noise_model: Apply Noise to Discrete-Valued Tables

In FunChisq: Model-Free Functional Chi-Squared and Exact Tests

Apply Noise to Discrete-Valued Tables

Description

The function can apply two types of noise to contingency tables of discrete values. A house noise model is designed for ordinal variables; a candle noise model is for categorical variables. Noise is applied independently for each data point in a table.

Usage

add.noise(tables, u, noise.model, margin=0)
add.house.noise(tables, u, margin=0)
add.candle.noise(tables, u, margin=0)

Arguments

tables	a list of tables or one table. A table can be either a matrix or a data frame of integer values.
u	a numeric value between 0 and 1 to specify the noise level to be applied to the input tables. See Details.
noise.model	a character string indicating the noise model of either "house" for ordinal variables or "candle" for categorical variables. See Details.
margin	a value of either 0, 1, or 2. Default is 0. 0: noise is applied along both rows and columns in a table. The sum of values in the table is the same before and after noise application. 1: noise is applied along each row. The sum of each row is the same before and after noise application. 2: noise is applied along each column. The sum of each column is the same before and after noise application.

Details

Each noise model defines a conditional probability function of a noisy version given an original discrete value and a noise level. In the house noise model for ordinal variables, defined in \insertCitezhang2015chinetFunChisq, the probability decreases as the noisy version deviates from the original ordinal value. The shape of the function is like a pitched house roof. In the candle noise model for categorical variables, the probability of the noisy version for any value other than the original categorical value is the same given the noise level. The function shape is like a candle.

At a minimum level of 0, no noise is applied on the input table(s). A maximum level of 1 indicates that the original sample will be changed to some other values with a probability of 1. For a discrete random variable of two possible values, a noise level of 1 will flip the values and create a non-random pattern; a noise level of 0.5 creates the most random pattern.

Value

If tables is a list, the function returns a list of tables with noised applied. If tables is a numeric matrix or a data frame, the function returns one table with noise applied.

Author(s)

Hua Zhong, Yang Zhang, and Joe Song.

References

\insertAllCited

See Also

simulate_tables.

Examples

  # Example 1. Add house noise to a single table

  # Create a 4x4 table
  t <- matrix(c(3,0,0,0,
                0,2,2,0,
                0,0,0,4,
                3,3,2,0),
              nrow=4, ncol=4, byrow=TRUE)
  # Two ways to apply house noise at level 0.1 along both rows
  # and columns of the table:
  add.noise(t, 0.1, "house", 0)
  add.house.noise(t, 0.1, 0)


  # Example 2. Add candle noise to a list of tables

  # Create a list of tables
  t.list <- list(t+5, t*10, t*2)
  # Two ways to apply candle noise at level 0.2 along the rows
  # of the table:
  add.noise(t.list, 0.2, "candle", 1)
  add.candle.noise(t.list, 0.2, 1)

FunChisq documentation built on May 31, 2023, 8:18 p.m.