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Distributional evaluation metrics for perturbation prediction.
Complements cell-eval (which focuses on conditional mean accuracy) with
metrics that measure distributional fidelity:
1. Per-perturbation MMD (Maximum Mean Discrepancy)
2. Per-perturbation Energy Distance
3. Variance Ratio (per-gene variance match)
4. Gene-Gene Correlation Preservation
5. Classifier Two-Sample Test (C2ST)
6. k-NN Precision / Recall
"""
import numpy as np
import anndata as ad
import pandas as pd
from scipy.spatial.distance import cdist
from scipy.stats import pearsonr
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import cross_val_score
from sklearn.preprocessing import StandardScaler
# ββ Helpers ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def _get_pert_cells(adata, pert):
mask = adata.obs["perturbation"] == pert
X = adata[mask].X
return np.asarray(X) if not isinstance(X, np.ndarray) else X
def _rbf_kernel(X, Y, sigma):
D2 = cdist(X, Y, metric="sqeuclidean")
return np.exp(-D2 / (2 * sigma ** 2))
# ββ 1. MMD (multi-sigma RBF) ββββββββββββββββββββββββββββββββββββββββ
def mmd_multi_sigma(X, Y, scales=(0.5, 1.0, 2.0, 4.0)):
D2_all = cdist(X, X, "sqeuclidean")
median_sq = np.median(D2_all[np.triu_indices(len(X), k=1)])
median_sq = max(median_sq, 1e-12)
vals = []
for s in scales:
sigma = np.sqrt(s * median_sq)
Kxx = _rbf_kernel(X, X, sigma)
Kyy = _rbf_kernel(Y, Y, sigma)
Kxy = _rbf_kernel(X, Y, sigma)
m, n = len(X), len(Y)
t_xx = (Kxx.sum() - np.trace(Kxx)) / (m * (m - 1))
t_yy = (Kyy.sum() - np.trace(Kyy)) / (n * (n - 1))
t_xy = Kxy.mean()
vals.append(t_xx + t_yy - 2 * t_xy)
return float(np.mean(vals))
# ββ 2. Energy Distance ββββββββββββββββββββββββββββββββββββββββββββββ
def energy_distance(X, Y):
Dxy = cdist(X, Y, "euclidean").mean()
Dxx = cdist(X, X, "euclidean").mean()
Dyy = cdist(Y, Y, "euclidean").mean()
return float(2 * Dxy - Dxx - Dyy)
# ββ 3. Variance Ratio βββββββββββββββββββββββββββββββββββββββββββββββ
def variance_ratio(pred_cells, real_cells, var_threshold=0.001):
"""Per-gene variance ratio: pred_var / real_var. Perfect = 1.0.
Only considers genes with real_var > var_threshold (skip sparse zeros)."""
pv = pred_cells.var(axis=0)
rv = real_cells.var(axis=0)
mask = rv > var_threshold
if mask.sum() < 10:
return {"var_ratio_median": np.nan, "var_ratio_mean": np.nan,
"var_ratio_q25": np.nan, "var_ratio_q75": np.nan,
"n_active_genes": int(mask.sum())}
ratio = pv[mask] / rv[mask]
return {
"var_ratio_median": float(np.median(ratio)),
"var_ratio_mean": float(np.mean(ratio)),
"var_ratio_q25": float(np.percentile(ratio, 25)),
"var_ratio_q75": float(np.percentile(ratio, 75)),
"n_active_genes": int(mask.sum()),
}
# ββ 4. Gene-Gene Correlation Preservation βββββββββββββββββββββββββββ
def gene_corr_preservation(pred_cells, real_cells, top_k=200):
"""Pearson correlation between flattened gene-gene correlation matrices.
Uses top_k highest-variance genes for tractability."""
gene_var = real_cells.var(axis=0)
top_idx = np.argsort(gene_var)[-top_k:]
pred_sub = pred_cells[:, top_idx]
real_sub = real_cells[:, top_idx]
pred_corr = np.corrcoef(pred_sub.T)
real_corr = np.corrcoef(real_sub.T)
idx = np.triu_indices(top_k, k=1)
r, _ = pearsonr(pred_corr[idx], real_corr[idx])
return float(r)
# ββ 5. C2ST (Classifier Two-Sample Test) ββββββββββββββββββββββββββββ
def c2st(pred_cells, real_cells, max_samples=500):
"""Logistic regression C2ST. Returns accuracy (0.5 = indistinguishable)."""
n_pred = min(len(pred_cells), max_samples)
n_real = min(len(real_cells), max_samples)
idx_p = np.random.choice(len(pred_cells), n_pred, replace=False)
idx_r = np.random.choice(len(real_cells), n_real, replace=False)
X = np.vstack([pred_cells[idx_p], real_cells[idx_r]])
y = np.concatenate([np.zeros(n_pred), np.ones(n_real)])
scaler = StandardScaler()
X_s = scaler.fit_transform(X)
clf = LogisticRegression(max_iter=500, C=1.0, solver="lbfgs")
n_cv = min(5, min(n_pred, n_real))
if n_cv < 2:
return float("nan")
scores = cross_val_score(clf, X_s, y, cv=n_cv, scoring="accuracy")
return float(scores.mean())
# ββ 6. k-NN Precision / Recall ββββββββββββββββββββββββββββββββββββββ
def knn_precision_recall(pred_cells, real_cells, k=10):
"""
Precision: fraction of pred cells whose k-NN ball overlaps real data.
Recall: fraction of real cells whose k-NN ball overlaps pred data.
