Capability index: GeoML
Layers: GeoStack · GeoNumerics · GeoML · GeoModels.
Every public name in the libraries geostack builds on, each listed
once under the shortest module path that exports it, with the first
sentence of its docstring. Search this page before writing a
loader, a model, a training step or a helper in a script or a
notebook: if what you need is here, use it; if it is almost here,
extend it where it lives. Regenerate with make capabilities after
changing a public API (tests/test_capabilities.py checks it is
current).
This page is the GeoML layer. It may import GeoNumerics, GeoStack.
Listed at geonnax 0.0.9, kernellib 0.0.21, optax-bayes 0.0.3, filterax 0.0.5, vardax 0.1.9, gauss-flows 0.1.9, xtremax 0.0.4, pyrox 0.1.1, pyrox-gp 0.1.9, pyrox-lgm 0.1.2, pyrox-nn 0.1.0.
Upstream: geonnax¶
Basis functions, neural layers and coordinate transforms in Equinox.
geonnax¶
| Name | Kind | What it does |
|---|---|---|
AbstractConditioner | class | Duck-typed protocol for (h, z) -> y conditioning layers. |
AffineModulation | class | Feature-wise Linear Modulation (FiLM): y = γ(z) ⊙ h + β(z). |
AntiAliasedActivation | class | A pointwise nonlinearity between band-limited function spaces. |
Attention | class | Pre-norm multi-head self-attention with cosine (QK-normalised) similarity. |
BasisSpectralConv | class | Spectral convolution in a precomputed basis: per-mode channel mixing. |
BasisTransform | class | Frozen analysis / synthesis pair for a precomputed basis. |
Block | class | Conv → GroupNorm → SiLU, the residual-block primitive. |
CNO | class | Convolutional Neural Operator: lift → U-Net of band-limited blocks → project. |
CNOBlock | class | Convolution then band-limited activation: the CNO I, D and U blocks. |
CNOResBlock | class | The CNO residual (R) block, . |
CPTensor | class | Canonical-Polyadic (CP / PARAFAC) factorization. |
Cartesian3DEncoder | class | Lift a single lon/lat coordinate onto the unit sphere . |
ConcatConditioner | class | Concatenate h and z then apply a single Linear. |
ConditionedINR | class | Wrap an inner network’s per-layer activations with conditioners. |
ConvNeXtBlock | class | ConvNeXt-V2 block: depthwise conv → norm → MLP with GRN (Woo et al., 2023). |
CyclicEncoder | class | Encode a single periodic input as concatenated cos/sin features. |
DeepVSSGPCore | class | Deterministic deep RFF spectral core. |
Deg2Rad | class | Element-wise degrees-to-radians conversion. |
DenseRank1 | class | Rank-1 ensemble dense layer (deterministic BatchEnsemble core). |
DenseTensor | class | A full, un-factorised tensor. |
DomainPadding | class | Zero-pad spatial axes by a fraction of their size, then crop back. |
Downsample | class | Memory-efficient factor-2 downsample: space-to-depth, then 1x1 conv. |
FNO | class | Fourier Neural Operator: lifting → Fourier blocks → projection. |
FNOBlock | class | One Fourier layer: spectral conv + pointwise skip, then an activation. |
FourierFilter | class | Single Fourier filter: . |
FourierNet | class | Multiplicative Fourier Filter Network (Fathony et al., ICLR 2021). |
GaborFilter | class | Single Gabor filter: . |
GaborNet | class | Multiplicative Gabor Filter Network (Fathony et al., ICLR 2021). |
GeneratedSiren | class | Wrapper around a SIREN whose layers consume generated weights. |
GeoContextEncoder | class | Encode geoscience metadata into a single context vector. |
GeoFNO | class | Geo-FNO: a Fourier neural operator on per-sample point clouds. |
GlobalResponseNorm | class | Global Response Normalization (Woo et al., 2023, “ConvNeXt-V2”). |
HeteroscedasticHead | class | Shared state and init for the FA-noise heteroscedastic layers. |
HybridSphericalSlepianEncoder | class | Concatenate low-bandwidth global SHs with local Slepian cap modes. |
HyperLinear | class | Generate a target Linear’s (W, b) from z, then apply. |
HyperSIREN | function | NIF-style ShapeNet/ParameterNet composite (Pan, Brunton, Kutz — JMLR 2023). |
LNO | class | Local Neural Operator: pad → local core → crop, marched with jax.lax.scan. |
LaplaceRandomFeatureCovariance | class | Laplace-approximation precision for an SNGP output head. |
LayerNormEnsemble | class | Per-ensemble-member LayerNorm (deterministic core). |
LearnedDeformation | class | A learned chart from the physical domain onto the latent torus (Geo-FNO). |
LinearAttention | class | Pre-norm linear attention — O(n) in the number of spatial positions. |
LinearChainCRF | class | Deterministic linear-chain CRF — forward algorithm plus Viterbi decoding. |
LonLatScale | class | Affine-rescale a single lon/lat pair into [-1, 1]. |
MCSigmoidDenseFA | class | Heteroscedastic multi-label output layer (FA noise + sigmoid). |
MCSoftmaxDenseFA | class | Heteroscedastic multi-class output layer (FA noise + softmax). |
MSWT | class | Multi-Scale Wavelet Transformer operator (Wang et al., 2026). |
MSWTBlock | class | Pre-norm wavelet-attention block: an attention residual, then an FFN residual. |
ManifoldNO | class | Manifold Neural Operator: lifting → basis blocks → projection. |
ManifoldNOBlock | class | One manifold-operator layer: basis spectral conv + pointwise skip. |
MixtureOfGaussiansDenseHead | class | Deterministic mixture-density-network output head. |
MultiHeadAttentionBE | class | Multi-head attention with BatchEnsemble rank-1 projections. |
MultiScaleSIREN | class | Parallel frequency-banded SIRENs summed at the readout. |
NCPContinuousPerturb | class | Input perturbation for the Noise Contrastive Prior pattern. |
NestedResidualUNet | class | A small residual U-Net used as one stage block (Qin et al., 2020, “U²-Net”). |
OrthogonalRandomFeatures | class | Orthogonal Random Features (Yu et al., 2016) — variance-reduced RFF. |
RandomFeatureGaussianProcess | class | SNGP output layer (Liu et al., 2020) — deterministic core. |
Rank1ProjInit | class | Per-projection BatchEnsemble inits used by MultiHeadAttentionBE. |
ResnetBlock | class | Two Blocks with squeeze-excitation and a residual skip. |
SFNO | class | Spherical Fourier Neural Operator: lift → spherical blocks → project. |
SIREN | class | Multi-layer sinusoidal representation network (Sitzmann et al., NeurIPS 2020). |
SirenDense | class | Sine-activated dense layer: y = sin(ω · (W x + b)) or y = W x + b. |
SirenLayerSpec | class | Static per-layer metadata shared by deterministic and Bayesian SIRENs. |
SirenLayerType | function | Re-exported from typing. |
SlepianEncoder | class | Deterministic Slepian-cap positional encoder on . |
SpectralConv | class | Fourier spectral convolution over num_spatial_dims = len(n_modes) axes. |
SpectralNormalization | class | Wrap an Equinox linear layer to be -Lipschitz via power iteration. |
SphericalFNOBlock | class | One spherical Fourier layer: spherical spectral conv + pointwise skip. |
SphericalHarmonicEncoder | class | Real spherical-harmonic features on the unit 2-sphere for a single point. |
SphericalHarmonicTransform | class | Dense, differentiable spherical harmonic analysis/synthesis on a grid. |
SphericalSpectralConv | class | Spherical spectral convolution: per-degree channel mixing in SH space. |
SphericalWaveletConv | class | Per-scale channel mixing in the spherical-wavelet domain. |
SphericalWaveletTransform | class | Scale-discretised (needlet) wavelet analysis/synthesis on the sphere. |
SqueezeExcitation | class | Squeeze-and-Excitation channel gating (Hu et al., 2018). |
Stage | class | One encoder/decoder stage: a leaf block, then an optional nested U-Net. |
StandardizedConv | class | Convolution with optional on-the-fly weight standardization. |
TTTensor | class | Tensor-Train (Matrix-Product) factorization. |
TuckerTensor | class | Tucker factorization: a small core contracted with per-mode factor matrices. |
UNet | class | Dimension-flexible U-Net with modern blocks, attention, and nested stages. |
Upsample | class | Factor-2 upsample via pixel-shuffle: 1x1 conv, then depth-to-space. |
WNO | class | Wavelet Neural Operator: lifting → wavelet blocks → projection. |
WNOBlock | class | One wavelet layer: wavelet conv + pointwise skip, then an activation. |
WaveletAttention | class | Self-attention performed inside the wavelet domain (Wang et al., 2026). |
WaveletConv | class | Wavelet-domain channel mixing — the wavelet analogue of SpectralConv. |
WindowedAttention | class | Swin-style windowed multi-head self-attention with cosine similarity. |
apply_rank1_proj | function | Apply y_i = ((x ⊙ s_i) @ W) ⊙ r_i + b_i per ensemble member. |
band_limited_resize | function | Resample a periodic field onto a new grid by Fourier truncation / zero-padding. |
build_siren_specs | function | Produce per-layer specs for a depth-depth SIREN, first + hidden… + last. |
cno_receptive_radius | function | Effective receptive radius, in grid points, of a CNO run on its input grid. |
hetero_noisy_logits | function | Sample num_mc_samples heteroscedastic logits for one example. |
init_factorized_tensor | function | Construct a factorized tensor of the requested kind. |
init_rank1_proj | function | Glorot-init shared kernel + per-member rank-1 vectors + zero bias. |
log_spaced_omegas | function | Return num_scales log-spaced frequencies spanning the closed band. |
mfn_forward | function | Pure-JAX MFN forward pass given user-supplied filter and linear callables. |
orthogonal_blocks | function | Build the ORF frequency matrix as [Q_1 S_1, ..., Q_K S_K]. |
rff_cosine_forward | function | Shared single-cosine RFF feature map: sqrt(2/D) cos(xW/l + b). |
rff_forward | function | Shared RFF feature map: sqrt(1/D) [cos(xW/l), sin(xW/l)]. |
siren_W_limit | function | Return the half-width a of the U(-a, a) weight init for a SIREN layer. |
Upstream: kernellib¶
Covariance kernels and scalable kernel methods on gaussx.
