///|
/// Double / debiased machine learning estimator for the partially
/// linear regression model
///
/// Y = D * theta_0 + g_0(X) + zeta, E[zeta | D, X] = 0
/// D = m_0(X) + V, E[V | X] = 0
///
/// with the *partialling out* score
///
/// psi_a(theta) = -(D - m_hat)^2,
/// psi_b(theta) = (D - m_hat) * (Y - l_hat),
/// psi(theta) = theta * psi_a + psi_b
///
/// where `l_hat = E_hat[Y | X]` and `m_hat = E_hat[D | X]` are obtained
/// from a `LinearRegression` learner (or any other `Learner`) trained
/// out-of-fold via K-fold cross-fitting.
///
/// The point estimate is
///
/// theta_hat = -mean(psi_b) / mean(psi_a)
/// = mean((D - m_hat)(Y - l_hat)) / mean((D - m_hat)^2).
///
/// The variance is estimated following `doubleml.utils._estimation._var_est`
/// (non-cluster case):
///
/// J = mean(psi_a) # expected derivative of psi w.r.t. theta
/// gamma = mean(psi(theta_hat)^2)
/// sigma2 = gamma / (J^2 * n)
/// se = sqrt(sigma2).
///
/// The implementation supports only the `partialling out` score and a
/// single treatment. It is intentionally minimal — see the README for
/// the matrix of features covered relative to the upstream package.
pub struct DoubleMLPLR {
data : DoubleMLData
// injected learner types (v0.54.0+): separate per-nuisance so
// l-step and m-step can use different model families
// (e.g. OLS for l, random forest for m). Both default to a
// fresh `LinearRegression`; can be overridden per-fit via
// `DoubleMLPLR::fit`'s labeled params.
learner_l : LearnerDispatch
learner_m : LearnerDispatch
n_folds : Int
n_rep : Int
seed : Int
// cross-fitted nuisance predictions
l_hat : Array[Double]
m_hat : Array[Double]
// point estimate, standard error
coef : Double
se : Double
fitted : Bool
// v0.58.0+: populated by `DoubleMLPLR::tune(...)` with the
// chosen candidate and per-candidate scores. `None` for models
// built via `DoubleMLPLR::new(...)` or re-fit via
// `DoubleMLPLR::fit(...)` (a re-fit discards the prior tune
// history because the nuisance learners may have changed).
tune_result : TuneResult?
} derive(Debug)
///|
pub extend DoubleMLPLR with @moonbitlang/core/debug.Debug::{to_repr}
///|
pub fn DoubleMLPLR::new(
data : DoubleMLData,
learner_l? : LearnerDispatch = LearnerDispatch::linear_regression(),
learner_m? : LearnerDispatch = LearnerDispatch::linear_regression(),
n_folds? : Int = 2,
n_rep? : Int = 1,
seed? : Int = 3141,
) -> DoubleMLPLR {
try {
require(n_folds >= 2)
require(n_folds <= data.n_obs())
require(n_rep >= 1)
{
data,
learner_l,
learner_m,
n_folds,
n_rep,
seed,
l_hat: Array::make(data.n_obs(), 0.0),
m_hat: Array::make(data.n_obs(), 0.0),
coef: 0.0,
se: 0.0,
fitted: false,
tune_result: None,
}
} catch {
PreconditionError::Violated(loc) =>
abort("precondition failed at " + loc.to_string())
}
}
///|
/// Number of observations.
pub fn DoubleMLPLR::n_obs(self : DoubleMLPLR) -> Int {
self.data.n_obs()
}
///|
/// Number of features (covariate columns).
pub fn DoubleMLPLR::n_features(self : DoubleMLPLR) -> Int {
self.data.n_features()
}
///|
/// Fitted causal parameter.
pub fn DoubleMLPLR::coef(self : DoubleMLPLR) -> Double {
try {
require(self.fitted)
self.coef
} catch {
PreconditionError::Violated(loc) =>
abort("precondition failed at " + loc.to_string())
}
}
///|
/// Standard error of the causal parameter, computed via the
/// DML variance formula.
