/
distributionally_robust_data.py
188 lines (163 loc) · 6.86 KB
/
distributionally_robust_data.py
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from math import inf
class OnlineCressieRead:
@staticmethod
def intervalimpl(
n,
sumw,
sumwsq,
sumwr,
sumwsqr,
sumwsqrsq,
wmin,
wmax,
alpha=0.05,
rmin=0,
rmax=1,
raiseonerr=False,
upper_bound=False,
):
from math import inf, isclose, sqrt
from scipy.stats import chi2
assert wmin < 1
assert wmax > 1
assert rmin <= rmax
uncwfake = wmax if sumw < n else wmin
if uncwfake == inf:
uncgstar = 1 + 1 / n
else:
unca = (uncwfake + sumw) / (1 + n)
uncb = (uncwfake**2 + sumwsq) / (1 + n)
uncgstar = (n + 1) * (unca - 1) ** 2 / (uncb - unca * unca)
Delta = chi2.isf(q=alpha, df=1)
phi = (-uncgstar - Delta) / (2 * (n + 1))
bounds = []
r_sign = (rmax, -1) if upper_bound else (rmin, 1)
for r, sign in (r_sign,):
candidates = []
for wfake in (wmin, wmax):
if wfake == inf:
x = sign * (r + (sumwr - sumw * r) / n)
y = (r * sumw - sumwr) ** 2 / (n * (1 + n)) - (
r**2 * sumwsq - 2 * r * sumwsqr + sumwsqrsq
) / (1 + n)
z = phi + 1 / (2 * n)
if isclose(y * z, 0, abs_tol=1e-9):
y = 0
if z <= 0 and y * z >= 0:
kappa = sqrt(y / (2 * z))
if isclose(kappa, 0):
candidates.append((sign * r, None))
else:
gstar = x - sqrt(2 * y * z)
gamma = -kappa * (1 + n) / n + sign * (r * sumw - sumwr) / n
beta = -sign * r
candidates.append(
(
gstar,
{
"kappastar": kappa,
"betastar": beta,
"gammastar": gamma,
"wfake": wfake,
# Q_{w,r} &= -\frac{\gamma + \beta w + w r}{(N+1) \kappa} \\
"qfunc": lambda c, w, r, k=kappa, g=gamma, b=beta, s=sign, num=n: -c
* (g + (b + s * r) * w)
/ ((num + 1) * k),
},
)
)
else:
barw = (wfake + sumw) / (1 + n)
barwsq = (wfake * wfake + sumwsq) / (1 + n)
barwr = sign * (wfake * r + sumwr) / (1 + n)
barwsqr = sign * (wfake * wfake * r + sumwsqr) / (1 + n)
barwsqrsq = (wfake * wfake * r * r + sumwsqrsq) / (1 + n)
if barwsq > barw**2:
x = barwr + (
(1 - barw) * (barwsqr - barw * barwr) / (barwsq - barw**2)
)
y = (barwsqr - barw * barwr) ** 2 / (barwsq - barw**2) - (
barwsqrsq - barwr**2
)
z = phi + (1 / 2) * (1 - barw) ** 2 / (barwsq - barw**2)
if isclose(y * z, 0, abs_tol=1e-9):
y = 0
if z <= 0 and y * z >= 0:
kappa = sqrt(y / (2 * z)) if y * z > 0 else 0
if isclose(kappa, 0):
candidates.append((sign * r, None))
else:
gstar = x - sqrt(2 * y * z)
beta = (
-kappa * (1 - barw) - (barwsqr - barw * barwr)
) / (barwsq - barw * barw)
gamma = -kappa - beta * barw - barwr
candidates.append(
(
gstar,
{
"kappastar": kappa,
"betastar": beta,
"gammastar": gamma,
"wfake": wfake,
# Q_{w,r} &= -\frac{\gamma + \beta w + w r}{(N+1) \kappa} \\
"qfunc": lambda c, w, r, k=kappa, g=gamma, b=beta, s=sign, num=n: -c
* (g + (b + s * r) * w)
/ ((num + 1) * k),
},
)
)
best = min(candidates, key=lambda x: x[0])
vbound = min(rmax, max(rmin, sign * best[0]))
bounds.append((vbound, best[1]))
return (bounds[0][0],), (bounds[0][1],)
def __init__(self, alpha, tau=1, wmin=0, wmax=inf):
import numpy as np
self.alpha = alpha
self.tau = tau
self.n = 0
self.sumw = 0
self.sumwsq = 0
self.sumwr = 0
self.sumwsqr = 0
self.sumwsqrsq = 0
self.wmin = wmin
self.wmax = wmax
self.duals = None
self.mleduals = None
def update(self, c, w, r):
if c > 0:
assert (
w + 1e-6 >= self.wmin and w <= self.wmax + 1e-6
), "w = {} < {} < {}".format(self.wmin, w, self.wmax)
assert r >= 0 and r <= 1, "r = {}".format(r)
decay = self.tau**c
self.n = decay * self.n + c
self.sumw = decay * self.sumw + c * w
self.sumwsq = decay * self.sumwsq + c * w**2
self.sumwr = decay * self.sumwr + c * w * r
self.sumwsqr = decay * self.sumwsqr + c * (w**2) * r
self.sumwsqrsq = decay * self.sumwsqrsq + c * (w**2) * (r**2)
self.duals = None
self.mleduals = None
return self
def recomputeduals(self, is_upper=False):
from crminustwo import CrMinusTwo as CrMinusTwo
self.duals = self.intervalimpl(
self.n,
self.sumw,
self.sumwsq,
self.sumwr,
self.sumwsqr,
self.sumwsqrsq,
self.wmin,
self.wmax,
self.alpha,
raiseonerr=True,
upper_bound=is_upper,
)
def qlb(self, w, r):
if self.duals is None:
self.recomputeduals()
assert self.duals is not None
return self.duals[1][0]["qfunc"](1, w, r) if self.duals[1][0] is not None else 1