kernellib¶
| Name | Kind | What it does |
|---|---|---|
AbstractEstimator | class | Configure, fit, predict. |
AbstractFeatureMap | class | A finite-dimensional approximation k(x, x') ≈ φ(x)ᵀ φ(x'). |
AbstractGraph | class | Weighted, undirected graph without self-loops. |
AbstractGreatCircleKernel | class | on (lon, lat) inputs. |
AbstractKernel | class | Anything that produces a Gram matrix. |
AbstractMeshKernel | class | A kernel on a triangle mesh given by its Laplace-Beltrami spectrum. |
AbstractPointwiseKernel | class | A kernel defined by k(x, x'). |
AbstractSphereSeriesKernel | class | A kernel on given by its Laplace-Beltrami spectrum . |
AbstractStationaryKernel | class | k(x, x') = variance * shape(||(x - x') / lengthscale||²). |
ActiveDims | class | Apply a kernel to a subset of input dimensions. |
Advected | class | A frozen spatial field moving at a constant velocity. |
CKAAccumulator | class | Running mini-batch CKA (Nguyen, Raghu & Kornblith, 2021). |
Chordal | class | A Euclidean kernel on points of the sphere, . |
Constant | class | Constant kernel, k(x, x') = sigma^2. |
Cosine | class | Cosine kernel, sigma^2 cos(2 pi ||x - x'|| / p). |
Cubic | class | Cubic covariance model, compactly supported. |
CurlFree | class | Curl-free kernel: the covariance of a gradient field . |
CurlFreeFeatures | class | Hilbert-space features of a curl-free 2-D vector field. |
Derivative | class | for fixed input dimensions. |
DerivativeIndexed | class | Joint covariance of a GP’s values and partial derivatives. |
Distance | class | Distance-induced kernel, k(x, x') = σ² (|x|^a + |x'|^a - |x - x'|^a) / 2. |
DivergenceFree | class | Divergence-free kernel: the covariance of a rotated gradient field. |
DivergenceFreeFeatures | class | Hilbert-space features of a divergence-free 2-D vector field. |
EARTH_RADIUS_KM | constant | 6371.0088 |
EigenPro | class | Kernel regression by EigenPro-preconditioned SGD (Ma & Belkin, 2017). |
EigenProPreconditioner | class | Spectral correction state for EigenPro kernel SGD. |
Falkon | class | Nyström kernel ridge regression solved by Falkon (Rudi et al., 2017). |
FalkonInfo | class | Convergence report of a falkon_solve run. |
FalkonPreconditioner | class | The two upper-triangular Cholesky factors of the Falkon preconditioner. |
FastFoodFeatures | class | FastFood random features (Le, Sarlós & Smola, 2013) for any kernel with a spectral sampler. |
FastFoodParams | class | The random structure of a FastFood feature map. |
FeatureKernel | class | Inner product of features, . |
GeneralizedCauchy | class | Generalized Cauchy covariance model. |
GeometricAnisotropy | class | A rotated, stretched stationary kernel: a correlation ellipse or ellipsoid. |
Gibbs | class | Gibbs kernel: a lengthscale that varies with location. |
Gneiting | class | Gneiting’s non-separable space-time covariance. |
Graph | class | Sparse weighted graph: a static topology and traced edge weights. |
GraphEigenFeatures | class | Low-rank features of GraphMatern / GraphHeat from Laplacian eigenpairs. |
GraphHeat | class | Graph heat (diffusion) kernel on node indices. |
GraphMatern | class | Graph Matérn kernel on node indices (Borovitskiy et al., 2021). |
GraphTopology | class | Static, hashable edge list of an undirected graph without self-loops. |
GreatCircleAskey | class | Askey’s truncated power kernel, . |
GreatCircleCauchy | class | Generalized Cauchy kernel, . |
GreatCircleExponential | class | Exponential kernel of the great-circle angle, . |
GreatCirclePoweredExponential | class | Powered exponential kernel, . |
GreatCircleSpherical | class | The geostatistics spherical model of the great-circle angle. |
GreatCircleWendland | class | C²- or C⁴-Wendland kernel of the great-circle angle. |
GridGraph | class | Regular lattice graph that never stores its edges. |
Helmholtz | class | Helmholtz-decomposition kernel: curl-free plus divergence-free parts. |
HelmholtzFeatures | class | Helmholtz features: curl-free plus divergence-free columns. |
HoleEffect | class | Hole-effect (cardinal sine, “wave”) covariance model. |
ImplicitCrossKernelOperator | class | Matrix-free rectangular kernel operator K(X, Z) \cdot v. |
ImplicitKernelOperator | class | Matrix-free kernel operator: (K + sigma^2 I) v via sequential scan. |
JunStein | class | Axially symmetric kernel of Jun & Stein (2008), . |
KNNGraph | class | A directed k-nearest-neighbour graph, self excluded. |
KRR | class | Kernel ridge regression. |
KernelLocalityPreservingProjections | class | Kernel locality preserving projections. |
KernelOperator | class | Kernel matrix operator with efficient first-order autodiff. |
KernelPCA | class | Kernel principal component analysis. |
KernelSchrodingerProjections | class | Kernel Schrödinger eigenmap projections. |
KroneckerFeatures | class | Features of a separable kernel as a product of two maps. |
LaplaceEigenfunctionFeatures | class | Hilbert-space (HSGP) approximation of a stationary kernel on a box. |
LaplacianEigenmaps | class | Laplacian eigenmaps (Belkin & Niyogi, 2003) of the k-NN graph of X. |
LatitudeScaled | class | Amplitude modulation by latitude, . |
LegendreLatitudeFn | class | A function of latitude, . |
Linear | class | Linear kernel, k(x, x') = sigma^2 x^T x' + b. |
LinearTransform | class | A stationary kernel of a linearly transformed lag. |
LocalityPreservingProjections | class | Locality preserving projections (He & Niyogi, 2003). |
Matern | class | Matern kernel with closed-form nu in {0.5, 1.5, 2.5}. |
MeshHeat | class | Heat (diffusion) kernel on a triangulated surface. |
MeshLaplaceFeatures | class | FEM Laplace-Beltrami eigenvector features of a mesh kernel. |
MeshMatern | class | Matérn kernel on a triangulated surface (Borovitskiy et al. 2020). |
Modulated | class | A kernel with an input-dependent amplitude, . |
NystromFeatures | class | Nyström features (Williams & Seeger, 2001) for any kernel. |
OrthogonalRandomFeatures | class | Orthogonal random features (Yu et al., 2016). |
PaciorekSchervish | class | Paciorek-Schervish kernel: a location-dependent anisotropy matrix. |
Pentaspherical | class | Pentaspherical covariance model, compactly supported. |
Periodic | class | Periodic (MacKay) kernel on the Euclidean distance. |
PeriodicFeatures | class | Exact truncated Fourier features of a 1-D Periodic kernel. |
Periodised | class | Make any kernel periodic: apply it to inputs wrapped onto circles. |
PermutationTestResult | class | Outcome of permutation_test. |
Polynomial | class | Polynomial kernel, k(x, x') = sigma^2 (x^T x' + b)^d. |
Product | class | Elementwise product of kernels, k(x, x') = prod_i k_i(x, x'). |
RBF | class | Radial basis function (squared exponential) kernel. |
RandomAdvectionRBF | class | The frozen-field RBF averaged over a Gaussian velocity. |
RandomFourierFeatures | class | Random Fourier features (Rahimi & Recht, 2007). |
RationalQuadratic | class | Rational quadratic kernel, a scale mixture of RBFs. |
Residual | class | What an approximation misses, . |
RootedTree | class | A tree with one root: every non-root node has exactly one parent. |
Scaled | class | A kernel times a scalar, k(x, x') = scale * k_0(x, x'). |
SchrodingerEigenmapProjections | class | Schrödinger eigenmap projections (SEP): linear Schrödinger eigenmaps. |
SchrodingerEigenmaps | class | Schrödinger eigenmaps (Czaja & Ehler, 2013) of the k-NN graph of X. |
Shift | class | Input warp x -> x - offset; offset is scalar or per dimension. |
SlepianFeatures | class | Features of a zonal kernel concentrated on a spherical cap. |
SphereHeat | class | Heat (diffusion, squared-exponential) kernel on the sphere. |
SphereMatern | class | Intrinsic Matérn kernel on the sphere (Borovitskiy et al. 2020). |
SphereSeries | class | A sphere kernel from any user spectrum . |
Spherical | class | Spherical covariance model, compactly supported. |
