Provides functions for coarse-to-fine spatial and spatio-temporal modeling, enabling fast prediction, regression, and uncertainty quantification for moderate to large datasets. For methodological details, see Murakami et al. (2026)
A scalable, covariance-free framework for spatial and spatio-temporal regression, prediction, and uncertainty quantification for moderate to large datasets. Available as both an R package and a Python package sharing the same algorithm and reference implementation.
Try the interactive map in your browser, no installation required: https://dmuraka.shinyapps.io/spCFmap/
Given response y, covariates x, and 2-D coordinates, spCF jointly fits a
linear / GLM regression and a multiscale spatial process. Holdout validation
selects the spatial scales adaptively, and the fit produces predictive means and
standard deviations at observed and unobserved locations. A scale-wise
decomposition (sp_scalewise) lets you isolate large-, medium-, and
small-scale spatial structure for interpretation.
Key features:
cf_lm) with scalable coarse-to-fine process modeling for large datasets.cf_glm) supporting Gaussian, Poisson, binomial, and Gamma families, as well as quasi-likelihood families in R.cf_dglm) designed to scale efficiently to large spatio-temporal datasets.cf_downscale) that disaggregates aggregate-level
responses to a finer grid under a pycnophylactic (mass-preserving) constraint.sp_scalewise) from the estimated spatial process based on user-specified bandwidth ranges.cf_lm only).se_type="prediction").spCF/
├── R/, src/, man/, vignettes/ # R package source
├── DESCRIPTION, NAMESPACE # R package metadata
├── deploy/ # Shiny deployment unit for spCFmap()
└── python/ # Python port (see python/README.md)
├── spCF/ # importable package
├── examples/, tests/
└── pyproject.toml
# CRAN
install.packages("spCF")
# Or the development version straight from GitHub:
remotes::install_github("dmuraka/spCF")
pip install "git+https://github.com/dmuraka/spCF#subdirectory=python"
The Python importable name is also spCF.
library(spCF)
library(sf); library(sp)
data(meuse); data(meuse.grid)
y <- log(meuse[, "zinc"])
coords <- meuse[, c("x", "y")]
x <- data.frame(dist = meuse[, "dist"])
x0 <- data.frame(dist = meuse.grid[, "dist"])
coords0<- meuse.grid[, c("x", "y")]
mod_hv <- cf_lm_hv(y = y, x = x, coords = coords)
mod <- cf_lm (y = y, x = x, x0 = x0,
coords = coords, coords0 = coords0,
mod_hv = mod_hv)
mod
import numpy as np
import spCF
rng = np.random.default_rng(0)
n = 500
coords = rng.uniform(0, 10, size=(n, 2))
x = rng.normal(size=(n, 2))
z = np.sin(coords[:, 0] / 2) * np.cos(coords[:, 1] / 2)
y = 1.0 + 2.0 * x[:, 0] - 0.5 * x[:, 1] + 1.5 * z + rng.normal(0, 0.3, n)
mod_hv = spCF.cf_lm_hv(y=y, x=x, coords=coords, kernel="exp", seed=42)
mod = spCF.cf_lm (y=y, x=x, coords=coords, mod_hv=mod_hv)
print(mod.beta["coef"])
print(mod.pred["pred"][:5])
spCFmap() opens a Shiny application that maps a fit over a basemap: predictive
mean and SD, the covariate effect, and any scale-wise component, with the time
range or bandwidth range chosen interactively.
A hosted instance runs at https://dmuraka.shinyapps.io/spCFmap/. It fits models from the bundled demo data (meuse, a space-time air-quality set, an areal downscaling set) or from your own CSV / GeoJSON upload; each upload box offers a worked example file and a ReadMe describing the columns it expects.
Locally, with the R package installed:
spCFmap() # the full app: upload data and fit inside it
spCFmap(mod, crs = 4326) # map a model that has already been fitted
crs is the coordinate reference system the model's coordinates are in. It has
no default, because coordinates carry no unit of their own and guessing would
put the map in the wrong part of the world.
The hosted instance runs on a free shinyapps.io tier, whose memory is shared
between everyone connected at once. That suits the demos and uploads of a few
thousand observations; larger fits are better mapped locally. deploy/ holds
the deployment unit and its instructions.
| Function | Purpose |
|---|---|
cf_lm_hv / cf_lm |
Train & holdout-validate / predict with the Gaussian CF spatial model |
cf_glm_hv / cf_glm |
Train & holdout-validate / predict with a CF spatial GLMM |
cf_dglm_hv / cf_dglm |
Train & holdout-validate / predict with a CF spatio-temporal GLMM |
cf_downscale_hv / cf_downscale |
Train & holdout-validate / predict spatial downscaling (areal → fine grid) |
sp_scalewise |
Extract the spatial process for a given bandwidth range |
spCFmap |
Interactive Shiny map explorer for CF outputs (R only) |
See the R walk-throughs in
vignettes/spCF_lm.Rmd,
vignettes/spCF_glm.Rmd,
vignettes/spCF_downscale.Rmd, and
vignettes/spCF_dglm.Rmd,
and python/README.md for Python-specific notes
(including the sd_method, se_type, and se_method options that control the
predictive SD and coefficient-SE estimators).
@article{Murakami2026,
author = {Murakami, Daisuke and Comber, Alexis and Yoshida, Takahiro and
Tsutsumida, Narumasa and Brunsdon, Chris and Nakaya, Tomoki},
title = {Coarse-to-fine spatial modeling: A scalable,
machine-learning-compatible framework},
journal = {Geographical Analysis},
volume = {58},
number = {2},
pages = {e70034},
year = {2026},
doi = {10.1111/gean.70034}
}
@article{Murakami2026b,
author = {Murakami, Daisuke and Comber, Alexis and Yoshida, Takahiro and
Tsutsumida, Narumasa and Brunsdon, Chris and Nakaya, Tomoki},
title = {Coarse-to-fine spatial GLMM for scalable prediction
and multiscale analysis},
journal = {ArXiv},
number = {2605.01157},
year = {2026},
}
@article{Murakami2026c,
author = {Murakami, Daisuke},
title = {Title: Fast covariance-free spatiotemporal modeling via coarse-to-fine learning},
journal = {ArXiv},
number = {2608.03449},
year = {2026},
}
GPL (≥ 2). See LICENSE (added via the GitHub license template).