Programming Machine Learning

Dependencies and Utilities

Mix.install([
  # :kino,
  :nimble_csv,
  :nx,
  # :vega_lite,
  {:vega_lite, "~> 0.1.4"},
  {:kino_vega_lite, "~> 0.1.1"}
])

alias NimbleCSV, as: CSV
alias VegaLite, as: Vl

Resolving Hex dependencies...
Resolution completed in 0.259s
New:
  complex 0.5.0
  fss 0.1.1
  kino 0.12.0
  kino_vega_lite 0.1.11
  nimble_csv 1.2.0
  nx 0.6.4
  table 0.1.2
  telemetry 1.2.1
  vega_lite 0.1.8
* Getting nimble_csv (Hex package)
* Getting nx (Hex package)
* Getting vega_lite (Hex package)
* Getting kino_vega_lite (Hex package)
* Getting kino (Hex package)
* Getting table (Hex package)
* Getting fss (Hex package)
* Getting complex (Hex package)
* Getting telemetry (Hex package)
==> table
Compiling 5 files (.ex)
Generated table app
==> vega_lite
Compiling 6 files (.ex)
Generated vega_lite app
===> Analyzing applications...
===> Compiling telemetry
==> nimble_csv
Compiling 1 file (.ex)
Generated nimble_csv app
==> fss
Compiling 4 files (.ex)
Generated fss app
==> complex
Compiling 2 files (.ex)
Generated complex app
==> nx
Compiling 32 files (.ex)
Generated nx app
==> kino
Compiling 47 files (.ex)
Generated kino app
==> kino_vega_lite
Compiling 4 files (.ex)
Generated kino_vega_lite app

VegaLite

defmodule Utilities do
  def integer(integer_string) do
    {integer, _} = Integer.parse(integer_string)
    integer
  end

  def float(float_string) do
    {float, _} = Float.parse(float_string)
    float
  end
end

{:module, Utilities, <<70, 79, 82, 49, 0, 0, 7, ...>>, {:float, 1}}

import Utilities

Utilities

Chapter 1

Load the pizza.txt data file and plot the data. The data lists an historical record of the number of pizzas ordered given a number of reservations earlier in the day.

CSV.define(MyParser, separator: "\s")

{reservations, pizza} =
  Path.join(__ENV__.file, "../data/pizza.txt")
  |> Path.expand()
  |> File.stream!()
  |> Enum.map(fn line ->
    String.replace(line, ~r/\s+/, "\s")
    |> String.trim()
  end)
  |> MyParser.parse_enumerable()
  |> Enum.map(fn [x, y] -> {float(x), float(y)} end)
  |> Enum.unzip()

reservations = Nx.tensor(reservations)
pizza = Nx.tensor(pizza)

Vl.new(width: 650, height: 300)
|> Vl.data_from_values(
  Reservations: Nx.to_flat_list(reservations),
  Pizzas: Nx.to_flat_list(pizza)
)
|> Vl.mark(:point, filled: true)
|> Vl.encode_field(:x, "Reservations", type: :quantitative)
|> Vl.encode_field(:y, "Pizzas", type: :quantitative)

{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"Pizzas":33.0,"Reservations":13.0},{"Pizzas":16.0,"Reservations":2.0},{"Pizzas":32.0,"Reservations":14.0},{"Pizzas":51.0,"Reservations":23.0},{"Pizzas":27.0,"Reservations":13.0},{"Pizzas":16.0,"Reservations":1.0},{"Pizzas":34.0,"Reservations":18.0},{"Pizzas":17.0,"Reservations":10.0},{"Pizzas":29.0,"Reservations":26.0},{"Pizzas":15.0,"Reservations":3.0},{"Pizzas":15.0,"Reservations":3.0},{"Pizzas":32.0,"Reservations":21.0},{"Pizzas":22.0,"Reservations":7.0},{"Pizzas":37.0,"Reservations":22.0},{"Pizzas":13.0,"Reservations":2.0},{"Pizzas":44.0,"Reservations":27.0},{"Pizzas":16.0,"Reservations":6.0},{"Pizzas":21.0,"Reservations":10.0},{"Pizzas":37.0,"Reservations":18.0},{"Pizzas":30.0,"Reservations":15.0},{"Pizzas":26.0,"Reservations":9.0},{"Pizzas":34.0,"Reservations":26.0},{"Pizzas":23.0,"Reservations":8.0},{"Pizzas":39.0,"Reservations":15.0},{"Pizzas":27.0,"Reservations":10.0},{"Pizzas":37.0,"Reservations":21.0},{"Pizzas":17.0,"Reservations":5.0},{"Pizzas":18.0,"Reservations":6.0},{"Pizzas":25.0,"Reservations":13.0},{"Pizzas":23.0,"Reservations":13.0}]},"encoding":{"x":{"field":"Reservations","type":"quantitative"},"y":{"field":"Pizzas","type":"quantitative"}},"height":300,"mark":{"filled":true,"type":"point"},"width":650}