SphericalHarmonicFeatures | class | Weighted real spherical harmonics up to degree for a zonal kernel. |
Stable | class | Stable (powered exponential) covariance model. |
Stretch | class | Input warp x -> x / scale; scale is scalar or per dimension. |
Sum | class | Sum of kernels, k(x, x') = sum_i k_i(x, x'). |
TailDown | class | Tail-down covariance on a rooted tree (Ver Hoef & Peterson, 2010). |
TailUp | class | Tail-up covariance on a rooted tree (Ver Hoef & Peterson, 2010). |
Tanh | class | Hyperbolic-tangent kernel, k(x, x') = sigma^2 tanh(gamma x^T x' + c0). |
Tapered | class | A covariance multiplied by a compactly supported taper. |
TaylorStatistics | class | The sides and angle of a kernel Taylor-diagram triangle. |
TreeSites | class | Pairwise geometry of N sites on a RootedTree (host-computed). |
Variogram | class | A binned empirical semivariogram. |
Warped | class | Apply a kernel to warped inputs, k(x, x') = k_0(w(x), w(x')). |
Wendland | class | Wendland covariance model, compactly supported. |
White | class | White-noise kernel, sigma^2 delta(x, x'). |
adjacency_matrix | function | Symmetric weighted adjacency matrix of a k-NN graph. |
barrier_potential | function | Diagonal potential that is strength at indices and 0 elsewhere. |
batched_kernel_matvec | function | Compute K(X, Z) @ v in memory-efficient batches. |
batched_kernel_rmatvec | function | Compute K(X, Z)^T @ u in memory-efficient batches. |
cka | function | Centred kernel alignment, . |
combine_potentials | function | Several Schrödinger potentials as one: . |
commute_time_kernel | function | Commute-time kernel , the Laplacian’s pseudo-inverse. |
cosine_graph_kernel | function | Inverse-cosine kernel (Smola & Kondor, 2003). |
curl | function | Per-point curl of a 2-D or 3-D vector field. |
delaunay_graph | function | The edge graph of the Delaunay triangulation of X. |
derivative_inputs | function | Rows [x, i] for DerivativeIndexed: values, then partials. |
diffusion_kernel | function | Diffusion (heat) kernel (Kondor & Lafferty, 2002). |
distance_correlation_squared | function | Squared distance correlation (Székely et al., 2007), cka. |
distance_covariance_squared | function | Squared distance covariance (Székely et al., 2007), 4 * hsic. |
divergence | function | Per-point divergence . |
draw_rff_cosine_basis | function | Draw (variance, lengthscale, omega, phase, weights) for a kernel. |
edge_weights | function | Reweight a graph’s edges by a kernel on the nodes’ features. |
eigenpro_correction | function | Compute the EigenPro eigenspace correction for one SGD mini-batch. |
eigenpro_preconditioner | function | Build an EigenPro spectral preconditioner from a kernel operator. |
eigenpro_step_size | function | Return the EigenPro preconditioned step size for a batch size. |
empirical_variogram | function | Binned empirical semivariogram of y observed at X. |
energy_distance | function | Energy distance (Székely & Rizzo, 2004), 2 * mmd_squared. |
estimate_lengthscale | function | A data-driven lengthscale for an RBF-type kernel. |
evaluate_rff_cosine_paths | function | Evaluate the zero-mean RFF prior path(s) at inputs X. |
falkon_preconditioner | function | Build the Falkon preconditioner from the inducing-point kernel matrix. |
falkon_predict | function | Predict with Nyström KRR weights: . |
falkon_solve | function | Nyström kernel ridge regression weights by Falkon’s preconditioned CG. |
fastfood_features | function | FastFood feature map, . |
fastfood_frequencies | function | The dense frequency matrix that FastFood applies implicitly. |
fastfood_operator | function | FastFood approximation of the RBF Gram matrix, . |
fastfood_params | function | Draw the random structure for a FastFood RBF feature map. |
fit_variogram | function | Fit a stationary kernel plus a nugget to an empirical variogram. |
funk_hecke_coefficients | function | Per-degree spherical-harmonic spectrum of a kernel on a sphere. |
gabriel_graph | function | The Gabriel graph of X. |
gamma_to_lengthscale | function | lengthscale = 1 / sqrt(2 gamma), the inverse of lengthscale_to_gamma. |
gradient | function | Per-point gradient of a scalar field. |
graph_from_adjacency | function | The sparse graph of a dense, symmetric adjacency matrix. |
graph_from_edges | function | The sparse graph of an edge list: the seam for other graph libraries. |
graph_from_neighbors | function | The sparse, symmetric graph of a k-nearest-neighbour relation. |
graph_laplacian | function | Graph Laplacian of a symmetric adjacency matrix. |
graph_null_space | function | Orthonormal basis of the Laplacian’s null space. |
grid_graph | function | The lattice graph of an array of shape shape. |
hadamard_transform | function | Re-exported from gaussx. |
hessian | function | Per-point Hessian . |
hsic | function | Hilbert-Schmidt Independence Criterion between paired samples. |
hsic_penalty | function | The HSIC penalty operator on protected attributes. |
implicit_cross_kernel | function | Create a matrix-free rectangular cross-kernel operator. |
jacobian | function | Per-point Jacobian . |
kernel_alignment | function | Uncentred kernel alignment, . |
knn_graph | function | The k-nearest-neighbour graph of X. |
label_potential | function | Non-diagonal potential pulling together points that share a label. |
laplacian | function | Per-point Laplacian . |
laplacian_eigenmap | function | Laplacian eigenmap of a weighted graph: smallest solutions of . |
laplacian_eigpairs | function | The n smallest eigenpairs of a graph Laplacian. |
laplacian_penalty | function | The graph-smoothness penalty operator . |
lengthscale_grid | function | Log-spaced lengthscales within decades orders of magnitude of center. |
lengthscale_to_gamma | function | gamma = 1 / (2 lengthscale^2), the scikit-learn RBF parameter. |
matern_graph_kernel | function | Graph Matérn kernel (Borovitskiy et al., 2021). |
mesh_graph | function | The edge graph of a triangle mesh. |
mmd_squared | function | Squared maximum mean discrepancy between samples X and Y. |
n_components_graph | function | Number of connected components (an isolated node is one). |
nearest_neighbors | function | The n_neighbors nearest other points of every point in X. |
nystrom_kernel | function | The Nyström kernel . |
nystrom_operator | function | Nystrom low-rank kernel approximation. |
permutation_test | function | Permutation p-value for a statistic that is large under the alternative. |
radius_graph | function | The graph joining points within radius of each other. |
radius_neighbors | function | The other points within radius of every point, at most max_neighbors of them. |
random_walk_kernel | function | -step random-walk kernel (Smola & Kondor, 2003). |
regularized_laplacian_kernel | function | Regularised Laplacian kernel . |
relative_neighborhood_graph | function | The relative neighbourhood graph of X. |
rff_operator | function | Random Fourier Features kernel approximation. |
schrodinger_eigenmap | function | Schrödinger eigenmap: smallest solutions of . |
select_landmarks | function | Indices into X of n_landmarks distinct landmarks. |
spatial_spectral_graph | function | Spatial-spectral graph for images (Cahill, Czaja & Messinger, 2014). |
spatial_spectral_potential | function | Spatial-spectral potential for images (Cahill, Czaja & Messinger, 2014). |
structure_matrix | function | The Besag (ICAR) structure matrix , optionally BYM2-scaled. |
tapered_operator | function | The tapered Gram as a sparse gaussx operator. |
taylor_statistics | function | Radii, correlation and distance for a kernel Taylor diagram. |
to_cross_operator | function | K(X1, X2) as a rectangular linear operator. |
to_operator | function | K(X, X) (+ noise * I) as a symmetric, PSD-tagged linear operator. |
vector_inputs | function | Point-major rows [x_n, i] for the vector-field kernels. |
Upstream: optax-bayes¶
The Bayesian learning rule as optax gradient transformations.
