Least-squares heterodistributional subspace search

Usage

lhss(
  df_numerator,
  df_denominator,
  m = NULL,
  intercept = TRUE,
  scale = "numerator",
  nsigma = 10,
  sigma_quantile = NULL,
  sigma = NULL,
  nlambda = 10,
  lambda = NULL,
  ncenters = 200,
  centers = NULL,
  maxit = 200,
  progressbar = TRUE
)

Arguments

df_numerator: data.frame with exclusively numeric variables with the numerator samples
df_denominator: data.frame with exclusively numeric variables with the denominator samples (must have the same variables as df_denominator)
m: Scalar indicating the dimensionality of the reduced subspace
intercept: logical Indicating whether to include an intercept term in the model. Defaults to TRUE.
scale: "numerator", "denominator", or NULL, indicating whether to standardize each numeric variable according to the numerator means and standard deviations, the denominator means and standard deviations, or apply no standardization at all.
nsigma: Integer indicating the number of sigma values (bandwidth parameter of the Gaussian kernel gram matrix) to use in cross-validation.
sigma_quantile: NULL or numeric vector with probabilities to calculate the quantiles of the distance matrix to obtain sigma values. If NULL, nsigma values between 0.05 and 0.95 are used.
sigma: NULL or a scalar value to determine the bandwidth of the Gaussian kernel gram matrix. If NULL, nsigma values between 0.05 and 0.95 are used.
nlambda: Integer indicating the number of lambda values (regularization parameter), by default, lambda is set to 10^seq(3, -3, length.out = nlambda).
lambda: NULL or numeric vector indicating the lambda values to use in cross-validation
ncenters: integer Maximum number of Gaussian centers in the kernel gram matrix.
centers: NULL or data.frame with the same dimensions as the data, indicating the centers for the Gaussian kernel gram matrix.
maxit: Maximum number of iterations in the updating scheme.
progressbar: Logical indicating whether or not to display a progressbar.

Value

lhss-object, containing all information to calculate the density ratio using optimal sigma, optimal lambda and optimal weights.

References

Sugiyama, M., Yamada, M., Von Bünau, P., Suzuki, T., Kanamori, T. & Kawanabe, M. (2011). Direct density-ratio estimation with dimensionality reduction via least-squares hetero-distributional subspace search. Neural Networks, 24, 183-198. doi:10.1016/j.neunet.2010.10.005 .

Examples



set.seed(123)
# Fit model (minimal example to limit computation time)
dr <- lhss(numerator_small, denominator_small,
           nsigma = 3, lambda = c(0.1, 1), ncenters = 50, maxit = 100)
# Inspect model object
dr
#> 
#> Call:
#> lhss(df_numerator = numerator_small, df_denominator = denominator_small,     nsigma = 3, lambda = c(0.1, 1), ncenters = 50, maxit = 100)
#> 
#> Kernel Information:
#>   Kernel type: Gaussian with L2 norm distances
#>   Number of kernels: 50
#>   sigma: num [1:3, 1:2] 0.0793 0.9371 2.677 0.0693 0.9633 ...
#> 
#> Regularization parameter (lambda): num [1:2] 0.1 1
#> 
#> Subspace dimension (m): 1
#> Optimal sigma: 2.677003
#> Optimal lambda: 0.1
#> Optimal kernel weights (loocv): num [1:51] 6.666 -0.3081 -0.0385 -0.0353 0.0108 ...
#>  
# Obtain summary of model object
summary(dr)
#> 
#> Call:
#> lhss(df_numerator = numerator_small, df_denominator = denominator_small,     nsigma = 3, lambda = c(0.1, 1), ncenters = 50, maxit = 100)
#> 
#> Kernel Information:
#>   Kernel type: Gaussian with L2 norm distances
#>   Number of kernels: 50
#> 
#> Subspace dimension (m): 1
#> Optimal sigma: 2.677003
#> Optimal lambda: 0.1
#> Optimal kernel weights (loocv): num [1:51] 6.666 -0.3081 -0.0385 -0.0353 0.0108 ...
#>  
#> Pearson divergence between P(nu) and P(de): 0.6358
#> For a two-sample homogeneity test, use 'summary(x, test = TRUE)'.
#> 
# Plot model object
plot(dr)
#> Warning: Negative estimated density ratios for 12 observation(s) converted to 0.01 before applying logarithmic transformation
#> `stat_bin()` using `bins = 30`. Pick better value `binwidth`.

# Plot density ratio for each variable individually
plot_univariate(dr)
#> Warning: Negative estimated density ratios for 12 observation(s) converted to 0.01 before applying logarithmic transformation
#> [[1]]

#> 
#> [[2]]

#> 
#> [[3]]

#> 
# Plot density ratio for each pair of variables
plot_bivariate(dr)
#> Warning: Negative estimated density ratios for 12 observation(s) converted to 0.01 before applying logarithmic transformation
#> [[1]]

#> 
#> [[2]]

#> 
#> [[3]]

#> 
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
#> , , 1
#> 
#>           [,1]
#> [1,] 2.1625009
#> [2,] 3.6694722
#> [3,] 2.7969688
#> [4,] 4.1387638
#> [5,] 0.1585054
#> [6,] 1.2616673
#>