Refactor Optional arg and Regression interface.

[rleonid]

• Renamed spec type to usage.
• Created special constructors for regression models to hide the
  optional arguments. Each type is now defined only in that module and
  does not pollute the main Regression module.
• Changed to using polymorphic variants to express regularizers.

[rleonid]

Before:

#show_module Regression ;;
module Regression :
  sig
    module type Linear_model_intf =
      sig
        type spec
        val default : spec
        type input
        type t
        val describe : t -> string
        val eval : t -> input -> float
        val regress : ?spec:spec -> input array -> resp:float array -> t
        val residuals : t -> float array
        val coefficients : t -> float array
        val residual_standard_error : t -> float
        val coeff_of_determination : t -> float
        val confidence_interval : t -> alpha:float -> input -> float * float
        val prediction_interval : t -> alpha:float -> input -> float * float
        val coefficient_tests : ?null:float -> t -> Inference.test array
        val f_statistic : t -> float
      end
    module Univariate : sig  end
    type lambda_spec = Spec of float | From of float array
    type multivariate_spec = { add_constant_column : bool; lambda_spec : lambda_spec option; }
    module Multivariate : sig  end
    type tikhonov_spec = { regularizer : float array array; lambda_spec : lambda_spec option; }
    module Tikhonov : sig  end
  end
utop # #show_module Regression.Multivariate ;;
module Multivariate :
  sig
    type spec = Regression.multivariate_spec
    val default : spec
    type input = float array
    type t
    val describe : t -> string
    val eval : t -> input -> float
    val regress : ?spec:spec -> input array -> resp:float array -> t
    val residuals : t -> float array
    val coefficients : t -> float array
    val residual_standard_error : t -> float
    val coeff_of_determination : t -> float
    val confidence_interval : t -> alpha:float -> input -> float * float
    val prediction_interval : t -> alpha:float -> input -> float * float
    val coefficient_tests : ?null:float -> t -> Inference.test array
    val f_statistic : t -> float
    val aic : t -> float
    val press : t -> float
  end

After:

utop # #show_module Regression ;;
module Regression :
  sig
    module type Linear_model_intf =
      sig
        type opt
        val default : opt
        type input
        type t
        val describe : t -> string
        val eval : t -> input -> float
        val regress : ?opt:opt -> input array -> resp:float array -> t
        val residuals : t -> float array
        val coefficients : t -> float array
        val residual_standard_error : t -> float
        val coeff_of_determination : t -> float
        val confidence_interval : t -> alpha:float -> input -> float * float
        val prediction_interval : t -> alpha:float -> input -> float * float
        val coefficient_tests : ?null:float -> t -> Oml.Inference.test array
        val f_statistic : t -> float
      end
    module Univariate : sig  end
    module Multivariate : sig  end
    module Tikhonov : sig  end
  end
utop # #show_module Regression.Univariate ;;
module Univariate :
  sig
    type opt = float array
    val opt : ?weights:float array -> unit -> opt
    val default : opt
    type input = float
    type t
    val describe : t -> string
    val eval : t -> input -> float
    val regress : ?opt:opt -> input array -> resp:float array -> t
    val residuals : t -> float array
    val coefficients : t -> float array
    val residual_standard_error : t -> float
    val coeff_of_determination : t -> float
    val confidence_interval : t -> alpha:float -> input -> float * float
    val prediction_interval : t -> alpha:float -> input -> float * float
    val coefficient_tests : ?null:float -> t -> Oml.Inference.test array
    val f_statistic : t -> float
    val alpha : t -> float
    val beta : t -> float
    val alpha_test : ?null:float -> t -> Oml.Inference.test
    val beta_test : ?null:float -> t -> Oml.Inference.test
  end
utop # #show_module Regression.Multivariate ;;
module Multivariate :
  sig
    type opt = { add_constant_column : bool; l2_regularizer : [ `From of float array | `S of float ] option; }
    val opt : ?l2_regularizer:[ `From of float array | `S of float ] -> ?add_constant_column:bool -> unit -> opt
    val default : opt
    type input = float array
    type t
    val describe : t -> string
    val eval : t -> input -> float
    val regress : ?opt:opt -> input array -> resp:float array -> t
    val residuals : t -> float array
    val coefficients : t -> float array
    val residual_standard_error : t -> float
    val coeff_of_determination : t -> float
    val confidence_interval : t -> alpha:float -> input -> float * float
    val prediction_interval : t -> alpha:float -> input -> float * float
    val coefficient_tests : ?null:float -> t -> Oml.Inference.test array
    val f_statistic : t -> float
    val aic : t -> float
    val press : t -> float
  end

[ihodes]

Why not just delete?

[rleonid]

No particular good reason, laziness I guess. I already filed an issue #130 that should address this.

[ihodes]

This looks great, definitely seems simpler to me.