Upstream: filterax¶
Differentiable ensemble Kalman filters and smoothers.
Upstream: vardax¶
Variational data assimilation: BLUE/OI, 3D-Var, 4D-Var and kin.
vardax¶
| Name | Kind | What it does |
|---|---|---|
AmortizedConfig | class | Configuration for an AmortizedPosterior. |
AmortizedPosterior | class | Amortized variational posterior . |
AnalysisStep | class | Re-exported from pipekit_cycle. |
AveragingKernel | class | RTM L2-style averaging-kernel obs operator. |
Batch1D | class | Batch of 1-D spatiotemporal data. |
Batch2D | class | Batch of 2-D spatiotemporal data. |
Batch2DMultivar | class | Batch of 2-D multivariate spatiotemporal data. |
BilinAEPrior1D | class | Bilinear autoencoder prior for 1-D data. |
BilinAEPrior2D | class | Bilinear autoencoder prior for 2-D data. |
BilinAEPrior2DMultivar | class | Bilinear autoencoder prior for 2-D multivariate data. |
CompositeBasis | class | Concatenate several reduced bases into one control vector. |
ConditionalFlowHead | class | Conditional normalising flow head (stub). |
ConvAEPrior1D | class | Convolutional autoencoder prior for 1-D spatially-structured data. |
ConvLSTMGradMod1D | class | 1-D ConvLSTM-based gradient modulator. |
ConvLSTMGradMod2D | class | 2-D ConvLSTM-based gradient modulator. |
CostFunction | class | Variational cost function J(x, batch, **kwargs) -> scalar. |
DynIncrements | class | One-step-increment dynamical prior. |
DynTrajectory | class | Full-rollout dynamical prior. |
DynamicalPrior | class | Base class for ODE-based dynamical priors. |
EnsembleCovariance | class | Sample-covariance posterior from an ensemble of analyses. |
ForwardModel | class | Re-exported from pipekit_cycle. |
FourDVarNet1D | class | End-to-end 4DVarNet model for 1-D spatiotemporal reconstruction. |
FourDVarNet2D | class | End-to-end 4DVarNet model for 2-D spatiotemporal reconstruction. |
GaussNewtonHessian | class | Gauss-Newton Hessian inversion at MAP. |
GaussianMarkLikelihood | class | Serialise a Gaussian posterior into a mark-likelihood dict. |
GradModulator | class | Learned gradient modulator for the FourDVarNet inner solver. |
IdentityObsEncoder | class | Concatenate input and mask into a flat context vector. |
IdentityPrior | class | Trivial identity prior: . |
ImplicitAdjoint | class | Re-exported from optimistix. |
Incremental4DVar | class | Reduced-basis 4DVar. |
IncrementalConfig | class | Configuration for IncrementalFourDVar. |
IncrementalFourDVar | class | Operational incremental 4DVar (Decision D11). |
InstrumentRegistry | class | Keyed lookup of InstrumentSpec by instrument_id. |
InstrumentSpec | class | Per-instrument (obs_op, mask, R_op, id) bundle. |
InterpObs | class | Grid → scattered-obs sparse bilinear interpolation. |
KStepAdjoint | class | K-step differentiation: warmup under stop_gradient, then k live steps. |
L63Prior | class | Learned prior for the Lorenz-63 system. |
L96Prior | class | Learned prior for the Lorenz-96 system. |
LSTMState1D | class | Hidden state for a 1-D ConvLSTM gradient modulator. |
LSTMState2D | class | Hidden state for a 2-D ConvLSTM gradient modulator. |
LaplaceCovariance | class | Laplace approximation at MAP. |
LinearBasis | class | Generic linear reduced basis with a diagonal- prior. |
LinearObs | class | H(x) = H_mat @ x. |
Lorenz63 | class | Lorenz-63 vector field as an Equinox module. |
Lorenz96 | class | Lorenz-96 vector field as an Equinox module. |
MLPAEPrior1D | class | MLP autoencoder prior for 1-D data. |
MLPObsEncoder | class | Two-layer MLP encoder from flat (input, mask) to context. |
MaskedIdentity | class | with optional element-wise mask. |
Minimiser | class | Wrapper protocol around optimistix.AbstractMinimiser. |
MultiInstrumentFusion | class | Compose per-instrument operators at the likelihood level. |
ObservationOperator | class | Re-exported from pipekit_cycle. |
OneStepAdjoint | class | One-step differentiation (Bolte et al., 2023). |
OptimalInterpolation | class | BLUE / OI — closed-form linear-Gaussian analysis. |
Posterior | class | Posterior container — Decision D10. |
PosteriorAdapter | class | Turns an analysis output into a Posterior container. |
Prior | class | Prior model: maps state to its regularised reconstruction. |
RecursiveCheckpointAdjoint | class | Re-exported from optimistix. |
ReducedBasis | class | Reduced-basis control-vector operator. |
RegressionHead | class | Gaussian regression head: q_φ(x|y) = N(μ_φ(y), diag(σ²_φ(y))). |
ScoreDiffusionHead | class | Score-based diffusion head (stub). |
SoftBoundedForward | class | ForwardModel adapter that softly confines states to a box. |
SolverState1D | class | Mutable solver state for 1-D problems. |
SolverState2D | class | Mutable solver state for 2-D problems. |
StrongFourDVar | class | Strong-constraint 4DVar. |
TemporalPrior | class | Time-dependent prior: dynamics-aware regularisation over a window. |
ThreeDVar | class | 3D variational analysis. |
VarDACycle | function | Build a pipekit_cycle.DACycle from a vardax model. |
VarSmootherCycle | function | Build a pipekit_cycle.SmootherCycle from a vardax model. |
WeakFourDVar | class | Weak-constraint 4DVar with augmented control vector. |
amortized_nll_loss_fn | function | Negative log-likelihood for amortized inference (Epic 8). |
amortized_train_step | function | Single training step for AmortizedPosterior. |
assert_adjoint_calibrated | function | Random-vector probe of the Jacobian agreement at y. |
assert_posterior_agreement | function | Check that p_fast.mean lies within tolerance_sigma standard deviations of p_oracle.mean. |
background_cost | function | Background cost . |
composite_basis | function | Build a CompositeBasis from a sequence of ReducedBasis components. |
decomposed_loss | function | Compute the decomposed variational loss. |
eof_basis | function | Data-driven EOF (PCA) reduced basis from a sample matrix. |
eval_step | function | Compute the evaluation loss for a single batch (no gradient). |
fourier_basis | function | Laplacian-eigenfunction (Dirichlet/HSGP) reduced basis on a box. |
fp_solver_step_1d | function | Perform a single 1-D fixed-point projection step. |
init_solver_state_1d | function | Initialise a 1-D solver state from a batch. |
init_solver_state_2d | function | Initialise a 2-D solver state from a batch. |
interp_obs_from_coords | function | Build an InterpObs from grid axis arrays + obs locations. |
linear_basis | function | Build a LinearBasis from an arbitrary precomputed design matrix. |
obs_cost_1d | function | Observation cost for 1-D data. |
obs_cost_2d | function | Observation cost for 2-D data. |
one_step_solve_4dvarnet_1d | function | Solve 4DVarNet-1D using k-step differentiation (Bolte et al., 2023). |
one_step_solve_4dvarnet_2d | function | Solve 4DVarNet-2D using k-step differentiation (Bolte et al., 2023). |
plot_l96_grid | function | Hovmöller-style image of Lorenz-96 states over time. |
plot_l96_trajectories | function | Line plot of selected Lorenz-96 variables over time. |
plot_reconstruction_comparison | function | Side-by-side comparison of target, masked input, and reconstruction. |
prior_cost | function | Prior cost based on learned autoencoder reconstruction. |
rbf_basis | function | Placeable radial-basis reduced basis (Gaussian or Wendland kernels). |
reconstruction_loss | function | Mean-squared reconstruction loss. |
simulate_lorenz63 | function | Simulate the Lorenz-63 system and return state trajectory. |
simulate_lorenz96 | function | Simulate the Lorenz-96 system and return state trajectory. |
simulation_based_calibration | function | Per Talts et al. 2018: rank histogram of true draws within posterior samples. |
solve_4dvarnet_1d | function | Run the full 1-D 4DVarNet solver for n_steps iterations. |
solve_4dvarnet_1d_fixedpoint | function | Run n_fp_steps fixed-point projection steps using jax.lax.scan. |
solve_4dvarnet_2d | function | Run the full 2-D 4DVarNet solver for n_steps iterations. |
solver_step_1d | function | Perform a single 1-D solver iteration. |
solver_step_2d | function | Perform a single 2-D solver iteration. |
strong_variational_cost | function | Strong-constraint variational cost . |
time_patches | function | Overlapping consecutive time pairs for one-step increment losses. |
to_optimistix_adjoint | function | Map an adjoint spec onto an optimistix.AbstractAdjoint. |
train_loss_fn | function | Compute the training loss for a single batch. |
train_step | function | Perform a single training step (forward + backward + update). |
variational_cost | function | Compute the variational cost . |
variational_cost_grad | function | Gradient of variational_cost w.r.t. x. |
wavelet_basis | function | Orthonormal wavelet (DWT) reduced basis on a periodic grid. |
Upstream: gauss-flows¶
Gaussianization (RBIG) and normalizing flows.
