The hubEnsembles package includes functionality for
aggregating model outputs, such as forecasts or projections, that are
submitted to a hub by multiple models and combined into ensemble model
outputs. The package includes two main functions:
simple_ensemble and linear_pool. We illustrate
these functions in this vignette, and briefly compare them.
This vignette uses the following R packages:
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
library(plotly)
#> Loading required package: ggplot2
#>
#> Attaching package: 'plotly'
#> The following object is masked from 'package:ggplot2':
#>
#> last_plot
#> The following object is masked from 'package:stats':
#>
#> filter
#> The following object is masked from 'package:graphics':
#>
#> layout
library(hubUtils)
library(hubEnsembles)The example-simple-forecast-hub has been created by the
Consortium of Infectious Disease Modeling Hubs as a simple example hub
to demonstrate the set up and functionality for the hubverse. The hub
includes both target data and example model output data.
hub_path <- system.file("example-data/example-simple-forecast-hub",
package = "hubEnsembles"
)
model_outputs <- hubData::connect_hub(hub_path) %>%
dplyr::collect()
head(model_outputs)
#> # A tibble: 6 × 8
#> origin_date horizon location target output_type output_type_id value model_id
#> <date> <int> <chr> <chr> <chr> <dbl> <int> <chr>
#> 1 2022-12-05 -6 20 inc co… quantile 0.01 22 UMass-ar
#> 2 2022-12-05 -6 20 inc co… quantile 0.025 24 UMass-ar
#> 3 2022-12-05 -6 20 inc co… quantile 0.05 26 UMass-ar
#> 4 2022-12-05 -6 20 inc co… quantile 0.1 28 UMass-ar
#> 5 2022-12-05 -6 20 inc co… quantile 0.15 30 UMass-ar
#> 6 2022-12-05 -6 20 inc co… quantile 0.2 32 UMass-ar
target_data_path <- file.path(
hub_path, "target-data",
"covid-hospitalizations.csv"
)
target_data <- read.csv(target_data_path)
head(target_data)
#> time_idx location value target
#> 1 2021-03-21 46 12 inc covid hosp
#> 2 2021-03-04 45 82 inc covid hosp
#> 3 2021-02-26 46 7 inc covid hosp
#> 4 2021-02-20 44 21 inc covid hosp
#> 5 2021-02-09 44 19 inc covid hosp
#> 6 2021-01-25 25 224 inc covid hospsimple_ensemble
The simple_ensemble function is used to summarize across
component model outputs; this function can be applied to predictions
with an output_type of mean,
median, quantile, cdf, or
pmf.
The simple_ensemble function defaults to calculating an
equally weighted mean across all component model outputs for each unique
output_type_id. For our example data, which contains two
output types (median and quantile), this means
the resulting ensemble will be the mean of component model submitted
values for each quantile.
mean_ens <- hubEnsembles::simple_ensemble(model_outputs)
head(mean_ens)
#> # A tibble: 6 × 8
#> model_id origin_date horizon location target output_type output_type_id value
#> <chr> <date> <int> <chr> <chr> <chr> <dbl> <dbl>
#> 1 hub-ense… 2022-12-05 -6 20 inc c… median NA 37.3
#> 2 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.01 14.7
#> 3 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.025 15.7
#> 4 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.05 17
#> 5 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.1 18.3
#> 6 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.15 21.7We can change the function used to aggregate across model outputs.
For example, we may want to calculate a median of component model
submitted values for each quantile. We will also use the
model_id argument to distinguish this ensemble.
median_ens <- hubEnsembles::simple_ensemble(model_outputs,
agg_fun = median,
model_id = "hub-ensemble-median"
)
head(median_ens)
#> # A tibble: 6 × 8
#> model_id origin_date horizon location target output_type output_type_id value
#> <chr> <date> <int> <chr> <chr> <chr> <dbl> <int>
#> 1 hub-ense… 2022-12-05 -6 20 inc c… median NA 37
#> 2 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.01 22
#> 3 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.025 23
#> 4 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.05 25
#> 5 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.1 27
#> 6 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.15 28Custom functions can also be passed into the agg_fun
argument. For example, a geometric mean may be a more appropriate way to
combine component model outputs. Any custom function to be used requires
an argument x for the vector of numeric values to
summarize, and if relevant, an argument w of numeric
weights.
geometric_mean <- function(x) {
n <- length(x)
return(prod(x)^(1 / n))
}
geometric_mean_ens <- hubEnsembles::simple_ensemble(model_outputs,
agg_fun = geometric_mean,
model_id = "hub-ensemble-geometric"
)
head(geometric_mean_ens)
#> # A tibble: 6 × 8
#> model_id origin_date horizon location target output_type output_type_id value
#> <chr> <date> <int> <chr> <chr> <chr> <dbl> <dbl>
#> 1 hub-ense… 2022-12-05 -6 20 inc c… median NA 37.3
#> 2 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.01 0
#> 3 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.025 0
#> 4 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.05 0
#> 5 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.1 0
#> 6 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.15 18.0In addition, we can weight the contributions of each model by
providing a table of weights, which are provided in a
data.frame with a model_id column and a
weight column.
