nemos.basis.RaisedCosineLogConv#

class nemos.basis.RaisedCosineLogConv(n_basis_funcs, window_size, width=2.0, time_scaling=None, enforce_decay_to_zero=True, label='RaisedCosineLogConv', conv_kwargs=None)[source]#

Bases: ConvBasisMixin, RaisedCosineBasisLog

Represent log-spaced raised cosine basis functions.

Similar to RaisedCosineLinearConv but the basis functions are log-spaced. This implementation is based on the cosine bumps used by Pillow et al. [1] to uniformly tile the internal points of the domain.

Parameters:

n_basis_funcs (int) – The number of basis functions.
width (float) – Width of the raised cosine.
time_scaling (float) – Non-negative hyper-parameter controlling the logarithmic stretch magnitude, with larger values resulting in more stretching. As this approaches 0, the transformation becomes linear.
enforce_decay_to_zero (bool) – If set to True, the algorithm first constructs a basis with n_basis_funcs + ceil(width) elements and subsequently trims off the extra basis elements. This ensures that the final basis element decays to 0.
window_size (int) – The window size for convolution. Required if mode is ‘conv’.
label (Optional[str]) – The label of the basis, intended to be descriptive of the task variable being processed. For example: velocity, position, spike_counts.
conv_kwargs (Optional[dict]) – Additional keyword arguments passed to nemos.convolve.create_convolutional_predictor(); These arguments are used to change the default behavior of the convolution. For example, changing the predictor_causality, which by default is set to "causal". Note that one cannot change the default value for the axis parameter. Basis assumes that the convolution axis is axis=0.

References

Examples

>>> import numpy as np
>>> from nemos.basis import RaisedCosineLogConv
>>> n_basis_funcs = 5
>>> raised_cosine_basis = RaisedCosineLogConv(n_basis_funcs, window_size=10)
>>> raised_cosine_basis
RaisedCosineLogConv(n_basis_funcs=5, window_size=10, width=2.0, time_scaling=50.0, enforce_decay_to_zero=True)
>>> sample_points = np.random.randn(100)
>>> # convolve the basis
>>> features = raised_cosine_basis.compute_features(sample_points)

Attributes

`conv_kwargs`	The convolutional kwargs.
`input_shape`	Expected per-sample input shape.
`is_complex`	Whether the basis is intrinsically complex.
`label`	Label for the basis.
`n_basis_funcs`	Number of basis functions.
`n_output_features`	Number of features returned by the basis.
`time_scaling`	Time scaling.
`width`	Return width of the raised cosine.
`window_size`	Duration of the convolutional kernel in number of samples.

__init__(n_basis_funcs, window_size, width=2.0, time_scaling=None, enforce_decay_to_zero=True, label='RaisedCosineLogConv', conv_kwargs=None)[source]#

Parameters:

n_basis_funcs (int)
window_size (int)
width (float)
time_scaling (float)
enforce_decay_to_zero (bool)
label (str | None)
conv_kwargs (dict | None)

Methods

`__init__`(n_basis_funcs, window_size[, ...])
`compute_features`(xi)	Convolve basis functions with input time series.
`evaluate`(sample_pts)	Evaluate the log-spaced raised cosine basis at the sample points.
`evaluate_on_grid`(n_samples)	Evaluate the basis set on a grid of equi-spaced sample points.
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	From scikit-learn, get parameters by inspecting init.
`set_input_shape`(xi)	Set the expected input shape for the basis object.
`set_params`(**params)	Set the parameters of this estimator.
`setup_basis`(*xi)	Set all basis states.
`split_by_feature`(x[, axis])	Decompose an array along a specified axis into sub-arrays based on the number of expected inputs.
`to_transformer`()	Turn the Basis into a TransformerBasis for use with scikit-learn.

__add__(other)#

Add two Basis objects together.

Parameters:: other (BasisMixin) – The other Basis object to add.
Returns:: The resulting Basis object.
Return type:: AdditiveBasis

classmethod __init_subclass__(**kwargs)#

Set the set_{method}_request methods.

