minimind: A Minimalist Machine Learning Library written in Swift

The main focus of this library is dimensionality reduction, manifold learning and multi-output regression. Minimind allows fast mobile app prototyping by providing a friendly numpy-like interface and native performance on iOS and MacOS. See playground files for examples. Some wrapper functions for Accelerate were borrowed from Surge.

Learning A Predictive Distribution

        let X = Matrix<Float>([[-1.50983293], [-1.11726642], [-0.89303372], [ 0.07971517], [ 0.29116607], [ 0.7494249 ], [ 0.93321463], [ 1.46661229]])
        
        let Y = Matrix<Float>([[ 0.04964821,  0.0866106,  0.16055375,  0.58936555,  0.71558366,  1.00004714,  1.08412273,  1.42418915]]).t
        
        // start with large variance and lengthscale
        let kern = RBF(variance: 300.0, lengthscale: 1000.0)
        
        let gp = GaussianProcessRegressor<Float, RBF>(kernel: kern, alpha: 1.0)
        gp.fit(X, Y, maxiters: 500)
        
        print(gp.kernel.get_params())
        
        let Xstar = Matrix<Float>(-1, 1, arange(-1.5, 1.5, 0.1))
        let (Mu, Sigma) = gp.predict(Xstar)

        // plot variance 
        _ = graph.plot(x: Xstar.grid.cgFloat, y: (Mu + diag(Sigma)).grid.cgFloat , c: UIColor.blue, s: 1.0)
        _ = graph.plot(x: Xstar.grid.cgFloat, y: (Mu - diag(Sigma)).grid.cgFloat, c: UIColor.blue, s: 1.0)
        
        // plot mean
        _ = graph.plot(x: Xstar.grid.cgFloat, y: Mu.grid.cgFloat, c: UIColor.red, s: 3.0)

        // plot training data
        _ = graph.scatter(x: X.grid.cgFloat, y: Y.grid.cgFloat, c: UIColor.green, s: 10.0)
        
        graph.autoscale()

Matrix Operations, side-by-side with numpy

import Foundation
import Surge
import minimind

// random matrix
let m: Matrix<Float> = randMatrix(3, 3)
let a = Matrix<Float>([[1.2, 0.2, 0.3],
                       [0.5, 1.5, 0.2],
                       [0.1, 0.2, 2.0]])

let subM = m[0∷2, 0∷2] // matrix slicing
let cmean = m.mean(0) // mean accross columns
let b = (m * a + a) ∘ m.t // linear math
let (u, s, v) = svd(a) // Singular values & vectors
let l = cholesky(a, "L") // Cholesky & LDLT
let (evals, evecs) = eigh(a, "L") // Eigen decom.

import numpy as np

# random matrix
m = np.random.rand(3, 3)
a = np.array([[1.2, 0.2, 0.3],
              [0.5, 1.5, 0.2],
              [0.1, 0.2, 2.0]])
              
subM = m[0::2, 0::2]
cmean = m.mean(0)

b = (m.dot(a) + a) * m.T

u, s, v = np.linalg.svd(a)
l = np.linalg.cholesky(a)
evals, evecs = np.linalg.eigh(a)

Sampling from a GP prior

Internal Design Philosophy

To maximise code reusability, Swift extensions are used extensively. For instance, Matrix is generically defined as Matrix<T>, with no constraints on T. This basically means that Matrix can contain any data types like Float, Double, Int, Bool and even String. Matrix<T> can be specialised to deal with a certain group of data such as ScalarType (Similar to Swift Numeric type, which will comes with XCode 9). Accelerations are used whenever possible by further specialising Matrix (e.g to Matrix<Float>, Matrix<Double>).