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README.Rmd
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---
output: github_document
---
<!-- README.md is generated from README.Rmd. Please edit that file -->
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
out.width = "100%"
)
```
# bayesRecon: BAyesian reCONciliation of hierarchical forecasts
<!--
<img src="./man/figures/logo.png" align="right" />
-->
<!-- badges: start -->
[](https://github.com/IDSIA/bayesRecon/actions/workflows/R-CMD-check.yaml)
[](https://CRAN.R-project.org/package=bayesRecon)
[](https://cran.r-project.org/package=bayesRecon)
[](https://lifecycle.r-lib.org/articles/stages.html#experimental)
[-yellow.svg)](https://www.gnu.org/licences/lgpl-3.0)
[](https://coveralls.io/github/IDSIA/bayesRecon)
<!-- badges: end -->
The package `bayesRecon` implements several methods for probabilistic reconciliation of hierarchical time series forecasts.
The main functions are:
* `reconc_gaussian`: reconciliation via conditioning of multivariate Gaussian base forecasts;
this is done analytically;
* `reconc_BUIS`: reconciliation via conditioning of any probabilistic forecast via importance sampling;
this is the recommended option for non-Gaussian base forecasts;
* `reconc_MCMC`: reconciliation via conditioning of discrete probabilistic forecasts via Markov Chain Monte Carlo;
* `reconc_MixCond`: reconciliation via conditioning of mixed hierarchies, where
the upper forecasts are multivariate Gaussian and the bottom forecasts are discrete distributions;
* `reconc_TDcond`: reconciliation via top-down conditioning of mixed hierarchies, where the upper forecasts are
multivariate Gaussian and the bottom forecasts are discrete distributions.
## News
:boom: [2024-05-29] Added `reconc_MixCond` and `reconc_TDcond` and the vignette "Reconciliation of M5 hierarchy with mixed-type forecasts".
:boom: [2023-12-19] Added the vignette "Properties of the reconciled distribution via conditioning".
:boom: [2023-08-23] Added the vignette "Probabilistic Reconciliation via Conditioning with bayesRecon". Added the `schaferStrimmer_cov` function.
:boom: [2023-05-26] bayesRecon v0.1.0 is released!
## Installation
You can install the **stable** version on [R
CRAN](https://cran.r-project.org/package=bayesRecon)
``` r
install.packages("bayesRecon", dependencies = TRUE)
```
You can also install the **development** version from
[Github](https://github.com/IDSIA/bayesRecon)
``` r
# install.packages("devtools")
devtools::install_github("IDSIA/bayesRecon", build_vignettes = TRUE, dependencies = TRUE)
```
## Usage
Let us consider the minimal temporal hierarchy in the figure,
where the bottom variables are the two 6-monthly forecasts and the upper variable is the yearly forecast. We denote the variables for the two semesters and the year by $S_1, S_2, Y$ respectively.
```{r echo=FALSE, out.width='50%', fig.align='center'}
knitr::include_graphics('./man/figures/minimal_hierarchy.png')
```
The hierarchy is described by the *aggregation matrix* A,
which can be obtained using the function `get_reconc_matrices`.
```{r}
library(bayesRecon)
rec_mat <- get_reconc_matrices(agg_levels = c(1, 2), h = 2)
A <- rec_mat$A
print(A)
```
### Example 1: Poisson base forecasts
We assume that the base forecasts are Poisson distributed, with parameters given by $\lambda_{Y} = 9$, $\lambda_{S_1} = 2$, and $\lambda_{S_2} = 4$.
```{r}
lambdaS1 <- 2
lambdaS2 <- 4
lambdaY <- 9
lambdas <- c(lambdaY, lambdaS1, lambdaS2)
n_tot = length(lambdas)
base_forecasts = list()
for (i in 1:n_tot) {
base_forecasts[[i]] = list(lambda = lambdas[i])
}
```
We recommend using the BUIS algorithm (Zambon et al., 2024) to sample from the reconciled distribution.