pub fn DoubleMLPLR::se(self : DoubleMLPLR) -> Double {
try {
require(self.fitted)
self.se
} catch {
PreconditionError::Violated(loc) =>
abort("precondition failed at " + loc.to_string())
}
}
///|
/// 95% Wald-style confidence interval `[coef - 1.96*se, coef + 1.96*se]`.
pub fn DoubleMLPLR::confint(self : DoubleMLPLR) -> (Double, Double) {
try {
require(self.fitted)
let lo = self.coef - 1.96 * self.se
let hi = self.coef + 1.96 * self.se
(lo, hi)
} catch {
PreconditionError::Violated(loc) =>
abort("precondition failed at " + loc.to_string())
}
}
///|
/// Cross-fitted nuisance predictions for the outcome (length `n`).
pub fn DoubleMLPLR::predictions_l(self : DoubleMLPLR) -> Array[Double] {
self.l_hat
}
///|
/// Cross-fitted nuisance predictions for the treatment (length `n`).
pub fn DoubleMLPLR::predictions_m(self : DoubleMLPLR) -> Array[Double] {
self.m_hat
}
///|
/// Accessor for the `tune_result` populated by
/// `DoubleMLPLR::tune(...)` (v0.58.0+). Returns `None` for
/// models built via `DoubleMLPLR::new(...)` or re-fit via
/// `DoubleMLPLR::fit(...)` (a re-fit discards the prior tune
/// history because the nuisance learners may have changed).
///
/// Inspect the returned `TuneResult` to see which `(learner_l,
/// learner_m)` combination won under the chosen scoring rule,
/// what the best score was, and the per-candidate score vector
/// (in `param_set` order).
pub fn DoubleMLPLR::tune_result(self : DoubleMLPLR) -> TuneResult? {
self.tune_result
}
///|
/// Run the DML estimation. The default learner is a closed-form
/// `LinearRegression`; a different `Learner` can be supplied for
/// experiments. The result is stored on the object and the object is
/// returned for chaining.
///
/// Per-repetition behaviour: each repetition `r` cross-fits the
/// nuisances from its own folds (seed `self.seed + r`), computes its
/// own `(theta_r, se_r)` from the `mean(psi_a) / mean(psi_b)` form,
/// and the two arrays are then aggregated by `aggregate_coef_se`
/// (median of thetas, then SE from the median of
/// `(theta_r + 1.96 * se_r)`). For `n_rep == 1` the aggregator
/// returns the single `(theta_1, se_1)` exactly, so the byte-equality
/// with the previous "average then estimate" implementation is
/// preserved. The `predictions_l/m` accessors return the nuisances
/// from the *last* repetition (the conventional choice in upstream
/// `doubleml`), not a cross-rep average.
///
/// When `self.data` carries a non-empty `cluster_vars` vector, the
/// estimator routes through the *clustered* DML path: folds are
/// drawn over the unique cluster ids, every row of a unit stays
/// on the same side of every split, the causal parameter is the
/// fold-weighted ratio of cluster score sums, and the SE is the
/// unit-level cluster-robust estimator (mirrors upstream's
/// `_var_est` one-cluster-variable branch and
/// `LinearScoreMixin._est_coef` cluster branch).
///
/// `score` selects the DML nuisance score (v0.55.0+):
/// - `"partialling-out"` (default, v0.54.0): the standard
/// partialling-out DML score `psi_a = -(d - m_hat)^2`,
/// `psi_b = (d - m_hat) * (y - l_hat)`. This is what
/// upstream calls `DoubleMLPLR._score_partialling_out`.
/// Works without `DoubleMLData.z` (the v0.54.0 default).
/// - `"IV-type"` / `"iv-type"` (v0.55.0+): the
/// instrument-residual-maker DML score
/// `psi_a = -z * (d - m_hat)`,
/// `psi_b = z * (y - l_hat)`,
/// where `z = DoubleMLData::new(..., z=...)`. Requires
/// `data.is_instrument_data()` to be true; calling `fit`
/// with this score and no instrument aborts with a
/// descriptive message naming the missing `z=` arg.
