fdars.regression¶

Regression and dimensionality reduction for functional data: FPCA, FPLS, scalar-on-function, function-on-scalar, ANOVA, and logistic regression.

Functions¶

Function	Description
`fpca`	Functional principal component analysis
`fpls`	Functional partial least squares
`fregre_lm`	Scalar-on-function linear regression
`fregre_pls`	Scalar-on-function PLS regression
`fregre_np`	Nonparametric kernel regression
`fregre_l1`	L1 (robust) regression
`fregre_huber`	Huber M-estimation regression
`functional_logistic`	Functional logistic regression
`fosr`	Function-on-scalar regression
`fanova`	Functional ANOVA
`model_selection_ncomp`	Cross-validated component selection

`fpca`¶

fdars.fpca(data, argvals, n_comp=3)

Functional principal component analysis with integration-weighted covariance.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional data
`argvals`	`ndarray (m,)`		Evaluation points
`n_comp`	`int`	`3`	Number of principal components

Returns	Type	Description
result	`dict`	Keys: `scores` (n, n_comp), `rotation` (m, n_comp), `singular_values` (n_comp,), `mean` (m,), `centered` (n, m), `weights` (m,)

t = np.linspace(0, 1, 100)
pca = fdars.fpca(data, t, n_comp=5)
scores = pca["scores"]  # project new data via these loadings

`fpls`¶

fdars.fpls(data, argvals, response, n_comp=3)

Functional partial least squares. Finds directions that maximize covariance between functional predictors and scalar response.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional predictors
`argvals`	`ndarray (m,)`		Evaluation points
`response`	`ndarray (n,)`		Scalar response
`n_comp`	`int`	`3`	Number of PLS components

Returns	Type	Description
result	`dict`	Keys: `scores` (n, n_comp), `loadings` (m, n_comp), `weights` (m, n_comp), `x_means` (m,), `integration_weights` (m,)

pls = fdars.fpls(data, t, y, n_comp=3)

`fregre_lm`¶

fdars.fregre_lm(data, response, n_comp=3)

Scalar-on-function linear regression via FPC scores. Projects data onto FPCs, then fits OLS.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional predictors
`response`	`ndarray (n,)`		Scalar response
`n_comp`	`int`	`3`	Number of FPC components

Returns	Type	Description
result	`dict`	Keys: `fitted_values` (n,), `residuals` (n,), `beta_t` (m,), `r_squared`, `coefficients` (n_comp,), `intercept`

fit = fdars.fregre_lm(data, y, n_comp=5)
print(f"R-squared: {fit['r_squared']:.3f}")

`fregre_pls`¶

fdars.fregre_pls(data, argvals, response, n_comp=3)

Scalar-on-function regression via PLS components.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional predictors
`argvals`	`ndarray (m,)`		Evaluation points
`response`	`ndarray (n,)`		Scalar response
`n_comp`	`int`	`3`	Number of PLS components

Returns	Type	Description
result	`dict`	Keys: `fitted_values` (n,), `residuals` (n,), `beta_t` (m,), `r_squared`

fit = fdars.fregre_pls(data, t, y, n_comp=3)

`fregre_np`¶

fdars.fregre_np(dist_matrix, response, h=0.0)

Nonparametric kernel regression from a precomputed distance matrix.

Parameter	Type	Default	Description
`dist_matrix`	`ndarray (n, n)`		Pairwise distance matrix
`response`	`ndarray (n,)`		Scalar response
`h`	`float`	`0.0`	Bandwidth; `0.0` for automatic selection

Returns	Type	Description
result	`dict`	Keys: `fitted_values` (n,), `residuals` (n,), `h_func`, `r_squared`

D = fdars.lp_self_1d(data, t)
fit = fdars.fregre_np(D, y)
print(f"Selected bandwidth: {fit['h_func']:.3f}")

`fregre_l1`¶

fdars.fregre_l1(data, response, n_comp=3)

