Estimate the shrunk Ledoit-Wolf covariance matrix.

Options

• :assume_centered? (boolean/0) - If true, data will not be centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If false, data will be centered before computation. The default value is false.

Return Values

The function returns a struct with the following parameters:

• :covariance - Tensor of shape {num_features, num_features}. Estimated covariance matrix.

• :shrinkage - Coefficient in the convex combination used for the computation of the shrunken estimate. Range is [0, 1].

• :location - Tensor of shape {num_features,}. Estimated location, i.e. the estimated mean.

Examples

iex> key = Nx.Random.key(0)
iex> {x, _new_key} = Nx.Random.multivariate_normal(key, Nx.tensor([0.0, 0.0]), Nx.tensor([[0.4, 0.2], [0.2, 0.8]]), shape: {50}, type: :f32)
iex> model = Scholar.Covariance.LedoitWolf.fit(x)
iex> model.covariance
#Nx.Tensor<
  f32[2][2]
  [
    [0.3557686507701874, 0.17340737581253052],
    [0.17340737581253052, 1.0300586223602295]
  ]
>
iex> model.shrinkage
#Nx.Tensor<
  f32
  0.15034137666225433
>
iex> model.location
#Nx.Tensor<
  f32[2]
  [0.17184630036354065, 0.3276958167552948]
>

iex> key = Nx.Random.key(0)
iex> {x, _new_key} = Nx.Random.multivariate_normal(key, Nx.tensor([0.0, 0.0, 0.0]), Nx.tensor([[3.0, 2.0, 1.0], [1.0, 2.0, 3.0], [1.3, 1.0, 2.2]]), shape: {10}, type: :f32)
iex> model = Scholar.Covariance.LedoitWolf.fit(x)
iex> model.covariance
#Nx.Tensor<
  f32[3][3]
  [
    [2.5945029258728027, 1.5078359842300415, 1.1623677015304565],
    [1.5078359842300415, 2.106797456741333, 1.1812156438827515],
    [1.1623677015304565, 1.1812156438827515, 1.4606266021728516]
  ]
>
iex> model.shrinkage
#Nx.Tensor<
  f32
  0.1908363401889801
>
iex> model.location
#Nx.Tensor<
  f32[3]
  [1.1228725910186768, 0.5419300198554993, 0.8678852319717407]
>

iex> key = Nx.Random.key(0)
iex> {x, _new_key} = Nx.Random.multivariate_normal(key, Nx.tensor([0.0, 0.0, 0.0]), Nx.tensor([[3.0, 2.0, 1.0], [1.0, 2.0, 3.0], [1.3, 1.0, 2.2]]), shape: {10}, type: :f32)
iex> cov = Scholar.Covariance.LedoitWolf.fit(x, assume_centered?: true)
iex> cov.covariance
#Nx.Tensor<
  f32[3][3]
  [
    [3.8574986457824707, 2.2048025131225586, 2.1504499912261963],
    [2.2048025131225586, 2.4572863578796387, 1.7215262651443481],
    [2.1504499912261963, 1.7215262651443481, 2.154898166656494]
  ]
>copy