained_zero
      • log_ess_from_log_weights
      • make_rwmh_kernel_fn
      • make_tqdm_progress_bar_fn
      • particle_filter
      • reconstruct_trajectories
      • remc_thermodynamic_integrals
      • resample_deterministic_minimum_error
      • resample_independent
      • resample_stratified
      • resample_systematic
      • retry_init
      • sample_chain
      • sample_chain_with_burnin
      • sample_fold
      • sample_sequential_monte_carlo
      • sample_snaper_hmc
      • simple_heuristic_tuning
      • snaper_criterion
      • step_kernel
      • windowed_adaptive_hmc
      • windowed_adaptive_nuts
    • nn
      • Overview
      • Affine
      • AffineVariationalFlipout
      • AffineVariationalReparameterization
      • AffineVariationalReparameterizationLocal
      • Convolution
      • ConvolutionTranspose
      • ConvolutionTransposeVariationalFlipout
      • ConvolutionTransposeVariationalReparameterization
      • ConvolutionV2
      • ConvolutionVariationalFlipout
      • ConvolutionVariationalFlipoutV2
      • ConvolutionVariationalReparameterization
      • ConvolutionVariationalReparameterizationV2
      • Layer
      • Sequential
      • VariationalLayer
      • initializers
        • Overview
        • glorot_normal
        • glorot_uniform
        • he_normal
        • he_uniform
      • losses
        • Overview
        • compute_extra_loss
        • kl_divergence_exact
        • kl_divergence_monte_carlo
        • negloglik
      • util
        • Overview
        • CallOnce
        • RandomVariable
        • batchify_op
        • display_imgs
        • expand_dims
        • flatten_rightmost
        • halflife_decay
        • im2row
        • im2row_index
        • make_convolution_fn
        • make_convolution_transpose_fn_with_dilation
        • make_convolution_transpose_fn_with_subkernels
        • make_convolution_transpose_fn_with_subkernels_matrix
        • make_fit_op
        • make_kernel_bias
        • make_kernel_bias_posterior_mvn_diag
        • make_kernel_bias_prior_spike_and_slab
        • prepare_conv_args
        • prepare_tuple_argument
        • tfcompile
        • trace
        • tune_dataset
        • variables_load
        • variables_save
        • variables_summary
    • parallel_filter
      • Overview
      • kalman_filter
      • sample_walk
    • psd_kernels
      • Overview
      • AdditiveKernel
      • ContinuousAndCategoricalValues
      • FeatureScaledWithCategorical
      • Independent
      • MultiTaskKernel
      • Separable
    • sequential
      • Overview
      • EnsembleKalmanFilterState
      • IteratedFilter
      • ensemble_adjustment_kalman_filter_update
      • ensemble_kalman_filter_log_marginal_likelihood
      • ensemble_kalman_filter_predict
      • ensemble_kalman_filter_update
      • extended_kalman_filter
      • geometric_cooling_schedule
      • inflate_by_scaled_identity_fn
    • stats
      • Overview
      • RunningCentralMoments
      • RunningCovariance
      • RunningMean
      • RunningPotentialScaleReduction
      • RunningVariance
    • sts_gibbs
      • Overview
      • GibbsSamplerState
      • build_model_for_gibbs_fitting
      • fit_with_gibbs_sampling
      • get_seasonal_latents_shape
      • one_step_predictive
    • substrates
      • Overview
    • tangent_spaces
      • Overview
      • AxisAlignedSpace
      • ConstantDiagonalSymmetricMatrixSpace
      • FullSpace
      • GeneralSpace
      • ProbabilitySimplexSpace
      • SphericalSpace
      • SymmetricMatrixSpace
      • TangentSpace
      • UnspecifiedTangentSpaceError
      • ZeroSpace
    • util
      • Overview
      • DeferredModule
      • JitPublicMethods
      • make_trainable
      • make_trainable_stateless
    • vi
      • Overview
      • build_affine_surrogate_posterior
      • build_affine_surrogate_posterior_from_base_distribution
      • build_affine_surrogate_posterior_from_base_distribution_stateless
      • build_affine_surrogate_posterior_stateless
