View Source Scholar.Linear.IsotonicRegression (Scholar v0.3.0)

Isotonic regression is a method of fitting a free-form line to a set of observations by solving a convex optimization problem. It is a form of regression analysis that can be used as an alternative to polynomial regression to fit nonlinear data.

Time complexity of isotonic regression is $O(N^2)$ where $N$ is the number of points.

Summary

Types

t()

Functions

check_preprocess(model)

fit(x, y, opts \\ [])

Fits a isotonic regression model for sample inputs x and sample targets y.

predict(model, x)

Makes predictions with the given model on input x and interpolating function.

preprocess(model, trim_duplicates \\ true)

Preprocesses the model for prediction.

Types

t()

@type t() :: %Scholar.Linear.IsotonicRegression{
  cutoff_index: Nx.Tensor.t(),
  increasing: Nx.Tensor.t(),
  preprocess: tuple() | Scholar.Interpolation.Linear.t(),
  x_max: Nx.Tensor.t(),
  x_min: Nx.Tensor.t(),
  x_thresholds: Nx.Tensor.t(),
  y_thresholds: Nx.Tensor.t()
}

Functions

check_preprocess(model)

fit(x, y, opts \\ [])

Fits a isotonic regression model for sample inputs x and sample targets y.

Options

:y_min (float/0) - Lower bound on the lowest predicted value. If if not provided, the lower bound is set to Nx.Constant.neg_infinity().
:y_max (float/0) - Upper bound on the highest predicted value. If if not provided, the lower bound is set to Nx.Constant.infinity().
:increasing - Whether the isotonic regression should be fit with the constraint that the function is monotonically increasing. If false, the constraint is that the function is monotonically decreasing. If :auto, the constraint is determined automatically based on the data. The default value is :auto.
:out_of_bounds - How to handle out-of-bounds points. If :clip, out-of-bounds points are mapped to the nearest valid value. If :nan, out-of-bounds points are replaced with Nx.Constant.nan(). The default value is :nan.
:sample_weights - The weights for each observation. If not provided, all observations are assigned equal weight.

Return Values

The function returns a struct with the following parameters:

:x_min - Minimum value of input tensor x.
:x_max - Maximum value of input tensor x.
:x_thresholds - Thresholds used for predictions.
:y_thresholds - Predicted values associated with each threshold.
:increasing - Whether the isotonic regression is increasing.
:cutoff_index - The index of the last valid threshold. Rest elements are placeholders for the sake of preserving shape of tensor.
:preprocess - Interpolation function to be applied on input tensor x. Before preprocess/1 is applied it is set to {}

Examples

iex> x = Nx.tensor([1, 4, 7, 9, 10, 11])
iex> y = Nx.tensor([1, 3, 6, 8, 9, 10])
iex> Scholar.Linear.IsotonicRegression.fit(x, y)
%Scholar.Linear.IsotonicRegression{
  x_min: Nx.tensor(
    1.0
  ),
  x_max: Nx.tensor(
    11.0
  ),
  x_thresholds: Nx.tensor(
    [1.0, 4.0, 7.0, 9.0, 10.0, 11.0]
  ),
  y_thresholds: Nx.tensor(
    [1.0, 3.0, 6.0, 8.0, 9.0, 10.0]
  ),
  increasing: Nx.u8(1),
  cutoff_index: Nx.tensor(
    5
  ),
  preprocess: {}
}

predict(model, x)

Makes predictions with the given model on input x and interpolating function.

Examples

iex> x = Nx.tensor([1, 4, 7, 9, 10, 11])
iex> y = Nx.tensor([1, 3, 6, 8, 9, 10])
iex> model = Scholar.Linear.IsotonicRegression.fit(x, y)
iex> model = Scholar.Linear.IsotonicRegression.preprocess(model)
iex> to_predict = Nx.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
iex> Scholar.Linear.IsotonicRegression.predict(model, to_predict)
#Nx.Tensor<
  f32[10]
  [1.0, 1.6666667461395264, 2.3333332538604736, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0]
>

preprocess(model, trim_duplicates \\ true)

Preprocesses the model for prediction.

Returns an updated model.

Examples

iex> x = Nx.tensor([1, 4, 7, 9, 10, 11])
iex> y = Nx.tensor([1, 3, 6, 8, 9, 10])
iex> model = Scholar.Linear.IsotonicRegression.fit(x, y)
iex> Scholar.Linear.IsotonicRegression.preprocess(model)
%Scholar.Linear.IsotonicRegression{
  x_min: Nx.tensor(
    1.0
  ),
  x_max: Nx.tensor(
    11.0
  ),
  x_thresholds: Nx.tensor(
    [1.0, 4.0, 7.0, 9.0, 10.0, 11.0]
  ),
  y_thresholds: Nx.tensor(
    [1.0, 3.0, 6.0, 8.0, 9.0, 10.0]
  ),
  increasing: Nx.u8(1),
  cutoff_index: Nx.tensor(
    5
  ),
  preprocess: %Scholar.Interpolation.Linear{
    coefficients: Nx.tensor(
      [
        [0.6666666865348816, 0.3333333134651184],
        [1.0, -1.0],
        [1.0, -1.0],
        [1.0, -1.0],
        [1.0, -1.0]
      ]
    ),
    x: Nx.tensor(
      [1.0, 4.0, 7.0, 9.0, 10.0, 11.0]
    )
  }
}