///
///|
/// Per-row DML score elements for `DoubleMLPLR`. v0.55.0:
/// factored out of `DoubleMLPLR::fit` / `fit_cluster` so the
/// `"partialling-out"` and `"IV-type"` score branches share
/// one helper.
///
/// `partialling-out` (the v0.54.0 default):
/// psi_a[i] = -v_hat[i] * v_hat[i]
/// psi_b[i] = v_hat[i] * u_hat[i]
///
/// `IV-type` (v0.55.0+; requires instrument vector Z):
/// psi_a[i] = -z[i] * v_hat[i]
/// psi_b[i] = z[i] * u_hat[i]
///
/// where `v_hat = d - m_hat`, `u_hat = y - l_hat`. The IV-type
/// score is the standard "instrumental residual-maker" DML
/// score (Chernozhukov et al. 2018): substituting `z` for `d`
/// in the partialling-out formula makes the score exogenous
/// from `X` (via the exclusion restriction), recovering a
/// consistent IV-style theta even when the treatment is
/// endogenous.
///
/// The caller must validate that `z.length() == n` (for IV-type)
/// or that `z.length() == 0` (the v0.54.0 default,
/// partialling-out path) before invoking this helper. No
/// precondition check here — the caller has richer error
/// context (e.g. names the offending `DoubleMLPLR::fit`
/// call site).
fn plr_score_elements(
n : Int,
v_hat : Array[Double],
u_hat : Array[Double],
z : Array[Double],
score : String,
) -> (Array[Double], Array[Double]) {
let psi_a : Array[Double] = Array::make(n, 0.0)
let psi_b : Array[Double] = Array::make(n, 0.0)
if score == "iv-type" || score == "IV-type" {
// IV-type: z[i] is the instrument (length n is caller's
// responsibility; the array index below would panic if z
// is shorter). The default `z = []` (length 0) on
// DoubleMLData never reaches here because the caller
// pre-validates with `require(z.length() == n)`.
for i = 0; i < n; i = i + 1 {
psi_a[i] = -z[i] * v_hat[i]
psi_b[i] = z[i] * u_hat[i]
}
} else {
// partialling-out (default): v_hat[i] is the treatment residual.
for i = 0; i < n; i = i + 1 {
psi_a[i] = -v_hat[i] * v_hat[i]
psi_b[i] = v_hat[i] * u_hat[i]
}
}
(psi_a, psi_b)
}
///|
/// The `learner_l` / `learner_m` labeled params accept any
/// `LearnerDispatch` (defaults to the constructor-set values,
/// i.e. a fresh `LinearRegression`). Per-fit overrides let
/// callers swap in alternative nuisance estimators
/// (`ConstantLearner`, `NoopLearner`, ...) without rebuilding
/// the `DoubleMLPLR` instance.
pub fn DoubleMLPLR::fit(
self : DoubleMLPLR,
learner_l? : LearnerDispatch = self.learner_l,
learner_m? : LearnerDispatch = self.learner_m,
max_attempts? : Int = 1,
score? : String = "partialling-out",
tune_result? : TuneResult? = None,
) -> DoubleMLPLR {
try {
require(
score == "partialling-out" || score == "iv-type" || score == "IV-type",
)
require(max_attempts >= 1)
// v0.55.0: real IV-type branch. Caller must have built
// `DoubleMLData` with a non-empty `z` vector of length `n_obs`.
// The require below is the v0.48.0+ cascade: false here
// throws `PreconditionError::Violated(loc)` which the outer
// `try` catches and re-aborts with a descriptive message.