This uses PEP-487 [1] to set the set_{method}_request methods. It looks for the information available in the set default values which are set using __metadata_request__* class attributes, or inferred from method signatures.

The __metadata_request__* class attributes are used when a method does not explicitly accept a metadata through its arguments or if the developer would like to specify a request value for those metadata which are different from the default None.

References

__iter__()#: Make basis iterable. Re-implemented for additive.

__len__()#: Return the number of additive basis.

__mul__(other)#

Multiply two Basis objects together.

Parameters:: other (BasisMixin | int) – The other Basis object to multiply.
Return type:: Basis
Returns:: The resulting Basis object.

__pow__(exponent)#

Exponentiation of a Basis object.

Define the power of a basis by repeatedly applying the method __multiply__. The exponent must be a positive integer.

Parameters:

exponent (int) – Positive integer exponent

Return type:

BasisMixin

Returns:

The product of the basis with itself “exponent” times. Equivalent to self * self * ... * self.

Raises:

TypeError – If the provided exponent is not an integer.
ValueError – If the integer is zero or negative.

__rmul__(other)#

Right multiplication operator for basis.

Parameters:: other (BasisMixin | int)

__sklearn_clone__()#

Clone the basis while preserving attributes related to input shapes.

This method ensures that input shape attributes (e.g., _input_shape_product, _input_shape_) are preserved during cloning. Reinitializing the class as in the regular sklearn clone would drop these attributes, rendering cross-validation unusable.

Return type:: Basis

compute_features(xi)[source]#

Convolve basis functions with input time series.

A bank of basis filters is convolved with the input data. All the dimensions except for the sample-axis are flattened, so that the method always returns a matrix.

For example, if inputs are of shape (num_samples, 2, 3), the output will be (num_samples, num_basis_funcs * 2 * 3).

Parameters:: *xi (ArrayLike) – The input data over which to apply the basis transformation. The samples can be passed as multiple arguments, each representing a different dimension for multivariate inputs.
Return type:: TsdFrame | ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]

Notes

This method is intended to be 1-to-1 mappable to sklearn transform method of transformer. This means that for the method to be callable, all the state attributes have to be pre-computed in a method that is mappable to fit, which for us is _fit_basis. It is fundamental that both methods behaves like the corresponding transformer method, with the only difference being the input structure: a single (X, y) pair for the transformer, a number of time series for the Basis.

Examples

>>> import numpy as np
>>> from nemos.basis import RaisedCosineLogConv

>>> # Generate data
>>> num_samples = 1000
>>> X = np.random.normal(size=(num_samples, ))  # raw time series
>>> basis = RaisedCosineLogConv(10, window_size=100)
>>> features = basis.compute_features(X)  # basis transformed time series
>>> features.shape
(1000, 10)

property conv_kwargs#

The convolutional kwargs.

Keyword arguments passed to nemos.convolve.create_convolutional_predictor().

evaluate(sample_pts)[source]#

Evaluate the log-spaced raised cosine basis at the sample points.

Parameters:: sample_pts (NDArray) – Spacing for basis functions. Samples will be rescaled to the interval [0, 1]. sample_pts is a n-dimensional (n >= 1) array with first axis being the samples, i.e. sample_pts.shape[0] == n_samples.
Returns:: Log-raised cosine basis functions, shape (n_samples, n_basis_funcs).
Return type:: basis_funcs
Raises:: ValueError – If the sample provided do not lie in [0,1].

Examples

>>> import numpy as np
>>> from nemos.basis import RaisedCosineLogConv
>>> raised_cos = RaisedCosineLogConv(n_basis_funcs=4, window_size=20)
>>> out = raised_cos.evaluate(np.random.randn(100, 5, 2))
>>> out.shape
(100, 5, 2, 4)

evaluate_on_grid(n_samples)[source]#

Evaluate the basis set on a grid of equi-spaced sample points.

