# Models

A statistical model combines a datafit and penalty. A solver supplies the numerical method; it is selected explicitly rather than inferred from the model's name. 

| Model | Construction | Prediction |
| --- | --- | --- |
| [Linear regression](<linear>) | Gaussian with a compatible penalty | Response mean |
| [Logistic regression](<logistic>) | Binomial with a compatible penalty | Logit; transform to a probability |
| [Multivariate regression](<multivariate>) | MultivariateGaussian with AxisPenalty | Response-major means |
| [Lasso convenience API](<lasso>) | Named Gaussian L1 configuration | Response mean |
| [SLOPE](<slope>) | Gaussian or binomial with Slope | Response mean or logit |
| [Clustered lasso](<clustered-lasso>) | Gaussian or binomial with ClusteredLasso | Response mean or logit |
| [Chain fused lasso](<chain-fused-lasso>) | Gaussian or binomial with ChainFusedLasso | Response mean or logit |

Use `Problem::new(&x, datafit, penalty).fit_with(&solver)` for typed composition. The type system checks supported combinations. Runtime problems permit dynamic selection with explicit capability checks; see the [solver compatibility table](<../reference/solvers/>). 

`Lasso` is currently the sole named convenience model. Other model families use composition. The [shared conventions](<../modeling>) describe intercepts, normalization, penalty scales, and original-scale output. The Python package exposes Gaussian lasso and composition with Gaussian or binomial datafits, the three MVP penalties, and explicit hybrid or proximal-gradient solvers. 

API: [`shrinkage::Problem`](<https://shrinkage.cc/packages/rust/reference/4fd51b866367bd6673d82fc698be06078f421c181aef012c7bc5b92a97232647>) and [`shrinkage::RuntimeProblem`](<https://shrinkage.cc/packages/rust/reference/6c4676e8a2d70e42d12ccb31a1ad91f9cca07ac8509696f4c1996761f69e7999>).