if score == "iv-type" || score == "IV-type" {
require(self.data.z.length() == self.n_obs())
}
if self.data.is_cluster_data() {
return self.fit_cluster(learner_l~, learner_m~, max_attempts~, score~, tune_result~)
}
let n = self.n_obs()
let nrep = self.n_rep
let coefs : Array[Double] = Array::make(nrep, 0.0)
let ses : Array[Double] = Array::make(nrep, 0.0)
// hold the last rep's predictions; final values land in l_hat / m_hat
let mut l_pred : Array[Double] = Array::make(n, 0.0)
let mut m_pred : Array[Double] = Array::make(n, 0.0)
for r = 0; r < nrep; r = r + 1 {
let folds = kfold(n, self.n_folds, self.seed + r)
l_pred = cross_fit_predict_dispatch(
learner_l,
self.data.x,
self.data.y,
folds,
)
m_pred = cross_fit_predict_dispatch(
learner_m,
self.data.x,
self.data.d,
folds,
)
// score elements for THIS rep's nuisances only
let v_hat : Array[Double] = Array::make(n, 0.0)
let u_hat : Array[Double] = Array::make(n, 0.0)
for i = 0; i < n; i = i + 1 {
v_hat[i] = self.data.d[i] - m_pred[i]
u_hat[i] = self.data.y[i] - l_pred[i]
}
let (psi_a, psi_b) = plr_score_elements(
n, v_hat, u_hat, self.data.z, score,
)
// point estimate + variance come from the shared DML formula
let (coef_r, se_r) = var_est(psi_a, psi_b)
coefs[r] = coef_r
ses[r] = se_r
}
// last iteration's predictions are now in l_pred / m_pred
let (coef, se) = aggregate_coef_se(coefs, ses)
{
data: self.data,
learner_l,
learner_m,
n_folds: self.n_folds,
n_rep: self.n_rep,
seed: self.seed,
l_hat: l_pred,
m_hat: m_pred,
coef,
se,
fitted: true,
// honor the caller's tune_result override (set by
// `DoubleMLPLR::tune`); default `None` preserves v0.57.0
// behavior for plain `fit(...)` callers.
tune_result,
}
} catch {
PreconditionError::Violated(loc) =>
abort("precondition failed at " + loc.to_string())
}
}
///|
/// Clustered-DML path for `DoubleMLPLR`. Folds partition whole
/// units (`kfold` on unique cluster ids, expanded to row folds);
/// coefficient is the fold-weighted ratio of cluster score sums
/// (`est_coef_cluster`); variance is unit-level cluster-robust
/// (`var_est_cluster`). `psi_a = -(d - m_hat)^2` and
/// `psi_b = (d - m_hat) * (y - l_hat)` are the per-row score
/// elements — the same ones the row-level path uses. The cluster
/// path differs from the row-level path only in the fold
/// partition and the two aggregation steps; the per-row score
/// elements are identical, so a single nuisances cross-fit
/// (with cluster-respecting folds) feeds both paths.
fn DoubleMLPLR::fit_cluster(
self : DoubleMLPLR,
learner_l~ : LearnerDispatch,
learner_m~ : LearnerDispatch,
max_attempts? : Int = 1,
score? : String = "partialling-out",
tune_result? : TuneResult? = None,
) -> DoubleMLPLR {
try {
require(max_attempts >= 1)
// v0.55.0: real IV-type branch. Caller must have built
// `DoubleMLData` with a non-empty `z` vector. Same
// require-cascade as `fit()` for the v0.48.0+
// `PreconditionError::Violated(loc)` -> `abort(...)` flow.
if score == "iv-type" || score == "IV-type" {
require(self.data.z.length() == self.n_obs())
}
let cluster = self.data.cluster_vars
let n = self.n_obs()
let nrep = self.n_rep
let uniq = unique_units(cluster)
let n_units = uniq.length()
require(self.n_folds <= n_units)
// row → unit-position map (linear scan, panels are small in
// tests and demos). v0.36.0: build_row_unit_map raises
// ClusterDataError::MissingUnit on a malformed cluster vector;
// we catch and re-abort to preserve pre-v0.36.0 behavior.
