| Type: | Package |
| Title: | Distribution Comparison Through Density Ratio Estimation |
| Version: | 0.2.2 |
| Description: | Fast, flexible and user-friendly tools for distribution comparison through direct density ratio estimation. The estimated density ratio can be used for covariate shift adjustment, outlier-detection, change-point detection, classification and evaluation of synthetic data quality. The package implements multiple non-parametric estimation techniques (unconstrained least-squares importance fitting, ulsif(), Kullback-Leibler importance estimation procedure, kliep(), spectral density ratio estimation, spectral(), kernel mean matching, kmm(), and least-squares hetero-distributional subspace search, lhss()). with automatic tuning of hyperparameters. Helper functions are available for two-sample testing and visualizing the density ratios. For an overview on density ratio estimation, see Sugiyama et al. (2012) <doi:10.1017/CBO9781139035613> for a general overview, and the help files for references on the specific estimation techniques. |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| LazyData: | true |
| Imports: | osqp, Rcpp, pbapply, ggplot2, ggh4x |
| LinkingTo: | Rcpp, RcppArmadillo, RcppProgress |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| Config/testthat/parallel: | true |
| Depends: | R (≥ 2.10) |
| RoxygenNote: | 7.3.2 |
| VignetteBuilder: | knitr |
| URL: | https://thomvolker.github.io/densityratio/, https://github.com/thomvolker/densityratio |
| BugReports: | https://github.com/thomvolker/densityratio/issues |
| NeedsCompilation: | yes |
| Packaged: | 2025-07-18 16:10:22 UTC; 5868777 |
| Author: | Thom Volker  [aut,
cre],
Carlos Gonzalez Poses [ctb],
Erik-Jan van Kesteren [ctb] |
| Maintainer: | Thom Volker <thombenjaminvolker@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-07-18 16:40:02 UTC |
colon
Description
Colon cancer data set from princeton, containing 2000 gene expressions from 22 colon tumor tissues and 40 non-tumor tissues. The data is collected by Alon et al. (1999) and can be obtained from here.
Format
A data.frame with 62 rows and 2001 columns (class variable and 2000 gene expressions).
Bivariate plot
Description
Bivariate plot
Usage
create_bivariate_plot(data, ext, vars, logscale, show.sample)
Arguments
data |
Data frame with the individual values and density ratio estimates |
ext |
Data frame with the density ratio estimates and sample indicator |
vars |
Character vector of variable names to be plotted. |
logscale |
Logical indicating whether the density ratio should be plotted in log scale. Defaults to TRUE. |
show.sample |
Logical indicating whether to give different shapes to observations, depending on the sample they come from (numerator or denominator). Defaults to FALSE. |
Value
Bivariate plot
Univariate plot
Description
Scatterplot of individual values and density ratio estimates. Used internally in create_univariate_plot()
Usage
create_univariate_plot(data, ext, var, y_lab, sample.facet = TRUE)
Arguments
data |
Data frame with the individual values and density ratio estimates |
ext |
Data frame with the density ratio estimates and sample indicator |
var |
Name of the variable to be plotted on the x-axis |
y_lab |
Name of the y-axis label, typically ("Density Ratio" or "Log Density Ratio") |
sample.facet |
Logical indicating whether to facet the plot by sample. Default is TRUE. |
Value
A scatterplot of variable values and density ratio estimates.
denominator_data
Description
Simulated data set (see data-raw/generate-data-densityratio.R) with five variables that are used in the examples.
Format
A data frame with 1000 rows and 5 columns:
- x1
Categorical variable with three categories, 'A', 'B' and 'C'
- x2
Categorical variable with two categories, 'G1' and 'G2'
- x3
Continuous variable (normally distributed given x1 and x2)
- x4
Continuous variable (normally distributed)
- x5
Continuous variable (normally distributed)
denominator_small
Description
Subset of the denominator_data with three variables and 50 observations
Format
A data frame with 100 rows and 3 columns:
- x1
Continuous variable (normally distributed given x1 and x2)
- x2
Continuous variable (normally distributed)
- x3
Continuous variable (normally distributed)
Create a Gram matrix with squared Euclidean distances between
observations in the input matrix X and the input matrix Y
Description
Create a Gram matrix with squared Euclidean distances between
observations in the input matrix X and the input matrix Y
Arguments
X |
A numeric input matrix |
Y |
A numeric input matrix with the same variables as |
intercept |
Logical indicating whether an intercept should be added to the estimation procedure. In this case, the first column is an all-zero column (which will be transformed into an all-ones column in the kernel). |
A histogram of density ratio estimates
Description
Creates a histogram of the density ratio estimates. Useful to understand the distribution of estimated density ratios in each sample, or compare it among samples. It is the default plotting method for density ratio objects.