Parameters:

n_samples (int) – The number of points in the uniformly spaced grid. A higher number of samples will result in a more detailed visualization of the basis functions.

Return type:

Tuple[NDArray, NDArray]

Returns:

X – Array of shape (n_samples,) containing the equi-spaced sample points where we’ve evaluated the basis.
basis_funcs – Raised cosine basis functions, shape (n_samples, n_basis_funcs)

Examples

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from nemos.basis import RaisedCosineLogConv
>>> n_basis_funcs = 5
>>> decay_rates = np.array([0.01, 0.02, 0.03, 0.04, 0.05]) # sample decay rates
>>> window_size=10
>>> ortho_basis = RaisedCosineLogConv(n_basis_funcs, window_size)
>>> sample_points, basis_values = ortho_basis.evaluate_on_grid(100)
>>> plt.plot(sample_points, basis_values)
[<matplotlib.lines.Line2D object at ...
>>> plt.show()

(Source code)

../../_images/nemos-basis-RaisedCosineLogConv-1.png — Fig. 15 Log Spaced Raised-Cosine#

get_metadata_routing()#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:: routing – A MetadataRequest encapsulating routing information.
Return type:: MetadataRequest

get_params(deep=True)#

From scikit-learn, get parameters by inspecting init.

Parameters:: deep – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Return type:: dict
Returns:: A dictionary containing the parameters. Key is the parameter name, value is the parameter value.

property input_shape#

Expected per-sample input shape.

Returns:: If inputs are shaped (n_samples, *shape), returns shape.

property is_complex#

Whether the basis is intrinsically complex.

Returns:: True if the basis is complex; False otherwise.

Notes

compute_features() always returns a real-valued design matrix. For complex bases (e.g., FourierEval), the real and imaginary parts are returned as separate columns.

property label: str#: Label for the basis.

property n_basis_funcs#: Number of basis functions.

property n_output_features: int | None#

Number of features returned by the basis.

Notes

The number of output features can be determined only when the number of inputs provided to the basis is known. Therefore, before the first call to compute_features, this property will return None. After that call, or after setting the input shape with set_input_shape, n_output_features will be available.

set_input_shape(xi)[source]#

Set the expected input shape for the basis object.

This method configures the shape of the input data that the basis object expects. xi can be specified as an integer, a tuple of integers, or derived from an array. The method also calculates the total number of input features and output features based on the number of basis functions.

Parameters:

xi (Union[int, tuple[int, ...], NDArray]) –

The input shape specification. - An integer: Represents the dimensionality of the input. A value of 1 is treated as scalar input. - A tuple: Represents the exact input shape excluding the first axis (sample axis).

All elements must be integers.

An array: The shape is extracted, excluding the first axis (assumed to be the sample axis).

Raises:

ValueError – If a tuple is provided and it contains non-integer elements.

Returns:

Returns the instance itself to allow method chaining.

Return type:

self

Notes

All state attributes that depends on the input must be set in this method in order for the API of basis to work correctly. In particular, this method is called by setup_basis, which is equivalent to fit for a transformer. If any input dependent state is not set in this method, then compute_features (equivalent to fit_transform) will break.

Examples

>>> import nemos as nmo
>>> import numpy as np
>>> basis = nmo.basis.RaisedCosineLogConv(5, 10)
>>> # Configure with an integer input:
>>> _ = basis.set_input_shape(3)
>>> basis.n_output_features
15
>>> # Configure with a tuple:
>>> _ = basis.set_input_shape((4, 5))
>>> basis.n_output_features
100
>>> # Configure with an array:
>>> x = np.ones((10, 4, 5))
>>> _ = basis.set_input_shape(x)
>>> basis.n_output_features
100

set_params(**params)#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance

setup_basis(*xi)#

Set all basis states.