      • build_asvi_surrogate_posterior
      • build_asvi_surrogate_posterior_stateless
      • build_factored_surrogate_posterior
      • build_factored_surrogate_posterior_stateless
      • build_split_flow_surrogate_posterior
      • util
        • Overview
        • build_linear_operator_zeros
        • build_trainable_linear_operator_block
        • build_trainable_linear_operator_diag
        • build_trainable_linear_operator_full_matrix
        • build_trainable_linear_operator_tril
  • tfp.glm
    • Overview
    • Bernoulli
    • BernoulliNormalCDF
    • Binomial
    • CustomExponentialFamily
    • ExponentialFamily
    • GammaExp
    • GammaSoftplus
    • LogNormal
    • LogNormalSoftplus
    • NegativeBinomial
    • NegativeBinomialSoftplus
    • Normal
    • NormalReciprocal
    • Poisson
    • PoissonSoftplus
    • compute_predicted_linear_response
    • convergence_criteria_small_relative_norm_weights_change
    • fit
    • fit_one_step
    • fit_sparse
    • fit_sparse_one_step
  • tfp.layers
    • Overview
    • AutoregressiveTransform
    • BlockwiseInitializer
    • CategoricalMixtureOfOneHotCategorical
    • Convolution1DFlipout
    • Convolution1DReparameterization
    • Convolution2DFlipout
    • Convolution2DReparameterization
    • Convolution3DFlipout
    • Convolution3DReparameterization
    • DenseFlipout
    • DenseLocalReparameterization
    • DenseReparameterization
    • DenseVariational
    • DistributionLambda
    • IndependentBernoulli
    • IndependentLogistic
    • IndependentNormal
    • IndependentPoisson
    • KLDivergenceAddLoss
    • KLDivergenceRegularizer
    • MixtureLogistic
    • MixtureNormal
    • MixtureSameFamily
    • MultivariateNormalTriL
    • OneHotCategorical
    • VariableLayer
    • VariationalGaussianProcess
    • default_loc_scale_fn
    • default_mean_field_normal_fn
    • default_multivariate_normal_fn
    • conv_variational
      • Overview
    • dense_variational
      • Overview
    • dense_variational_v2
      • Overview
      • kullback_leibler
        • Overview
        • augment_kl_xent_docs
    • distribution_layer
      • Overview
    • initializers
      • Overview
    • masked_autoregressive
      • Overview
    • util
      • Overview
      • deserialize_function
      • serialize_function
    • variable_input
      • Overview
    • weight_norm
      • Overview
      • WeightNorm
  • tfp.math
    • Overview
    • MinimizeTraceableQuantities
    • atan_difference
    • batch_interp_rectilinear_nd_grid
    • batch_interp_regular_1d_grid
    • batch_interp_regular_nd_grid
    • bessel_iv_ratio
    • bessel_ive
    • bessel_kve
    • betainc
    • betaincinv
    • bracket_root
    • cholesky_concat
    • cholesky_update
    • clip_by_value_preserve_gradient
    • custom_gradient
    • dawsn
    • dense_to_sparse
    • diag_jacobian
    • erfcinv
    • erfcx
    • fill_triangular
    • fill_triangular_inverse
    • find_root_chandrupatla
    • find_root_secant
    • gram_schmidt
    • hpsd_logdet
    • hpsd_quadratic_form_solve
    • hpsd_quadratic_form_solvevec
    • hpsd_solve
    • hpsd_solvevec
    • igammacinv
    • igammainv
    • interp_regular_1d_grid
    • lambertw
    • lambertw_winitzki_approx
    • lbeta
    • log1mexp
    • log1psquare
    • log_add_exp
    • log_bessel_ive
    • log_bessel_kve
    • log_combinations
    • log_cosh
    • log_cumsum_exp
    • log_gamma_correction
    • log_gamma_difference
    • log_sub_exp
    • logerfc
    • logerfcx
    • low_rank_cholesky
    • lu_matrix_inverse
    • lu_reconstruct
    • lu_solve
    • minimize
    • minimize_stateless
    • owens_t
    • pivoted_cholesky
    • reduce_kahan_sum
    • reduce_log_harmonic_mean_exp
    • reduce_logmeanexp
    • reduce_weighted_logsumexp
    • round_exponential_bump_function
    • scan_associative
    • secant_root
    • smootherstep
    • soft_sorting_matrix
    • soft_threshold
    • softplus_inverse
    • sparse_or_dense_matmul
    • sparse_or_dense_matvecmul
    • sqrt1pm1
    • trapz
