Expertium
commented
11 months ago For grade-derived R, I have this code (it's mostly leftover from that one time we tried making a weighted average of predicted and grade-derived R):
from scipy.optimize import curve_fit
dataset = pd.read_csv("./revlog_history.tsv", sep='\t', index_col=None, dtype={'r_history': str ,'t_history': str} )
dataset = dataset[(dataset['i'] > 1) & (dataset['delta_t'] > 0) & (dataset['t_history'].str.count(',0') == 0)]
dataset['y'] = dataset['r'].map({1: 0, 2: 1, 3: 1, 4: 1})
dataset['lapse'] = dataset['r_history'].str.count('1')
dataset['delta_t'] = dataset['delta_t'].map(lambda x: round(1.2 * math.pow(1.4, math.floor(math.log(x, 1.4))), 2))
dataset['i'] = dataset['i'].map(lambda x: round(1.115 * math.pow(1.1, math.floor(math.log(x, 1.1))), 2))
dataset['lapse'] = dataset['lapse'].map(lambda x: min(x, 8))
grade_r_matrix = dataset.groupby(by=["delta_t", "i", "lapse"]).agg({'y': ['count', 'mean'], 'r': 'mean'}).reset_index()
grade_r_matrix.sort_values(by=[('r', 'mean')], inplace=True, ignore_index=True)
grade_means = grade_r_matrix['r']['mean']
r_means = (grade_r_matrix['y']['mean'] * grade_r_matrix['y']['count'] + 1 * grade_r_matrix['y']['mean'].mean()) / (grade_r_matrix['y']['count'] + 1)
count = grade_r_matrix['y']['count']
def func(x, a, b):
return 1-(np.power(1-np.power((x-1)/3, a), b))
params, covs = curve_fit(func, grade_means, r_means, bounds=((0.25, 0.25), (4, 4)), sigma=1/np.sqrt(count))
grade_derived_r_values = [func(x, *params) for x in [1, 2, 3, 4]]
grade_derived_r = dict(zip([1, 2, 3, 4], grade_derived_r_values))The value for Again is always 0, the value for Easy is always 1. These 4 values will then be used in the hybrid loss function for optimization. Also, I tried using minimize instead of curve_fit, but for some reason it always sets parameters to their maximum or minimum values that are allowed by bounds.
As for weighing by recency, I suggest something like this:
alpha = 0.9
exp_weights = [alpha ** x for x in range(0, 10)]Every value of the loss will be weighted based on how recent that review was. The most recent review will always have a weight of 1.0, more distant past reviews will have weight <1. This way D will depend more on recent reviews. Alpha will be an optimizable parameter.
L-M-Sherlock
dae
user1823
This will obviously be very computationally expensive since we are running an optimization procedure after every review, but I still want to try it. There is one more problem. Since Hard, Good and Easy all count as 1 when it comes to recall, this history: 3,3,3 And this history: 4,4,4 Will result in exactly the same value of D. Solution: derive R from grades and use a weighted average of two losses, like this:
loss = a * WozLoss(r, binary_recall) + (1-a) * WozLoss(r, grade_derived_r)I could try to implement this myself, but there is one major obstacle (well, a lot of obstacles): I have no idea how to make a function that goes through the card's entire history, calculates the value of the loss for each review, an then outputs it, and it has to be withinstep(), something like this:Originally posted by @Expertium in https://github.com/open-spaced-repetition/fsrs4anki/issues/461#issuecomment-1792359565
Simply put, the key idea is to perform an optimization procedure after each review to find a value of D that provides the best fit to this card's review history.
EDIT: there should be 2 optimizable parameters. The first one is a in
loss = a * WozLoss(r, binary_recall) + (1-a) * WozLoss(r, grade_derived_r), 0<a<1. The second one is alpha for exponential weights for each value of the loss, it determines how quickly weights decrease as we get further into the past, 0<alpha<1. See my next comment, I gave a very simple example of what exponential weights would look like.