reservations[0..4]

#Nx.Tensor<
  f32[5]
  [13.0, 2.0, 14.0, 23.0, 13.0]
>

pizza[0..4]

#Nx.Tensor<
  f32[5]
  [33.0, 16.0, 32.0, 51.0, 27.0]
>

defmodule Chapter1.LinearRegression do
  import Nx.Defn

  @doc """
  For a given weight, predict the output for a given input
  """
  @spec predict(Nx.Tensor.t(), number()) :: Nx.Tensor.t()
  defn predict(x, weight) do
    x * weight
  end

  @doc """
  Calculate the loss, as a mean squared error, for the given weight
  """
  @spec loss(Nx.Tensor.t(), Nx.Tensor.t(), number()) :: number()
  def loss(x, y, weight) do
    Nx.subtract(predict(x, weight), y)
    |> Nx.power(2)
    |> Nx.mean()
    |> Nx.to_number()
  end

  @doc """
  Train a linear regression model with a maximum number of iterations
  """
  @spec train(Nx.Tensor.t(), Nx.Tensor.t(), non_neg_integer(), float()) ::
          {:ok, float()} | {:error, String.t()}
  def train(x, y, iterations, lr = _learning_rate) do
    0..iterations
    |> Enum.reduce_while({0, 0}, fn iteration, {weight, _} ->
      current_loss = loss(x, y, weight)

      IO.puts("Iteration #{iteration} => Loss: #{current_loss |> Nx.to_number()}")

      cond do
        loss(x, y, weight + lr) < current_loss -> {:cont, {weight + lr, iteration}}
        loss(x, y, weight - lr) < current_loss -> {:cont, {weight - lr, iteration}}
        true -> {:halt, {weight, iteration}}
      end
    end)
    |> case do
      {_weight, ^iterations} -> {:error, "Couldn't converge within #{iterations}"}
      {weight, number_of_iterations} -> {:ok, weight, number_of_iterations}
    end
  end
end

warning: Nx.power/2 is deprecated. Use pow/2 instead
  Documents/GitHub/programming-machine-learning/elixir-programming-machine-learning.livemd#cell:nqqujb6hpyj5ccz47utn3mxcrjwgqju7:18: Chapter1.LinearRegression.loss/3

{:module, Chapter1.LinearRegression, <<70, 79, 82, 49, 0, 0, 18, ...>>, {:train, 4}}

alias Chapter1.LinearRegression

Chapter1.LinearRegression

Train the system with 10,000 iterations and a learning rate of 0.01.

{:ok, weight, iterations} = LinearRegression.train(reservations, pizza, 10_000, 0.01)

