# shrinkage::Binomial Shrinkage for Rust · 0.3.0 [Source]() ```rust pub struct Binomial<'a> ``` Bernoulli negative log likelihood with a logit link, averaged over rows. Responses must be finite and lie in `[0, 1]`; fractional responses represent proportions with equal observation weights. The complete linear predictor includes an optional unpenalized intercept, fitted by default. The predictor Hessian is diagonal with entries at most `1 / (4n)`. Consequently, for an optimization-scale design augmented with an intercept column, the coefficient gradient has Lipschitz constant at most `||[X, 1]||² / (4n)`. [`crate::ProximalGradient`]() uses backtracking to enforce the corresponding quadratic upper bound without computing this norm. [`crate::Irls`](<38d3c0c77c3a369dc72fa82940fe75e00e04888f78613113e69bdc12b1c8d7dd>) uses the exact diagonal predictor Hessian to construct weighted quadratic models solved by coordinate descent. ```rust use faer::{Col, Mat}; use shrinkage::{Binomial, Problem, ProximalGradient, Ridge}; let x = Mat::from_fn(4, 1, |i, _| i as f64); let y = [0.0, 0.0, 1.0, 1.0]; let fit = Problem::new(&x, Binomial::new(&y), Ridge::new(0.1)) .fit_with(&ProximalGradient::>::new())?; // Predictions are logits; apply the logistic function for probabilities. let logits = fit.predict(&x)?; ``` ## Inherent implementation [Source]() ```rust impl<'a> Binomial<'a> ``` ### `fit_intercept` ```rust pub fn fit_intercept(self, enabled: bool) -> Self ``` [Source]() Enable or disable the unpenalized fitted intercept. Explicit column centering can still induce an original-scale intercept. ### `fits_intercept` ```rust pub fn fits_intercept(&self) -> bool ``` [Source]() Whether fitting includes a free, unpenalized intercept. ### `inverse_link` ```rust pub fn inverse_link(&self, eta: f64) -> Result ``` [Source]() Transform a predictor to a mean with the default link. #### Errors Reject nonfinite predictors or arithmetic. ### `link` ```rust pub fn link(&self, mu: f64) -> Result ``` [Source]() Transform a mean with the default logit link. #### Errors Reject means outside the link domain or nonfinite arithmetic. ### `new` ```rust pub fn new(response: &'a [f64]) -> Self ``` [Source]() Borrow responses, fitting an intercept by default. ### `response` ```rust pub fn response(&self) -> &[f64] ``` [Source]() Borrow the observed responses. ### `with_link` ```rust pub fn with_link( self, link: L ) -> shrinkage::LinkedDatafit ``` [Source]() Compose this family with a link for Fisher-scoring IRLS. ## Implementation of Clone [Source]() ```rust impl<'a> Clone for Binomial<'a> ``` ### `clone` ```rust fn clone(&self) -> Self ``` [Source]() ## [Implementation of ConvexLink](<45ae855dae253e1bbc77e093683e36c85f95b348ea7c924f536c479638434084>) [Source]() ```rust impl ConvexLink> for Logit ``` ## [Implementation of ConvexLink](<45ae855dae253e1bbc77e093683e36c85f95b348ea7c924f536c479638434084>) [Source]() ```rust impl ConvexLink> for Probit ``` ## Implementation of Copy [Source]() ```rust impl<'a> Copy for Binomial<'a> ``` ## [Implementation of CrossValidationDatafit](<98601fc9b50fbe6c319e8c6f7936102bb90fb9e942a9ce7e6cbd3d48de803c74>) [Source]() ```rust impl CrossValidationDatafit for shrinkage::Binomial<'_> ``` ### `WithResponse` ```rust type WithResponse<'a> = Binomial<'a>; ``` [Source]() ### `response` ```rust fn response(&self) -> &[f64] ``` [Source]() ### `supports_metric` ```rust fn supports_metric(&self, metric: ValidationMetric) -> bool ``` [Source]() ### `validate_training` ```rust fn validate_training(&self) -> Result<(), FitError> ``` [Source]() ### `validation_metric` ```rust fn validation_metric(&self) -> ValidationMetric ``` [Source]() ### `with_response` ```rust fn with_response<'a>(&self, response: &'a [f64]) -> Binomial<'a> ``` [Source]() ## [Implementation of Datafit](<9d16367f3210bbbb9bf039290cf9c94f447e51d4ea33aea446a7f30e965d873a>) [Source]() ```rust impl Datafit for Binomial<'_> ``` ### `Error` ```rust type Error = FitError; ``` [Source]() ### `value` ```rust fn value(&self, predictor: &[f64]) -> Result ``` [Source]() ## Implementation of Debug [Source]() ```rust impl<'a> Debug for Binomial<'a> ``` ### `fmt` ```rust fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result ``` [Source]() ## [Implementation of DiagonalHessianDatafit](<0c7a483f4e622180bfcc5efab524b3377e2104e91e0d263eb5a204d4a4ab722e>) [Source]() ```rust impl DiagonalHessianDatafit for Binomial<'_> ``` ### `hessian_diagonal` ```rust fn hessian_diagonal( &self, predictor: &[f64], output: &mut [f64] ) -> Result<(), FitError> ``` [Source]() ## [Implementation of DifferentiableDatafit](<52561c3cc593c87f940a70abf79b463b0c969e6ea2f86d60ef4f213626b07d4b>) [Source]() ```rust