gauss_flows¶
| Name | Kind | What it does |
|---|---|---|
AbstractStochastic | class | Base class for transforms that are stochastic in both directions. |
AbstractSurjection | class | Base class for SurVAE surjective transforms. |
ActNorm | class | Activation normalization (ActNorm) for image-shaped events. |
ActNorm1D | class | Activation normalization (ActNorm) for 1-D events. |
AffineCoupling | class | Affine coupling layer. |
Augment | class | Generative surjection that appends conditionally sampled dimensions. |
BatchNorm | class | Invertible batch normalization layer for 1D inputs. |
CircularRQSplineCoupling | class | Coupling layer whose transformer is a circular rational quadratic spline. |
CircularRationalQuadraticSpline | class | Scalar rational quadratic spline with tied endpoint derivatives. |
ClassCondDiagGaussian | class | Class-conditional diagonal Gaussian with learned per-class parameters. |
ClassCondFlow | class | Class-conditional flow built on a ClassCondDiagGaussian base. |
ConditionalDiagGaussian | class | Diagonal Gaussian whose (loc, log_scale) are produced by a single net. |
Conditioner | class | Wrap an unconditional bijection with a context-amortised affine. |
ConjugateTransformFilter | class | Ensemble Kalman analysis performed in a Gaussianised latent space. |
ContinuousAffineCoupling | class | Time-gated affine coupling with optional control conditioning. |
DeepSigmoidCoupling | class | Coupling layer with a monotone single-layer sigmoidal transformer. |
DiffeqConcat | class | MLP vector field with a learnable scalar time embedding. |
DiffeqMLP | class | MLP vector field f(ode_time, x, condition) via concatenation. |
FFJORD | class | Continuous normalizing flow via a learned ODE. |
FixedRotation | class | Fixed (non-trainable) orthogonal rotation matrix. |
FlowDist | class | Wrap a flowjax Transformed distribution as a NumPyro distribution. |
FlowGuide | class | NumPyro variational guide using a Gaussianization flow. |
GINCoupling | class | Volume-preserving affine coupling from Sorrenson et al. (2020). |
GaussianMixture | class | Trainable multivariate Gaussian-mixture base distribution. |
GaussianPCA | class | Probabilistic-PCA Gaussian base distribution (low-rank + diagonal Σ). |
GeneralizedDivisiveNormalization | class | Generalized divisive normalization for image-shaped events (..., C). |
GeneralizedDivisiveNormalization1D | class | 1-D Generalized divisive normalization with full D x D coupling. |
HaarWavelet | class | Haar wavelet transform bijection (1-D, last axis). |
HistogramCDF | class | Marginal Gaussianization via a per-dimension empirical histogram CDF. |
HouseholderRotation | class | Orthogonal rotation via a sequence of Householder reflections. |
InverseGaussCDF | class | Apply the inverse Gaussian CDF (probit) element-wise. |
Invertible1x1Conv | class | Invertible 1×1 convolution with LU-parameterised weight (Glow). |
LULinearPermute | class | Invertible linear layer via LU decomposition composed with a fixed permutation. |
MatrixExponential | class | Closed-form linear neural flow parameterised by exp(W · t). |
MixtureGaussianCDF | class | Marginal Gaussianization via a mixture-of-Gaussians CDF. |
MixtureGaussianCDFCoupling | class | Coupling layer whose transformed half goes through a mixture-CDF. |
MixtureLogisticCDF | class | Marginal Gaussianization via a mixture-of-logistics CDF. |
NumpyroBase | class | Wrap any numpyro.distributions.Distribution as a flowjax base. |
Orthogonal1x1Conv | class | Orthogonal 1x1 convolution (Cayley-parameterised orthogonal mixing). |
OrthogonalConvExponential | class | Orthogonal convolution via the exponential of a skew-symmetric operator. |
OrthogonalRotation | class | Learnable orthogonal rotation via the Cayley map. |
PeriodicShift | class | Learnable circular shift on selected periodic dimensions. |
PeriodicWrap | class | Canonical projection of selected dimensions onto [−bound, bound]. |
PlanarFlow | class | Planar normalizing-flow bijection (Rezende & Mohamed 2015). |
RQSplineCoupling | class | Rational quadratic spline coupling layer. |
RQSplineMarginal | class | Marginal Gaussianization via rational-quadratic splines. |
SimpleAbsSurjection | class | Elementwise absolute-value surjection with a random-sign inverse. |
SimpleMaxPoolSurjection2d | class | 2D max-pooling surjection with a learned residual decoder. |
SimpleSortSurjection | class | Sort along one axis; invert via independent per-slice permutations. |
Slice | class | Inference surjection that drops the trailing dimensions of a 1D event. |
Squeeze | class | Volume-preserving squeeze that trades spatial extent for channels. |
StochasticPermutation | class | Uniform random permutation along one axis (zero log-det). |
SurVAEFlow | class | Container that threads PRNG keys through a mixed bijection / surjection chain. |
SylvesterFlow | class | Sylvester normalizing flow (van den Berg et al. 2018). |
TimeFourier | class | Fourier-feature time gate with g(0) = 0 by construction. |
TimeIdentity | class | Identity time gate g(t) = t. |
TimeTanh | class | Tanh time gate with g(0) = 0 by construction. |
TransformFilter | class | Run a Gaussian filter in warped coordinates. |
UniformOnSphere | class | Uniform distribution on the unit sphere Sᵈ ⊂ ℝ^{d+1}. |
VAE | class | Variational autoencoder as a SurVAE stochastic transform. |
VonMisesFisher | class | Von Mises–Fisher distribution on the unit sphere Sᵈ ⊂ ℝ^{d+1}. |
coupling_gaussianization_flow | function | Construct a coupling-based Gaussianization flow. |
entropy | function | Differential entropy of a flow (flow-based Monte-Carlo estimator). |
entropy_reduction | function | Differential entropy of x via a Gaussianization flow (RBIG-way). |
expmap_sphere | function | Map a tangent vector at x to the sphere via the exponential map. |
fit_gaussianization_flow | function | Fit a Gaussianization flow to data by maximum likelihood. |
fit_rbig | function | Fit an iterative-Gaussianization (RBIG) flow to data in closed form. |
fit_rbig_coupling | function | Warm-start an RBIG-style coupling flow in closed form. |
gaussian_entropy | function | Differential entropy of a Gaussian (analytical Gaussian closed form). |
gaussian_kl_divergence | function | KL divergence of two Gaussians (analytical Gaussian closed form). |
gaussian_mutual_information | function | Mutual information of Gaussian blocks (analytical Gaussian closed form). |
gaussian_total_correlation | function | Total correlation of a Gaussian (analytical Gaussian closed form). |
gaussianization_flow | function | Construct a Gaussianization flow. |
information_reduction | function | Total correlation removed between two representations (RBIG-way reduction). |
iterative_rbig | function | Construct an iterative RBIG (Rotation-Based Iterative Gaussianization) flow. |
kl_divergence | function | KL divergence KL(P ‖ Q) of flows (flow-based Monte-Carlo estimator). |
kl_divergence_reduction | function | KL divergence KL(P || Q) via a reference Gaussianization (RBIG-way). |
logmap_sphere | function | Return the tangent vector at x whose exp-map reaches y. |
mutual_information | function | Mutual information I(X; Y) of flows (flow-based Monte-Carlo estimator). |
negentropy | function | Negentropy of a flow (flow-based Monte-Carlo estimator). |
normalizing_kalman_filter | function | Compose a state-space base with a per-timestep observation warp. |
pack_time_control | function | Pack time and optional control vector into one condition array. |
rbig_conjugate_filter | function | Fit a Gaussianising warp to a prior ensemble with RBIG. |
tangent_basis | function | Return an orthonormal basis of the tangent space Tₓ Sᵈ. |
time_control_cond_shape | function | Return the FlowJax cond_shape for packed (time, control) inputs. |
total_correlation | function | Total correlation of a flow (flow-based Monte-Carlo estimator). |
total_correlation_reduction | function | Total correlation of x via a Gaussianization flow (RBIG-way). |
unpack_time_control | function | Unpack a packed (time, control) condition. |
Upstream: xtremax¶
Extreme-value and point-process models in NumPyro.