    • value_and_gradient
    • hypergeometric
      • Overview
      • hyp2f1_small_argument
    • ode
      • Overview
      • BDF
      • ChosenBySolver
      • Diagnostics
      • DormandPrince
      • Results
      • Solver
    • psd_kernels
      • Overview
      • AutoCompositeTensorPsdKernel
      • ChangePoint
      • Constant
      • ExpSinSquared
      • ExponentialCurve
      • ExponentiatedQuadratic
      • FeatureScaled
      • FeatureTransformed
      • GammaExponential
      • GeneralizedMatern
      • KumaraswamyTransformed
      • Linear
      • MaternFiveHalves
      • MaternOneHalf
      • MaternThreeHalves
      • Parabolic
      • PointwiseExponential
      • Polynomial
      • PositiveSemidefiniteKernel
      • RationalQuadratic
      • SchurComplement
      • SpectralMixture
  • tfp.mcmc
    • Overview
    • CheckpointableStatesAndTrace
    • DualAveragingStepSizeAdaptation
    • HamiltonianMonteCarlo
    • MetropolisAdjustedLangevinAlgorithm
    • MetropolisHastings
    • NoUTurnSampler
    • RandomWalkMetropolis
    • ReplicaExchangeMC
    • SimpleStepSizeAdaptation
    • SliceSampler
    • StatesAndTrace
    • TransformedTransitionKernel
    • TransitionKernel
    • UncalibratedHamiltonianMonteCarlo
    • UncalibratedLangevin
    • UncalibratedRandomWalk
    • default_swap_proposal_fn
    • effective_sample_size
    • even_odd_swap_proposal_fn
    • make_simple_step_size_update_policy
    • potential_scale_reduction
    • random_walk_normal_fn
    • random_walk_uniform_fn
    • sample_annealed_importance_chain
    • sample_chain
    • sample_halton_sequence
  • tfp.monte_carlo
    • Overview
    • expectation
  • tfp.optimizer
    • Overview
    • StochasticGradientLangevinDynamics
    • VariationalSGD
    • bfgs_minimize
    • converged_all
    • converged_any
    • differential_evolution_minimize
    • differential_evolution_one_step
    • lbfgs_minimize
    • nelder_mead_minimize
    • nelder_mead_one_step
    • proximal_hessian_sparse_minimize
    • proximal_hessian_sparse_one_step
    • convergence_criteria
      • Overview
      • ConvergenceCriterion
      • LossNotDecreasing
      • SuccessiveGradientsAreUncorrelated
    • linesearch
      • Overview
      • hager_zhang
  • tfp.random
    • Overview
    • rademacher
    • rayleigh
    • sanitize_seed
    • spherical_uniform
    • split_seed
  • tfp.stats
    • Overview
    • assign_log_moving_mean_exp
    • assign_moving_mean_variance
    • auto_correlation
    • brier_decomposition
    • brier_score
    • cholesky_covariance
    • correlation
    • count_integers
    • covariance
    • cumulative_variance
    • expected_calibration_error
    • expected_calibration_error_quantiles
    • find_bins
    • histogram
    • kendalls_tau
    • log_average_probs
    • log_loomean_exp
    • log_loosum_exp
    • log_soomean_exp
    • log_soosum_exp
    • moving_mean_variance_zero_debiased
    • percentile
    • quantile_auc
    • quantiles
    • stddev
    • variance
    • windowed_mean
    • windowed_variance
  • tfp.sts
    • Overview
    • AdditiveStateSpaceModel
    • Autoregressive
    • AutoregressiveIntegratedMovingAverage
    • AutoregressiveMovingAverageStateSpaceModel
    • AutoregressiveStateSpaceModel
    • ConstrainedSeasonalStateSpaceModel
    • DynamicLinearRegression
    • DynamicLinearRegressionStateSpaceModel
    • IntegratedStateSpaceModel
    • LinearRegression
    • LocalLevel
    • LocalLevelStateSpaceModel
    • LocalLinearTrend
    • LocalLinearTrendStateSpaceModel
    • MaskedTimeSeries
    • MissingValuesTolerance
    • Seasonal
    • SeasonalStateSpaceModel
    • SemiLocalLinearTrend
    • SemiLocalLinearTrendStateSpaceModel
    • SmoothSeasonal
    • SmoothSeasonalStateSpaceModel
    • SparseLinearRegression
    • StructuralTimeSeries
    • Sum
    • build_factored_surrogate_posterior
    • build_factored_surrogate_posterior_stateless
    • decompose_by_component
    • decompose_forecast_by_component
    • fit_with_hmc
    • forecast
