package owl

Linear regression: linear ~i x y fits the measurements x and the observations y into a linear model. x is a m by n row-based matrix and each row represents one measurement. y is a m by 1 matrix and each number is an observation. The parameters will be returned as a column vector. ~i indicates wether to include intercept, the default value is false. The intercept will be the first elelment in the returned parameters.

polynomial regression: polynomial x y d fits the measurements x and the observations y into a polynomial model. Both x and y are m by 1 matrices. Parameter d specifies the highest degree of the polynomial model. The function returns a (d+1) by 1 matrix where the first element is the intercept and the rest are the corresponding coefficients of each degree from 1 to d.

Exponential regression: exponential x y fits the measurements x and the observations y into a exponential model: y = a * exp^(-lambda * x) + b . Both x and y are m by 1 matrices. The returned result is a matrix of three model parameters [a, lambda, b].

Nonlinear regression: nonlinear f p x y fits the measurements x and the observations y into a user-defined nonlinear model. Both x and y are m x 1 matrices; p is the initial guess of the parameters, f is the user-defined function, its first parameter is the parameter array, and the second is the variable.

E.g., if we want to fit x and y using y = a *. (log x) +. b model, we first define the function f as

let f p x = p.{0} *. (log x) + p.{1}

where p.{0} represents a and p.{1} represents b. Then we also need to make an initial guess of the parameters (i.e., a and b) by defining

let p = [0.1; 0.1].

Finally, we can perform the nonlinear regression by calling nonlinear f p x y.

Ordinary Least Square regression: in ols ~i x y, i : whether or not to include intercept bias in parameters, the default is true; ; x is the measurements, and y is the observations. THe return is the model.

Ridge regression: in ridge ~i ~a x y, i : whether or not to include intercept bias in parameters, the default is true; a : the weight on the regularisation term; x is the measurements, and y is the observations. The return is the model.

LASSO regression: in lasso ~i ~a x y, i : whether or not to include intercept bias in parameters, the default is true; a : the weight on the regularisation term; x is the measurements, and y is the observations. The return is the model.

Logistic regression: in logistic ~i x y, i : whether or not to include intercept bias in parameters, the default is true; ; x is the measurements, and y is the observations.

Note that the values in y are either +1 or 0. The return is the model.

Support Vector Machine regression: in svm ~i p x y, i : whether or not to include intercept bias in parameters, the default is true; p : the initial guess of the model; x is the measurements, and y is the observations.

Note that the values in y are either +1 or -1.

K-means clustering: kmeans x c divides x which is a row-based matrix into c clusters. The return is (y,a) where y is the model and a is the membership list of all nodes in x.