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LinearCountRegressor

LinearCountRegressor

A model type for constructing a linear count regressor, based on GLM.jl, and implementing the MLJ model interface.

From MLJ, the type can be imported using

LinearCountRegressor = @load LinearCountRegressor pkg=GLM

Do model = LinearCountRegressor() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in LinearCountRegressor(fit_intercept=...).

LinearCountRegressor is a generalized linear model, specialised to the case of a Count target variable (non-negative, unbounded integer) with user-specified link function. Options exist to specify an intercept or offset feature.

Training data

In MLJ or MLJBase, bind an instance model to data with one of:

mach = machine(model, X, y)
mach = machine(model, X, y, w)

Here

  • X: is any table of input features (eg, a DataFrame) whose columns are of scitype Continuous; check the scitype with schema(X)
  • y: is the target, which can be any AbstractVector whose element scitype is Count; check the scitype with schema(y)
  • w: is a vector of Real per-observation weights

Train the machine using fit!(mach, rows=...).

Hyper-parameters

  • fit_intercept=true: Whether to calculate the intercept for this model. If set to false, no intercept will be calculated (e.g. the data is expected to be centered)
  • distribution=Distributions.Poisson(): The distribution which the residuals/errors of the model should fit.
  • link=GLM.LogLink(): The function which links the linear prediction function to the probability of a particular outcome or class. This should be one of the following: GLM.IdentityLink(), GLM.InverseLink(), GLM.InverseSquareLink(), GLM.LogLink(), GLM.SqrtLink().
  • offsetcol=nothing: Name of the column to be used as an offset, if any. An offset is a variable which is known to have a coefficient of 1.
  • maxiter::Integer=30: The maximum number of iterations allowed to achieve convergence.
  • atol::Real=1e-6: Absolute threshold for convergence. Convergence is achieved when the relative change in deviance is less than `max(rtol*dev, atol). This term exists to avoid failure when deviance is unchanged except for rounding errors.
  • rtol::Real=1e-6: Relative threshold for convergence. Convergence is achieved when the relative change in deviance is less than `max(rtol*dev, atol). This term exists to avoid failure when deviance is unchanged except for rounding errors.
  • minstepfac::Real=0.001: Minimum step fraction. Must be between 0 and 1. Lower bound for the factor used to update the linear fit.
  • report_keys: Vector of keys for the report. Possible keys are: :deviance, :dof_residual, :stderror, :vcov, :coef_table and :glm_model. By default only :glm_model is excluded.

Operations

  • predict(mach, Xnew): return predictions of the target given new features Xnew having the same Scitype as X above. Predictions are probabilistic.
  • predict_mean(mach, Xnew): instead return the mean of each prediction above
  • predict_median(mach, Xnew): instead return the median of each prediction above.

Fitted parameters

The fields of fitted_params(mach) are:

  • features: The names of the features encountered during model fitting.
  • coef: The linear coefficients determined by the model.
  • intercept: The intercept determined by the model.

Report

The fields of report(mach) are:

  • deviance: Measure of deviance of fitted model with respect to a perfectly fitted model. For a linear model, this is the weighted residual sum of squares
  • dof_residual: The degrees of freedom for residuals, when meaningful.
  • stderror: The standard errors of the coefficients.
  • vcov: The estimated variance-covariance matrix of the coefficient estimates.
  • coef_table: Table which displays coefficients and summarizes their significance and confidence intervals.
  • glm_model: The raw fitted model returned by GLM.lm. Note this points to training data. Refer to the GLM.jl documentation for usage.

Examples

using MLJ
import MLJ.Distributions.Poisson

## Generate some data whose target y looks Poisson when conditioned on
## X:
N = 10_000
w = [1.0, -2.0, 3.0]
mu(x) = exp(w'x) ## mean for a log link function
Xmat = rand(N, 3)
X = MLJ.table(Xmat)
y = map(1:N) do i
    x = Xmat[i, :]
    rand(Poisson(mu(x)))
end;

CountRegressor = @load LinearCountRegressor pkg=GLM
model = CountRegressor(fit_intercept=false)
mach = machine(model, X, y)
fit!(mach)

Xnew = MLJ.table(rand(3, 3))
yhat = predict(mach, Xnew)
yhat_point = predict_mean(mach, Xnew)

## get coefficients approximating `w`:
julia> fitted_params(mach).coef
3-element Vector{Float64}:
  0.9969008753103842
 -2.0255901752504775
  3.014407534033522

report(mach)

See also LinearRegressor, LinearBinaryClassifier