Usage
dr.histogram(
x,
samples = "both",
logscale = TRUE,
binwidth = NULL,
bins = NULL,
tol = 0.01,
...
)
## S3 method for class 'ulsif'
plot(
x,
samples = "both",
logscale = TRUE,
binwidth = NULL,
bins = NULL,
tol = 0.01,
...
)
## S3 method for class 'kliep'
plot(
x,
samples = "both",
logscale = TRUE,
binwidth = NULL,
bins = NULL,
tol = 0.01,
...
)
## S3 method for class 'kmm'
plot(
x,
samples = "both",
logscale = TRUE,
binwidth = NULL,
bins = NULL,
tol = 0.01,
...
)
## S3 method for class 'spectral'
plot(
x,
samples = "both",
logscale = TRUE,
binwidth = NULL,
bins = NULL,
tol = 0.01,
...
)
## S3 method for class 'lhss'
plot(
x,
samples = "both",
logscale = TRUE,
binwidth = NULL,
bins = NULL,
tol = 0.01,
...
)
## S3 method for class 'naivedensityratio'
plot(
x,
samples = "both",
logscale = TRUE,
binwidth = NULL,
bins = NULL,
tol = 0.01,
...
)
Arguments
x |
Density ratio object created with e.g., |
samples |
Character string indicating whether to plot the 'numerator', 'denominator', or 'both' samples. Default is 'both'. |
logscale |
Logical indicating whether to plot the density ratio estimates on a log scale. Default is TRUE. |
binwidth |
Numeric indicating the width of the bins, passed on to
|
bins |
Numeric indicating the number of bins. Overriden by binwidth, and
passed on to |
tol |
Numeric indicating the tolerance: values below this value will be set to the tolerance value, for legibility of the plots |
... |
Additional arguments passed on to |
Value
A histogram of density ratio estimates.
A histogram of density ratio estimates.
A histogram of density ratio estimates.
A histogram of density ratio estimates.
A histogram of density ratio estimates.
A histogram of density ratio estimates.
A histogram of density ratio estimates.
See Also
ulsif for example usage
kliep for example usage
kmm for example usage
spectral for example usage
lhss for example usage
naive for example usage
Extract parameters
Description
Extract parameters
Usage
extract_params(object, ...)
Obtain parameters from a kliep object
Description
Obtain parameters from a kliep object
Usage
## S3 method for class 'kliep'
extract_params(object, sigma, ...)
Obtain parameters from a kmm object
Description
Obtain parameters from a kmm object
Usage
## S3 method for class 'kmm'
extract_params(object, sigma, ...)
Obtain parameters from a lhss object
Description
Obtain parameters from a lhss object
Usage
## S3 method for class 'lhss'
extract_params(object, lambda, lambdasigma, ...)
Obtain parameters from a spectral object
Description
Obtain parameters from a spectral object
Usage
## S3 method for class 'spectral'
extract_params(object, sigma, m, ...)
Obtain parameters from a ulsif object
Description
Obtain parameters from a ulsif object
Usage
## S3 method for class 'ulsif'
extract_params(object, sigma, lambda, ...)
insurance
Description
Insurance data that is openly available (e.g., on Kaggle).
Format
A data.frame with 1338 rows and 7 columns:
- age
Age of the insured (continuous)
- sex
Sex of the insured (binary)
- bmi
Body mass index of the insured (continuous)
- children
Number of children/dependents covered by the insurance (integer)
- smoker
Whether the insured is a smoker (binary)
- region
The region in which the insured lives (categorical)
- charges
The medical costs billed by the insurance (continuous)
Create gaussian kernel gram matrix from distance matrix
Description
Create gaussian kernel gram matrix from distance matrix
Arguments
dist |
A numeric distance matrix |
sigma |
A scalar with the length-scale parameter |
kidiq
Description
The kidiq data stems from the National Longitudinal Survey of Youth and is used in Gelman and Hill (2007). The data set contains 434 observations measured on five variables, and is obtained from https://github.com/jknowles/BDAexampleR.
