geoml.likelihood

class geoml.likelihood.Gaussian(warping=None, sharpness=1)[source]

Bases: _ContinuousLikelihood

Gaussian likelihood.

Equivalent to a squared error model. The latent variable maps to the mean, while the noise variance is a parameter.

class geoml.likelihood.Laplace(warping=None, sharpness=1)[source]

Bases: _ContinuousLikelihood

Laplace’s likelihood.

Equivalent to a linear error model. The latent variable maps to the mean, while the distribution’s scale factor is a parameter.

class geoml.likelihood.Gamma(warping=None, sharpness=1)[source]

Bases: _ContinuousLikelihood

Gamma likelihood.

Used for strictly positive variables. The latent variable is shifted by a parameter and then mapped to the distribution’s shape. The rate parameter is fixed at 1.0.

class geoml.likelihood.StudentT(warping=None, sharpness=1)[source]

Bases: _ContinuousLikelihood

Student-T likelihood.

A heavy-tailed distribution. The latent variable maps to the mean, while the scale and degrees of freedom are parameters.

class geoml.likelihood.EpsilonInsensitive(warping=None, sharpness=1)[source]

Bases: _ContinuousLikelihood

Epsilon-insensitive likelihood.

Similar to the Laplace likelihood, with an addition epsilon parameter, below which error are not penalized. Can be used to obtain a model similar to the Support Vector Machine.

class geoml.likelihood.Huber(warping=None, sharpness=1)[source]

Bases: _ContinuousLikelihood

Huber’s likelihood.

Based on the Huber loss.

class geoml.likelihood.MultivariateGaussian(n_components, warping=None, sharpness=1)[source]

Bases: Gaussian

class geoml.likelihood.MultivariateLaplace(n_components, warping=None, sharpness=1)[source]

Bases: _ContinuousLikelihood

class geoml.likelihood.MultivariateEpsilonInsensitive(n_components, warping=None, sharpness=1)[source]

Bases: EpsilonInsensitive

class geoml.likelihood.MultivariateHuber(n_components, warping=None, sharpness=1)[source]

Bases: Huber

class geoml.likelihood.Mixture(warping, n_components=2, family='gaussian', separation=3.0, weights=None, contamination=None, sharpness=1)[source]

Bases: _ContinuousLikelihood

A likelihood whose noise is a mixture of scales.

The noise on a measurement comes from one of n_components copies of family, all sharing the latent location and differing in width, with trainable proportions. It fits data whose scatter is not one number – a careful assay and a rushed one, a fresh core and a weathered one – and, unlike a heavy-tailed likelihood, it says which mechanism each measurement came from (responsibilities()).

Parameters:

warping (geoml.warping.Warping) – The mixture’s own warping, applied once to the data. It sizes the mixture, and the components with it.
n_components (int) – How many noise scales, at least two.
family (str) – The distribution every component takes: “gaussian”, “laplace”, “studentt”, “epsiloninsensitive” or “huber”.
separation (float) – How much wider each component is than the one before it, at construction. Only the family’s width parameters move.
weights (array-like, optional) – Initial mixing proportions, one per component, summing to one. Default: 0.95 on the narrowest, the rest split evenly.
contamination (list of bool, optional) – Which components describe error rather than ground. Default: none of them. At least one component must be genuine.
sharpness (int) – Data augmentation factor, as in every likelihood.

components

The noise scales, narrowest first.

Type:: list of _ContinuousLikelihood

contamination

Which of them describe error rather than ground.

Type:: list of bool

Raises:: ValueError – If fewer than two components are asked for, if family is not one of the names above, if the contamination flags do not match the components, or if every component is marked as contamination.

See also

responsibilities: which component each measurement came from.
geoml.warping.ZScore: pair the mixture with robust=True.

Notes

The mixture is over the row. In a vector or compositional variable the columns are one observation, so the densities are multiplied across them before the components are weighted, giving one responsibility per location rather than one per element. The components’ scales stay per column. That density does not factorize, so a vector mixture takes its latent expectation over the joint posterior samples rather than each column’s quadrature.

Contamination is declared, not assumed. By default every component describes the ground and the mixture is a noise model. Marking a component as contamination says its readings replace a measurement rather than report one: integrated_backward() then leaves it out of the value while keeping it in the spread reported beside it. Training and measurement_samples() always use the full mixture.

Components of equal width do not pull apart in training, which is why separation spreads them at construction. Pair the mixture with a warping led by ZScore(size, robust=True), so that a gross outlier cannot set the scale everything else is normalized by.

References

Kuss, M. (2006) Gaussian Process Models for Robust Regression, Classification, and Reinforcement Learning. PhD thesis, TU Darmstadt.

Stegle, O., Fallert, S. V., MacKay, D. J. C. and Brage, S. (2008) Gaussian process robust regression for noisy heart rate data. IEEE Transactions on Biomedical Engineering 55(9), 2143-2151.

Examples

>>> warping = geoml.warping.ChainedWarping(
...     geoml.warping.ZScore(1, robust=True),
...     geoml.warping.Spline(1))
>>> likelihood = geoml.likelihood.Mixture(
...     warping, n_components=2, contamination=[False, True])

responsibilities(latent_mean, latent_variance, values)[source]

Posterior probability that each row came from each component.

One answer per row: the densities are multiplied across the columns before the components are weighted, as the likelihood fits them.

Parameters:

latent_mean (ArrayLike) – The model’s posterior at the measured locations, of shape (n_data,) or (n_data, size), as predict stores them.
latent_variance (ArrayLike) – The model’s posterior at the measured locations, of shape (n_data,) or (n_data, size), as predict stores them.
values (ArrayLike) – The measurements, in their own units, of the same shape.

Returns:

ndarray – Of shape (n_data, n_components), rows summing to one.

Return type:

NDArray[float64]