xtremax¶
| Name | Kind | What it does |
|---|---|---|
FrechetType2GEVD | class | Fréchet Type II Generalized Extreme Value Distribution for NumPyro. |
GeneralizedExtremeValueDistribution | class | Generalized Extreme Value Distribution (GEVD) for NumPyro. |
GeneralizedParetoDistribution | class | Generalized Pareto Distribution (GPD) for NumPyro. |
GumbelType1GEVD | class | Gumbel Type I Generalized Extreme Value Distribution for NumPyro. |
WeibullType3GEVD | class | Weibull Type III Generalized Extreme Value Distribution for NumPyro. |
assemble_nonstationary_gev_fields | function | Build non-stationary spatio-temporal GEV parameter fields. |
design_matrix | function | Prepend an intercept column to a static-covariate matrix. |
expected_exceedances | function | Expected number of block exceedances of a threshold. |
frechet_cdf | function | Fréchet CDF. |
frechet_icdf | function | Fréchet quantile function. |
frechet_log_prob | function | Fréchet log PDF (assumes shape > 0). |
frechet_mean | function | Fréchet mean (+inf when shape >= 1). |
frechet_return_level | function | T-period return level. |
gev_cdf | function | CDF of the Generalized Extreme Value distribution. |
gev_icdf | function | Quantile function (inverse CDF) of the GEV distribution. |
gev_log_prob | function | Log PDF of the Generalized Extreme Value distribution. |
gev_log_survival | function | Log survival function :math:\log S(x) = \log(1 - F(x)) of the GEV. |
gev_mean | function | Mean of the GEV distribution (+inf when :math:\xi \ge 1). |
gev_return_level | function | T-period return level: :math:z_T = F^{-1}(1 - 1/T). |
gev_survival | function | Survival function :math:S(x) = 1 - F(x) of the GEV distribution. |
gpd_cdf | function | CDF of the Generalized Pareto Distribution. |
gpd_icdf | function | Quantile function (inverse CDF) of the GPD. |
gpd_log_prob | function | Log PDF of the Generalized Pareto Distribution (loc = 0). |
gpd_log_survival | function | Log survival :math:\log S(x) = -\tfrac{1}{\xi}\log(1 + \xi x/\sigma). |
gpd_mean | function | GPD mean: :math:\sigma / (1 - \xi) for :math:\xi < 1, else +inf. |
gpd_return_level | function | T-period return level: :math:Q(1 - 1/T). |
gpd_survival | function | Survival function :math:S(x) = (1 + \xi x/\sigma)^{-1/\xi} of the GPD. |
gumbel_cdf | function | Gumbel CDF: :math:F(x) = \exp(-\exp(-z)). |
gumbel_icdf | function | Gumbel quantile: :math:Q(p) = \mu - \sigma\log(-\log p). |
gumbel_log_prob | function | Gumbel log PDF: :math:-\log\sigma - z - e^{-z}, :math:z=(x-\mu)/\sigma. |
gumbel_mean | function | Gumbel mean: :math:\mu + \sigma\gamma_E. |
gumbel_return_level | function | T-period return level: :math:Q(1 - 1/T). |
nonstationary_return_level | function | Return level for stationary or non-stationary GEV parameter fields. |
nonstationary_return_period | function | Return period associated with a threshold under (non-)stationary GEV. |
pairwise_distances | function | Euclidean distance matrix between sites. |
two_range_correlation | function | Two-range exponential correlation matrix with unit diagonal. |
weibull_cdf | function | Reverse-Weibull CDF. |
weibull_icdf | function | Reverse-Weibull quantile function. |
weibull_log_prob | function | Reverse-Weibull log PDF (assumes shape < 0). |
weibull_mean | function | Reverse-Weibull mean (always finite for shape < 0). |
weibull_return_level | function | T-period return level. |
xtremax.extraction¶
| Name | Kind | What it does |
|---|---|---|
XarrayQuantileRegressor | class | Quantile regressor that operates on :class:xr.DataArray inputs. |
constant_threshold | function | Return a constant threshold value. |
decluster_runs | function | Decluster exceedances using the runs method. |
decluster_separation | function | Decluster by enforcing minimum separation between peaks. |
declustered_block_maxima | function | Extract declustered block maxima by identifying independent extreme events. |
estimate_extremal_index | function | Estimate the extremal index (theta), a measure of clustering. |
quantile_regression_threshold | function | Estimate a time-varying threshold via linear quantile regression. |
quantile_threshold | function | Calculate threshold based on a percentile of the data. |
r_largest_block_maxima | function | Extract r-largest order statistics from each block. |
rolling_threshold | function | Calculate time-varying threshold using a rolling window. |
seasonal_threshold | function | Calculate seasonal threshold (backward compatibility wrapper). |
sliding_block_maxima | function | Extract block maxima using a sliding window approach. |
spatial_block_maxima | function | Extract spatial block maximum values from an xarray DataArray. |
temporal_block_maxima | function | Extract temporal block maximum values from an xarray DataArray. |
temporal_threshold | function | Calculate time-varying threshold based on temporal grouping. |
xtremax.point_processes¶
| Name | Kind | What it does |
|---|---|---|
EventHistory | class | Fixed-size buffer of events + optional marks. |
GoodnessOfFit | class | Bundle of diagnostics returned by goodness_of_fit. |
MarkedSampleResult | class | Marked temporal sample: (times, mask, marks). |
MarkedSpatialSampleResult | class | Marked spatial sample: (locations, mask, marks). |
MarkedSpatiotemporalSampleResult | class | Marked spatiotemporal sample: (locations, times, mask, marks). |
RectangularDomain | class | Axis-aligned rectangle [lo, hi] ⊂ ℝᵈ. |
SampleResult | class | Unmarked temporal sample: (times, mask, n_events). |
SpatialSampleResult | class | Unmarked spatial sample: (locations, mask, n_events). |
SpatiotemporalSampleResult | class | Unmarked spatiotemporal sample: (locations, times, mask, n_events). |
TemporalDomain | class | Half-open temporal interval [t0, t1) ⊂ ℝ. |
constant_mark_distribution | function | Mark distribution that ignores time and history and returns d. |
constant_retention | function | Retention that always returns the same probability p. |
cumulative_log_intensity | function | Shorthand for :math:\Lambda(t) = \int_0^t \lambda(s) ds. |
integrate_log_intensity | function | Compute :math:\int_{t_0}^{t_1} \exp(\log\lambda(s))\, ds. |
integrate_log_intensity_spatial | function | Compute :math:\int_D \exp(\log\lambda(s))\, ds. |
integrate_log_intensity_spatiotemporal | function | Compute :math:\int_{t_0}^{t_1} \int_D \exp(\log\lambda(s, t))\, ds\, dt. |
time_varying_marks | function | Wrap a time → Distribution callable into the full signature. |
time_varying_retention | function | Wrap a pure function of time into the full retention signature. |
xtremax.simulations¶
| Name | Kind | What it does |
|---|---|---|
SpatialFeatureExtractor | class | Static methods to derive physical features from a Digital Elevation Model (DEM). |
augment_spatial_features | function | Pipeline to run all extractors and merge into Dataset. |
compute_advanced_climate_signal | function | Generates Tmax and Precip Mean fields using advanced physics proxies. |
compute_climate_signal | function | Combines Spatial and Temporal fields to create a mean climate signal (Mu). |
create_iberian_domain | function | Creates the master spatial dataset with Lat, Lon, Elevation, and Land Mask. |
generate_fractal_terrain | function | Generates coherent terrain using Fractal Brownian Motion (fBm). |
generate_gmst_trajectory | function | Generates a synthetic Global Mean Surface Temperature (GMST) anomaly curve. |
generate_iberia_mask | function | Procedurally generates a boolean mask approximating the Iberian Peninsula and Balearic Islands using geometrical primitives. |
generate_physical_gmst | function | Simulates Global Mean Surface Temperature (GMST) using a 0-D Energy Balance Model. |
generate_spatial_field | function | Generates static spatial data: Lat, Lon, Elevation, Distance to Coast. |
simulate_precip_extremes | function | Simulates Precipitation Extremes: 1. |
simulate_temp_extremes | function | Simulates Block Maxima Temperature via the GEV distribution. |
simulate_wind_extremes | function | Simulates Extreme Wind Speeds (Gusts) using Weibull distribution. |
Upstream: pyrox¶
Equinox modules with NumPyro sample and param sites.