Format
A data.frame with 434 rows and 5 columns
- kid_score
Child's IQ score (continuous)
- mom_hs
Whether the mother obtained a high school degree (binary)
- mom_iq
Mother's IQ score (continuous)
- mom_work
Whether the mother worked in the first three years of the child's life (1: not in the first three years; 2: in the second or third year; 3: parttime in the first year; 4: fulltime in the first year)
- mom_age
Mother's age (continuous)
Kullback-Leibler importance estimation procedure
Description
Kullback-Leibler importance estimation procedure
Usage
kliep(
df_numerator,
df_denominator,
scale = "numerator",
nsigma = 10,
sigma_quantile = NULL,
sigma = NULL,
ncenters = 200,
centers = NULL,
cv = TRUE,
nfold = 5,
epsilon = NULL,
maxit = 5000,
progressbar = TRUE
)
Arguments
df_numerator |
|
df_denominator |
|
scale |
|
nsigma |
Integer indicating the number of sigma values (bandwidth parameter of the Gaussian kernel gram matrix) to use in cross-validation. |
sigma_quantile |
|
sigma |
|
ncenters |
Maximum number of Gaussian centers in the kernel gram matrix. Defaults to all numerator samples. |
centers |
Option to specify the Gaussian samples manually. |
cv |
Logical indicating whether or not to do cross-validation |
nfold |
Number of cross-validation folds used in order to calculate the
optimal |
epsilon |
Numeric scalar or vector with the learning rate for the
gradient-ascent procedure. If a vector, all values are used as the learning
rate. By default, |
maxit |
Maximum number of iterations for the optimization scheme. |
progressbar |
Logical indicating whether or not to display a progressbar. |
Value
kliep-object, containing all information to calculate the
density ratio using optimal sigma and optimal weights.
References
Sugiyama, M., Suzuki, T., Nakajima, S., Kashima, H., Von Bünau, P., & Kawanabe, M. (2008). Direct importance estimation for covariate shift adaptation. Annals of the Institute of Statistical Mathematics 60, 699-746. Doi: https://doi.org/10.1007/s10463-008-0197-x.
Examples
set.seed(123)
# Fit model
dr <- kliep(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kliep(numerator_small, denominator_small,
nsigma = 1, ncenters = 100, nfold = 10,
epsilon = 10^{2:-5}, maxit = 500)
Kernel mean matching approach to density ratio estimation
Description
Kernel mean matching approach to density ratio estimation
Usage
kmm(
df_numerator,
df_denominator,
scale = "numerator",
constrained = FALSE,
nsigma = 10,
sigma_quantile = NULL,
sigma = NULL,
ncenters = 200,
centers = NULL,
cv = TRUE,
nfold = 5,
parallel = FALSE,
nthreads = NULL,
progressbar = TRUE,
osqp_settings = NULL,
cluster = NULL
)
Arguments
df_numerator |
|
df_denominator |
|
scale |
|
constrained |
|
nsigma |
Integer indicating the number of sigma values (bandwidth parameter of the Gaussian kernel gram matrix) to use in cross-validation. |
sigma_quantile |
|
sigma |
|
ncenters |
Maximum number of Gaussian centers in the kernel gram matrix. Defaults to all numerator samples. |
centers |
Option to specify the Gaussian samples manually. |
cv |
Logical indicating whether or not to do cross-validation |
nfold |
Number of cross-validation folds used in order to calculate the
optimal |
parallel |
logical indicating whether to use parallel processing in the cross-validation scheme. |
nthreads |
|
progressbar |
Logical indicating whether or not to display a progressbar. |
osqp_settings |
Optional: settings to pass to the |
cluster |
Optional: a cluster object to use for parallel processing,
see |
Value
kmm-object, containing all information to calculate the
density ratio using optimal sigma and optimal weights.
References
Huang, J., Smola, A. J., Gretton, A., Borgwardt, K. M., & Schölkopf, B. (2006). Correcting sample selection bias by unlabeled data. In Advances in Neural Information Processing Systems, edited by B. Schölkopf, J. Platt and T. Hoffman. Available from https://proceedings.neurips.cc/paper/2006/hash/a2186aa7c086b46ad4e8bf81e2a3a19b-Abstract.html.
Examples
set.seed(123)
# Fit model
dr <- kmm(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kmm(numerator_small, denominator_small,
nsigma = 5, ncenters = 100, nfold = 10,
constrained = TRUE)
Least-squares heterodistributional subspace search
Description
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 |
|
df_denominator |
|
m |
Scalar indicating the dimensionality of the reduced subspace |
intercept |
|
scale |
|
nsigma |
Integer indicating the number of sigma values (bandwidth parameter of the Gaussian kernel gram matrix) to use in cross-validation. |
sigma_quantile |
|
sigma |
|
nlambda |
Integer indicating the number of |
lambda |
|
ncenters |
Maximum number of Gaussian centers in the kernel gram matrix. Defaults to all numerator samples. |
centers |
Numeric matrix with the same variables as |
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
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
naive(numerator_small, denominator_small, m=2, kernel="epanechnikov")
Naive density ratio estimation
Description
The naive approach creates separate kernel density estimates for
the numerator and the denominator samples, and then evaluates their
ratio for the denominator samples. For multivariate data, the density ratio
is computed after a orthogonal linear transformation, such that the new
variables can be treated as independent. To reduce the dimensionality of
the PCA solution, one can set the number of components by setting the
m parameter to an integer value smaller than the number of variables.