Iteration 0 => Loss: 812.8666381835938
Iteration 1 => Loss: 804.820556640625
Iteration 2 => Loss: 796.8181762695312
Iteration 3 => Loss: 788.8595581054688
Iteration 4 => Loss: 780.9447021484375
Iteration 5 => Loss: 773.0736694335938
Iteration 6 => Loss: 765.246337890625
Iteration 7 => Loss: 757.4628295898438
Iteration 8 => Loss: 749.7229614257812
Iteration 9 => Loss: 742.0269775390625
Iteration 10 => Loss: 734.3746948242188
Iteration 11 => Loss: 726.7661743164062
Iteration 12 => Loss: 719.2013549804688
Iteration 13 => Loss: 711.680419921875
Iteration 14 => Loss: 704.203125
Iteration 15 => Loss: 696.7696533203125
Iteration 16 => Loss: 689.3799438476562
Iteration 17 => Loss: 682.0339965820312
Iteration 18 => Loss: 674.7317504882812
Iteration 19 => Loss: 667.473388671875
Iteration 20 => Loss: 660.2586669921875
Iteration 21 => Loss: 653.0877685546875
Iteration 22 => Loss: 645.9606323242188
Iteration 23 => Loss: 638.877197265625
Iteration 24 => Loss: 631.8375854492188
Iteration 25 => Loss: 624.8416748046875
Iteration 26 => Loss: 617.8895263671875
Iteration 27 => Loss: 610.981201171875
Iteration 28 => Loss: 604.1165771484375
Iteration 29 => Loss: 597.2957763671875
Iteration 30 => Loss: 590.5186767578125
Iteration 31 => Loss: 583.7853393554688
Iteration 32 => Loss: 577.0957641601562
Iteration 33 => Loss: 570.4500122070312
Iteration 34 => Loss: 563.8479614257812
Iteration 35 => Loss: 557.2896728515625
Iteration 36 => Loss: 550.775146484375
Iteration 37 => Loss: 544.3043823242188
Iteration 38 => Loss: 537.8773803710938
Iteration 39 => Loss: 531.494140625
Iteration 40 => Loss: 525.1546630859375
Iteration 41 => Loss: 518.8589477539062
Iteration 42 => Loss: 512.6069946289062
Iteration 43 => Loss: 506.3988037109375
Iteration 44 => Loss: 500.234375
Iteration 45 => Loss: 494.1136779785156
Iteration 46 => Loss: 488.0367431640625
Iteration 47 => Loss: 482.0035705566406
Iteration 48 => Loss: 476.0141906738281
Iteration 49 => Loss: 470.06854248046875
Iteration 50 => Loss: 464.1666564941406
Iteration 51 => Loss: 458.30853271484375
Iteration 52 => Loss: 452.49420166015625
Iteration 53 => Loss: 446.7236022949219
Iteration 54 => Loss: 440.9967346191406
Iteration 55 => Loss: 435.31365966796875
Iteration 56 => Loss: 429.6743469238281
Iteration 57 => Loss: 424.0787658691406
Iteration 58 => Loss: 418.5269775390625
Iteration 59 => Loss: 413.0189514160156
Iteration 60 => Loss: 407.5546569824219
Iteration 61 => Loss: 402.1341247558594
Iteration 62 => Loss: 396.75738525390625
Iteration 63 => Loss: 391.42437744140625
Iteration 64 => Loss: 386.1351623535156
Iteration 65 => Loss: 380.8896789550781
Iteration 66 => Loss: 375.68792724609375
Iteration 67 => Loss: 370.52996826171875
Iteration 68 => Loss: 365.4158020019531
Iteration 69 => Loss: 360.3453369140625
Iteration 70 => Loss: 355.3186950683594
Iteration 71 => Loss: 350.33575439453125
Iteration 72 => Loss: 345.3965759277344
Iteration 73 => Loss: 340.50115966796875
Iteration 74 => Loss: 335.6495361328125
Iteration 75 => Loss: 330.8416748046875
Iteration 76 => Loss: 326.0775451660156
Iteration 77 => Loss: 321.3572082519531
Iteration 78 => Loss: 316.68060302734375
Iteration 79 => Loss: 312.0477600097656
Iteration 80 => Loss: 307.4586486816406
Iteration 81 => Loss: 302.9133605957031
Iteration 82 => Loss: 298.4117736816406
Iteration 83 => Loss: 293.9540100097656
Iteration 84 => Loss: 289.53997802734375
Iteration 85 => Loss: 285.1696472167969
Iteration 86 => Loss: 280.8431396484375
Iteration 87 => Loss: 276.5603942871094
Iteration 88 => Loss: 272.3213806152344
Iteration 89 => Loss: 268.12615966796875
Iteration 90 => Loss: 263.97467041015625
Iteration 91 => Loss: 259.8669128417969
Iteration 92 => Loss: 255.80299377441406
Iteration 93 => Loss: 251.78277587890625