model_weights <- data.frame(
model_id = c("UMass-ar", "UMass-gbq", "simple_hub-baseline"),
weight = c(0.4, 0.4, 0.2)
)
weighted_mean_ens <- hubEnsembles::simple_ensemble(model_outputs,
weights = model_weights,
model_id = "hub-ensemble-weighted-mean"
)
head(weighted_mean_ens)
#> # A tibble: 6 × 8
#> model_id origin_date horizon location target output_type output_type_id value
#> <chr> <date> <int> <chr> <chr> <chr> <dbl> <dbl>
#> 1 hub-ense… 2022-12-05 -6 20 inc c… median NA 37.6
#> 2 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.01 17.6
#> 3 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.025 18.8
#> 4 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.05 20.4
#> 5 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.1 22
#> 6 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.15 24.6linear_pool
An alternative approach to generate an ensemble is a linear pool, or
a distributional mixture; this function can be applied to predictions
with an output_type of mean,
quantile, cdf, or pmf. Our
example hub includes median output type, so we exclude it
from the calculation.
For mean, cdf and pmf output
types, the linear pool is equivalent to using a mean
simple_ensemble. For quantile model outputs,
the linear_pool function needs to approximate a full
probability distribution using the value-quantile pairs from each
component model. As a default, this is done with functions in the
distfromq package, which defaults to fitting a monotonic
cubic spline.
linear_pool_ens <- model_outputs %>%
filter(output_type != "median") %>%
hubEnsembles::linear_pool()
head(linear_pool_ens)
#> # A tibble: 6 × 8
#> model_id origin_date horizon location target output_type output_type_id value
#> <chr> <date> <int> <chr> <chr> <chr> <dbl> <dbl>
#> 1 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.01 0
#> 2 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.025 0
#> 3 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.05 7.01
#> 4 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.1 21.1
#> 5 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.15 25.6
#> 6 hub-ense… 2022-12-05 -6 20 inc c… quantile 0.2 27.6
basic_plot_function <- function(plot_df, truth_df, plain_line = 0.5, ribbon = c(0.975, 0.025),
forecast_date) {
plain_df <- dplyr::filter(plot_df, .data$output_type_id == plain_line)
ribbon_df <- dplyr::filter(plot_df, .data$output_type_id %in% ribbon) %>%
dplyr::mutate(output_type_id = ifelse(.data$output_type_id == min(ribbon),
"min", "max"
)) %>%
tidyr::pivot_wider(names_from = .data$output_type_id, values_from = .data$value)
plot_model <- plot_ly(height = 600, colors = scales::hue_pal()(50))
if (!is.null(truth_df)) {
plot_model <- plot_model %>%
add_trace(
data = truth_df, x = ~time_idx, y = ~value, type = "scatter",
mode = "lines+markers", line = list(color = "#6e6e6e"),
hoverinfo = "text", name = "ground truth",
hovertext = paste("Date: ", truth_df$time_value, "<br>",
"Ground truth: ",
format(truth_df$value, big.mark = ","),
sep = ""
),
marker = list(color = "#6e6e6e", size = 7)
)
}
plot_model <- plot_model %>%
add_lines(
data = plain_df, x = ~target_date, y = ~value,
color = ~model_id
) %>%
add_ribbons(
data = ribbon_df, x = ~target_date, ymin = ~min,
ymax = ~max, color = ~model_id, opacity = 0.25,
line = list(width = 0), showlegend = FALSE
) %>%
plotly::layout(shapes = list(
type = "line", y0 = 0, y1 = 1, yref = "paper",
x0 = forecast_date, x1 = forecast_date,
line = list(color = "gray")
))
}
plot_df <- dplyr::bind_rows(model_outputs, mean_ens) %>%
dplyr::filter(location == "US", origin_date == "2022-12-12") %>%
dplyr::mutate(target_date = origin_date + horizon)
plot <- basic_plot_function(
plot_df,
truth_df = target_data %>%
dplyr::filter(
location == "US",
time_idx >= "2022-10-01",
time_idx <= "2023-03-01"
),
forecast_date = "2022-12-12"
)
#> Warning: Use of .data in tidyselect expressions was deprecated in tidyselect 1.2.0.
#> ℹ Please use `"output_type_id"` instead of `.data$output_type_id`
#> This warning is displayed once every 8 hours.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.
#> Warning: Use of .data in tidyselect expressions was deprecated in tidyselect 1.2.0.
#> ℹ Please use `"value"` instead of `.data$value`
#> This warning is displayed once every 8 hours.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.
plot
#> Warning: Can't display both discrete & non-discrete data on same axis