Usage
naive(
df_numerator,
df_denominator,
m = NULL,
bw = "SJ",
kernel = "gaussian",
n = 2L^11,
...
)
Arguments
df_numerator |
|
df_denominator |
|
m |
|
bw |
the smoothing bandwidth to be used. See stats::density for more information. |
kernel |
the kernel to be used. See stats::density for more information. |
n |
|
... |
further arguments passed to stats::density |
Value
naivedensityratio object
See Also
Examples
set.seed(123)
# Fit model
dr <- naive(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
naive(numerator_small, denominator_small, m=2, kernel="epanechnikov")
numerator_data
Description
Simulated data set (see data-raw/generate-data-densityratio.R) with five variables that are used in the examples.
Format
A data frame with 1000 rows and 5 columns:
- x1
Categorical variable with three categories, 'A', 'B' and 'C'
- x2
Categorical variable with two categories, 'G1' and 'G2'
- x3
Continuous variable (normally distributed given x1 and x2)
- x4
Continuous variable (normally distributed given x3)
- x5
Continuous variable (mixture of two normally distributed variables)
numerator_small
Description
Subset of the numerator_data with three variables and 50 observations
Format
A data frame with 50 rows and 3 columns:
- x1
Continuous variable (normally distributed given x1 and x2)
- x2
Continuous variable (normally distributed given x3)
- x3
Continuous variable (mixture of two normally distributed variables)
Single permutation
Description
Single permutation
Single permutation statistic of ulsif object
Single permutation statistic of kliep object
Single permutation statistic of kmm object
Single permutation statistic of lhss object
Single permutation statistic of spectral object
Single permutation statistic of naivedensityratio object
Usage
permute(object, ...)
## S3 method for class 'ulsif'
permute(object, stacked, nnu, nde, ...)
## S3 method for class 'kliep'
permute(object, stacked, nnu, nde, min_pred = sqrt(.Machine$double.eps), ...)
## S3 method for class 'kmm'
permute(object, stacked, nnu, nde, ...)
## S3 method for class 'lhss'
permute(object, stacked, nnu, nde, ...)
## S3 method for class 'spectral'
permute(object, stacked, nnu, nde, ...)
## S3 method for class 'naivedensityratio'
permute(object, stacked, nnu, nde, min_pred, max_pred, ...)
Arguments
object |
|
... |
Additional arguments to pass through to specific permute functions. |
stacked |
|
nnu |
Scalar with numerator sample size |
nde |
Scalar with denominator sample size |
min_pred |
Minimum value of the predicted density ratio |
max_pred |
Maximum value of the predicted density ratio |
Value
permutation statistic for a single permutation of the data
permutation statistic for a single permutation of the data
permutation statistic for a single permutation of the data
permutation statistic for a single permutation of the data
permutation statistic for a single permutation of the data
permutation statistic for a single permutation of the data
permutation statistic for a single permutation of the data
Densityratio in two-dimensional plot
Description
Plots a scatterplot of two variables, with densityratio mapped to the colour scale.
Usage
plot_bivariate(
x,
vars = NULL,
samples = "both",
grid = FALSE,
logscale = TRUE,
show.sample = FALSE,
tol = 0.01,
...
)
Arguments
x |
Density ratio object created with e.g., |
vars |
Character vector of variable names for which all pairwise bivariate plots are created |
samples |
Character string indicating whether to plot the 'numerator', 'denominator', or 'both' samples. Default is 'both'. |
grid |
Logical indicating whether output should be a list of individual plots ("individual"), or one facetted plot with all variables ("assembled"). Defaults to "individual". |
logscale |
Logical indicating whether to plot the density ratio
estimates on a log scale. Default is |
show.sample |
Logical indicating whether to give different shapes to
observations, depending on the sample they come from (numerator or
denominator). Defaults to |
tol |
Numeric indicating the tolerance: values below this value will be set to the tolerance value, for legibility of the plots |
... |
Additional arguments passed to the predict() function. |
Value
Bivariate scatter plots of all combinations of variables in vars.
Examples
set.seed(123)
# Fit model
dr <- ulsif(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
ulsif(numerator_small, denominator_small, sigma = 2, lambda = 2)
Scatter plot of density ratios and individual variables
Description
A scatter plot showing the relationship between estimated density ratios and individual variables.
