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Helper utilities

RxGP exports several utility functions used throughout the message passing rules and by end users.

Mean function application

RxGP.apply_mean_fn — Function
apply_mean_fn(x, mf)

Apply a scalar mean function mf to input x, handling different input types:

  • If x is a scalar, apply mf directly, e.g. mf(x) = x^2 gives apply_mean_fn(3, mf) == 9.
  • If x is a length-1 vector of numbers, apply mf to the single element.
  • If x is a longer vector of numbers, apply mf to the entire vector.
  • If x is a vector of vectors, use apply_mean_fn.(x, mf) to broadcast over sub-vectors.
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Applies the scalar mean function mf to an input x. Handles dispatch for PointMass, Distribution, scalar, and vector inputs.

Mean and covariance extraction

RxGP.mean_cov_scalar_matrix — Function
mean_cov_scalar_matrix(x)

Return (mean, cov) where mean is a scalar and cov is a 1×1 matrix. Input x must be one-dimensional (scalar, length-1 vector, PointMass, or univariate distribution).

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RxGP.mean_cov_vector_matrix — Function
mean_cov_vector_matrix(x)

Return (mean, cov) where mean is a vector and cov is a matrix, regardless of the dimensionality of x. Accepts Real, AbstractVector, PointMass, or any NormalDistributionsFamily.

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These convenience functions extract (mean, cov) from various input types (PointMass, Real, distribution) and normalise the output shapes:

FunctionReturns
mean_cov_scalar_matrix(scalar, 1×1 matrix)
mean_cov_vector_matrix(vector, matrix)

Linear algebra helpers

RxGP.jdotavx — Function
jdotavx(a, b)

Vectorised dot product of arrays a and b using LoopVectorization.@turbo.

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Inducing variable buffer

RxGP.BufferUniSGP — Type
BufferUniSGP{D,M}

Wraps an inducing-variable message qv together with its UniSGPMeta. When the product of all N incoming messages has been accumulated (tracked via meta.counter), updates the Cholesky factor meta.Uv.

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BufferUniSGP wraps an inducing-variable message together with its meta object. When the product of all incoming messages to v has been accumulated (tracked via meta.counter), it updates the Cholesky factor of the second moment meta.Uv. This ensures that the free-energy computation remains efficient.

Hyperparameter optimisation

The following functions compute the negative log backward message and its gradient with respect to the kernel hyperparameters $\theta$. They are designed to be used with gradient-based optimisers (e.g. Optim.jl or Flux.jl).

RxGP.neg_log_backwardmess_fast — Function
neg_log_backwardmess_fast(θ; y_data, x_y_data, q_v, q_w, kernel, mean_fn, Xu, ...)

Negative log backward message toward θ for the univariate VSGP. Supports function-value observations (y_data/x_y_data), gradient observations (ω_data/x_ω_data), and either point or distributional inputs. Used as the M-step objective in grad_llh_default!.

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RxGP.neg_log_backwardmess_uncertain — Function
neg_log_backwardmess_uncertain(θ; y_data, qx, v, Uv, w, kernel, Xu, method)

Negative log backward message toward θ when inputs qx are distributions. Uses Gauss–Hermite cubature to compute kernel expectations Ψ0, Ψ1, Ψ2.

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RxGP.neg_log_backwardmess_msg — Function
neg_log_backwardmess_msg(θ; in_data_, out_data_, q_v, q_W_, meta_)

Negative log backward message toward θ computed via @call_rule on UniSGP_dID(:θ, Marginalisation). Sums log-pdf contributions over all data points and batches in in_data_.

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RxGP.neg_log_backwardmess_multi — Function
neg_log_backwardmess_multi(θ; y_data, qx, sumRv_Wbar, v, W, tr_W, kernel, Xu, method)

Negative log backward message toward θ for the multivariate (MultiSGP) VSGP with C = I. Expects pre-computed sumRv_Wbar = sum(Rv_blk .* W) and tr_W = tr(W) for efficiency.

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