pyrox.inference¶
| Name | Kind | What it does |
|---|---|---|
EnsembleMAP | class | NumPyro-like ensemble MAP/MLE runner. |
EnsembleResult | class | Output of a full EnsembleMAP.run / EnsembleVI.run. |
EnsembleState | class | Stacked state for an ensemble of optimizer runs. |
EnsembleVI | class | NumPyro-like ensemble variational-inference runner. |
ensemble_init | function | Initialize an ensemble of (params, opt_state) by vmap over keys. |
ensemble_loss | function | Build the filter_value_and_grad loss from a log-joint. |
ensemble_map | function | One-shot wrapper around EnsembleMAP. |
ensemble_predict | function | Vmap predict_fn over the leading ensemble axis of params. |
ensemble_step | function | Perform one ensemble update step on a batch. |
ensemble_vi | function | One-shot wrapper around EnsembleVI. |
param_group_optimizer | function | Apply a different optimizer to each labelled parameter group. |
Upstream: pyrox-gp¶
Gaussian processes for pyrox.
pyrox_gp¶
| Name | Kind | What it does |
|---|---|---|
BernoulliLikelihood | class | Binary classification likelihood with logit link. |
ConditionedGP | class | GP conditioned on Gaussian-likelihood training observations. |
ConditionedLatentFactorGP | class | Latent-factor posterior — MAP latents plus the decoder posterior. |
ConditionedMarkovGP | class | Markov GP conditioned on Gaussian-likelihood observations. |
ConditionedOILMMGP | class | OILMM posterior — Q conditioned scalar GPs plus the mixing. |
ConjugateVI | class | Natural-gradient / CVI update for sparse variational GPs. |
Constant | class | Constant kernel k(x, x') = sigma^2. |
ConstantSDE | class | Re-exported from gaussx. |
Cosine | class | Cosine kernel sigma^2 cos(2 pi ||x - x'|| / period). |
CosineSDE | class | Re-exported from gaussx. |
DecoupledInducingFeatures | class | Decoupled mean / covariance inducing-feature bases (Cheng & Boots 2017). |
DecoupledPathwiseSampler | class | Sparse/decoupled pathwise sampler with RFF prior + inducing update. |
DeltaGuide | class | Point-mass (MAP-style) variational posterior over inducing values. |
DistLikelihood | class | Generic likelihood wrapping any numpyro.distributions.Distribution. |
ExpectationPropagation | class | Parallel expectation propagation (Minka 2001) with damping. |
ExpectationPropagationMarkov | class | Parallel Expectation Propagation for MarkovGPPrior. |
FourierInducingFeatures | class | VFF — Variational Fourier inducing features on . |
FullRankGuide | class | Full-rank Gaussian variational posterior over inducing values u. |
GPPrior | class | Finite-dimensional GP prior over a fixed training input set. |
GaussNewtonInference | class | Gauss-Newton inference: Newton loop with PSD-projected curvature. |
GaussNewtonMarkovInference | class | Gauss-Newton (Markov) inference: Newton with a strict PSD floor. |
GaussianLikelihood | class | Gaussian observation model . |
Guide | class | Abstract base for variational posterior families. |
HeteroscedasticGaussianLikelihood | class | Gaussian regression with input-dependent noise. |
ICMKernel | class | Intrinsic coregionalization model with one shared latent kernel. |
InducingFeatures | class | Protocol for inter-domain inducing features. |
IntegratedWienerSDE | class | Re-exported from gaussx. |
LMCKernel | class | Linear model of coregionalization for vector-valued GPs. |
LaplaceInference | class | Laplace approximation via Newton iteration on the log posterior. |
LaplaceMarkovInference | class | Laplace approximation for MarkovGPPrior. |
LaplacianInducingFeatures | class | Inducing features from low-frequency graph Laplacian eigenvectors. |
LatentFactorGPPrior | class | GP latent factors with an analytically marginalized linear decoder. |
Likelihood | class | Abstract base for observation models. |
Linear | class | Linear kernel sigma^2 x^T x' + bias. |
MarkovGPPrior | class | Linear-time temporal GP prior over a sorted 1-D grid. |
Matern | class | Matern kernel with nu in {0.5, 1.5, 2.5}. |
MaternSDE | class | Re-exported from gaussx. |
MeanFieldGuide | class | Diagonal Gaussian variational posterior over inducing values u. |
MultiOutputConditionedGP | class | Multi-output GP conditioned on Gaussian-likelihood observations. |
MultiOutputGPPrior | class | Finite-dimensional multi-output GP prior over fixed training inputs. |
MultiOutputInducingVariables | class | Shared inducing-point structure for LMC-style sparse workflows. |
MultiOutputSparseGPPrior | class | Sparse multi-output GP prior over shared inducing inputs. |
NaturalGuide | class | Natural-parameter Gaussian variational posterior over inducing values. |
NonGaussConditionedGP | class | GP conditioned on a non-Gaussian likelihood via an advanced strategy. |
NonGaussConditionedMarkovGP | class | Markov GP conditioned on a non-Gaussian likelihood via a site-based strategy. |
NormalizingKalmanPrior | class | Normalizing Kalman Filter prior over a multivariate time grid. |
OILMMGPPrior | class | Orthogonal-mixing multi-output GP prior with a projected exact posterior. |
OILMMKernel | class | Orthogonal instantaneous linear mixing model. |
PathwiseFunction | class | Callable posterior function draw(s) produced by a pathwise sampler. |
PathwiseSampler | class | Exact-GP pathwise posterior sampler using Matheron’s rule. |
Periodic | class | Periodic (MacKay) kernel. |
PeriodicSDE | class | Re-exported from gaussx. |
PoissonLikelihood | class | Count likelihood with log-link. |
Polynomial | class | Polynomial kernel sigma^2 (x^T x' + bias)^degree. |
PosteriorLinearization | class | Iterated statistical-linearization site updates. |
PosteriorLinearizationMarkov | class | Posterior linearization for MarkovGPPrior (Markov IPLF). |
ProductSDE | class | Re-exported from gaussx. |
QuasiNewtonInference | class | MAP optimization via L-BFGS, Laplace covariance at convergence. |
QuasiPeriodicSDE | class | Re-exported from gaussx. |
RBF | class | Radial basis function (squared exponential) kernel. |
RationalQuadratic | class | Rational quadratic kernel. |
SDEKernel | class | Re-exported from gaussx. |
SDEParams | class | Re-exported from gaussx. |
SharedInducingPoints | class | Shared inducing inputs for multi-output latent GP collections. |
SlepianInducingFeatures | class | Region-localized Slepian inducing features on . |
SoftmaxLikelihood | class | Multi-class classification likelihood with softmax link. |
SparseConditionedMarkovGP | class | Sparse Markov GP fitted to a guide. |
SparseGPPrior | class | GP prior parameterized over inducing inputs Z. |
SparseMarkovGPPrior | class | Sparse variational GP prior over an SDE kernel and inducing time grid. |
SphericalHarmonicInducingFeatures | class | VISH — inducing harmonics on (Dutordoir et al. 2020). |
StudentTLikelihood | class | Heavy-tailed regression: p(y | f) = StudentT(nu, f, sigma). |
SumSDE | class | Re-exported from gaussx. |
WarpedGaussianLikelihood | class | -- the transformed-GP model. |
White | class | White-noise kernel sigma^2 delta(x, x'). |
WhitenedGuide | class | Whitened-coordinate Gaussian variational posterior over inducing values. |
collapsed_lfr_log_prob | function | Log-likelihood with the linear decoder marginalized analytically. |
decoder_posterior | function | Closed-form matrix-normal posterior over the decoder. |
funk_hecke_coefficients | function | Funk-Hecke coefficients of a zonal kernel on . |
gp_factor | function | Register the collapsed GP log marginal likelihood with NumPyro. |
gp_sample | function | Sample a latent function f at the prior’s training inputs. |
init_inducing | function | Inducing inputs (M, D): rows of X picked by kernellib.select_landmarks. |
latent_init | function | Initial latents (N, n_latent) for a GPLVM or latent-factor model. |
latent_total_correlation | function | Total correlation of the fitted latent factors. |
lfr_factor | function | Register the collapsed latent-factor log-likelihood with NumPyro. |
lfr_model | function | MAP-over-latents collapsed latent-factor regression model. |
lfr_predictive_moments | function | Exact moments of the product of two independent Gaussians. |
markov_gp_factor | function | Register the collapsed Markov-GP marginal log-likelihood with NumPyro. |
markov_gp_sample | function | Sample a latent function f at the prior’s training times. |
mo_gp_factor | function | Register the collapsed multi-output GP marginal likelihood with NumPyro. |
mo_svgp_elbo | function | Structured multi-output SVGP ELBO as a differentiable scalar. |
mo_svgp_factor | function | Register the multi-output SVGP ELBO as a NumPyro factor site. |
normalizing_kalman_factor | function | Register the NKF marginal log-likelihood with NumPyro. |
preconditioned_cg_solver | function | A gaussx solver strategy for exact GPs: preconditioned CG plus SLQ. |
sparse_markov_elbo | function | Sparse variational ELBO for SparseMarkovGPPrior. |
sparse_markov_factor | function | Register sparse_markov_elbo as a NumPyro factor site. |
svgp_elbo | function | Structured SVGP ELBO as a differentiable scalar. |
svgp_factor | function | Register the structured SVGP ELBO as a NumPyro factor site. |
warp_to_base | function | Map observations into the space where the factor model is linear. |
warped_decoder_posterior | function | Matrix-normal decoder posterior, read in the warped space. |
warped_lfr_log_prob | function | Collapsed latent-factor log-likelihood on warped observations. |
warped_predictive_moments | function | Moments of under , by quadrature. |
Upstream: pyrox-lgm¶
Latent Gaussian models for pyrox.