Usage
plot_univariate(
x,
vars = NULL,
samples = "both",
logscale = TRUE,
grid = FALSE,
sample.facet = FALSE,
nrow.panel = NULL,
tol = 0.01,
...
)
Arguments
x |
Density ratio object created with e.g., |
vars |
Character vector of variable names to be plotted. |
samples |
Character string indicating whether to plot the 'numerator', 'denominator', or 'both' samples. Default is 'both'. |
logscale |
Logical indicating whether to plot the density ratio estimates on a log scale. Default is TRUE. |
grid |
Logical indicating whether output should be a list of individual plots ("individual"), or one facetted plot with all variables ("assembled"). Defaults to "individual". |
sample.facet |
Logical indicating whether to facet the plot by sample, i.e, showing plots separate for each sample, and side to side. Defaults to FALSE. |
nrow.panel |
Integer indicating the number of rows in the assembled plot. If NULL, the number of rows is automatically calculated. |
tol |
Numeric indicating the tolerance: values below this value will be set to the tolerance value, for legibility of the plots |
... |
Additional arguments passed to the predict() function. |
Value
Scatter plot of density ratios and individual variables.
Examples
set.seed(123)
# Fit model
dr <- ulsif(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
ulsif(numerator_small, denominator_small, sigma = 2, lambda = 2)
Obtain predicted density ratio values from a kliep object
Description
Obtain predicted density ratio values from a kliep object
Usage
## S3 method for class 'kliep'
predict(object, newdata = NULL, sigma = c("sigmaopt", "all"), ...)
Arguments
object |
A |
newdata |
Optional |
sigma |
A scalar with the Gaussian kernel width |
... |
Additional arguments to be passed to the function |
Value
An array with predicted density ratio values from possibly new data, but otherwise the numerator samples.
See Also
Examples
set.seed(123)
# Fit model
dr <- kliep(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kliep(numerator_small, denominator_small,
nsigma = 1, ncenters = 100, nfold = 10,
epsilon = 10^{2:-5}, maxit = 500)
Obtain predicted density ratio values from a kmm object
Description
Obtain predicted density ratio values from a kmm object
Usage
## S3 method for class 'kmm'
predict(object, newdata = NULL, sigma = c("sigmaopt", "all"), ...)
Arguments
object |
A |
newdata |
Optional |
sigma |
A scalar with the Gaussian kernel width |
... |
Additional arguments to be passed to the function |
Value
An array with predicted density ratio values from possibly new data, but otherwise the numerator samples.
See Also
Examples
set.seed(123)
# Fit model
dr <- kmm(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kmm(numerator_small, denominator_small,
nsigma = 5, ncenters = 100, nfold = 10,
constrained = TRUE)
Obtain predicted density ratio values from a lhss object
Description
Obtain predicted density ratio values from a lhss object
Usage
## S3 method for class 'lhss'
predict(
object,
newdata = NULL,
sigma = c("sigmaopt", "all"),
lambda = c("lambdaopt", "all"),
...
)
Arguments
object |
A |
newdata |
Optional |
sigma |
A scalar with the Gaussian kernel width |
lambda |
A scalar with the regularization parameter |
... |
Additional arguments to be passed to the function |
Value
An array with predicted density ratio values from possibly new data, but otherwise the numerator samples.
See Also
Examples
set.seed(123)
# Fit model (minimal example to limit computation time)
dr <- lhss(numerator_small, denominator_small,
nsigma = 5, nlambda = 3, ncenters = 50, maxit = 100)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
Obtain predicted density ratio values from a naivedensityratio object
Description
Obtain predicted density ratio values from a naivedensityratio object
Usage
## S3 method for class 'naivedensityratio'
predict(object, newdata = NULL, log = FALSE, tol = 1e-06, ...)
Arguments
object |
A |
newdata |
Optional |
log |
A logical indicating whether to return the log of the density ratio |
tol |
Minimal density value to avoid numerical issues |
... |
Additional arguments to be passed to the function |
Value
An array with predicted density ratio values from possibly new data, but otherwise the numerator samples.
See Also
Examples
set.seed(123)
# Fit model
dr <- naive(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
naive(numerator_small, denominator_small, m=2, kernel="epanechnikov")
Obtain predicted density ratio values from a spectral object
Description
Obtain predicted density ratio values from a spectral object
Usage
## S3 method for class 'spectral'
predict(
object,
newdata = NULL,
sigma = c("sigmaopt", "all"),
m = c("opt", "all"),
...