    • impute_missing_values
    • moments_of_masked_time_series
    • one_step_predictive
    • regularize_series
    • sample_uniform_initial_state
  • tfp.substrates
    • Overview
    • jax
      • Overview
      • bijectors
        • Overview
        • AbsoluteValue
        • Ascending
        • AutoCompositeTensorBijector
        • AutoregressiveNetwork
        • Bijector
        • Blockwise
        • Chain
        • CholeskyOuterProduct
        • CholeskyToInvCholesky
        • Composition
        • CorrelationCholesky
        • Cumsum
        • Exp
        • Expm1
        • FFJORD
        • FillScaleTriL
        • FillTriangular
        • FrechetCDF
        • GeneralizedExtremeValueCDF
        • GeneralizedPareto
        • GompertzCDF
        • GumbelCDF
        • Householder
        • Identity
        • Inline
        • Invert
        • IteratedSigmoidCentered
        • JointMap
        • KumaraswamyCDF
        • LambertWTail
        • Log
        • Log1p
        • MaskedAutoregressiveFlow
        • MatrixInverseTriL
        • MatvecLU
        • MoyalCDF
        • NormalCDF
        • Pad
        • Permute
        • Power
        • PowerTransform
        • RationalQuadraticSpline
        • RayleighCDF
        • RealNVP
        • Reciprocal
        • Reshape
        • Restructure
        • Scale
        • ScaleMatvecDiag
        • ScaleMatvecLU
        • ScaleMatvecLinearOperator
        • ScaleMatvecLinearOperatorBlock
        • ScaleMatvecTriL
        • Shift
        • ShiftedGompertzCDF
        • Sigmoid
        • Sinh
        • SinhArcsinh
        • SoftClip
        • Softfloor
        • SoftmaxCentered
        • Softplus
        • Softsign
        • Split
        • Square
        • Tanh
        • TransformDiagonal
        • Transpose
        • UnitVector
        • WeibullCDF
        • masked_autoregressive_default_template
        • masked_dense
        • pack_sequence_as
        • real_nvp_default_template
        • tree_flatten
      • distributions
        • Overview
        • AutoCompositeTensorDistribution
        • Autoregressive
        • BatchBroadcast
        • BatchReshape
        • Bates
        • Bernoulli
        • Beta
        • BetaBinomial
        • BetaQuotient
        • Binomial
        • Blockwise
        • Categorical
        • Cauchy
        • Chi
        • Chi2
        • CholeskyLKJ
        • DeterminantalPointProcess
        • Deterministic
        • Dirichlet
        • DirichletMultinomial
        • Distribution
        • DoublesidedMaxwell
        • Empirical
        • ExpGamma
        • ExpInverseGamma
        • ExpRelaxedOneHotCategorical
        • Exponential
        • ExponentiallyModifiedGaussian
        • FiniteDiscrete
        • Gamma
        • GammaGamma
        • GaussianProcess
        • GaussianProcessRegressionModel
        • GeneralizedExtremeValue
        • GeneralizedNormal
        • GeneralizedPareto
        • Geometric
        • Gumbel
        • HalfCauchy
        • HalfNormal
        • HalfStudentT
        • HiddenMarkovModel
        • Horseshoe
        • Independent
        • Inflated
        • InverseGamma
        • InverseGaussian
        • JohnsonSU
        • JointDistribution
        • JointDistribution.Root
        • JointDistributionCoroutine
        • JointDistributionCoroutineAutoBatched
        • JointDistributionNamed
        • JointDistributionNamedAutoBatched
        • JointDistributionSequential
        • JointDistributionSequentialAutoBatched
        • Kumaraswamy
        • LKJ
        • LambertWDistribution
        • LambertWNormal
        • Laplace
        • LinearGaussianStateSpaceModel
        • LogLogistic
        • LogNormal
        • Logistic
        • LogitNormal
        • MarkovChain
        • Masked
        • MatrixNormalLinearOperator
        • MatrixTLinearOperator
        • Mixture
        • MixtureSameFamily
        • Moyal
        • Multinomial
        • MultivariateNormalDiag
        • MultivariateNormalDiagPlusLowRank
        • MultivariateNormalDiagPlusLowRankCovariance
