Constructs prediction intervals using Conformalized Quantile Regression (Romano et al. 2019). Requires two models: one for the lower quantile and one for the upper quantile. The conformal step adjusts these quantile predictions to achieve valid coverage.
Usage
conformal_cqr(
x,
y,
model_lower,
model_upper,
x_new,
alpha = 0.1,
cal_fraction = 0.5,
quantiles = c(0.05, 0.95),
seed = NULL
)Arguments
- x
A numeric matrix or data frame of predictor variables.
- y
A numeric vector of response values.
- model_lower
A
make_model()specification for the lower quantile model.- model_upper
A
make_model()specification for the upper quantile model.- x_new
A numeric matrix or data frame of new predictor variables.
- alpha
Miscoverage level. Default
0.10.- cal_fraction
Fraction of data used for calibration. Default
0.5.- quantiles
The target quantiles. Default
c(0.05, 0.95).- seed
Optional random seed.
Value
A predictset_reg object. See conformal_split() for details.
The method component is "cqr".
Details
Interval quality depends on the underlying quantile models. Poorly
calibrated quantile models produce valid but potentially wide intervals.
For best results, use proper quantile regression models (e.g.
quantreg::rq()) rather than shifted mean predictions.
References
Romano, Y., Patterson, E. and Candes, E.J. (2019). Conformalized quantile regression. Advances in Neural Information Processing Systems, 32. doi:10.48550/arXiv.1905.03222
See also
Other regression methods:
conformal_aci(),
conformal_cv(),
conformal_jackknife(),
conformal_mondrian(),
conformal_split(),
conformal_weighted()
Examples
set.seed(42)
n <- 200
x <- matrix(rnorm(n * 3), ncol = 3)
y <- x[, 1] * 2 + rnorm(n)
x_new <- matrix(rnorm(20 * 3), ncol = 3)
# Approximating quantile regression with shifted linear models.
# In practice, use quantile regression models, e.g.:
# quantreg::rq(y ~ ., data = df, tau = 0.05)
model_lo <- make_model(
train_fun = function(x, y) lm(y ~ ., data = data.frame(y = y, x)),
predict_fun = function(obj, x_new) {
predict(obj, newdata = as.data.frame(x_new)) - 1.5
},
type = "regression"
)
model_hi <- make_model(
train_fun = function(x, y) lm(y ~ ., data = data.frame(y = y, x)),
predict_fun = function(obj, x_new) {
predict(obj, newdata = as.data.frame(x_new)) + 1.5
},
type = "regression"
)
result <- conformal_cqr(x, y, model_lo, model_hi, x_new = x_new)
print(result)
#>
#> ── Conformal Prediction Intervals (Conformalized Quantile Regression) ──────────
#> • Coverage target: "90%"
#> • Training: 100 | Calibration: 100 | Predictions: 20
#> • Conformal quantile: -0.038
#> • Median interval width: 2.924