cma.sampler.GaussDiagonalSampler

class documentation

class GaussDiagonalSampler(GaussSampler):

Multi-variate normal distribution with zero mean and diagonal covariance matrix.

Provides methods to sample from and update a multi-variate normal distribution with zero mean and diagonal covariance matrix.

Arguments to `init`

standard_deviations (required) define the diagonal of the initial covariance matrix, and consequently also the dimensionality (attribute dim) of the normal distribution. If standard_deviations is an int, np.ones(standard_deviations) is used.

constant_trace='None': 'arithmetic' or 'geometric' or 'aeigen' or 'geigen' (geometric mean of eigenvalues) are available to be constant.

randn=np.random.randn is used to generate N(0,1) numbers.

>>> import cma, numpy as np
>>> s = cma.sampler.GaussDiagonalSampler(np.ones(4))
>>> z = s.sample(1)[0]
>>> assert s.norm([1,0,0,0]) == 1
>>> s.update([[1., 0., 0., 0]], [.9])
>>> assert s.norm([1,0,0,0]) == 1
>>> s.update([[4., 0., 0.,0]], [.5])
>>> g *= 2

TODO

o DONE implement CMA_diagonal with samplers

o Clean up CMAEvolutionStrategy attributes related to sampling (like usage of B, C, D, dC, sigma_vec, these are pretty substantial changes). In particular this should become compatible with any StatisticalModelSampler. Plan: keep B, C, D, dC for the time being as output-info attributes, keep sigma_vec (55 appearances) either as constant scaling or as a class. Current favorite: make a class (DONE) .

o combination of sigma_vec and C:

update sigma_vec with y (this is wrong: use "z")
rescale y according to the inverse update of sigma_vec (as if y is expressed in the new sigma_vec while C in the old)
update C with the "new" y.

Method	`__imul__`	`sm *= factor` is a shortcut for `sm = sm.__imul__(factor)`.
Method	`__init__`	declarative init, doesn't need to be executed
Method	`correlation`	return correlation between variables i and j.
Method	`multiply_C`	multiply `self.C` with `factor` updating internal states.
Method	`norm`	compute the Mahalanobis norm that is induced by the statistical model / sample distribution, specifically by covariance matrix `C`. The expected Mahalanobis norm is about `sqrt(dimension)`.
Method	`reset`	reset distribution while keeping all other parameters
Method	`sample`	return list of i.i.d. samples.
Method	`to_correlation_matrix`	"re-scale" C to a correlation matrix and return the scaling factors as standard deviations.
Method	`to_linear_transformation`	return associated linear transformation.
Method	`to_linear_transformation_inverse`	return associated inverse linear transformation.
Method	`transform`	apply linear transformation `C**0.5` to `x`.
Method	`transform_inverse`	apply inverse linear transformation `C**-0.5` to `x`.
Method	`update`	update/learn by natural gradient ascent.
Instance Variable	`C`	covariance matrix diagonal
Instance Variable	`constant_trace`	Undocumented
Instance Variable	`count_tell`	Undocumented
Instance Variable	`dimension`	Undocumented
Instance Variable	`quadratic`	Undocumented
Instance Variable	`randn`	Undocumented
Property	`condition_number`	Undocumented
Property	`correlation_matrix`	return correlation matrix of the distribution.
Property	`covariance_matrix`	Undocumented
Property	`variances`	vector of coordinate-wise (marginal) variances

Inherited from GaussSampler:

Method	`set_H`	set Hessian w.r.t. which to compute the eigen spectrum.
Method	`set_H_by_f`	set Hessian from f at x0.
Property	`chin`	approximation of the expected length when isotropic with variance 1.
Property	`corr_condition`	condition number of the correlation matrix
Property	`eigenspectrum`	return eigen spectrum w.r.t. H like sqrt(H) C sqrt(H)
Instance Variable	`_left`	Undocumented
Instance Variable	`_right`	Undocumented

Inherited from StatisticalModelSamplerWithZeroMeanBaseClass (via GaussSampler):

Method	`inverse_hessian_scalar_correction`	return scalar correction `alpha` such that `X` and `f` fit to `f(x) = (x-mean) (alpha * C)**-1 (x-mean)`
Method	`parameters`	return `dict` with (default) parameters, e.g., `c1` and `cmu`.
Instance Variable	`_lam`	Undocumented
Instance Variable	`_mueff`	Undocumented
Instance Variable	`_parameters`	Undocumented

def __imul__(self, factor): ¶

overrides cma.interfaces.StatisticalModelSamplerWithZeroMeanBaseClass.__imul__

sm *= factor is a shortcut for sm = sm.__imul__(factor).

Multiplies the covariance matrix with factor.

def __init__(self, dimension, constant_trace='None', randn=np.random.randn, quadratic=False, **kwargs): ¶

overrides cma.sampler.GaussSampler.__init__

declarative init, doesn't need to be executed

def correlation(self, i, j): ¶

return correlation between variables i and j.

def multiply_C(self, factor): ¶

multiply self.C with factor updating internal states.

factor can be a scalar, a vector or a matrix. The vector is used as outer product, i.e. multiply_C(diag(C)**-0.5) generates a correlation matrix.

def norm(self, x): ¶

overrides cma.interfaces.StatisticalModelSamplerWithZeroMeanBaseClass.norm

compute the Mahalanobis norm that is induced by the statistical model / sample distribution, specifically by covariance matrix C. The expected Mahalanobis norm is about sqrt(dimension).

Example

>>> import cma, numpy as np
>>> sm = cma.sampler.GaussFullSampler(np.ones(10))
>>> x = np.random.randn(10)
>>> d = sm.norm(x)

d is the norm "in" the true sample distribution, sampled points have a typical distance of sqrt(2*sm.dim), where sm.dim is the dimension, and an expected distance of close to dim**0.5 to the sample mean zero. In the example, d is the Euclidean distance, because C = I.

def reset(self): ¶

reset distribution while keeping all other parameters

def sample(self, number, same_length=False): ¶

overrides cma.interfaces.StatisticalModelSamplerWithZeroMeanBaseClass.sample

return list of i.i.d. samples.

Parameters
number	is the number of samples.
same_length	Undocumented
update	controls a possibly lazy update of the sampler.

def to_correlation_matrix(self): ¶

"re-scale" C to a correlation matrix and return the scaling factors as standard deviations.

cma.sampler.GaussDiagonalSampler

Arguments to __init__

TODO

Example

`cma.sampler.GaussDiagonalSampler`

Arguments to `init`