        • MultivariateNormalFullCovariance
        • MultivariateNormalLinearOperator
        • MultivariateNormalTriL
        • MultivariateStudentTLinearOperator
        • NegativeBinomial
        • NoncentralChi2
        • Normal
        • NormalInverseGaussian
        • OneHotCategorical
        • OrderedLogistic
        • PERT
        • Pareto
        • PlackettLuce
        • Poisson
        • PoissonLogNormalQuadratureCompound
        • PowerSpherical
        • ProbitBernoulli
        • QuantizedDistribution
        • RegisterKL
        • RelaxedBernoulli
        • RelaxedOneHotCategorical
        • Sample
        • SigmoidBeta
        • SinhArcsinh
        • Skellam
        • SphericalUniform
        • StoppingRatioLogistic
        • StudentT
        • StudentTProcess
        • StudentTProcessRegressionModel
        • TransformedDistribution
        • Triangular
        • TruncatedCauchy
        • TruncatedNormal
        • TwoPieceNormal
        • TwoPieceStudentT
        • Uniform
        • VariationalGaussianProcess
        • VectorDeterministic
        • VonMises
        • VonMisesFisher
        • Weibull
        • WishartLinearOperator
        • WishartTriL
        • ZeroInflatedNegativeBinomial
        • Zipf
        • independent_joint_distribution_from_structure
        • kl_divergence
        • mvn_conjugate_linear_update
        • normal_conjugates_known_scale_posterior
        • normal_conjugates_known_scale_predictive
        • quadrature_scheme_lognormal_gauss_hermite
        • quadrature_scheme_lognormal_quantiles
      • glm
        • Overview
        • Bernoulli
        • BernoulliNormalCDF
        • Binomial
        • CustomExponentialFamily
        • ExponentialFamily
        • GammaExp
        • GammaSoftplus
        • LogNormal
        • LogNormalSoftplus
        • NegativeBinomial
        • NegativeBinomialSoftplus
        • Normal
        • NormalReciprocal
        • Poisson
        • PoissonSoftplus
        • compute_predicted_linear_response
        • convergence_criteria_small_relative_norm_weights_change
        • fit
        • fit_one_step
      • math
        • Overview
        • MinimizeTraceableQuantities
        • atan_difference
        • batch_interp_rectilinear_nd_grid
        • batch_interp_regular_1d_grid
        • batch_interp_regular_nd_grid
        • bessel_iv_ratio
        • bessel_ive
        • bessel_kve
        • betainc
        • betaincinv
        • bracket_root
        • cholesky_concat
        • cholesky_update
        • clip_by_value_preserve_gradient
        • custom_gradient
        • dawsn
        • diag_jacobian
        • erfcinv
        • erfcx
        • fill_triangular
        • fill_triangular_inverse
        • find_root_chandrupatla
        • find_root_secant
        • gram_schmidt
        • hpsd_logdet
        • hpsd_quadratic_form_solve
        • hpsd_quadratic_form_solvevec
        • hpsd_solve
        • hpsd_solvevec
        • igammacinv
        • igammainv
        • interp_regular_1d_grid
        • lambertw
        • lambertw_winitzki_approx
        • lbeta
        • log1mexp
        • log1psquare
        • log_add_exp
        • log_bessel_ive
        • log_bessel_kve
        • log_combinations
        • log_cosh
        • log_cumsum_exp
        • log_gamma_correction
        • log_gamma_difference
        • log_sub_exp
        • logerfc
        • logerfcx
        • low_rank_cholesky
        • lu_matrix_inverse
        • lu_reconstruct
        • lu_solve
        • minimize
        • minimize_stateless
        • owens_t
        • pivoted_cholesky
        • reduce_kahan_sum
        • reduce_log_harmonic_mean_exp
        • reduce_logmeanexp
        • reduce_weighted_logsumexp
        • round_exponential_bump_function
        • scan_associative
        • smootherstep
        • soft_sorting_matrix
        • soft_threshold
        • softplus_inverse
        • sparse_or_dense_matmul
        • sparse_or_dense_matvecmul
        • sqrt1pm1
        • trapz
        • value_and_gradient
