Randomly selecting from Pandas groups with equal probability -- unexpected behavior

Question

I have 12 unique groups that I am trying to randomly sample from, each with a different number of observations. I want to randomly sample from the entire population (dataframe) with each group having the same probability of being selected from. The simplest example of this would be a dataframe with 2 groups.

    groups  probability
0       a       0.25
1       a       0.25
2       b       0.5

using np.random.choice(df['groups'], p=df['probability'], size=100) Each iteration will now have a 50% chance of selecting group a and a 50% chance of selecting group b

To come up with the probabilities I used the formula:

(1. / num_groups) / size_of_groups

or in Python:

num_groups = len(df['groups'].unique())  # 2
size_of_groups = df.groupby('label').size()  # {a: 2, b: 1}
(1. / num_groups) / size_of_groups

Which returns

    groups
a    0.25
b    0.50

This works great until I get past 10 unique groups, after which I start getting weird distributions. Here is a small example:

np.random.seed(1234)

group_size = 12
groups = np.arange(group_size)

probs = np.random.uniform(size=group_size)
probs = probs / probs.sum()

g = np.random.choice(groups, size=10000, p=probs)
df = pd.DataFrame({'groups': g})

prob_map = ((1. / len(df['groups'].unique())) / df.groupby('groups').size()).to_dict()

df['probability'] = df['groups'].map(prob_map)

plt.hist(np.random.choice(df['groups'], p=df['probability'], size=10000, replace=True))
plt.xticks(np.arange(group_size))
plt.show()

I would expect a fairly uniform distribution with a large enough sample size, but I am getting these wings when the number of groups is 11+. If I change the group_size variable to 10 or lower, I do get the desired uniform distribution.

I can't tell if the problem is with my formula for calculating the probabilities, or possibly a floating point precision problem? Anyone know a better way to accomplish this, or a fix for this example?

Thanks in advance!

Answer 1

There is no problem about your calculations. Your resulting array is:

arr = np.random.choice(df['groups'], p=df['probability'], size=10000, replace=True)

If you check the value counts:

pd.Series(arr).value_counts().sort_index()
Out: 
0     855
1     800
2     856
3     825
4     847
5     835
6     790
7     847
8     834
9     850
10    806
11    855
dtype: int64

It is pretty close to a uniform distribution. The problem is with the default number of bins (10) of the histogram. Instead, try this:

bins = np.linspace(-0.5, 10.5, num=12)
pd.Series(arr).plot.hist(bins=bins)

Answer 2

you are using hist which defaults to 10 bins...

plt.rcParams['hist.bins']

10

---

pass group_size as the bins parameter.

plt.hist(
    np.random.choice(df['groups'], p=df['probability'], size=10000, replace=True),
    bins=group_size)