This method corresponds sklearn transformer fit. As fit, it must receive the input and it must set all basis states, i.e. kernel_ and all the states relative to the input shape. The difference between this method and the transformer fit is in the expected input structure, where the transformer fit method requires the inputs to be concatenated in a 2D array, while here each input is provided as a separate time series for each basis element.

Parameters:: xi (NDArray) – Input arrays.
Return type:: Basis
Returns:: The basis with ready for evaluation.

split_by_feature(x, axis=1)[source]#

Decompose an array along a specified axis into sub-arrays based on the number of expected inputs.

This function takes an array (e.g., a design matrix or model coefficients) and splits it along a designated axis.

How it works:

If the basis expects an input shape (n_samples, n_inputs), then the feature axis length will be total_n_features = n_inputs * n_basis_funcs. This axis is reshaped into dimensions (n_inputs, n_basis_funcs).
If the basis expects an input of shape (n_samples,), then the feature axis length will be total_n_features = n_basis_funcs. This axis is reshaped into (1, n_basis_funcs).

For example, if the input array x has shape (1, 2, total_n_features, 4, 5), then after applying this method, it will be reshaped into (1, 2, n_inputs, n_basis_funcs, 4, 5).

The specified axis (axis) determines where the split occurs, and all other dimensions remain unchanged. See the example section below for the most common use cases.

Parameters:

x (NDArray) –
The input array to be split, representing concatenated features, coefficients, or other data. The shape of x along the specified axis must match the total number of features generated by the basis, i.e., self.n_output_features.

Examples:
- For a design matrix: (n_samples, total_n_features)
- For model coefficients: (total_n_features,) or (total_n_features, n_neurons).
axis (int, optional) – The axis along which to split the features. Defaults to 1. Use axis=1 for design matrices (features along columns) and axis=0 for coefficient arrays (features along rows). All other dimensions are preserved.

Raises:

ValueError – If the shape of x along the specified axis does not match self.n_output_features.

Returns:

A dictionary where:

Key: Label of the basis.
Value: the array reshaped to: (..., n_inputs, n_basis_funcs, ...)

Return type:

dict

Examples

>>> import numpy as np
>>> from nemos.basis import RaisedCosineLogConv
>>> from nemos.glm import GLM
>>> basis = RaisedCosineLogConv(n_basis_funcs=6, window_size=10, label="two_inputs")
>>> X_multi = basis.compute_features(np.random.randn(20, 2))
>>> split_features_multi = basis.split_by_feature(X_multi, axis=1)
>>> for feature, sub_dict in split_features_multi.items():
...        print(f"{feature}, shape {sub_dict.shape}")
two_inputs, shape (20, 2, 6)

property time_scaling#

Time scaling.

Time scaling parameter regulating the logarithmic stretch of the basis.

to_transformer()#

Turn the Basis into a TransformerBasis for use with scikit-learn.

Return type:: TransformerBasis

Examples

Jointly cross-validating basis and GLM parameters with scikit-learn.

>>> import nemos as nmo
>>> from sklearn.pipeline import Pipeline
>>> from sklearn.model_selection import GridSearchCV
>>> # load some data
>>> X, y = np.random.normal(size=(30, 1)), np.random.poisson(size=30)
>>> basis = nmo.basis.RaisedCosineLinearEval(10).set_input_shape(1).to_transformer()
>>> glm = nmo.glm.GLM(regularizer="Ridge", regularizer_strength=1.)
>>> pipeline = Pipeline([("basis", basis), ("glm", glm)])
>>> param_grid = dict(
...     glm__regularizer_strength=(0.1, 0.01, 0.001, 1e-6),
...     basis__n_basis_funcs=(3, 5, 10, 20, 100),
... )
>>> gridsearch = GridSearchCV(
...     pipeline,
...     param_grid=param_grid,
...     cv=5,
... )
>>> gridsearch = gridsearch.fit(X, y)

property width#: Return width of the raised cosine.

property window_size#: Duration of the convolutional kernel in number of samples.

nemos.basis.RaisedCosineLogConv#

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