        • hypergeometric
          • Overview
          • hyp2f1_small_argument
        • ode
          • Overview
          • BDF
          • ChosenBySolver
          • Diagnostics
          • DormandPrince
          • Results
          • Solver
        • psd_kernels
          • Overview
          • AutoCompositeTensorPsdKernel
          • ChangePoint
          • Constant
          • ExpSinSquared
          • ExponentialCurve
          • ExponentiatedQuadratic
          • FeatureScaled
          • FeatureTransformed
          • GammaExponential
          • GeneralizedMatern
          • KumaraswamyTransformed
          • Linear
          • MaternFiveHalves
          • MaternOneHalf
          • MaternThreeHalves
          • Parabolic
          • PointwiseExponential
          • Polynomial
          • PositiveSemidefiniteKernel
          • RationalQuadratic
          • SchurComplement
          • SpectralMixture
      • mcmc
        • Overview
        • CheckpointableStatesAndTrace
        • DualAveragingStepSizeAdaptation
        • HamiltonianMonteCarlo
        • MetropolisAdjustedLangevinAlgorithm
        • MetropolisHastings
        • NoUTurnSampler
        • RandomWalkMetropolis
        • ReplicaExchangeMC
        • SimpleStepSizeAdaptation
        • SliceSampler
        • StatesAndTrace
        • TransformedTransitionKernel
        • TransitionKernel
        • UncalibratedHamiltonianMonteCarlo
        • UncalibratedLangevin
        • UncalibratedRandomWalk
        • default_swap_proposal_fn
        • effective_sample_size
        • even_odd_swap_proposal_fn
        • make_simple_step_size_update_policy
        • potential_scale_reduction
        • random_walk_normal_fn
        • random_walk_uniform_fn
        • sample_annealed_importance_chain
        • sample_chain
        • sample_halton_sequence
      • monte_carlo
        • Overview
        • expectation
      • optimizer
        • Overview
        • bfgs_minimize
        • converged_all
        • converged_any
        • lbfgs_minimize
        • nelder_mead_minimize
        • nelder_mead_one_step
        • convergence_criteria
          • Overview
          • ConvergenceCriterion
          • LossNotDecreasing
          • SuccessiveGradientsAreUncorrelated
        • linesearch
          • Overview
          • hager_zhang
      • random
        • Overview
        • rademacher
        • rayleigh
        • sanitize_seed
        • spherical_uniform
        • split_seed
      • stats
        • Overview
        • assign_log_moving_mean_exp
        • assign_moving_mean_variance
        • auto_correlation
        • brier_decomposition
        • brier_score
        • cholesky_covariance
        • correlation
        • count_integers
        • covariance
        • cumulative_variance
        • expected_calibration_error
        • expected_calibration_error_quantiles
        • find_bins
        • histogram
        • kendalls_tau
        • log_average_probs
        • log_loomean_exp
        • log_loosum_exp
        • log_soomean_exp
        • log_soosum_exp
        • moving_mean_variance_zero_debiased
        • percentile
        • quantiles
        • stddev
        • variance
        • windowed_mean
        • windowed_variance
      • sts
        • Overview
        • AdditiveStateSpaceModel
        • Autoregressive
        • AutoregressiveIntegratedMovingAverage
        • AutoregressiveMovingAverageStateSpaceModel
        • AutoregressiveStateSpaceModel
        • ConstrainedSeasonalStateSpaceModel
        • DynamicLinearRegression
        • DynamicLinearRegressionStateSpaceModel
        • IntegratedStateSpaceModel
        • LinearRegression
        • LocalLevel
        • LocalLevelStateSpaceModel
        • LocalLinearTrend
        • LocalLinearTrendStateSpaceModel
        • MaskedTimeSeries
        • MissingValuesTolerance
        • Seasonal
        • SeasonalStateSpaceModel
        • SemiLocalLinearTrend
        • SemiLocalLinearTrendStateSpaceModel
        • SmoothSeasonal
