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b381c58 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 | """Section 5.1 -- personalized warfarin dosing on the PharmGKB/IWPC cohort.
Paper setup (verbatim, Section 5.1 "RCB Setup"):
"The total number of trials is set at T = 5528, with reward noise sigma_hat = 0.054
estimated from the true optimal dosing of warfarin after scaling. To create an
online decision-making scenario, we simulate the process across 10 random
permutations of patient arrivals, averaging the results over these permutations.
The exploration budget eps is varied among [0.025, 0.035, 0.045]. The minimum gap
tau_P0 is set at 0.005. The prior variance is defined as Sigma = [0.4, 0.6, 0.8] Id,
and the prior means are beta_{2,0} = 0.05 x Id, beta_{1,0} = beta_{3,0} = 0_d."
Full grid: 3 budgets x 3 prior variances x 10 permutations = 90 runs of T = 5528.
"""
import argparse, json, os, sys, time
import numpy as np
from sklearn.linear_model import LinearRegression
os.chdir(os.path.abspath(os.path.join(os.path.dirname(__file__), "..")))
sys.path.insert(0, os.path.join(os.path.dirname(__file__), ".."))
from rcb.core import RCB, N_eps, L_eps
from rcb.env import build_warfarin
PREV = None # true class prevalences p_k, filled from the data
def ground_truth(X, arm, dose):
"""Appendix F.4 / Section 5.1 ground truth: scale the optimal dose into [0,1]
(min 0, max 1); per dosage group, regress the scaled dose on the covariates to
get beta_i; the true mean reward of a patient is x'beta_i for the *optimal* arm
and 0 for every counterfactual arm."""
s = (dose - dose.min()) / (dose.max() - dose.min())
betas = []
for i in range(3):
m = arm == i
lr = LinearRegression(fit_intercept=False).fit(X[m], s[m])
betas.append(lr.coef_)
betas = np.array(betas)
mu_opt = np.einsum("ij,ij->i", X, betas[arm]) # x'beta_{optimal arm}
sigma_hat = float(np.std(s))
return betas, mu_opt, s, sigma_hat
def weighted_risk_score(correct, arm, prev):
"""Section 5.1: Score = sum_k p_k ( I(Correct|k) - I(Incorrect|k) ) = sum_k p_k (2 a_k - 1)."""
sc = 0.0
for k in range(3):
m = arm == k
a = correct[m].mean() if m.sum() else 0.0
sc += prev[k] * (2 * a - 1)
return sc
def effective_phi0(X):
"""Assumption 3 requires lambda_min(E[xx']) >= phi0 > 0. On the IWPC design this
eigenvalue is exactly 0 (the dummy encoding is rank deficient), so we substitute
the smallest *positive* eigenvalue -- the tightest value for which the assumption
is not vacuous. This substitution is reported in the logbook."""
ev = np.linalg.eigvalsh(X.T @ X / len(X))
return float(ev[ev > 1e-8].min())
def run_one(X, arm, mu_opt, sigma, eps, prior_var, seed, tau_P0=0.005, rho_P0=0.95,
C_N=None, gamma_const=4.0, phi0=None, use_empirical_EF=True,
reward="continuous", rng_noise=None, N_override=None):
rng = np.random.default_rng(seed)
n, d = X.shape
K = 3
order = rng.permutation(n)
beta0 = [np.zeros(d), 0.05 * np.ones(d), np.zeros(d)] # Medium arm is prior-best
Sigma0 = [prior_var * np.eye(d) for _ in range(K)]
if phi0 is None:
phi0 = effective_phi0(X)
N = N_eps(K, d, sigma, eps, tau_P0, phi0, C=C_N) if N_override is None else float(N_override)
L = L_eps(eps, tau_P0, rho_P0)
algo = RCB(K, d, sigma, beta0, Sigma0, N=max(1, N), L=L, offset=0.0,
phi0=phi0, trust_mode="linear", trust_rate=1.0,
gamma_const=gamma_const, use_empirical_EF=use_empirical_EF, rng=rng)
regret = np.empty(n); gains = np.empty(n); correct = np.empty(n, bool)
rec_by_patient = np.empty(n, int)
cum = 0.0
for t, idx in enumerate(order):
x = X[idx]
rec, info = algo.recommend(x)
rec_by_patient[idx] = rec
gains[t] = algo.dbic_gain_expected(x, algo.rec_kernel(x, info))
ok = rec == arm[idx]
correct[t] = ok
# mu(x, i) = x'beta_i for the optimal arm, 0 for counterfactuals
cum += mu_opt[idx] - (mu_opt[idx] if ok else 0.0)
regret[t] = cum
if reward == "binary":
y = 1.0 if ok else 0.0
else:
# y_t = mu(x_t, a_t) + eta_t, mu = x'beta_i for the optimal arm and 0
# for counterfactual arms (Section 5.1 "Ground Truth"), eta ~ N(0, sigma^2)
y = (mu_opt[idx] if ok else 0.0) + sigma * rng.standard_normal()
algo.update(x, rec, y, info)
return dict(regret=regret, gain=gains, correct=correct, order=order,
rec_by_patient=rec_by_patient,
Tcold=algo.Tcold if algo.Tcold else n, N=N, L=L, phi0=phi0)
def main():
ap = argparse.ArgumentParser()
ap.add_argument("--data", default="data/iwpc_warfarin_5528.csv")
ap.add_argument("--out", default="outputs/warfarin.json")
ap.add_argument("--perms", type=int, default=10)
ap.add_argument("--C_N", type=float, default=None, required=True,
help="implementation constant multiplying Theorem 1's N(eps)")
ap.add_argument("--N", type=int, default=None,
help="explicit per-arm cold-start size (overrides C_N * Theorem 1)")
ap.add_argument("--reward", default="binary", choices=["binary", "continuous"],
help="Section 5.1 states y_t = 1{correct arm} (binary); the "
"'Ground Truth' paragraph instead implies y = x'beta_opt.")
