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Semi-supervised learning: small labeled set plus large unlabeled pool

Source: R/geron_w4d_native.R
morie_geron_semisupervised.Rd

theta = (X_l'X_l + alpha X_u'LX_u)^-1 X_l'y_l, with L = D - W the graph Laplacian of the RBF affinity on the unlabeled pool.

Usage

morie_geron_semisupervised(
  X_l,
  y_l,
  X_u,
  alpha = 1,
  gamma = 1,
  fit_intercept = TRUE
)

Arguments

X_l

Labeled inputs (n_l, d).

y_l

Labels, length n_l.

X_u

Unlabeled pool (n_u, d).

alpha

Smoothness weight (>=0).

gamma

RBF width (>0).

fit_intercept

Prepend intercept column.

Value

list with theta, fitted, unlabeled_pred, sup_loss, roughness, objective, laplacian, affinity, alpha, estimate, n, method.

Examples

morie_geron_semisupervised(X_l = c(1, 2, 3, 4, 5, 6, 7, 8), y_l = c(1, 2, 3, 4, 5, 6, 7, 8),
  X_u = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $theta
#> [1] 0.3018931 0.9329127
#> 
#> $fitted
#> [1] 1.234806 2.167718 3.100631 4.033544 4.966456 5.899369 6.832282 7.765194
#> 
#> $unlabeled_pred
#> [1] 1.234806 2.167718 3.100631 4.033544 4.966456 5.899369 6.832282 7.765194
#> 
#> $sup_loss
#> [1] 0.02362874
#> 
#> $roughness
#> [1] 2.628639
#> 
#> $objective
#> [1] 2.817669
#> 
#> $laplacian
#>               [,1]          [,2]          [,3]          [,4]          [,5]
#> [1,]  3.863186e-01 -3.678794e-01 -1.831564e-02 -1.234098e-04 -1.125352e-07
#> [2,] -3.678794e-01  7.541980e-01 -3.678794e-01 -1.831564e-02 -1.234098e-04
#> [3,] -1.831564e-02 -3.678794e-01  7.725137e-01 -3.678794e-01 -1.831564e-02
#> [4,] -1.234098e-04 -1.831564e-02 -3.678794e-01  7.726371e-01 -3.678794e-01
#> [5,] -1.125352e-07 -1.234098e-04 -1.831564e-02 -3.678794e-01  7.726371e-01
#> [6,] -1.388794e-11 -1.125352e-07 -1.234098e-04 -1.831564e-02 -3.678794e-01
#> [7,] -2.319523e-16 -1.388794e-11 -1.125352e-07 -1.234098e-04 -1.831564e-02
#> [8,] -5.242886e-22 -2.319523e-16 -1.388794e-11 -1.125352e-07 -1.234098e-04
#>               [,6]          [,7]          [,8]
#> [1,] -1.388794e-11 -2.319523e-16 -5.242886e-22
#> [2,] -1.125352e-07 -1.388794e-11 -2.319523e-16
#> [3,] -1.234098e-04 -1.125352e-07 -1.388794e-11
#> [4,] -1.831564e-02 -1.234098e-04 -1.125352e-07
#> [5,] -3.678794e-01 -1.831564e-02 -1.234098e-04
#> [6,]  7.725137e-01 -3.678794e-01 -1.831564e-02
#> [7,] -3.678794e-01  7.541980e-01 -3.678794e-01
#> [8,] -1.831564e-02 -3.678794e-01  3.863186e-01
#> 
#> $affinity
#>              [,1]         [,2]         [,3]         [,4]         [,5]
#> [1,] 0.000000e+00 3.678794e-01 1.831564e-02 1.234098e-04 1.125352e-07
#> [2,] 3.678794e-01 0.000000e+00 3.678794e-01 1.831564e-02 1.234098e-04
#> [3,] 1.831564e-02 3.678794e-01 0.000000e+00 3.678794e-01 1.831564e-02
#> [4,] 1.234098e-04 1.831564e-02 3.678794e-01 0.000000e+00 3.678794e-01
#> [5,] 1.125352e-07 1.234098e-04 1.831564e-02 3.678794e-01 0.000000e+00
#> [6,] 1.388794e-11 1.125352e-07 1.234098e-04 1.831564e-02 3.678794e-01
#> [7,] 2.319523e-16 1.388794e-11 1.125352e-07 1.234098e-04 1.831564e-02
#> [8,] 5.242886e-22 2.319523e-16 1.388794e-11 1.125352e-07 1.234098e-04
#>              [,6]         [,7]         [,8]
#> [1,] 1.388794e-11 2.319523e-16 5.242886e-22
#> [2,] 1.125352e-07 1.388794e-11 2.319523e-16
#> [3,] 1.234098e-04 1.125352e-07 1.388794e-11
#> [4,] 1.831564e-02 1.234098e-04 1.125352e-07
#> [5,] 3.678794e-01 1.831564e-02 1.234098e-04
#> [6,] 0.000000e+00 3.678794e-01 1.831564e-02
#> [7,] 3.678794e-01 0.000000e+00 3.678794e-01
#> [8,] 1.831564e-02 3.678794e-01 0.000000e+00
#> 
#> $alpha
#> [1] 1
#> 
#> $estimate
#> [1] 0.02362874
#> 
#> $n
#> [1] 16
#> 
#> $method
#> [1] "Laplacian-regularised least squares: supervised loss + alpha * graph smoothness on the unlabeled pool"
#>