        • SmoothSeasonalStateSpaceModel
        • SparseLinearRegression
        • StructuralTimeSeries
        • Sum
        • build_factored_surrogate_posterior
        • build_factored_surrogate_posterior_stateless
        • decompose_by_component
        • decompose_forecast_by_component
        • fit_with_hmc
        • forecast
        • impute_missing_values
        • moments_of_masked_time_series
        • one_step_predictive
        • regularize_series
        • sample_uniform_initial_state
      • util
        • Overview
        • BatchedComponentProperties
        • DeferredTensor
        • ParameterProperties
        • SeedStream
        • TransformedVariable
      • vi
        • Overview
        • GradientEstimators
        • amari_alpha
        • arithmetic_geometric
        • chi_square
        • csiszar_vimco
        • dual_csiszar_function
        • fit_surrogate_posterior_stateless
        • jeffreys
        • jensen_shannon
        • kl_forward
        • kl_reverse
        • log1p_abs
        • modified_gan
        • monte_carlo_variational_loss
        • pearson
        • squared_hellinger
        • symmetrized_csiszar_function
        • t_power
        • total_variation
        • triangular
    • numpy
      • Overview
      • bijectors
        • Overview
        • AbsoluteValue
        • Ascending
        • AutoCompositeTensorBijector
        • AutoregressiveNetwork
        • Bijector
        • Blockwise
        • Chain
        • CholeskyOuterProduct
        • CholeskyToInvCholesky
        • Composition
        • CorrelationCholesky
        • Cumsum
        • Exp
        • Expm1
        • FFJORD
        • FillScaleTriL
        • FillTriangular
        • FrechetCDF
        • GeneralizedExtremeValueCDF
        • GeneralizedPareto
        • GompertzCDF
        • GumbelCDF
        • Householder
        • Identity
        • Inline
        • Invert
        • IteratedSigmoidCentered
        • JointMap
        • KumaraswamyCDF
        • LambertWTail
        • Log
        • Log1p
        • MaskedAutoregressiveFlow
        • MatrixInverseTriL
        • MatvecLU
        • MoyalCDF
        • NormalCDF
        • Pad
        • Permute
        • Power
        • PowerTransform
        • RationalQuadraticSpline
        • RayleighCDF
        • RealNVP
        • Reciprocal
        • Reshape
        • Restructure
        • Scale
        • ScaleMatvecDiag
        • ScaleMatvecLU
        • ScaleMatvecLinearOperator
        • ScaleMatvecLinearOperatorBlock
        • ScaleMatvecTriL
        • Shift
        • ShiftedGompertzCDF
        • Sigmoid
        • Sinh
        • SinhArcsinh
        • SoftClip
        • Softfloor
        • SoftmaxCentered
        • Softplus
        • Softsign
        • Split
        • Square
        • Tanh
        • TransformDiagonal
        • Transpose
        • UnitVector
        • WeibullCDF
        • masked_autoregressive_default_template
        • masked_dense
        • pack_sequence_as
        • real_nvp_default_template
        • tree_flatten
      • distributions
        • Overview
        • AutoCompositeTensorDistribution
        • Autoregressive
        • BatchBroadcast
        • BatchReshape
        • Bates
        • Bernoulli
        • Beta
        • BetaBinomial
        • BetaQuotient
        • Binomial
        • Blockwise
        • Categorical
        • Cauchy
        • Chi
        • Chi2
        • CholeskyLKJ
        • DeterminantalPointProcess
        • Deterministic
        • Dirichlet
        • DirichletMultinomial
        • Distribution
        • DoublesidedMaxwell
        • Empirical
        • ExpGamma
        • ExpInverseGamma
        • ExpRelaxedOneHotCategorical
        • Exponential
        • ExponentiallyModifiedGaussian
        • FiniteDiscrete
        • Gamma
        • GammaGamma
        • GaussianProcess
        • GaussianProcessRegressionModel
        • GeneralizedExtremeValue
        • GeneralizedNormal
        • GeneralizedPareto
        • Geometric
        • Gumbel
        • HalfCauchy
        • HalfNormal