Iteration 94 => Loss: 247.8063507080078
Iteration 95 => Loss: 243.87368774414062
Iteration 96 => Loss: 239.98477172851562
Iteration 97 => Loss: 236.13958740234375
Iteration 98 => Loss: 232.3381805419922
Iteration 99 => Loss: 228.58055114746094
Iteration 100 => Loss: 224.86666870117188
Iteration 101 => Loss: 221.19654846191406
Iteration 102 => Loss: 217.57020568847656
Iteration 103 => Loss: 213.9875946044922
Iteration 104 => Loss: 210.44876098632812
Iteration 105 => Loss: 206.95367431640625
Iteration 106 => Loss: 203.50238037109375
Iteration 107 => Loss: 200.0947723388672
Iteration 108 => Loss: 196.73097229003906
Iteration 109 => Loss: 193.4109344482422
Iteration 110 => Loss: 190.13465881347656
Iteration 111 => Loss: 186.9021453857422
Iteration 112 => Loss: 183.71337890625
Iteration 113 => Loss: 180.56838989257812
Iteration 114 => Loss: 177.46714782714844
Iteration 115 => Loss: 174.40966796875
Iteration 116 => Loss: 171.39596557617188
Iteration 117 => Loss: 168.42599487304688
Iteration 118 => Loss: 165.4998016357422
Iteration 119 => Loss: 162.61734008789062
Iteration 120 => Loss: 159.77865600585938
Iteration 121 => Loss: 156.98373413085938
Iteration 122 => Loss: 154.23257446289062
Iteration 123 => Loss: 151.52517700195312
Iteration 124 => Loss: 148.86154174804688
Iteration 125 => Loss: 146.24166870117188
Iteration 126 => Loss: 143.66554260253906
Iteration 127 => Loss: 141.13319396972656
Iteration 128 => Loss: 138.64459228515625
Iteration 129 => Loss: 136.1997528076172
Iteration 130 => Loss: 133.79867553710938
Iteration 131 => Loss: 131.4413604736328
Iteration 132 => Loss: 129.12777709960938
Iteration 133 => Loss: 126.85798645019531
Iteration 134 => Loss: 124.6319351196289
Iteration 135 => Loss: 122.44966125488281
Iteration 136 => Loss: 120.31114196777344
Iteration 137 => Loss: 118.21638488769531
Iteration 138 => Loss: 116.16539001464844
Iteration 139 => Loss: 114.15814971923828
Iteration 140 => Loss: 112.19467163085938
Iteration 141 => Loss: 110.27494812011719
Iteration 142 => Loss: 108.39899444580078
Iteration 143 => Loss: 106.5667953491211
Iteration 144 => Loss: 104.77833557128906
Iteration 145 => Loss: 103.03366088867188
Iteration 146 => Loss: 101.3327407836914
Iteration 147 => Loss: 99.67557525634766
Iteration 148 => Loss: 98.06217956542969
Iteration 149 => Loss: 96.49254608154297
Iteration 150 => Loss: 94.96666717529297
Iteration 151 => Loss: 93.48454284667969
Iteration 152 => Loss: 92.04618835449219
Iteration 153 => Loss: 90.65159606933594
Iteration 154 => Loss: 89.3007583618164
Iteration 155 => Loss: 87.99366760253906
Iteration 156 => Loss: 86.73035430908203
Iteration 157 => Loss: 85.51078033447266
Iteration 158 => Loss: 84.3349838256836
Iteration 159 => Loss: 83.20294952392578
Iteration 160 => Loss: 82.11466217041016
Iteration 161 => Loss: 81.07015228271484
Iteration 162 => Loss: 80.06938171386719
Iteration 163 => Loss: 79.11238861083984
Iteration 164 => Loss: 78.19914245605469
Iteration 165 => Loss: 77.32966613769531
Iteration 166 => Loss: 76.50394439697266
Iteration 167 => Loss: 75.72199249267578
Iteration 168 => Loss: 74.9837875366211
Iteration 169 => Loss: 74.28933715820312
Iteration 170 => Loss: 73.63866424560547
Iteration 171 => Loss: 73.03173828125
Iteration 172 => Loss: 72.46858215332031
Iteration 173 => Loss: 71.94918823242188
Iteration 174 => Loss: 71.47354125976562
Iteration 175 => Loss: 71.04166412353516
Iteration 176 => Loss: 70.65354919433594
Iteration 177 => Loss: 70.30918884277344
Iteration 178 => Loss: 70.00858306884766
Iteration 179 => Loss: 69.75174713134766
Iteration 180 => Loss: 69.5386734008789
Iteration 181 => Loss: 69.36934661865234
Iteration 182 => Loss: 69.24378204345703
Iteration 183 => Loss: 69.1619873046875
Iteration 184 => Loss: 69.12394714355469