```{r}
buis <- reconc_BUIS(
A,
base_forecasts,
in_type = "params",
distr = "poisson",
num_samples = 100000,
seed = 42
)
samples_buis <- buis$reconciled_samples
```
Since there is a positive incoherence in the forecasts ($\lambda_Y > \lambda_{S_1}+\lambda_{S_2}$), the mean of the bottom reconciled forecast increases. We show below this behavior for $S_1$.
```{r, out.width='80%', fig.align='center'}
reconciled_forecast_S1 <- buis$bottom_reconciled_samples[1,]
range_forecats <- range(reconciled_forecast_S1)
hist(
reconciled_forecast_S1,
breaks = seq(range_forecats[1] - 0.5, range_forecats[2] + 0.5),
freq = F,
xlab = "S_1",
ylab = NULL,
main = "base vs reconciled"
)
points(
seq(range_forecats[1], range_forecats[2]),
stats::dpois(seq(range_forecats[1], range_forecats[2]), lambda =
lambdaS1),
pch = 16,
col = 4,
cex = 2
)
```
The blue circles represent the probability mass function of a Poisson with parameter $\lambda_{S_1}$ plotted on top of the histogram of the reconciled bottom forecasts for $S_1$. Note how the histogram is shifted to the right.
Moreover, while the base bottom forecast were assumed independent, the operation of reconciliation introduced a negative correlation between $S_1$ and $S_2$. We can visualize it with the plot below which shows the empirical correlations between the reconciled samples of $S_1$ and the reconciled samples of $S_2$.
```{r, out.width='80%', fig.align='center'}
AA <-
xyTable(buis$bottom_reconciled_samples[1, ],
buis$bottom_reconciled_samples[2, ])
plot(
AA$x ,
AA$y ,
cex = AA$number * 0.001 ,
pch = 16 ,
col = rgb(0, 0, 1, 0.4) ,
xlab = "S_1" ,
ylab = "S_2" ,
xlim = range(buis$bottom_reconciled_samples[1, ]) ,
ylim = range(buis$bottom_reconciled_samples[2, ])
)
```
We also provide a function for sampling using Markov Chain Monte Carlo (Corani et al., 2023).
```{r}
mcmc = reconc_MCMC(
A,
base_forecasts,
distr = "poisson",
num_samples = 30000,
seed = 42
)
samples_mcmc <- mcmc$reconciled_samples
```
### Example 2: Gaussian base forecasts
We now assume that the base forecasts are Gaussian distributed, with parameters given by
* $\mu_{Y} = 9$, $\mu_{S_1} = 2$, and $\mu_{S_2} = 4$;
* $\sigma_{Y} = 2$, $\sigma_{S_1} = 2$, and $\sigma_{S_2} = 3$.
```{r}
muS1 <- 2
muS2 <- 4
muY <- 9
mus <- c(muY, muS1, muS2)
sigmaS1 <- 2
sigmaS2 <- 2
sigmaY <- 3
sigmas <- c(sigmaY, sigmaS1, sigmaS2)
base_forecasts = list()
for (i in 1:n_tot) {
base_forecasts[[i]] = list(mean = mus[[i]], sd = sigmas[[i]])
}
```
We use the BUIS algorithm to sample from the reconciled distribution:
```{r}
buis <- reconc_BUIS(
A,
base_forecasts,
in_type = "params",
distr = "gaussian",
num_samples = 100000,
seed = 42
)
samples_buis <- buis$reconciled_samples
buis_means <- rowMeans(samples_buis)
```
If the base forecasts are Gaussian, the reconciled distribution is still Gaussian and can be computed in closed form:
```{r}
Sigma <- diag(sigmas ^ 2) #transform into covariance matrix
analytic_rec <- reconc_gaussian(A,
base_forecasts.mu = mus,
base_forecasts.Sigma = Sigma)
analytic_means_bottom <- analytic_rec$bottom_reconciled_mean
analytic_means_upper <- A %*% analytic_means_bottom
analytic_means <- rbind(analytic_means_upper,analytic_means_bottom)
```
The base means of $Y$, $S_1$, and $S_2$ are
`r round(mus,2)`.
