def sample_trivariate_xyz(size=1000, seed=42):
"""Sample from three dimensional toy dataset.
The output is a DataFrame containing three columns:
* ``x``: Beta distribution with a=0.1 and b=0.1
* ``y``: Beta distribution with a=0.1 and b=0.5
* ``z``: Normal distribution + 10 times ``y``
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.DataFrame:
DataFrame with three columns, ``x``, ``y`` and ``z``.
"""
with random_seed(seed):
x = stats.beta.rvs(a=0.1, b=0.1, size=size)
y = stats.beta.rvs(a=0.1, b=0.5, size=size)
return pd.DataFrame({
'x': x,
'y': y,
'z': np.random.normal(size=size) + y * 10
})
def sample_bivariate_age_income(size=1000, seed=42):
"""Sample from a bivariate toy dataset.
This dataset contains two columns which correspond to the simulated age and
income which are positively correlated with outliers.
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.DataFrame:
DataFrame with two columns, ``age`` and ``income``.
"""
with random_seed(seed):
age = stats.beta.rvs(a=2.0, b=6.0, loc=18, scale=100, size=size)
income = np.log(age) * 100
income += np.random.normal(loc=np.log(age) / 100, scale=10, size=size)
income[np.random.randint(0, 10, size=size) == 0] /= 1000
return pd.DataFrame({
"age": age,
"income": income
})
def sample_univariate_beta(size=1000, seed=42):
"""Sample from a beta distribution with a=3 and b=1 and loc=4.
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.Series:
Series with the sampled values.
"""
with random_seed(seed):
return pd.Series(stats.beta.rvs(a=3, b=1, loc=4, size=size))
def sample_univariate_degenerate(size=1000, seed=42):
"""Sample from a degenerate distribution that only takes one random value.
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.Series:
Series with the sampled values.
"""
with random_seed(seed):
return pd.Series(np.full(size, np.random.random()))
def sample_univariate_exponential(size=1000, seed=42):
"""Sample from an exponential distribution at 3.0 with rate 1.0.
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.Series:
Series with the sampled values.
"""
with random_seed(seed):
return pd.Series(np.random.exponential(size=size) + 3.0)
def sample_univariate_normal(size=1000, seed=42):
"""Sample from a normal distribution with mean 1 and stdev 1.
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.Series:
Series with the sampled values.
"""
with random_seed(seed):
return pd.Series(np.random.normal(size=size, loc=1.0))
def sample_univariate_uniform(size=1000, seed=42):
"""Sample from a uniform distribution in [-1.0, 3.0].
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.Series:
Series with the sampled values.
"""
with random_seed(seed):
return pd.Series(4.0 * np.random.random(size=size) - 1.0)
def load_age_income(seed=42):
"""
This dataset contains two columns which correspond to the simulated age and
income which are positively correlated with outliers.
"""
N = 500
with random_seed(seed):
age = stats.beta.rvs(a=2.0, b=6.0, loc=18, scale=100, size=N)
income = np.log(age) * 100
income += np.random.normal(loc=np.log(age) / 100, scale=10, size=N)
income[np.random.randint(0, 10, size=N) == 0] /= 1000
return pd.DataFrame({
"age": age,
"income": income
})
def sample_univariate_bernoulli(size=1000, seed=42):
"""Sample from a Bernoulli distribution with p=0.3.
The distribution is built by sampling a uniform random and then setting
0 or 1 depending on whether the value is above or below 0.3.
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.Series:
Series with the sampled values.
"""
with random_seed(seed):
return pd.Series(np.random.random(size=size) < 0.3).astype(float)
def load_three_dimensional(seed=42):
"""
This dataset contains 6 columns, each of which corresponds to a different
univariate distribution:
bernoulli - a Bernoulli distribution with p=0.3
bimodal - a mixture of two Gaussians at 0.0 and 10.0 with stdev=1
uniform - a uniform distribution in [-1.0, 3.0]
normal - a normal distribution at 1.0 with stdev=1
constant - a constant value
exponential - an exponential distribution at 3.0 with rate 1.0
"""
data = np.zeros((1000, 3))
with random_seed(seed):
data[:, 0] = stats.beta.rvs(a=0.1, b=0.1, size=data.shape[0])
data[:, 1] = stats.beta.rvs(a=0.1, b=0.5, size=data.shape[0])
data[:, 2] = np.random.normal(size=data.shape[0]) + data[:, 1] * 10
return pd.DataFrame(data, columns=["x", "y", "z"])
def sample_univariate_bimodal(size=1000, seed=42):
"""Sample from a bimodal distribution which mixes two Gaussians at 0.0 and 10.0 with stdev=1.
The distribution is built by sampling a standard normal and a normal with mean ``10``
and then selecting one or the other based on a bernoulli distribution.
Args:
size (int):
Amount of samples to generate. Defaults to 1000.
seed (int):
Random seed to use. Defaults to 42.
Retruns:
pandas.Series:
Series with the sampled values.
"""
with random_seed(seed):
bernoulli = sample_univariate_bernoulli(size, seed)
mode1 = np.random.normal(size=size) * bernoulli
mode2 = np.random.normal(size=size, loc=10) * (1.0 - bernoulli)
return pd.Series(mode1 + mode2)
def load_diverse_univariates(seed=42):
"""
This dataset contains 6 columns, each of which corresponds to a different
univariate distribution:
bernoulli - a Bernoulli distribution with p=0.3
bimodal - a mixture of two Gaussians at 0.0 and 10.0 with stdev=1
uniform - a uniform distribution in [-1.0, 3.0]
normal - a normal distribution at 1.0 with stdev=1
constant - a constant value
exponential - an exponential distribution at 3.0 with rate 1.0
"""
size = 1000
df = pd.DataFrame()
with random_seed(seed):
df["bernoulli"] = (np.random.random(size=size) < 0.3).astype(float)
df["bimodal"] = np.random.normal(size=size) * df["bernoulli"] + \
np.random.normal(size=size, loc=10) * (1.0 - df["bernoulli"])
df["uniform"] = 4.0 * np.random.random(size=size) - 1.0
df["normal"] = np.random.normal(size=size, loc=1.0)
df["constant"] = np.random.random() # a single random number
df["exponential"] = np.random.exponential(size=size) + 3.0
return df