"""
D_rr = cdist(real_cells, real_cells, "euclidean")
np.fill_diagonal(D_rr, np.inf)
real_knn_dist = np.sort(D_rr, axis=1)[:, k - 1]
D_pp = cdist(pred_cells, pred_cells, "euclidean")
np.fill_diagonal(D_pp, np.inf)
pred_knn_dist = np.sort(D_pp, axis=1)[:, k - 1]
D_pr = cdist(pred_cells, real_cells, "euclidean")
precision = float((D_pr <= real_knn_dist[None, :]).any(axis=1).mean())
D_rp = D_pr.T
recall = float((D_rp <= pred_knn_dist[None, :]).any(axis=1).mean())
return precision, recall
# ββ Main βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def evaluate_model(pred_path, real_path, name):
pred = ad.read_h5ad(pred_path)
real = ad.read_h5ad(real_path)
perts = [p for p in pred.obs["perturbation"].unique() if p != "control"]
rows = []
for pert in perts:
pc = _get_pert_cells(pred, pert)
rc = _get_pert_cells(real, pert)
if len(pc) < 5 or len(rc) < 5:
continue
mmd = mmd_multi_sigma(pc, rc)
edist = energy_distance(pc, rc)
vr = variance_ratio(pc, rc)
gc = gene_corr_preservation(pc, rc, top_k=min(200, pc.shape[1]))
c2st_acc = c2st(pc, rc)
prec, rec = knn_precision_recall(pc, rc, k=min(5, len(rc) - 1))
rows.append({
"perturbation": pert,
"mmd": mmd,
"energy_distance": edist,
**vr,
"gene_corr_preservation": gc,
"c2st_accuracy": c2st_acc,
"knn_precision": prec,
"knn_recall": rec,
})
df = pd.DataFrame(rows)
return df
def print_comparison(results: dict[str, pd.DataFrame]):
metrics = [
"mmd", "energy_distance",
"var_ratio_median", "var_ratio_mean",
"gene_corr_preservation", "c2st_accuracy",
"knn_precision", "knn_recall",
]
lower_better = {"mmd", "energy_distance"}
target_metrics = {
"var_ratio_median": 1.0,
"var_ratio_mean": 1.0,
"c2st_accuracy": 0.5,
}
names = list(results.keys())
short = {n: n[:12] for n in names}
header = f"{'Metric':<28}" + "".join(f"{short[n]:>14}" for n in names) + " Best"
print(header)
print("-" * len(header))
for m in metrics:
vals = []
for n in names:
vals.append(float(results[n][m].mean()))
if m in target_metrics:
target = target_metrics[m]
dists = [abs(v - target) for v in vals]
best_idx = dists.index(min(dists))
elif m in lower_better:
best_idx = vals.index(min(vals))
else:
best_idx = vals.index(max(vals))
short_names = [short[n] for n in names]
line = f"{m:<28}" + "".join(f"{v:>14.4f}" for v in vals)
line += f" <- {short_names[best_idx]}"
print(line)
print("\n=== Variance Ratio (median [Q25, Q75], 1.0 = perfect) ===")
for n in names:
df = results[n]
med = df["var_ratio_median"].mean()
q25 = df["var_ratio_q25"].mean()
q75 = df["var_ratio_q75"].mean()
print(f" {short[n]:<14} {med:.3f} [{q25:.3f}, {q75:.3f}]")
if __name__ == "__main__":
np.random.seed(42)
BASE = "/home/hp250092/ku50001222/qian/aivc/lfj"
models = {
"A6_SDE50": (
f"{BASE}/GRN/result/SB/A6_dsm_aniso/iteration_195000/pred.h5ad",
f"{BASE}/GRN/result/SB/A6_dsm_aniso/iteration_195000/real.h5ad",
),
"A6_ODE_RK4": (
f"{BASE}/GRN/result/SB/A6_dsm_aniso/eval_only/pred.h5ad",
f"{BASE}/GRN/result/SB/A6_dsm_aniso/eval_only/real.h5ad",
),
"A1_Euler": (
f"{BASE}/GRN/result/SB/A1_baseline/iteration_195000/pred.h5ad",
f"{BASE}/GRN/result/SB/A1_baseline/iteration_195000/real.h5ad",
),
"A1_RK4": (
f"{BASE}/GRN/result/SB/A1_baseline/eval_only/pred.h5ad",
f"{BASE}/GRN/result/SB/A1_baseline/eval_only/real.h5ad",
),
"scDFM": (
f"{BASE}/GRN/baseline/flow-fusion_differential_perceiver-norman-origin-predict_y-gamma_0.5-perturbation_function_crisper-lr_5e-05-dim_model_128-infer_top_gene_1000-split_method_additive-use_mmd_loss_True-fold_1-use_negative_edge_True-topk_30/iteration_200000/pred.h5ad",
f"{BASE}/GRN/baseline/flow-fusion_differential_perceiver-norman-origin-predict_y-gamma_0.5-perturbation_function_crisper-lr_5e-05-dim_model_128-infer_top_gene_1000-split_method_additive-use_mmd_loss_True-fold_1-use_negative_edge_True-topk_30/iteration_200000/real.h5ad",
),
}
results = {}
for name, (pred_path, real_path) in models.items():
print(f"\n>>> Evaluating {name} ...")
df = evaluate_model(pred_path, real_path, name)
results[name] = df
out_dir = str(pred_path).rsplit("/", 1)[0]
df.to_csv(f"{out_dir}/distributional_results.csv", index=False)
print(f" saved to {out_dir}/distributional_results.csv")
print("\n" + "=" * 100)
print("DISTRIBUTIONAL METRICS COMPARISON (mean over 39 perturbations)")
print("=" * 100 + "\n")
print_comparison(results)
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