impl DifferentiableDatafit for Binomial<'_> ``` ### `fits_intercept` ```rust fn fits_intercept(&self) -> bool ``` [Source]() ### `gradient` ```rust fn gradient( &self, predictor: &[f64], output: &mut [f64] ) -> Result<(), FitError> ``` [Source]() ### `n_obs` ```rust fn n_obs(&self) -> usize ``` [Source]() ## [Implementation of GapSafeDatafit]() [Source]() ```rust impl GapSafeDatafit for Binomial<'_> ``` ### `dual_candidate` ```rust fn dual_candidate( &self, predictor: &[f64], output: &mut [f64] ) -> Result<(), FitError> ``` [Source]() ### `dual_objective` ```rust fn dual_objective(&self, dual: &[f64]) -> Result ``` [Source]() ### `fenchel_gap` ```rust fn fenchel_gap(&self, predictor: &[f64], dual: &[f64]) -> Result ``` [Source]() ### `finalize_dual` ```rust fn finalize_dual(&self, dual: &mut [f64]) -> Result<(), FitError> ``` [Source]() ### `strong_concavity` ```rust fn strong_concavity(&self) -> f64 ``` [Source]() ## Implementation of HybridPathDatafit [Source]() ```rust impl HybridPathDatafit for shrinkage::Binomial<'_> ``` ### `Outer` ```rust type Outer = Outer; ``` [Source]() ### `fit` ```rust fn fit( &self, design: &mut NativeDesign, penalty: &P, solver: &HybridCoordinateDescent, threshold: f64, work: (&mut Workspace

, &mut ::Outer) ) -> Result::Error>> where M: RawColumns + MatVecInto + MatTransposeVecInto, V: ProximalVector, P: ReducedCoordinatePenalty ``` [Source]() ### `outer` ```rust fn outer(n: usize, p: usize) -> ::Outer ``` [Source]() ### `path_deviance` ```rust fn path_deviance( &self, _: &Workspace

, outer: &::Outer ) -> Result, FitError> ``` [Source]() ### `validate_solver` ```rust fn validate_solver( &self, solver: &HybridCoordinateDescent ) -> Result ``` [Source]() ## [Implementation of NullModelDatafit](<12ebbf9584faa968bb3fcbf1175e4e131dd6c7466b719c62ad9d7628739d9dac>) [Source]() ```rust impl NullModelDatafit for shrinkage::Binomial<'_> ``` ### `deviance` ```rust fn deviance(&self, predictor: &[f64]) -> Result, FitError> ``` [Source]() ### `null_intercepts` ```rust fn null_intercepts(&self) -> Result, FitError> ``` [Source]() ## [Implementation of QuadraticModelDatafit](<31d7fcbcbb4b2013239104910cbd830452b304788def6134cdeee718040312eb>) [Source]() ```rust impl QuadraticModelDatafit for Binomial<'_> ``` ### `working_curvature` ```rust fn working_curvature( &self, predictor: &[f64], output: &mut [f64] ) -> Result<(), FitError> ``` [Source]() ## [Implementation of SmoothDatafit]() [Source]() ```rust impl SmoothDatafit for Binomial<'_> ``` ### `gap_safe` ```rust fn gap_safe(&self) -> Option<&dyn shrinkage::GapSafeDatafit> ``` [Source]() ## Implementation of Freeze ```rust impl<'a> Freeze for Binomial<'a> ``` ## Implementation of RefUnwindSafe ```rust impl<'a> RefUnwindSafe for Binomial<'a> ``` ## Implementation of Send ```rust impl<'a> Send for Binomial<'a> ``` ## Implementation of Sync ```rust impl<'a> Sync for Binomial<'a> ``` ## Implementation of Unpin ```rust impl<'a> Unpin for Binomial<'a> ``` ## Implementation of UnsafeUnpin ```rust impl<'a> UnsafeUnpin for Binomial<'a> ``` ## Implementation of UnwindSafe ```rust impl<'a> UnwindSafe for Binomial<'a> ``` ## Implementation of Any ```rust impl Any for T where T: 'static + ?Sized ``` ## Implementation of Borrow ```rust impl Borrow for T where T: ?Sized ``` ## Implementation of BorrowMut ```rust impl BorrowMut for T where T: ?Sized ``` ## Implementation of ByRef ```rust impl ByRef for T ``` ## Implementation of CastableFrom ```rust impl CastableFrom for DT where ST: ?Sized, DT: ?Sized ``` ## Implementation of CastableFrom ```rust impl CastableFrom for DT where ST: ?Sized, DT: ?Sized ``` ## Implementation of CloneToUninit ```rust impl CloneToUninit for T where T: Clone ``` ## Implementation of From ```rust impl From for T ``` ## Implementation of Imply ```rust impl Imply for U where T: ?Sized, U: ?Sized ``` ## Implementation of Into ```rust impl Into for T where U: From ``` ## Implementation of IntoEither ```rust impl IntoEither for T ``` ## [Implementation of PathDatafit]() [Source]() ```rust impl PathDatafit for D where D: SmoothDatafit + NullModelDatafit + ?Sized ``` ## Implementation of Pointable ```rust impl Pointable for T ``` ## Implementation of Read ```rust impl Read for T where T: ?Sized ``` ## Implementation of Same ```rust impl Same for T ``` ## Implementation of SupersetOf ```rust impl SupersetOf for SP where SS: SubsetOf ``` ## Implementation of ToOwned ```rust impl ToOwned for T where T: Clone ``` ## Implementation of TryFrom ```rust impl TryFrom for T where U: Into ``` ## Implementation of TryInto ```rust impl TryInto for T where U: TryFrom ```