Chapter 5

Mix.install([
  {:nx, "~> 0.6.4"},
  {:vega_lite, "~> 0.1.8"},
  {:kino_vega_lite, "~> 0.1.11"}
])

alias VegaLite, as: Vl

Data

data =
  (__DIR__ <> "/data/police.txt")
  |> Path.expand()
  |> File.read!()
  |> String.split()
  |> Enum.drop(4)
  |> Enum.map(&amp;String.to_integer/1)
  |> Enum.chunk_every(4)
  |> Nx.tensor()

{reservations, police} = {data[[.., 0]], data[[.., -1]]}

plot =
  Vl.new(width: 600, height: 600)
  |> Vl.data_from_values(%{
    "Reservations" => Nx.to_list(reservations),
    "Police Call" => Nx.to_list(police)
  })
  |> Vl.mark(:point)
  |> Vl.encode_field(:x, "Reservations", type: :quantitative)
  |> Vl.encode_field(:y, "Police Call", type: :quantitative)

Sigmoid

defmodule Classifier do
  import Nx.Defn

  defn sigmoid(z) do
    1 / (1 + Nx.exp(-z))
  end

  defn forward(x, w) do
    Nx.dot(x, w)
    |> sigmoid()
  end

  defn classify(x, w) do
    forward(x, w)
    |> Nx.round()
  end

  defn loss(x, y, w) do
    y_hat = forward(x, w)
    first_term = y * Nx.log(y_hat)
    second_term = (1 - y) * Nx.log(1 - y_hat)
    -Nx.mean(first_term + second_term)
  end

  defn gradient(x, y, w) do
    (forward(x, w) - y)
    |> Nx.dot(x)
    |> Nx.divide(Nx.axis_size(x, 0))
  end

  def train(x, y, iterations, lr) do
    Enum.reduce(1..iterations, Nx.broadcast(0.0, {Nx.axis_size(x, 1)}), fn i, w ->
      IO.puts("Iteration #{i}, loss #{Nx.to_number(loss(x, y, w))}")
      Nx.subtract(w, Nx.multiply(gradient(x, y, w), lr))
    end)
  end

  def test(x, y, w) do
    Nx.equal(classify(x, w), y)
    |> then(&[correct: Nx.sum(&1), total: Nx.size(&1), accuracy: Nx.mean(&1)])
    |> Enum.map(fn {k, v} -> {k, Nx.to_number(v)} end)
  end
end

x = Nx.pad(data[[.., 0..2]], 1, [{0, 0, 0}, {1, 0, 0}])
y = data[[.., 3]]
w = Classifier.train(x, y, 10000, 0.001)

Classifier.test(x, y, w)

classifications = Classifier.classify(x, w)

Vl.new()
|> Vl.layers([
  plot,
  Vl.new()
  |> Vl.data_from_values(%{
    "Reservations" => Nx.to_list(reservations),
    "Police Call" => Nx.to_list(classifications)
  })
  |> Vl.mark(:tick)
  |> Vl.encode_field(:x, "Reservations", type: :quantitative)
  |> Vl.encode_field(:y, "Police Call", type: :quantitative)
])