L1 (least absolute deviations) robust regression for functional data via FPCs.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional predictors
`response`	`ndarray (n,)`		Scalar response
`n_comp`	`int`	`3`	Number of FPC components

Returns	Type	Description
result	`dict`	Keys: `fitted_values` (n,), `residuals` (n,), `beta_t` (m,)

fit = fdars.fregre_l1(data, y, n_comp=3)

`fregre_huber`¶

fdars.fregre_huber(data, response, n_comp=3, huber_k=1.345)

Huber M-estimation robust regression for functional data.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional predictors
`response`	`ndarray (n,)`		Scalar response
`n_comp`	`int`	`3`	Number of FPC components
`huber_k`	`float`	`1.345`	Huber tuning constant

Returns	Type	Description
result	`dict`	Keys: `fitted_values` (n,), `residuals` (n,), `beta_t` (m,)

fit = fdars.fregre_huber(data, y, n_comp=3, huber_k=1.345)

`functional_logistic`¶

fdars.functional_logistic(data, labels, n_comp=3, max_iter=25, tol=1e-6)

Functional logistic regression for binary classification via IRLS.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional predictors
`labels`	`ndarray (n,)` of `float64`		Binary labels (0.0/1.0)
`n_comp`	`int`	`3`	Number of FPC components
`max_iter`	`int`	`25`	Maximum IRLS iterations
`tol`	`float`	`1e-6`	Convergence tolerance

Returns	Type	Description
result	`dict`	Keys: `probabilities` (n,), `predicted_classes` (n,), `beta_t` (m,), `intercept`, `coefficients` (n_comp,)

fit = fdars.functional_logistic(data, labels.astype(float), n_comp=3)
pred = fit["predicted_classes"]

`fosr`¶

fdars.fosr(response, predictors, lambda_=0.0)

Function-on-scalar regression. Models a functional response as a linear combination of scalar predictors.

Parameter	Type	Default	Description
`response`	`ndarray (n, m)`		Functional response
`predictors`	`ndarray (n, p)`		Scalar predictors
`lambda_`	`float`	`0.0`	Roughness penalty; negative for GCV selection

Returns	Type	Description
result	`dict`	Keys: `fitted` (n, m), `beta` (p, m), `residuals` (n, m), `r_squared`

fit = fdars.fosr(Y_func, X_scalar, lambda_=-1.0)  # GCV selection
beta = fit["beta"]  # coefficient functions

`fanova`¶

fdars.fanova(data, groups, n_perm=999)

Functional ANOVA with permutation-based p-values.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional data
`groups`	`ndarray (n,)` of `int64`		Group labels
`n_perm`	`int`	`999`	Number of permutations

Returns	Type	Description
result	`dict`	Keys: `f_statistic_t` (m,), `p_value`, `group_means` (k, m), `global_statistic`

result = fdars.fanova(data, groups.astype(np.int64), n_perm=999)
print(f"p-value: {result['p_value']:.4f}")

`model_selection_ncomp`¶

fdars.model_selection_ncomp(data, response, max_comp=10, criterion="gcv")

Cross-validated selection of the number of FPC components for scalar-on-function regression.

Parameter	Type	Default	Description
`data`	`ndarray (n, m)`		Functional predictors
`response`	`ndarray (n,)`		Scalar response
`max_comp`	`int`	`10`	Maximum number of components to test
`criterion`	`str`	`"gcv"`	`"gcv"`, `"aic"`, or `"bic"`

Returns	Type	Description
result	`dict`	Keys: `best_ncomp`, `criteria` (list of (ncomp, aic, bic, gcv) tuples)

result = fdars.model_selection_ncomp(data, y, max_comp=10, criterion="bic")
print(f"Best n_comp: {result['best_ncomp']}")

fdars.regression¶

Functions¶

fpca¶

fpls¶

fregre_lm¶

fregre_pls¶

fregre_np¶

fregre_l1¶

fregre_huber¶

functional_logistic¶

fosr¶

fanova¶

model_selection_ncomp¶