spectrochempy.LSTSQ

class LSTSQ(*, log_level='WARNING', warm_start=False, fit_intercept=True, positive=False)[source][source]

Ordinary least squares Linear Regression (LSTSQ).

Use sklearn.linear_model.LinearRegression

LinearRegression fits a linear model with coefficients w = (w1, ..., wp) to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.

Parameters:

log_level (any of ["INFO", "DEBUG", "WARNING", "ERROR"], optional, default: "WARNING") – The log level at startup. It can be changed later on using the set_log_level method or by changing the log_level attribute.
warm_start (bool, optional, default: False) – When fitting repeatedly on the same dataset, but for multiple parameter values (such as to find the value maximizing performance), it may be possible to reuse previous model learned from the previous parameter value, saving time.

When warm_start is True, the existing fitted model attributes is used to initialize the new model in a subsequent call to fit.
fit_intercept (bool, optional, default: True) – Whether to calculate the intercept for this model. If set to False, no intercept will be used in calculations (i.e., data is expected to be centered).
positive (bool, optional, default: False) – When set to True , forces the coefficients (coef) to be positive.

See also

NNLS: Non-Negative least squares Linear Regression.

Initialize the BaseConfigurable class.

Parameters:

log_level (int, optional) – The log level at startup. Default is logging.WARNING.
**kwargs (dict) – Additional keyword arguments for configuration.

Attributes Summary

`X`	Return the X input dataset (eventually modified by the model).
`Y`	Return the `Y` input dataset.
`coef`	Estimated coefficients for the linear regression problem.
`config`	`traitlets.config.Config` object.
`description`
`fit_intercept`	Whether to calculate the `intercept` for this model.
`intercept`	Return a float or an array of shape (n_targets,).
`log`	Return `log` output.
`name`
`positive`	When set to `True` , forces the coefficients (`coef`) to be positive.

Methods Summary

`fit`(X[, Y, sample_weight])	Fit linear model.
`parameters`([replace, removed, default])	Alias for `params` method.
`params`([default])	Return current or default configuration values.
`predict`([X])	Predict features using the linear model.
`reset`()	Reset configuration parameters to their default values.
`score`([X, Y, sample_weight])	Return the coefficient of determination of the prediction.
`to_dict`()	Return config value in a dict form.

Attributes Documentation

X: Return the X input dataset (eventually modified by the model).

Y: Return the Y input dataset.

coef

Estimated coefficients for the linear regression problem.

If multiple targets are passed during the fit (Y 2D), this is a 2D array of shape (n_targets, n_features), while if only one target is passed, this is a 1D array of length n_features.

config: traitlets.config.Config object.

description = 'Ordinary Least Squares Linear Regression'

fit_intercept: Whether to calculate the intercept for this model. If set to False, no intercept will be used in calculations (i.e., data is expected to be centered).

intercept

Return a float or an array of shape (n_targets,).

Independent term in the linear model. Set to 0.0 if fit_intercept is False. If Y has units, then intercept has the same units.

log: Return log output.

name = 'LSTSQ'

positive: When set to True , forces the coefficients (coef) to be positive.

Methods Documentation

fit(X, Y=None, sample_weight=None)[source]

Fit linear model.

Parameters:

X (NDDataset or array-like of shape (n_observations,:term:n_features)) – Training data, where n_observations is the number of observations and n_features is the number of features.
Y (array-like of shape (n_observations,) or (n_observations,:term:n_targets)) – Target values. Will be cast to X’s dtype if necessary.
sample_weight (array-like of shape (n_observations,), default: None) – Individual weights for each observation.

Returns:

self – Returns the instance itself.

parameters(replace="params", removed="0.7.1") def parameters(self, default=False)[source]: Alias for params method.

params(default=False)[source]

Return current or default configuration values.

Parameters:: default (bool, optional, default: False) – If default is True, the default parameters are returned, else the current values.
Returns:: dict – Current or default configuration values.

predict(X=None)[source]

Predict features using the linear model.

Parameters:: X (NDDataset or array-like matrix, shape (n_observations,:term:n_features)) – Observations. If X is not set, the input X for fit is used.
Returns:: NDDataset – Predicted values (object of type of the input) using a ahape (n_observations,).

reset()[source]: Reset configuration parameters to their default values.

score(X=None, Y=None, sample_weight=None)[source]

Return the coefficient of determination of the prediction.

The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\) , where \(u\) is the residual sum of squares ((y_true - y_pred)** 2).sum() and \(v\) is the total sum of squares ((y_true - y_true.mean()) ** 2).sum() . The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of Y, disregarding the input features, would get a \(R^2\) score of 0.0.

Parameters:

X (NDDataset or array-like of shape (n_observations, n_features)) – Test samples.
Y (NDDataset or array-like of shape (n_observations,)) – True values for X.
sample_weight (array-like of shape (n_observations,), default: None) – Sample weights.

Returns:

float – \(R^2\) of predict (X ) wrt. Y .

to_dict()[source]

Return config value in a dict form.

Returns:: dict – A regular dictionary.

Examples using spectrochempy.LSTSQ

Solve a linear equation using LSTSQ