)
Arguments
object |
A |
newdata |
Optional |
sigma |
A scalar with the Gaussian kernel width |
m |
integer indicating the dimension of the eigenvector expansion |
... |
Additional arguments to be passed to the function |
Value
An array with predicted density ratio values from possibly new data, but otherwise the numerator samples.
See Also
Obtain predicted density ratio values from a ulsif object
Description
Obtain predicted density ratio values from a ulsif object
Usage
## S3 method for class 'ulsif'
predict(
object,
newdata = NULL,
sigma = c("sigmaopt", "all"),
lambda = c("lambdaopt", "all"),
...
)
Arguments
object |
A |
newdata |
Optional |
sigma |
A scalar with the Gaussian kernel width |
lambda |
A scalar with the regularization parameter |
... |
Additional arguments to be passed to the function |
Value
An array with predicted density ratio values from possibly new data, but otherwise the numerator samples.
See Also
Examples
set.seed(123)
# Fit model
dr <- ulsif(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
ulsif(numerator_small, denominator_small, sigma = 2, lambda = 2)
Print a kliep object
Description
Print a kliep object
Usage
## S3 method for class 'kliep'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted kliep object.
See Also
Examples
set.seed(123)
# Fit model
dr <- kliep(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kliep(numerator_small, denominator_small,
nsigma = 1, ncenters = 100, nfold = 10,
epsilon = 10^{2:-5}, maxit = 500)
Print a kmm object
Description
Print a kmm object
Usage
## S3 method for class 'kmm'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted kmm object.
See Also
Examples
set.seed(123)
# Fit model
dr <- kmm(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kmm(numerator_small, denominator_small,
nsigma = 5, ncenters = 100, nfold = 10,
constrained = TRUE)
Print a lhss object
Description
Print a lhss object
Usage
## S3 method for class 'lhss'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted lhss object.
See Also
Examples
set.seed(123)
# Fit model (minimal example to limit computation time)
dr <- lhss(numerator_small, denominator_small,
nsigma = 5, nlambda = 3, ncenters = 50, maxit = 100)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
Print a naivedensityratio object
Description
Print a naivedensityratio object
Usage
## S3 method for class 'naivedensityratio'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted naivedensityratio object.
See Also
Examples
set.seed(123)
# Fit model
dr <- naive(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
naive(numerator_small, denominator_small, m=2, kernel="epanechnikov")
Print a spectral object
Description
Print a spectral object
Usage
## S3 method for class 'spectral'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted spectral object.
See Also
Examples
set.seed(123)
# Fit model
dr <- spectral(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
spectral(numerator_small, denominator_small, sigma = 2)
Print a summary.kliep object
Description
Print a summary.kliep object
Usage
## S3 method for class 'summary.kliep'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted summary.kliep object.
See Also
Examples
set.seed(123)
# Fit model
dr <- kliep(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kliep(numerator_small, denominator_small,
nsigma = 1, ncenters = 100, nfold = 10,
epsilon = 10^{2:-5}, maxit = 500)
Print a summary.kmm object
Description
Print a summary.kmm object
Usage
## S3 method for class 'summary.kmm'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted summary.kmm object.
See Also
Examples
set.seed(123)
# Fit model
dr <- kmm(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kmm(numerator_small, denominator_small,
nsigma = 5, ncenters = 100, nfold = 10,
constrained = TRUE)
Print a summary.lhss object
Description
Print a summary.lhss object
Usage
## S3 method for class 'summary.lhss'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted summary.lhss object.
See Also
Examples
set.seed(123)
# Fit model (minimal example to limit computation time)
dr <- lhss(numerator_small, denominator_small,
nsigma = 5, nlambda = 3, ncenters = 50, maxit = 100)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
Print a summary.naivedensityratio object
Description
Print a summary.naivedensityratio object
Usage
## S3 method for class 'summary.naivedensityratio'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted summary.naivedensityratio object.
See Also
print, summary.naivedensityratio,
naive
Examples
set.seed(123)
# Fit model
dr <- naive(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
naive(numerator_small, denominator_small, m=2, kernel="epanechnikov")
Print a summary.spectral object
Description
Print a summary.spectral object
Usage
## S3 method for class 'summary.spectral'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted summary.spectral object.