        • HalfStudentT
        • HiddenMarkovModel
        • Horseshoe
        • Independent
        • Inflated
        • InverseGamma
        • InverseGaussian
        • JohnsonSU
        • JointDistribution
        • JointDistribution.Root
        • JointDistributionCoroutine
        • JointDistributionCoroutineAutoBatched
        • JointDistributionNamed
        • JointDistributionNamedAutoBatched
        • JointDistributionSequential
        • JointDistributionSequentialAutoBatched
        • Kumaraswamy
        • LKJ
        • LambertWDistribution
        • LambertWNormal
        • Laplace
        • LinearGaussianStateSpaceModel
        • LogLogistic
        • LogNormal
        • Logistic
        • LogitNormal
        • MarkovChain
        • Masked
        • MatrixNormalLinearOperator
        • MatrixTLinearOperator
        • Mixture
        • MixtureSameFamily
        • Moyal
        • Multinomial
        • MultivariateNormalDiag
        • MultivariateNormalDiagPlusLowRank
        • MultivariateNormalDiagPlusLowRankCovariance
        • MultivariateNormalFullCovariance
        • MultivariateNormalLinearOperator
        • MultivariateNormalTriL
        • MultivariateStudentTLinearOperator
        • NegativeBinomial
        • NoncentralChi2
        • Normal
        • NormalInverseGaussian
        • OneHotCategorical
        • OrderedLogistic
        • PERT
        • Pareto
        • PlackettLuce
        • Poisson
        • PoissonLogNormalQuadratureCompound
        • PowerSpherical
        • ProbitBernoulli
        • QuantizedDistribution
        • RegisterKL
        • RelaxedBernoulli
        • RelaxedOneHotCategorical
        • Sample
        • SigmoidBeta
        • SinhArcsinh
        • Skellam
        • SphericalUniform
        • StoppingRatioLogistic
        • StudentT
        • StudentTProcess
        • StudentTProcessRegressionModel
        • TransformedDistribution
        • Triangular
        • TruncatedCauchy
        • TruncatedNormal
        • TwoPieceNormal
        • TwoPieceStudentT
        • Uniform
        • VariationalGaussianProcess
        • VectorDeterministic
        • VonMises
        • VonMisesFisher
        • Weibull
        • WishartLinearOperator
        • WishartTriL
        • ZeroInflatedNegativeBinomial
        • Zipf
        • independent_joint_distribution_from_structure
        • kl_divergence
        • mvn_conjugate_linear_update
        • normal_conjugates_known_scale_posterior
        • normal_conjugates_known_scale_predictive
        • quadrature_scheme_lognormal_gauss_hermite
        • quadrature_scheme_lognormal_quantiles
      • glm
        • Overview
        • Bernoulli
        • BernoulliNormalCDF
        • Binomial
        • CustomExponentialFamily
        • ExponentialFamily
        • GammaExp
        • GammaSoftplus
        • LogNormal
        • LogNormalSoftplus
        • NegativeBinomial
        • NegativeBinomialSoftplus
        • Normal
        • NormalReciprocal
        • Poisson
        • PoissonSoftplus
        • compute_predicted_linear_response
        • convergence_criteria_small_relative_norm_weights_change
        • fit
        • fit_one_step
      • math
        • Overview
        • MinimizeTraceableQuantities
        • atan_difference
        • batch_interp_rectilinear_nd_grid
        • batch_interp_regular_1d_grid
        • batch_interp_regular_nd_grid
        • bessel_iv_ratio
        • bessel_ive
        • bessel_kve
        • betainc
        • betaincinv
        • bracket_root
        • cholesky_concat
        • cholesky_update
        • clip_by_value_preserve_gradient
        • custom_gradient
        • dawsn
        • diag_jacobian
        • erfcinv
        • erfcx
        • fill_triangular
        • fill_triangular_inverse
        • find_root_chandrupatla
        • find_root_secant
        • gram_schmidt
        • hpsd_logdet
        • hpsd_quadratic_form_solve
        • hpsd_quadratic_form_solvevec
        • hpsd_solve
        • hpsd_solvevec
        • igammacinv</