Gaussian (Normal)

Data Type: float

The Gaussian distribution is a symmetric bell-shaped distribution on the real line. The probability density function is given by

\[f\left(x | \mu, \sigma^2 \right) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}, \; x \in \mathbb{R}.\]

For more info see Gaussian Distribution.

GaussianDistribution

class dml.stats.gaussian.GaussianDistribution(mu, sigma2, name=None, keys=None)

Gaussian distribution with mean mu and variance sigma2.

mu

Mean of the Gaussian distribution.

Type:: float

sigma2

Variance of the Gaussian distribution.

Type:: float

name

Name of the object.

Type:: Optional[str]

const

Normalizing constant of the Gaussian (depends on sigma2).

Type:: float

log_const

Log of the normalizing constant.

Type:: float

keys

Key for the distribution.

Type:: Optional[str]

__init__(mu, sigma2, name=None, keys=None)

Initialize GaussianDistribution.

Parameters:

mu (float) – Mean of the Gaussian distribution.
sigma2 (float) – Variance of the Gaussian distribution (must be positive).
name (Optional[str], optional) – Name for the object.
keys (Optional[str], optional) – Key for the distribution.

density(x)

Evaluate the density of the Gaussian distribution at x.

Parameters:: x (float) – Observation.
Returns:: Density at x.
Return type:: float

dist_to_encoder()

Return a GaussianDataEncoder for this distribution.

Returns:: Encoder object.
Return type:: GaussianDataEncoder

estimator(pseudo_count=None)

Return a GaussianEstimator for this distribution.

Parameters:: pseudo_count (Optional[float], optional) – Pseudo-count for regularization.
Returns:: Estimator object.
Return type:: GaussianEstimator

log_density(x)

Evaluate the log-density of the Gaussian distribution at x.

Parameters:: x (float) – Observation.
Returns:: Log-density at x.
Return type:: float

sampler(seed=None)

Return a GaussianSampler for this distribution.

Parameters:: seed (Optional[int], optional) – Seed for random number generator.
Returns:: Sampler object.
Return type:: GaussianSampler

seq_ld_lambda()

Return a list containing the seq_log_density method.

Return type:: List[Callable]

seq_log_density(x)

Vectorized log-density for encoded data.

Parameters:: x (GaussianEncodedDataSequence) – Encoded data sequence.
Returns:: Log-density values.
Return type:: np.ndarray

GaussianEstimator

class dml.stats.gaussian.GaussianEstimator(pseudo_count=(None, None), suff_stat=(None, None), name=None, keys=None)

Estimator for the Gaussian distribution from aggregated sufficient statistics.

pseudo_count

Weights for sufficient statistics.

Type:: Tuple[Optional[float], Optional[float]]

suff_stat

Tuple of mean (mu) and variance (sigma2).

Type:: Tuple[Optional[float], Optional[float]]

name

Name of the estimator.

Type:: Optional[str]

keys

Key for mean and variance.

Type:: Optional[str]

__init__(pseudo_count=(None, None), suff_stat=(None, None), name=None, keys=None)

Initialize GaussianEstimator.

Parameters:

pseudo_count (Tuple[Optional[float], Optional[float]]) – Tuple of two positive floats.
suff_stat (Tuple[Optional[float], Optional[float]]) – Tuple of mean and variance.
name (Optional[str], optional) – Name for the estimator.
keys (Optional[str], optional) – Key for mean and variance.

Raises:

TypeError – If keys is not a string or None.

accumulator_factory()

Return a GaussianAccumulatorFactory for this estimator.

Returns:: Factory object.
Return type:: GaussianAccumulatorFactory

estimate(nobs, suff_stat)

Estimate a GaussianDistribution from sufficient statistics.

Parameters:

nobs (Optional[float]) – Number of observations (not used).
suff_stat (Tuple[float, float, float, float]) – (sum, sum2, count, count2) sufficient statistics.

Returns:

Estimated distribution.

Return type:

GaussianDistribution

GaussianSampler

class dml.stats.gaussian.GaussianSampler(dist, seed=None)

Sampler for drawing samples from a GaussianDistribution instance.

dist

GaussianDistribution instance to sample from.

Type:: GaussianDistribution

rng

Random number generator.

Type:: RandomState

sample(size=None)

Draw iid samples from the Gaussian distribution.

Parameters:: size (Optional[int], optional) – Number of samples to draw. If None, returns a single sample.
Returns:: Single sample or array of samples.
Return type:: Union[float, np.ndarray]