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: Maximum number of Gaussian centers in the kernel gram matrix. Defaults to all numerator samples.
centers: Numeric matrix with the same variables as nu and de that are used as Gaussian centers in the kernel Gram matrix. By default, the matrix nu is used as the matrix with Gaussian centers.
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
dr <- naive(numerator_small, denominator_small)
# Inspect model object
dr
#> 
#> Call:
#> naive(df_numerator = numerator_small, df_denominator = denominator_small)
#> 
#> Naive density ratio
#>   Number of variables: 3
#>   Number of numerator samples: 50
#>   Number of denominator samples: 100
#>   Numerator density: num [1:50] 1.41 5.74 1.87 4.13 1.67 ...
#>   Denominator density: num [1:100] 2.93 0.071 1.065 1.59 2.115 ...
#>  
# Obtain summary of model object
summary(dr)
#> 
#> Call:
#> naive(df_numerator = numerator_small, df_denominator = denominator_small)
#> 
#> Naive density ratio estimate:
#>   Number of variables: 
#>   Number of numerator samples: 50
#>   Number of denominator samples: 100
#>   Density ratio for numerator samples: num [1:50] 0.344 1.747 0.628 1.419 0.511 ...
#>   Density ratio for denominator samples: num [1:100] 1.0751 -2.6454 0.0626 0.464 0.7493 ...
#>  
#> 
#> Squared average log density ratio difference for numerator and denominator samples (SALDRD): 13.56
#> For a two-sample homogeneity test, use 'summary(x, test = TRUE)'.
#> 
# Plot model object
plot(dr)
#> Warning: Negative estimated density ratios for 25 observation(s) converted to 0.01 before applying logarithmic transformation
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# Plot density ratio for each variable individually
plot_univariate(dr)
#> Warning: Negative estimated density ratios for 25 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 25 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] 1.410607 5.739287 1.874031 4.131255 1.666760 4.095855
# Fit model with custom parameters
naive(numerator_small, denominator_small, m=2, kernel="epanechnikov")
#> 
#> Call:
#> naive(df_numerator = numerator_small, df_denominator = denominator_small,     m = 2, kernel = "epanechnikov")
#> 
#> Naive density ratio
#>   Number of variables: 3
#>   Number of numerator samples: 50
#>   Number of denominator samples: 100
#>   Numerator density: num [1:50] 0.572 1.421 0.945 1.058 0.936 ...
#>   Denominator density: num [1:100] 1.391 1.459 0.572 0.943 1.314 ...
#>