{:ok, 1.8400000000000014, 184}

Predict the number of pizzas for 20 reservations.

prediction = LinearRegression.predict(20, weight) |> Nx.to_number()
IO.puts("Prediction: x=20 => y=#{prediction}")

Prediction: x=20 => y=36.79999923706055

:ok

Plot the model overlayed on top of the data.

min = reservations |> Nx.reduce_min() |> Nx.to_number() |> round() |> IO.inspect(label: "min")
max = reservations |> Nx.reduce_max() |> Nx.to_number() |> round() |> IO.inspect(label: "max")

Vl.new(width: 650, height: 300)
|> Vl.layers([
  Vl.new()
  |> Vl.mark(:point, filled: true)
  |> Vl.data_from_values(
    Reservations: Nx.to_flat_list(reservations),
    Pizzas: Nx.to_flat_list(pizza)
  )
  |> Vl.encode_field(:x, "Reservations", type: :quantitative)
  |> Vl.encode_field(:y, "Pizzas", type: :quantitative),
  Vl.new()
  |> Vl.mark(:line, color: :pink)
  |> Vl.data_from_values(
    Reservations: [min, max],
    Pizzas: Nx.to_flat_list(Nx.multiply(Nx.tensor([min, max]), weight))
  )
  |> Vl.encode_field(:x, "Reservations", type: :quantitative)
  |> Vl.encode_field(:y, "Pizzas", type: :quantitative)
])

min: 1
max: 27

{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":300,"layer":[{"data":{"values":[{"Pizzas":33.0,"Reservations":13.0},{"Pizzas":16.0,"Reservations":2.0},{"Pizzas":32.0,"Reservations":14.0},{"Pizzas":51.0,"Reservations":23.0},{"Pizzas":27.0,"Reservations":13.0},{"Pizzas":16.0,"Reservations":1.0},{"Pizzas":34.0,"Reservations":18.0},{"Pizzas":17.0,"Reservations":10.0},{"Pizzas":29.0,"Reservations":26.0},{"Pizzas":15.0,"Reservations":3.0},{"Pizzas":15.0,"Reservations":3.0},{"Pizzas":32.0,"Reservations":21.0},{"Pizzas":22.0,"Reservations":7.0},{"Pizzas":37.0,"Reservations":22.0},{"Pizzas":13.0,"Reservations":2.0},{"Pizzas":44.0,"Reservations":27.0},{"Pizzas":16.0,"Reservations":6.0},{"Pizzas":21.0,"Reservations":10.0},{"Pizzas":37.0,"Reservations":18.0},{"Pizzas":30.0,"Reservations":15.0},{"Pizzas":26.0,"Reservations":9.0},{"Pizzas":34.0,"Reservations":26.0},{"Pizzas":23.0,"Reservations":8.0},{"Pizzas":39.0,"Reservations":15.0},{"Pizzas":27.0,"Reservations":10.0},{"Pizzas":37.0,"Reservations":21.0},{"Pizzas":17.0,"Reservations":5.0},{"Pizzas":18.0,"Reservations":6.0},{"Pizzas":25.0,"Reservations":13.0},{"Pizzas":23.0,"Reservations":13.0}]},"encoding":{"x":{"field":"Reservations","type":"quantitative"},"y":{"field":"Pizzas","type":"quantitative"}},"mark":{"filled":true,"type":"point"}},{"data":{"values":[{"Pizzas":1.840000033378601,"Reservations":1},{"Pizzas":49.68000030517578,"Reservations":27}]},"encoding":{"x":{"field":"Reservations","type":"quantitative"},"y":{"field":"Pizzas","type":"quantitative"}},"mark":{"color":"pink","type":"line"}}],"width":650}

defmodule Chapter1.LinearRegressionWithBias do
  import Nx.Defn

  @doc """
  For a given weight and bias, predict the output for a given input
  """
  @spec predict(Nx.Tensor.t(), number(), number()) :: Nx.Tensor.t()
  defn predict(x, weight, bias) do
    x * weight + bias
  end

