File size: 8,856 Bytes
698308b | 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 | """Shared helpers for browsecomp-plus-mini: loading the run matrix, system weights,
weighted rank metrics, pair agreement by gap, and the select/validate/test protocol.
Input (not redistributed here): a 0/1 matrix `matrix.csv` (rows = BrowseComp-Plus query_id,
columns = published runs, 1 = answer matched the gold answer under normalized exact match,
see grader.py), `runs.json` (one record per run: run, system, ...), and
`short_single_gold.json` ({query_id: bool}, true when the gold answer is a short single entity).
"""
import csv, json, collections
import numpy as np
def load(dirpath):
rows = list(csv.reader(open(f"{dirpath}/matrix.csv")))
runs = rows[0][1:]
qids = [r[0] for r in rows[1:]]
X = np.array([[float(v) for v in r[1:]] for r in rows[1:]]).T # runs x queries
meta = {m["run"]: m for m in json.load(open(f"{dirpath}/runs.json"))}
systems = [meta[r]["system"] for r in runs]
k = collections.Counter(systems)
w = np.array([1.0 / k[s] for s in systems]) # 1/k per system
short = json.load(open(f"{dirpath}/short_single_gold.json"))
pool = np.array([bool(short[q]) for q in qids])
return dict(runs=runs, qids=qids, X=X, full=X.mean(1), systems=systems, w=w, pool=pool, meta=meta)
def rankdata(a):
order = np.argsort(a, kind="mergesort")
r = np.empty(len(a)); r[order] = np.arange(len(a))
# average ties
vals, inv = np.unique(a, return_inverse=True)
sums = np.bincount(inv, r); cnts = np.bincount(inv)
return (sums / cnts)[inv]
def wpearson(a, b, w):
am = (w * a).sum() / w.sum(); bm = (w * b).sum() / w.sum()
da, db = a - am, b - bm
den = np.sqrt((w * da * da).sum() * (w * db * db).sum())
return float((w * da * db).sum() / den) if den > 0 else 0.0
def wspearman(a, b, w):
"""weighted Spearman: weighted Pearson correlation of the (unweighted) ranks"""
return wpearson(rankdata(a), rankdata(b), w)
def wspearman_cols(S, f, w):
"""weighted Spearman of each column of S (runs x candidates) against f"""
rf = rankdata(f)
R = np.apply_along_axis(rankdata, 0, S)
wn = w / w.sum()
Rc = R - (wn[:, None] * R).sum(0); fc = rf - (wn * rf).sum()
num = (wn[:, None] * Rc * fc[:, None]).sum(0)
den = np.sqrt((wn[:, None] * Rc ** 2).sum(0) * (wn * fc ** 2).sum())
return np.where(den > 0, num / np.where(den > 0, den, 1), 0.0)
BANDS = [("more than 10 points", 0.10, 9.0), ("5 to 10 points", 0.05, 0.10), ("2 to 5 points", 0.02, 0.05), ("under 2 points", 0.0, 0.02)]
def pair_agreement(full, sub, w, idx, systems=None, cross_system_only=False):
"""weighted share of run pairs ordered the same way by the subset, by size of the full-benchmark gap.
A tie on the subset counts as not agreeing."""
out = []
idx = list(idx)
for name, lo, hi in BANDS:
ok = tot = 0.0; n = 0
for a_ in range(len(idx)):
for b_ in range(a_ + 1, len(idx)):
i, j = idx[a_], idx[b_]
if cross_system_only and systems[i] == systems[j]:
continue
g = abs(full[i] - full[j])
if lo <= g < hi:
pw = w[i] * w[j]; n += 1; tot += pw
if (full[i] - full[j]) * (sub[i] - sub[j]) > 0:
ok += pw
out.append(dict(gap=name, n_pairs=n, agreement_pct=round(100 * ok / tot, 1) if tot else None))
return out
def calibrated_mae(full, sub, w, fit_idx, eval_idx):
co = np.polyfit(sub[fit_idx], full[fit_idx], 1, w=np.sqrt(w[fit_idx]))
pred = np.polyval(co, sub[eval_idx])
return float((w[eval_idx] * np.abs(pred - full[eval_idx])).sum() / w[eval_idx].sum()), co
def split_systems(systems, full, w, seed):
"""three-way split of SYSTEMS, stratified by system accuracy: sort systems by mean full score,
take them in blocks of three and deal one to each split in random order."""