See Also
print, summary.spectral, spectral
Examples
set.seed(123)
# Fit model
dr <- spectral(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
spectral(numerator_small, denominator_small, sigma = 2)
Print a summary.ulsif object
Description
Print a summary.ulsif object
Usage
## S3 method for class 'summary.ulsif'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted summary.ulsif object.
See Also
Examples
set.seed(123)
# Fit model
dr <- ulsif(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
ulsif(numerator_small, denominator_small, sigma = 2, lambda = 2)
Print a ulsif object
Description
Print a ulsif object
Usage
## S3 method for class 'ulsif'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
Arguments
x |
Object of class |
digits |
Number of digits to use when printing the output. |
... |
further arguments on how to format the number of digits. |
Value
invisble The inputted ulsif object.
See Also
Examples
set.seed(123)
# Fit model
dr <- ulsif(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
ulsif(numerator_small, denominator_small, sigma = 2, lambda = 2)
Spectral series based density ratio estimation
Description
Spectral series based density ratio estimation
Usage
spectral(
df_numerator,
df_denominator,
m = NULL,
scale = "numerator",
nsigma = 10,
sigma_quantile = NULL,
sigma = NULL,
ncenters = NULL,
cv = TRUE,
nfold = 10,
parallel = FALSE,
nthreads = NULL,
progressbar = TRUE
)
Arguments
df_numerator |
|
df_denominator |
|
m |
Integer vector indicating the number of eigenvectors to use in the spectral series expansion. Defaults to 50 evenly spaced values between 1 and the number of denominator samples (or the largest number of samples that can be used as centers in the cross-validation scheme). |
scale |
|
nsigma |
Integer indicating the number of sigma values (bandwidth parameter of the Gaussian kernel gram matrix) to use in cross-validation. |
sigma_quantile |
|
sigma |
|
ncenters |
integer If smaller than the number of denominator observations,
an approximation to the eigenvector expansion based on only ncenters samples
is performed, instead of the full expansion. This can be useful for large
datasets. Defaults to |
cv |
logical indicating whether to use cross-validation to determine the optimal sigma value and the optimal number of eigenvectors. |
nfold |
Integer indicating the number of folds to use in the
cross-validation scheme. If |
parallel |
logical indicating whether to use parallel processing in the cross-validation scheme. |
nthreads |
|
progressbar |
Logical indicating whether or not to display a progressbar. |
Value
spectral-object, containing all information to calculate the
density ratio using optimal sigma and optimal spectral series expansion.
References
Izbicki, R., Lee, A. & Schafer, C. (2014). High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation. Proceedings of Machine Learning Research 33, 420-429. Available from https://proceedings.mlr.press/v33/izbicki14.html.
Examples
set.seed(123)
# Fit model
dr <- spectral(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
spectral(numerator_small, denominator_small, sigma = 2)
Extract summary from kliep object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Description
Extract summary from kliep object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Usage
## S3 method for class 'kliep'
summary(
object,
test = FALSE,
n_perm = 100,
parallel = FALSE,
cluster = NULL,
min_pred = 1e-06,
...
)
Arguments
object |
Object of class |
test |
logical indicating whether to statistically test for homogeneity of the numerator and denominator samples. |
n_perm |
Scalar indicating number of permutation samples |
parallel |
|
cluster |
|
min_pred |
Scalar indicating the minimum value for the predicted density ratio values (used in the divergence statistic) to avoid negative density ratio values. |
... |
further arguments passed to or from other methods. |
Value
Summary of the fitted density ratio model
Examples
set.seed(123)
# Fit model
dr <- kliep(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kliep(numerator_small, denominator_small,
nsigma = 1, ncenters = 100, nfold = 10,
epsilon = 10^{2:-5}, maxit = 500)
Extract summary from kmm object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Description
Extract summary from kmm object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Usage
## S3 method for class 'kmm'
summary(
object,
test = FALSE,
n_perm = 100,
parallel = FALSE,
cluster = NULL,
min_pred = 1e-06,
...
)
Arguments
object |
Object of class |
test |
logical indicating whether to statistically test for homogeneity of the numerator and denominator samples. |
n_perm |
Scalar indicating number of permutation samples |
parallel |
|
cluster |
|
min_pred |
Scalar indicating the minimum value for the predicted density ratio values (used in the divergence statistic) to avoid negative density ratio values. |
... |
further arguments passed to or from other methods. |
Value
Summary of the fitted density ratio model
Examples
set.seed(123)
# Fit model
dr <- kmm(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
kmm(numerator_small, denominator_small,
nsigma = 5, ncenters = 100, nfold = 10,
constrained = TRUE)
Extract summary from lhss object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Description
Extract summary from lhss object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Usage
## S3 method for class 'lhss'
summary(
object,
test = FALSE,
n_perm = 100,
parallel = FALSE,
cluster = NULL,
...
