F#で重み付き回帰

F# for Machine Learning Essentialsから。
この本は、各種アルゴリズムを最低限の行列ライブラリで書いた後、機械学習ライブラリを使って結果が同じになるよねって構成の本です。かなり好きなタイプの構成なのですが、肝心の数式の説明はほとんどないので、そこは別の教科書が必要になるのが欠点。

重み付きの回帰問題。グラフの部分をXplotに書き換えてます。

#load "../../FsLab.Templates-basic/packages/FsLab/FsLab.fsx"

open System
open System.IO
open MathNet.Numerics
open MathNet.Numerics.LinearAlgebra
open MathNet.Numerics.LinearAlgebra.Double
open MathNet.Numerics.LinearRegression
open XPlot.GoogleCharts

let tof (t : string) = float t

let rows = File.ReadAllLines("C:\\home\\myproj\\fsharp\\FS_for_ML\\chap2\\data\\mpg.csv")
           |> Array.map(fun t -> t.Split(',') |> Array.toSeq |> Seq.take 6 |> Seq.toArray |> Array.map tof)
           |> Array.toSeq
           |> Seq.take 350
           |> Seq.toArray

let created1 = DenseMatrix.OfRowArrays rows
let milePerGallon = created1.Column 0
let created2 = created1.RemoveColumn 0
let Y_MPG = milePerGallon

let tau = 1.

let unknownCarDetails = vector [4.;140.;90.;2264.;15.5]
let values = [|for i in 0 .. 349 -> (created2.Row i).Subtract(unknownCarDetails).L2Norm() / (2. * tau ** 2.) |]

let weightedMPG = DiagonalMatrix.ofDiagArray values

let Theta_MPG = (created2.Transpose() * weightedMPG * created2).Inverse() * created2.Transpose() * weightedMPG * milePerGallon

let predictedMPG = Theta_MPG * unknownCarDetails

// Graph
let mpgPairs = [|for i in 0 .. 349 -> (i, milePerGallon.At(i)) |]
let predeictedMPGPairs = [|for i in 0 .. 349 -> (i, Theta_MPG * created2.Row(i))|]
let mpgResidual = [| for i in 0 .. 349 -> (milePerGallon.At(i),
                                           Theta_MPG * created2.Row(i),
                                           milePerGallon.At(i) - Theta_MPG * created2.Row(i)) |]

let mpgResidualPair = [|for i in 0 .. 349 -> (i, abs(milePerGallon.At(i) - Theta_MPG * created2.Row(i))) |]

let graph = ["scatter"; "lines" ; "bars"]
[mpgPairs;  predeictedMPGPairs; mpgResidualPair]
|> Chart.Combo
|> Chart.WithOptions 
     (Options(series = [| for typ in graph -> Series(typ) |]))

グラフ