Chapter 2

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

alias VegaLite, as: Vl

Data

[reservations, pizzas] =
  (__DIR__ <> "/data/pizza.txt")
  |> Path.expand()
  |> File.read!()
  |> String.split()
  |> Enum.drop(2)
  |> Enum.map(&amp;String.to_integer/1)
  |> Enum.chunk_every(2)
  |> Enum.zip_with(&amp;Nx.tensor/1)

plot =
  Vl.new(width: 300, height: 300)
  |> Vl.data_from_values(%{
    "Reservations" => Nx.to_list(reservations),
    "Pizzas" => Nx.to_list(pizzas)
  })
  |> Vl.mark(:circle)
  |> Vl.encode_field(:x, "Reservations", type: :quantitative)
  |> Vl.encode_field(:y, "Pizzas", type: :quantitative)

Linear Regression

defmodule LinearRegression do
  import Nx.Defn

  defn predict(x, w, b) do
    Nx.dot(x, w) + b
  end

  defn loss(x, y, w, b) do
    predict(x, w, b)
    |> Nx.subtract(y)
    |> Nx.pow(2)
    |> Nx.mean()
  end

  def train(x, y, iterations, lr) do
    Enum.reduce_while(1..iterations, {:training, 0, 0}, fn i, {:training, w, b} ->
      current_loss = Nx.to_number(loss(x, y, w, b))
      IO.puts("Iteration #{i}, loss #{current_loss}")

      cond do
        Nx.to_number(loss(x, y, w + lr, b)) < current_loss -> {:cont, {:training, w + lr, b}}
        Nx.to_number(loss(x, y, w - lr, b)) < current_loss -> {:cont, {:training, w - lr, b}}
        Nx.to_number(loss(x, y, w, b + lr)) < current_loss -> {:cont, {:training, w, b + lr}}
        Nx.to_number(loss(x, y, w, b - lr)) < current_loss -> {:cont, {:training, w, b - lr}}
        true -> {:halt, {:ok, w, b}}
      end
    end)
  end
end

{:ok, w, b} = LinearRegression.train(reservations, pizzas, 10000, 0.01)

LinearRegression.predict(20, w, b)

Vl.new()
|> Vl.layers([
  plot,
  Vl.new()
  |> Vl.data_from_values(%{
    "Reservations" => [0, 50],
    "Pizzas" => [b, LinearRegression.predict(50, w, b) |> Nx.to_number()]
  })
  |> Vl.mark(:line)
  |> Vl.encode_field(:x, "Reservations", type: :quantitative)
  |> Vl.encode_field(:y, "Pizzas", type: :quantitative)
])

Tuning hyperparameters

LinearRegression.train(reservations, pizzas, 100_000, 0.001)

LinearRegression.train(reservations, pizzas, 10000, 0.1)

LinearRegression.train(reservations, pizzas, 10000, 1)