The reconciled means obtained analytically are
`r round(analytic_means,2)`,
while the reconciled means obtained via BUIS are
`r round(buis_means,2)`.
## References
Corani, G., Azzimonti, D., Augusto, J.P.S.C., Zaffalon, M. (2021).
*Probabilistic Reconciliation of Hierarchical Forecast via Bayes’ Rule*.
ECML PKDD 2020. Lecture Notes in Computer Science, vol 12459.
[DOI](https://doi.org/10.1007/978-3-030-67664-3_13)
Corani, G., Azzimonti, D., Rubattu, N. (2024).
*Probabilistic reconciliation of count time series*.
International Journal of Forecasting 40 (2), 457-469.
[DOI](https://doi.org/10.1016/j.ijforecast.2023.04.003)
Zambon, L., Azzimonti, D. & Corani, G. (2024).
*Efficient probabilistic reconciliation of forecasts for real-valued and count time series*.
Statistics and Computing 34 (1), 21.
[DOI](https://doi.org/10.1007/s11222-023-10343-y)
Zambon, L., Agosto, A., Giudici, P., Corani, G. (2024).
*Properties of the reconciled distributions for Gaussian and count forecasts*.
International Journal of Forecasting (in press).
[DOI](https://doi.org/10.1016/j.ijforecast.2023.12.004)
Zambon, L., Azzimonti, D., Rubattu, N., Corani, G. (2024).
*Probabilistic reconciliation of mixed-type hierarchical time series*.
The 40th Conference on Uncertainty in Artificial Intelligence, accepted.
## Contributors
<!-- prettier-ignore-start -->
<!-- markdownlint-disable -->
<table>
<tbody>
<tr>
<td align="center" valign="top" width="14.28%">
<a href="https://sites.google.com/view/darioazzimonti/home">
<img src="https://github.com/dazzimonti.png" width="100px;" alt="Dario Azzimonti" style="border-radius:50%;border:1px solid #646464;"/><br />
<sub><b>Dario Azzimonti</b></sub></a><br />
<sub>(Maintainer)</sub><br />
<a href="mailto:[email protected]?subject=bayesRecon package!">[email protected]</a>
</td>
<td align="center" valign="top" width="14.28%">
<a href="#">
<img src="https://github.com/nicorbtt.png" width="100px;" alt="Nicolò Rubattu" style="border-radius:50%;border:1px solid #646464;"/><br />
<sub><b>Nicolò Rubattu</b></sub></a><br />
<a href="mailto:[email protected]?subject=bayesRecon package!">[email protected]</a>
</td>
<td align="center" valign="top" width="14.28%">
<a href="#">
<img src="https://github.com/LorenzoZambon.png" width="100px;" alt="Lorenzo Zambon" style="border-radius:50%;border:1px solid #646464;"/><br />
<sub><b>Lorenzo Zambon</b></sub></a><br />
<a href="mailto:[email protected]?subject=bayesRecon package!">[email protected]</a>
</td>
<td align="center" valign="top" width="14.28%">
<a href="https://sites.google.com/site/awerbhjkl678214/home">
<img src="https://github.com/gcorani.png" width="100px;" alt="Giorgio Corani" style="border-radius:50%;border:1px solid #646464;"/><br />
<sub><b>Giorgio Corani</b></sub></a><br />
<a href="mailto:[email protected]">[email protected]</a>
</td>
</tr>
</tbody>
</table>
<!-- markdownlint-restore -->
<!-- prettier-ignore-end -->
## Getting help
If you encounter a clear bug, please file a minimal reproducible example
on [GitHub](https://github.com/IDSIA/bayesRecon/issues).