pyrox_lgm¶
| Name | Kind | What it does |
|---|---|---|
AR1 | class | Stationary AR(1), . |
AbstractComponent | class | A latent field with hyperpriors and a projector to observations. |
AbstractObservation | class | y | eta for an LGM, with its own hyperparameters. |
BYM2 | class | BYM2 (Riebler et al., 2016), a mixture of unstructured and ICAR effects. |
Bernoulli | class | y ~ Bernoulli(sigmoid(eta)), y in {0, 1}. |
Besag | class | Intrinsic CAR (ICAR / Besag): precision , . |
Binomial | class | y ~ Binomial(n, sigmoid(eta)) with n = data["n_trials"]. |
CAR | class | Proper CAR: precision , . |
Diagnostics | class | Leave-one-out and information criteria of an INLAResult. |
FixedEffects | class | Fixed effects , columns of . |
Gaussian | class | y ~ N(eta, 1/prec); prec under PCPrecision(1, 0.01). |
Generic | class | A field with precision for a user-supplied structure . |
IID | class | Independent effects , . |
INLAResult | class | What inla() returns. |
Kronecker | class | Separable product (R-INLA group). |
LGM | class | A latent Gaussian model: components, fixed effects and an observation model. |
Leroux | class | Leroux CAR: precision , . |
NegativeBinomial | class | y ~ NegBin(mean exp(eta), size); size under Gamma(1, 0.1). |
PCAR1Rho | class | PC prior on the lag-one correlation of an AR(1) process. |
PCBYM2Phi | class | PC prior on the BYM2 mixing parameter . |
PCMatern | class | Joint PC prior on the range and marginal sd of a Matérn field. |
PCPrecision | class | PC prior on the precision of a Gaussian effect. |
Poisson | class | y ~ Poisson(exp(eta)); put the log exposure in data["offset"]. |
RW1 | class | First-order random walk, . |
RW2 | class | Second-order random walk, . |
Replicate | class | n_rep independent copies of a component, sharing its hyperparameters. |
SPDE | class | Matérn field via the SPDE, on a triangle mesh or a regular grid. |
StructureSpectrum | class | Spectral measure of , the generalised inverse of a structure. |
Summary | class | Posterior summary: mean, sd and the 2.5 / 50 / 97.5 % quantiles. |
diagnostics | function | DIC, WAIC, CPO and PIT of an INLAResult, with no refits. |
f | function | Build a latent component named after the data column it indexes. |
inla | function | Integrated nested Laplace approximation of a latent Gaussian model. |
structure_spectrum | function | The spectrum of that PCBYM2Phi needs, computed once. |
Upstream: pyrox-nn¶
Bayesian neural networks for pyrox.
pyrox_nn¶
| Name | Kind | What it does |
|---|---|---|
ArcCosineFourierFeatures | class | Random features for the arc-cosine kernel (Cho & Saul, 2009). |
BayesianAffineModulation | class | geonnax.AffineModulation with Normal priors on the FiLM generator. |
BayesianConcatConditioner | class | geonnax.ConcatConditioner with Normal priors on the projection. |
BayesianFourierNet | class | FourierNet with Bayesian priors on all filter and linear weights. |
BayesianGaborNet | class | GaborNet with Bayesian priors on all filter and linear weights. |
BayesianHyperLinear | class | geonnax.HyperLinear with Normal priors on the generator only. |
BayesianNeuralField | class | The full Bayesian Neural Field architecture. |
BayesianSIREN | class | SIREN with regime-scaled Normal priors on all layer weights. |
BayesianSlepianEncoder | class | Slepian encoder with NumPyro sites for cap radius and centre. |
ConditionedRFFNet | class | Conditional analogue of pyrox_nn.RandomKitchenSinks. |
DeepVSSGP | class | Deep Random Feature Expansion for Variational SSGP (Cutajar et al. 2017). |
DenseDVI | class | Deterministic Variational Inference dense layer (Wu et al., 2018). |
DenseFlipout | class | Bayesian dense layer with Flipout sign-flip structure. |
DenseHierarchical | class | Hierarchical Bayesian dense layer with multiplicative shrinkage. |
DenseNCP | class | Noise Contrastive Prior dense layer (Hafner et al., 2019). |
DenseRank1 | class | Rank-1 ensemble dense layer. |
DenseReparameterization | class | Bayesian dense layer via the reparameterization trick. |
DenseVariational | class | Dense layer with a user-supplied prior factory. |
DenseVariationalDropout | class | Sparse variational dropout dense layer. |
FourierFeatures | class | Per-input dyadic-frequency Fourier basis. |
HSGPFeatures | class | Hilbert-Space Gaussian Process feature layer (Riutort-Mayol et al., 2023). |
HyperFourierFeatures | class | Random Fourier features with (W, b, log_lengthscale) from a parameter net. |
InteractionFeatures | class | Element-wise products on selected pairs of input columns. |
LaplaceCosineFeatures | class | Cosine-bias variant of random Fourier features for the Laplace kernel. |
LaplaceFourierFeatures | class | SSGP-style RFF layer with Laplace (Matern-1/2) spectral density. |
LayerNormEnsemble | class | Per-ensemble-member LayerNorm. |
MCSigmoidDenseFA | class | Heteroscedastic multi-label output layer (FA noise + sigmoid). |
MCSoftmaxDenseFA | class | Heteroscedastic multi-class output layer (FA noise + softmax). |
MaternCosineFeatures | class | Cosine-bias variant of random Fourier features for the Matern kernel. |
MaternFourierFeatures | class | SSGP-style RFF layer with Matern spectral density. |
MultiHeadAttentionBE | class | Multi-head attention with BatchEnsemble rank-1 projections. |
NCPNormalOutput | class | Output-side Noise Contrastive Prior layer (Hafner et al., 2018). |
RBFCosineFeatures | class | Cosine-bias variant of random Fourier features for the RBF kernel. |
RBFFourierFeatures | class | SSGP-style RFF layer with RBF spectral density. |
RandomFeatureGaussianProcess | class | SNGP output layer (Liu et al., 2020). |
RandomKitchenSinks | class | Random Kitchen Sinks: RFF + a learned linear head. |
SeasonalFeatures | class | Period-and-harmonic cos/sin basis on a scalar time axis. |
Standardization | class | Apply a fixed-coefficient affine standardization. |
VariationalFourierFeatures | class | VSSGP — RFF with a learnable variational posterior over frequencies. |
cyclic_encode | function | Re-exported from geonnax. |
deg2rad | function | Re-exported from geonnax. |
fourier_features | function | Re-exported from geonnax. |
interaction_features | function | Re-exported from geonnax. |
lonlat_scale | function | Re-exported from geonnax. |
lonlat_to_cartesian3d | function | Re-exported from geonnax. |
seasonal_features | function | Re-exported from geonnax. |
seasonal_frequencies | function | Re-exported from geonnax. |
spherical_harmonic_encode | function | Re-exported from geonnax. |
standardize | function | Re-exported from geonnax. |
unstandardize | function | Re-exported from geonnax. |