def updateTest(prior: Tuple[float, float, float], result: bool, tnow: float):
"""Alternate to ebisu.updateRecall that returns several posterior Beta models"""
(alpha, beta, t) = prior
delta = tnow / t
if result:
gb1 = (1.0 / delta, 1.0, alpha + delta, beta, tnow)
mom = gb1Moments(*gb1[:-1])
else:
mom = np.array(failureMoments(prior, result, tnow, num=2))
def f(bd):
b, d = bd
this = np.array(gb1Moments(1 / d, 1., alpha, b, num=2))
return this - mom
from scipy.optimize import least_squares
res = least_squares(f, [beta, delta],
bounds=((1.01, 0), (np.inf, np.inf)))
# print("optimization cost", res)
newBeta, newDelta = res.x
gb1 = (1 / newDelta, 1, alpha, newBeta, tnow)
moved2 = moveBeta(gb1ToBeta(gb1))
return dict(
simple=gb1ToBeta(gb1),
moved=gb1ToBeta(moveGb1(gb1, prior[2])),
moved2=moved2,
moved3=moveBeta2(gb1ToBeta(gb1)),
moveBetasOnly=moveBeta(ebisu.updateRecall(prior, result, tnow)),
postToBeta=posteriorMomToBeta(mom, moved2, tnow),
)
def right(self):
r = self.card_list[self.index]
if not r.learning or not r.last:
r.last = today
r.learning = True
r.alpha, r.beta, r.t = spaced_rep.a_right, spaced_rep.b_right, spaced_rep.t_right
ebisu.updateRecall(prior=(r.alpha, r.beta, r.t),
successes=1,
total=1,
tnow=(today - r.last).days + .1)
self.card_list[self.index] = r
self.index += 1
if self.index < len(self.card_list):
self.frames[Back].update(self.card_list[self.index])
self.frames[Front].update(self.card_list[self.index])
self.show_frame(Front)
else:
self.show_frame(StartPage)
def update_item(hid, result):
time_passed = 0.1
word = db.fetchone("SELECT model, last_date FROM spaced_repetition WHERE hid=%s", (hid,))
if word[1] is not None:
lastTest = datetime.strptime(word[1], "%Y-%m-%dT%H:%M:%S.%f")
time_passed = (datetime.now() - lastTest) / oneHour
model = tuple(json.loads(word[0]))
recall = ebisu.predictRecall(model, time_passed, exact=True)
print(str(hid), str(recall))
new_model = ebisu.updateRecall(model, result, time_passed)
print(hid, result)
print(model)
print(new_model)
db.update_sr_item(hid, json.dumps(new_model), datetime.now().isoformat())
return True
def wrong(self):
w = self.card_list.pop(self.index)
if w.learning:
w.alpha, w.beta, w.t = ebisu.updateRecall(
prior=(w.alpha, w.beta, w.t),
successes=0,
total=1,
tnow=(w.last - today).days + .1)
if not w.learning:
w.learning = True
w.alpha, w.beta, w.t = spaced_rep.a_wrong, spaced_rep.b_wrong, spaced_rep.t_wrong
w.last = today
self.card_list.insert((self.index + len(self.card_list)) // 2, w)
self.frames[Back].update(self.card_list[self.index])
self.frames[Front].update(self.card_list[self.index])
self.show_frame(Front)
def process_result(self, user_id: int, results: bool) -> None:
"""
Saves a review with the test results (for eventual statistics)
"""
if not isinstance(results, bool):
raise ValueError(
"Invalid test result for Ebisu: {}".format(results))
user = User.objects.get(id=user_id)
# Compute the prior
alpha, beta, t = None, None, None
try:
if self.deck.reviewing_card.last_review:
previous_model, time_from_last_review = self._get_card_model(
self.deck.reviewing_card)
alpha, beta, t = ebisu.updateRecall(prior=previous_model,
successes=int(results),
total=1,
tnow=time_from_last_review)
except AssertionError as e:
logging.error(
"Assertion Error on card " + str(self.deck.reviewing_card) +
": ", e)
finally:
if (alpha, beta, t) == (None, None, None):
# Set defaults if this is the first review
alpha = self.deck.initial_alpha
beta = self.deck.initial_beta
t = self.deck.initial_t
# Save review
new_review = Review(
alpha=alpha,
beta=beta,
t=t,
user=user,
test_results=results,
review_time=datetime.utcnow(),
)
self.deck.reviewing_card.update(push__reviews=new_review)
self.deck.reviewing_card.save()
import ebisu t_init = 1 a_init = 3.0 b_init = 3.0 default_model = ebisu.defaultModel(t=t_init, alpha=a_init, beta=b_init) (a_wrong, b_wrong, t_wrong) = ebisu.updateRecall(default_model, 0, 1, 0.1) (a_right, b_right, t_right) = ebisu.updateRecall(default_model, 1, 1, 0.1)
def simulation(model, result, tnow):
gold = ebisu.updateRecall(model, result, tnow)
newModel = updateTest(model, result, tnow)
print(newModel)
t = np.linspace(.1, 100 * 1, 50 * 1)
def trace(model):
return np.vectorize(lambda t: ebisu.predictRecall(model, t))(t)
def yerr(model):
return np.vstack([
np.vectorize(lambda t: ebisu.alternate.predictRecallMedian(
model, t, 0.25))(t),
np.vectorize(lambda t: ebisu.alternate.predictRecallMedian(
model, t, 0.75))(t),
])
def both(model):
y = trace(model)
return dict(y=y, yerr=np.abs(yerr(model) - y))
plt.ion()
plt.figure()
plt.semilogy(t, trace(model), linewidth=6, label='prior')
# plt.semilogy(t, trace(gold), linewidth=5, label='orig')
plt.semilogy(t,
trace(newModel['simple']),
'--',
linewidth=4,
label='via GB1')
# plt.semilogy(t, trace(newModel['moved']), linewidth=3, label='via GB1@HL')
plt.semilogy(t,
trace(newModel['moved2']),
'--',
linewidth=2,
label='Beta@HL')
plt.semilogy(t,
trace(newModel['postToBeta']),
linewidth=1,
label='post2beta')
# plt.semilogy(t, trace(newModel['moveBetasOnly']), '-', linewidth=2, label='orig@HL')
plt.legend()
plt.title('Model=({},{},{}), Quiz={} @ Tnow={}'.format(
*model, result, tnow))
result = False
import scipy.stats as stats
alpha, beta, tau = model
N = 10 * 1000 * 1000
priorTau = stats.beta.rvs(alpha, beta, size=N)
tQuiz = 3.
priorTQuiz = priorTau**(tQuiz / tau)
posteriorWeights = (priorTQuiz)**result * (
(1 - priorTQuiz)**(1 - result))
posteriorModel = updateGb1(model, result, tQuiz)
posteriorNewTau = (priorTQuiz)**(posteriorModel[2] / tQuiz)
weightedMean = np.sum(
posteriorWeights * posteriorNewTau) / np.sum(posteriorWeights)
weightedVar = np.sum(
posteriorWeights *
(posteriorNewTau - weightedMean)**2) / np.sum(posteriorWeights)
print('expected', summarizeBeta(posteriorModel[0], posteriorModel[1]))
print('actual', [weightedMean, weightedVar])
def summarizeBeta(a, b):
return dict(mean=a / (a + b), var=a * b / (a + b)**2 / (a + b + 1))