let row_unit = build_row_unit_map(cluster, uniq) catch {
ClusterDataError::MissingUnit(g) =>
abort(
"expand_unit_folds_to_rows: row without a unit id (unit_id=" +
g.to_string() +
")",
)
}
// ascending row indices per unit
let unit_rows : Array[Array[Int]] = Array::makei(n_units, fn(_) {
let rows : Array[Int] = []
rows
})
for i = 0; i < n; i = i + 1 {
unit_rows[row_unit[i]].push(i)
}
let coefs : Array[Double] = Array::make(nrep, 0.0)
let ses : Array[Double] = Array::make(nrep, 0.0)
let mut l_pred : Array[Double] = Array::make(n, 0.0)
let mut m_pred : Array[Double] = Array::make(n, 0.0)
for r = 0; r < nrep; r = r + 1 {
// v0.40.0: retry loop on J-floor. Each retry uses a different
// fold split (seed = self.seed + r + attempt*nrep) so the
// fold-mean J is different. If all max_attempts attempts hit
// the J-floor for this rep, we record the failure and the
// post-loop re-aborts (preserves pre-v0.40.0 behavior when
// max_attempts=1).
let mut theta_r = 0.0
let mut se_r = 0.0
let mut attempt = 0
let mut succeeded = false
while attempt < max_attempts && !succeeded {
let rep_seed = self.seed + r + attempt * nrep
let folds_u = kfold(n_units, self.n_folds, rep_seed)
let (folds_row, unit_fold, fold_n_units) = expand_unit_folds_to_rows(
cluster, folds_u, row_unit,
)
l_pred = cross_fit_predict_dispatch(
learner_l,
self.data.x,
self.data.y,
folds_row,
)
m_pred = cross_fit_predict_dispatch(
learner_m,
self.data.x,
self.data.d,
folds_row,
)
let v_hat : Array[Double] = Array::make(n, 0.0)
let u_hat : Array[Double] = Array::make(n, 0.0)
for i = 0; i < n; i = i + 1 {
v_hat[i] = self.data.d[i] - m_pred[i]
u_hat[i] = self.data.y[i] - l_pred[i]
}
// v0.55.0: route through the shared score helper so the
// IV-type branch (cluster-aware variant) uses the same
// psi_a / psi_b formula as `DoubleMLPLR::fit`.
let (psi_a, psi_b) = plr_score_elements(
n, v_hat, u_hat, self.data.z, score,
)
// The cluster helper can raise VarEstClusterError::JTooSmall
// on a fold split where mean(psi_deriv) lands below 1e-6.
// The catch arm below records the failure and tries again
// with the next attempt's seed; we don't re-abort here
// because v0.40.0 adds max_attempts retries.
let (t, s) = cluster_causal_param_and_se(
psi_a,
psi_b,
folds_row,
fold_n_units,
unit_rows,
unit_fold,
folds_u.length(),
self.n_folds,
) catch {
_ => {
attempt = attempt + 1
// Sentinel (0.0, 0.0): the catch arm's return value is
// never observed because we re-enter the while loop
// (succeeded stays false) until attempt == max_attempts.
// The post-loop check `if !succeeded` then re-aborts.
(0.0, 0.0)
}
}
// If we got here without the catch arm running, the try
// expression returned (t, s) and we succeeded. The catch
// arm's (0.0, 0.0) is never observed because succeeded
// is still false in that branch (we set attempt += 1 but
// didn't reach this code).
theta_r = t
se_r = s
succeeded = true
}
if !succeeded {
// All max_attempts attempts hit the J-floor; give up and
// re-abort (preserves pre-v0.40.0 behavior when
// max_attempts=1).
abort(
"var_est_cluster: J-floor fired " +
max_attempts.to_string() +
" times for rep=" +
r.to_string() +
" (cluster SE numerically unstable across multiple fold splits, try a different seed or larger n_units)",
)
}
coefs[r] = theta_r
ses[r] = se_r
}
let (coef, se) = aggregate_coef_se(coefs, ses)
{
data: self.data,
learner_l,
learner_m,
n_folds: self.n_folds,
n_rep: self.n_rep,
seed: self.seed,
l_hat: l_pred,
m_hat: m_pred,
coef,
se,
fitted: true,
// cluster path: honor caller's tune_result override
// (set by `DoubleMLPLR::tune`); default `None` preserves
// v0.57.0 behavior for plain `fit(...)` callers.
tune_result,
}
} catch {
PreconditionError::Violated(loc) =>
abort("precondition failed at " + loc.to_string())
}
}