  @doc """
  Calculate the loss, as a mean squared error, for the given weight
  """
  @spec loss(Nx.Tensor.t(), Nx.Tensor.t(), number(), number()) :: number()
  def loss(x, y, weight, bias) do
    Nx.subtract(predict(x, weight, bias), y)
    |> Nx.power(2)
    |> Nx.mean()
    |> Nx.to_number()
  end

  @doc """
  Train a linear regression model with a maximum number of iterations
  """
  @spec train(Nx.Tensor.t(), Nx.Tensor.t(), non_neg_integer(), float()) ::
          {:ok, float()} | {:error, String.t()}
  def train(x, y, iterations, lr = _learning_rate) do
    0..iterations
    |> Enum.reduce_while({0, 0, 0}, fn iteration, {weight, bias, _} ->
      current_loss = loss(x, y, weight, bias)

      IO.puts("Iteration #{iteration} => Loss: #{current_loss |> Nx.to_number()}")

      cond do
        loss(x, y, weight + lr, bias) < current_loss ->
          {:cont, {weight + lr, bias, iteration}}

        loss(x, y, weight - lr, bias) < current_loss ->
          {:cont, {weight - lr, bias, iteration}}

        loss(x, y, weight, bias + lr) < current_loss ->
          {:cont, {weight, bias + lr, iteration}}

        loss(x, y, weight, bias - lr) < current_loss ->
          {:cont, {weight, bias - lr, iteration}}

        true ->
          {:halt, {weight, bias, iteration}}
      end
    end)
    |> case do
      {_weight, _bias, ^iterations} -> {:error, "Couldn't converge within #{iterations}"}
      {weight, bias, number_of_iterations} -> {:ok, weight, bias, number_of_iterations}
    end
  end
end

warning: Nx.power/2 is deprecated. Use pow/2 instead
  Documents/GitHub/programming-machine-learning/elixir-programming-machine-learning.livemd#cell:b5epztx5m4c3j37x3tmrdkfuk32ajm5i:18: Chapter1.LinearRegressionWithBias.loss/4

{:module, Chapter1.LinearRegressionWithBias, <<70, 79, 82, 49, 0, 0, 20, ...>>, {:train, 4}}

alias Chapter1.LinearRegressionWithBias

Chapter1.LinearRegressionWithBias

Train the system, using both a weight and bias, with 10,000 iterations and a learning rate of 0.01.

{:ok, weight, bias, iterations} =
  LinearRegressionWithBias.train(reservations, pizza, 10_000, 0.01)

...
Iteration 553 => Loss: 47.847782135009766
Iteration 554 => Loss: 47.795814514160156
Iteration 555 => Loss: 47.74403762817383
Iteration 556 => Loss: 47.69247817993164
Iteration 557 => Loss: 47.64110565185547
Iteration 558 => Loss: 47.58994674682617
Iteration 559 => Loss: 47.538978576660156
Iteration 560 => Loss: 47.488216400146484
Iteration 561 => Loss: 47.43764114379883
Iteration 562 => Loss: 47.38727951049805
Iteration 563 => Loss: 47.33710861206055
Iteration 564 => Loss: 47.28713607788086
Iteration 565 => Loss: 47.23737716674805
Iteration 566 => Loss: 47.236087799072266
Iteration 567 => Loss: 47.183982849121094
Iteration 568 => Loss: 47.13208770751953
Iteration 569 => Loss: 47.080387115478516
Iteration 570 => Loss: 47.02888870239258
Iteration 571 => Loss: 46.97758865356445
Iteration 572 => Loss: 46.926490783691406
Iteration 573 => Loss: 46.875587463378906
Iteration 574 => Loss: 46.82488250732422
Iteration 575 => Loss: 46.77438735961914
Iteration 576 => Loss: 46.724082946777344
Iteration 577 => Loss: 46.67399215698242
Iteration 578 => Loss: 46.624088287353516
Iteration 579 => Loss: 46.57439041137695
Iteration 580 => Loss: 46.52488708496094
Iteration 581 => Loss: 46.475582122802734
Iteration 582 => Loss: 46.426490783691406
Iteration 583 => Loss: 46.37758255004883
Iteration 584 => Loss: 46.37697982788086
Iteration 585 => Loss: 46.32575607299805
Iteration 586 => Loss: 46.27471923828125
Iteration 587 => Loss: 46.2238883972168
Iteration 588 => Loss: 46.173255920410156
Iteration 589 => Loss: 46.12281799316406
Iteration 590 => Loss: 46.07258605957031
Iteration 591 => Loss: 46.02254867553711
Iteration 592 => Loss: 45.97271728515625
Iteration 593 => Loss: 45.92308807373047
Iteration 594 => Loss: 45.873653411865234
Iteration 595 => Loss: 45.82441711425781
Iteration 596 => Loss: 45.775390625
Iteration 597 => Loss: 45.7265510559082
Iteration 598 => Loss: 45.677921295166016
Iteration 599 => Loss: 45.62948989868164
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Iteration 1550 => Loss: 22.863733291625977
Iteration 1551 => Loss: 22.86355972290039

