Module Owl_optimise (.ml)

module Owl_optimise: sig .. end


  Machine learning library
  Note: C layout row-major matrix

module MX: Owl_dense_real

module UT: Owl_utils

val kmeans : MX.mat -> int -> MX.mat * int array


  K-means clustering algorithm
  x is the row-based data points and c is the number of clusters.

val numerical_gradient : ('a -> MX.mat -> MX.mat) -> MX.mat -> MX.mat -> 'a -> 'b -> MX.mat


  a numberical way of calculating gradient.
  x is a k x m matrix containing m classifiers of k features.

val l1 : MX.mat -> MX.mat

L1 regularisation and its subgradient

val l1_grad : MX.mat -> MX.mat

val l2 : MX.mat -> MX.mat

L2 regularisation and its grandient

val l2_grad : 'a -> 'a

val elastic : float -> MX.mat -> MX.mat

 Elastic net regularisation and its gradient
  "a" is the weight on l1 regularisation term.

val elastic_grad : float -> MX.mat -> MX.mat

val noreg : MX.mat -> MX.mat

No regularisation and its gradient

val noreg_grad : MX.mat -> MX.mat

val square_loss : MX.mat -> MX.mat -> MX.mat

least square loss function

val square_grad : MX.mat -> MX.mat -> MX.mat -> MX.mat

val hinge_loss : MX.mat -> MX.mat -> MX.mat

hinge loss function

val hinge_grad : MX.mat -> MX.mat -> MX.mat -> MX.mat

val hinge2_loss : MX.mat -> MX.mat -> MX.mat

squared hinge loss function

val hinge2_grad : 'a -> 'b -> 'c -> 'd option

val softmax_loss : 'a -> 'b -> 'c option

softmax loss function

val softmax_grad : 'a -> 'b -> 'c -> 'd option

logistic loss function

val log_loss : MX.mat -> MX.mat -> MX.mat

val log_grad : MX.mat -> MX.mat -> MX.mat -> MX.mat

val constant_rate : 'a -> 'b -> 'c -> float

val optimal_rate : float -> float -> int -> float

val decr_rate : float -> 'a -> int -> float

val when_stable : float -> 'a -> bool

val when_enough : float -> int -> bool

val _sgd_basic : int ->
       (float -> float -> int -> float) ->
       (float -> int -> bool) ->
       (MX.mat -> MX.mat -> MX.mat) ->
       (MX.mat -> MX.mat -> MX.mat -> MX.mat) ->
       (MX.mat -> MX.mat) ->
       (MX.mat -> MX.mat) -> float -> bool -> MX.mat -> MX.mat -> MX.mat -> MX.mat


  Stochastic Gradient Descent (SGD) algorithm
  b : batch size
  s : step size
  t : stop criteria
  l : loss function
  g : gradient function of the loss function
  r : regularisation function
  o : gradient fucntion of the regularisation function
  a : weight on the regularisation term, common setting is 0.0001
  i : whether to include intercept or not, default value is false
  p : model parameters (k * m), each column is a classifier. So we have m classifier of k features.
  x : data matrix (n x k), each row is a data point. So we have n datea points of k features each.
  y : labeled data (n x m), n data points and each is labeled with m classifiers

val sgd : ?b:int ->
       ?s:(float -> float -> int -> float) ->
       ?t:(float -> int -> bool) ->
       ?l:(MX.mat -> MX.mat -> MX.mat) ->
       ?g:(MX.mat -> MX.mat -> MX.mat -> MX.mat) ->
       ?r:(MX.mat -> MX.mat) ->
       ?o:(MX.mat -> MX.mat) ->
       ?a:float -> ?i:bool -> MX.mat -> MX.mat -> MX.mat -> MX.mat


  wrapper of the _sgd_basic fucntion

val gradient_descent : 'a option

val svm_regression : ?i:bool -> MX.mat -> MX.mat -> MX.mat -> MX.mat

 Support Vector Machine regression
  i : whether to include intercept bias in parameters
  note that the values in y are either +1 or -1.

val ols_regression : ?i:bool -> MX.mat -> MX.mat -> MX.mat

 Ordinary Least Square regression
  i : whether to include intercept bias in parameters

val ridge_regression : ?i:bool -> ?a:float -> MX.mat -> MX.mat -> MX.mat

 Ridge regression
  i : whether to include intercept bias in parameters
  a : weight on the regularisation term
  TODO: how to choose a automatically

val lasso_regression : ?i:bool -> ?a:float -> MX.mat -> MX.mat -> MX.mat

 Lasso regression
  i : whether to include intercept bias in parameters
  a : weight on the regularisation term
  TODO: how to choose a automatically

val logistic_regression : ?i:bool -> MX.mat -> MX.mat -> MX.mat

 Logistic regression
  i : whether to include intercept bias in parameters
  a : weight on the regularisation term
  note that the values in y are either +1 or 0.