)
Arguments
object |
Object of class |
test |
logical indicating whether to statistically test for homogeneity of the numerator and denominator samples. |
n_perm |
Scalar indicating number of permutation samples |
parallel |
|
cluster |
|
... |
further arguments passed to or from other methods. |
Value
Summary of the fitted density ratio model
Examples
set.seed(123)
# Fit model (minimal example to limit computation time)
dr <- lhss(numerator_small, denominator_small,
nsigma = 5, nlambda = 3, ncenters = 50, maxit = 100)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
Extract summary from naivedensityraito object, including two-sample
significance test for homogeneity of the numerator and denominator samples
Description
Extract summary from naivedensityraito object, including two-sample
significance test for homogeneity of the numerator and denominator samples
Usage
## S3 method for class 'naivedensityratio'
summary(
object,
test = FALSE,
n_perm = 100,
parallel = FALSE,
cluster = NULL,
...
)
Arguments
object |
Object of class |
test |
logical indicating whether to statistically test for homogeneity of the numerator and denominator samples. |
n_perm |
Scalar indicating number of permutation samples |
parallel |
|
cluster |
|
... |
further arguments passed to or from other methods. |
Value
Summary of the fitted density ratio model
Examples
set.seed(123)
# Fit model
dr <- naive(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
naive(numerator_small, denominator_small, m=2, kernel="epanechnikov")
Extract summary from spectral object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Description
Extract summary from spectral object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Usage
## S3 method for class 'spectral'
summary(
object,
test = FALSE,
n_perm = 100,
parallel = FALSE,
cluster = NULL,
...
)
Arguments
object |
Object of class |
test |
logical indicating whether to statistically test for homogeneity of the numerator and denominator samples. |
n_perm |
Scalar indicating number of permutation samples |
parallel |
|
cluster |
|
... |
further arguments passed to or from other methods. |
Value
Summary of the fitted density ratio model
Examples
set.seed(123)
# Fit model
dr <- spectral(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
spectral(numerator_small, denominator_small, sigma = 2)
Extract summary from ulsif object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Description
Extract summary from ulsif object, including two-sample significance
test for homogeneity of the numerator and denominator samples
Usage
## S3 method for class 'ulsif'
summary(
object,
test = FALSE,
n_perm = 100,
parallel = FALSE,
cluster = NULL,
...
)
Arguments
object |
Object of class |
test |
logical indicating whether to statistically test for homogeneity of the numerator and denominator samples. |
n_perm |
Scalar indicating number of permutation samples |
parallel |
|
cluster |
|
... |
further arguments passed to or from other methods. |
Value
Summary of the fitted density ratio model
Examples
set.seed(123)
# Fit model
dr <- ulsif(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
ulsif(numerator_small, denominator_small, sigma = 2, lambda = 2)
Unconstrained least-squares importance fitting
Description
Unconstrained least-squares importance fitting
Usage
ulsif(
df_numerator,
df_denominator,
intercept = TRUE,
scale = "numerator",
nsigma = 10,
sigma_quantile = NULL,
sigma = NULL,
nlambda = 20,
lambda = NULL,
ncenters = 200,
centers = NULL,
parallel = FALSE,
nthreads = NULL,
progressbar = TRUE
)
Arguments
df_numerator |
|
df_denominator |
|
intercept |
|
scale |
|
nsigma |
Integer indicating the number of sigma values (bandwidth parameter of the Gaussian kernel gram matrix) to use in cross-validation. |
sigma_quantile |
|
sigma |
|
nlambda |
Integer indicating the number of |
lambda |
|
ncenters |
Maximum number of Gaussian centers in the kernel gram matrix. Defaults to all numerator samples. |
centers |
|
parallel |
logical indicating whether to use parallel processing in the cross-validation scheme. |
nthreads |
|
progressbar |
Logical indicating whether or not to display a progressbar. |
Value
ulsif-object, containing all information to calculate the
density ratio using optimal sigma and optimal weights.
References
Kanamori, T., Hido, S., & Sugiyama, M. (2009). A least-squares approach to direct importance estimation. Journal of Machine Learning Research, 10, 1391-1445. Available from https://jmlr.org/papers/v10/kanamori09a.html
Examples
set.seed(123)
# Fit model
dr <- ulsif(numerator_small, denominator_small)
# Inspect model object
dr
# Obtain summary of model object
summary(dr)
# Plot model object
plot(dr)
# Plot density ratio for each variable individually
plot_univariate(dr)
# Plot density ratio for each pair of variables
plot_bivariate(dr)
# Predict density ratio and inspect first 6 predictions
head(predict(dr))
# Fit model with custom parameters
ulsif(numerator_small, denominator_small, sigma = 2, lambda = 2)