{:ok, 1.1000000000000008, 12.929999999999769, 1551}

Predict the number of pizzas for 20 reservations, this time using a bias in addition to a weight.

prediction = LinearRegressionWithBias.predict(20, weight, bias) |> Nx.to_number()
IO.puts("Prediction: x=20 => y=#{prediction}")

Prediction: x=20 => y=34.93000030517578

:ok

Plot the model overlayed on top of the data.

Vl.new(width: 650, height: 300)
|> Vl.layers([
  Vl.new()
  |> Vl.mark(:point, filled: true)
  |> Vl.data_from_values(
    Reservations: Nx.to_flat_list(reservations),
    Pizzas: Nx.to_flat_list(pizza)
  )
  |> Vl.encode_field(:x, "Reservations", type: :quantitative)
  |> Vl.encode_field(:y, "Pizzas", type: :quantitative),
  Vl.new()
  |> Vl.mark(:line, color: :pink)
  |> Vl.data_from_values(
    Reservations: [min, max],
    Pizzas:
      Nx.tensor([min, max])
      |> Nx.multiply(weight)
      |> Nx.add(bias)
      |> Nx.to_flat_list()
  )
  |> Vl.encode_field(:x, "Reservations", type: :quantitative)
  |> Vl.encode_field(:y, "Pizzas", type: :quantitative)
])

{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":300,"layer":[{"data":{"values":[{"Pizzas":33.0,"Reservations":13.0},{"Pizzas":16.0,"Reservations":2.0},{"Pizzas":32.0,"Reservations":14.0},{"Pizzas":51.0,"Reservations":23.0},{"Pizzas":27.0,"Reservations":13.0},{"Pizzas":16.0,"Reservations":1.0},{"Pizzas":34.0,"Reservations":18.0},{"Pizzas":17.0,"Reservations":10.0},{"Pizzas":29.0,"Reservations":26.0},{"Pizzas":15.0,"Reservations":3.0},{"Pizzas":15.0,"Reservations":3.0},{"Pizzas":32.0,"Reservations":21.0},{"Pizzas":22.0,"Reservations":7.0},{"Pizzas":37.0,"Reservations":22.0},{"Pizzas":13.0,"Reservations":2.0},{"Pizzas":44.0,"Reservations":27.0},{"Pizzas":16.0,"Reservations":6.0},{"Pizzas":21.0,"Reservations":10.0},{"Pizzas":37.0,"Reservations":18.0},{"Pizzas":30.0,"Reservations":15.0},{"Pizzas":26.0,"Reservations":9.0},{"Pizzas":34.0,"Reservations":26.0},{"Pizzas":23.0,"Reservations":8.0},{"Pizzas":39.0,"Reservations":15.0},{"Pizzas":27.0,"Reservations":10.0},{"Pizzas":37.0,"Reservations":21.0},{"Pizzas":17.0,"Reservations":5.0},{"Pizzas":18.0,"Reservations":6.0},{"Pizzas":25.0,"Reservations":13.0},{"Pizzas":23.0,"Reservations":13.0}]},"encoding":{"x":{"field":"Reservations","type":"quantitative"},"y":{"field":"Pizzas","type":"quantitative"}},"mark":{"filled":true,"type":"point"}},{"data":{"values":[{"Pizzas":14.030000686645508,"Reservations":1},{"Pizzas":42.630001068115234,"Reservations":27}]},"encoding":{"x":{"field":"Reservations","type":"quantitative"},"y":{"field":"Pizzas","type":"quantitative"}},"mark":{"color":"pink","type":"line"}}],"width":650}