ap.add_argument("--EF", default="theory", choices=["theory", "empirical"],
help="source of E_{F,delta}(|T_{m-1}|) in Algorithm 2 line 10")
ap.add_argument("--phi0", type=float, default=1.0,
help="Assumption 3 lambda_min(E[xx']); <=0 means use the smallest "
"positive eigenvalue of the empirical design")
args = ap.parse_args()
X, arm, dose, cols = build_warfarin(args.data)
betas, mu_opt, s, sigma_hat = ground_truth(X, arm, dose)
n, d = X.shape
prev = np.bincount(arm, minlength=3) / n
phi0 = args.phi0 if args.phi0 > 0 else effective_phi0(X)
print(f"patients={n} features={d} sigma_hat={sigma_hat:.3f} prevalence={prev.round(3)}")
print(f"reward={args.reward} EF={args.EF} phi0={phi0:.6g}")
# Physician baseline: always Medium
phys_correct = (arm == 1)
phys_score = weighted_risk_score(phys_correct, arm, prev)
print(f"physician weighted risk score = {phys_score:.3f} (paper: 0.20)")
# Offline full-information ceiling for the paper's own oracle class (per-arm
# ridge on ALL 5528 patients). No online policy using this oracle can beat it.
lam = 1e-2
bh = []
for i in range(3):
yv = (arm == i).astype(float) if args.reward == "binary" else np.where(arm == i, mu_opt, 0.0)
bh.append(np.linalg.solve(X.T @ X + lam * np.eye(d), X.T @ yv))
pred = (X @ np.array(bh).T).argmax(1)
ceil_cm = np.array([[float((pred[arm == k] == j).mean()) for j in range(3)] for k in range(3)])
print(f"offline oracle ceiling: err={1 - (pred == arm).mean():.4f} "
f"score={weighted_risk_score(pred == arm, arm, prev):+.4f}")
# Theorem 1's own requirement at this scale, with C = 1 (no fudge factor).
N_thm1 = {e: N_eps(3, d, sigma_hat, e, 0.005, phi0, C=1.0) for e in [0.025, 0.035, 0.045]}
print("Theorem 1 required N(eps) at C=1: " +
" ".join(f"{e}:{v:.0f}" for e, v in N_thm1.items()) + f" (T = {n})")
res = {"meta": dict(n=n, d=d, sigma_hat=sigma_hat, prevalence=prev.tolist(),
physician_score=phys_score,
physician_error=float(1 - phys_correct.mean()),
C_N=args.C_N, reward=args.reward, EF=args.EF, phi0=phi0,
ceiling_error=float(1 - (pred == arm).mean()),
ceiling_score=weighted_risk_score(pred == arm, arm, prev),
ceiling_confusion=ceil_cm.tolist(),
N_theorem1_C1={str(k): v for k, v in N_thm1.items()},
columns=cols), "runs": []}
t0 = time.time()
for eps in [0.025, 0.035, 0.045]:
for pv in [0.4, 0.6, 0.8]:
regs, errs, gns, scores, conf, tcolds = [], [], [], [], [], []
for p in range(args.perms):
r = run_one(X, arm, mu_opt, sigma_hat, eps, pv, seed=1000 * p + 7,
C_N=args.C_N, reward=args.reward, phi0=phi0,
use_empirical_EF=(args.EF == "empirical"),
N_override=args.N)
regs.append(r["regret"]); gns.append(r["gain"])
errs.append(1 - np.cumsum(r["correct"]) / np.arange(1, n + 1))
rp = r["rec_by_patient"]
scores.append(weighted_risk_score(rp == arm, arm, prev))
# Table 2: rows = true dosage stratum, cols = RCB assigned dosage
cm = np.zeros((3, 3))
for k in range(3):
m = arm == k
for j in range(3):
cm[k, j] = (rp[m] == j).mean()
conf.append(cm)
tcolds.append(r["Tcold"])
entry = dict(eps=eps, prior_var=pv,
regret_mean=float(np.mean([g[-1] for g in regs])),
regret_curve=np.mean(regs, 0)[::20].tolist(),
error_final=float(np.mean([e[-1] for e in errs])),
error_curve=np.mean(errs, 0)[::20].tolist(),
gain_curve=np.mean(gns, 0)[::20].tolist(),
gain_min=float(np.min(np.mean(gns, 0))),
frac_gain_below_negeps=float(np.mean(np.mean(gns, 0) < -eps)),
score=float(np.mean(scores)), score_sd=float(np.std(scores)),
confusion=np.mean(conf, 0).tolist(),
Tcold=float(np.mean(tcolds)), N=r["N"], L=r["L"])
res["runs"].append(entry)
print(f"eps={eps} Sigma={pv}I | N={r['N']:.1f} L={r['L']:.1f} "
f"Tcold={np.mean(tcolds):.0f} | err={entry['error_final']:.3f} "
f"score={entry['score']:.3f} regret={entry['regret_mean']:.0f} "
f"min-gain={entry['gain_min']:+.4f}")
res["physician_confusion"] = [[0, 1, 0], [0, 1, 0], [0, 1, 0]]
res["wall_clock_s"] = time.time() - t0
os.makedirs(os.path.dirname(args.out), exist_ok=True)
json.dump(res, open(args.out, "w"))
print(f"wrote {args.out} in {res['wall_clock_s']:.0f}s")
if __name__ == "__main__":
main()
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