rng = np.random.default_rng(seed)
sysacc = collections.defaultdict(list)
for s, f in zip(systems, full):
sysacc[s].append(f)
order = sorted(sysacc, key=lambda s: np.mean(sysacc[s]))
parts = ([], [], [])
for b in range(0, len(order), 3):
block = order[b:b + 3]
for p, s in zip(rng.permutation(3), block):
parts[p].append(s)
return parts # select, validate, test
def run_idx(systems, sysset):
return np.array([i for i, s in enumerate(systems) if s in sysset])
def objective(S, f, w, mae_pen=1.0):
rho = wspearman_cols(S, f, w)
mae = (w[:, None] * np.abs(S - f[:, None])).sum(0) / w.sum()
return rho - mae_pen * mae
def greedy(D, idx, n, cand_mask):
X, full, w = D["X"][idx], D["full"][idx], D["w"][idx]
p = (w[:, None] * X).sum(0) / w.sum()
var = p * (1 - p)
ok = cand_mask & (p > 0) & (p < 1)
pool = list(np.where(ok)[0])
sub = sorted(pool, key=lambda t: -var[t])[:3]
pool = [t for t in pool if t not in sub]
while len(sub) < n:
base = X[:, sub].sum(1)
S = (base[:, None] + X[:, pool]) / (len(sub) + 1)
j = int(np.argmax(objective(S, full, w)))
sub.append(pool.pop(j))
return sub
def climb(D, idx, start, cand_mask, rounds=6):
X, full, w = D["X"][idx], D["full"][idx], D["w"][idx]
p = (w[:, None] * X).sum(0) / w.sum()
allowed = np.where(cand_mask & (p > 0) & (p < 1))[0]
sub = list(start); n = len(sub)
cur = float(objective((X[:, sub].mean(1))[:, None], full, w)[0])
for _ in range(rounds):
moved = False
for i in range(n):
rest = [t for t in allowed if t not in sub]
base = X[:, sub].sum(1) - X[:, sub[i]]
S = (base[:, None] + X[:, rest]) / n
sc = objective(S, full, w)
j = int(np.argmax(sc))
if sc[j] > cur + 1e-9:
sub[i] = rest[j]; cur = float(sc[j]); moved = True
if not moved:
break
return sub
def candidates(D, sel_idx, n, cand_mask, seed, restarts=6):
rng = np.random.default_rng(seed)
allowed = np.where(cand_mask)[0]
c = [greedy(D, sel_idx, n, cand_mask)]
c.append(climb(D, sel_idx, c[0], cand_mask))
X = D["X"][sel_idx]
p = X.mean(0)
allowed = [t for t in allowed if 0 < p[t] < 1]
for _ in range(restarts):
c.append(climb(D, sel_idx, list(rng.choice(allowed, n, replace=False)), cand_mask))
return c
def rho_on(D, sub, idx):
return wspearman(D["X"][idx][:, sub].mean(1), D["full"][idx], D["w"][idx])
def stratified(D, idx, n, cand_mask, nbins):
"""difficulty-stratified pick: split candidate queries into `nbins` bands of solve rate and take the
most discriminating queries in each (discrimination = weighted point-biserial correlation between
solving the query and the run's full-benchmark score)."""
X, f, w = D["X"][idx], D["full"][idx], D["w"][idx]
p = (w[:, None] * X).sum(0) / w.sum()
fc = f - (w * f).sum() / w.sum(); Xc = X - p
disc = (w[:, None] * Xc * fc[:, None]).sum(0) / np.sqrt((w[:, None] * Xc ** 2).sum(0) * (w * fc ** 2).sum() + 1e-12)
ok = np.where(cand_mask & (p > 0.02) & (p < 0.98))[0]
qs = np.quantile(p[ok], np.linspace(0, 1, nbins + 1))
per = [n // nbins + (1 if i < n % nbins else 0) for i in range(nbins)]
sel = []
for b in range(nbins):
inb = ok[(p[ok] >= qs[b]) & ((p[ok] < qs[b + 1]) if b < nbins - 1 else (p[ok] <= qs[b + 1]))]
sel += [int(t) for t in inb[np.argsort(-disc[inb])][:per[b]] if t not in sel]
return sel
def methods(seed):
"""candidate selection methods; each maps (D, run_idx, n, mask) -> list of query indices"""
m = {f"stratified_{b}": (lambda b: lambda D, i, n, c: stratified(D, i, n, c, b))(b) for b in (1, 2, 3, 4, 5)}
m["greedy"] = lambda D, i, n, c: greedy(D, i, n, c)
m["greedy_climb"] = lambda D, i, n, c: climb(D, i, greedy(D, i, n, c), c)
for r in range(3):
def f(D, i, n, c, r=r):
rng = np.random.default_rng(1000 * seed + r)
p = D["X"][i].mean(0)
allowed = [t for t in np.where(c)[0] if 0 < p[t] < 1]
return climb(D, i, list(rng.choice(allowed, n, replace=False)), c)
m[f"climb_restart_{r}"] = f
return m
def honest_pick(D, n, seed):
"""SELECT fits every method; VALIDATE chooses the method; the chosen method is refit on SELECT+VALIDATE;
TEST is only used to score the result."""
S, V, T = split_systems(D["systems"], D["full"], D["w"], seed)
si, vi, ti = run_idx(D["systems"], S), run_idx(D["systems"], V), run_idx(D["systems"], T)
M = methods(seed)
val = {k: rho_on(D, f(D, si, n, D["pool"]), vi) for k, f in M.items()}
best = max(val, key=val.get)
sub = M[best](D, np.concatenate([si, vi]), n, D["pool"])
return dict(subset=sub, method=best, validate_rho=val, split=(S, V, T), idx=(si, vi, ti))
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