Class PoissonRegressionOptions<T>

Namespace

AiDotNet.Models.Options

Assembly

AiDotNet.dll

Configuration options for Poisson Regression, a specialized form of regression analysis used for modeling count data and contingency tables where the dependent variable consists of non-negative integers.

public class PoissonRegressionOptions<T> : RegressionOptions<T>

Type Parameters

T

Inheritance

object

ModelOptions

RegressionOptions<T>

PoissonRegressionOptions<T>

Inherited Members

RegressionOptions<T>.DecompositionMethod

RegressionOptions<T>.UseIntercept

ModelOptions.Seed

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Remarks

Poisson Regression is particularly suited for analyzing count data where the response variable represents the number of occurrences of an event within a fixed period or space. Unlike linear regression, which assumes a normal distribution of errors, Poisson regression assumes the response variable follows a Poisson distribution. This makes it appropriate for cases where data is discrete, non-negative, and often skewed. The model uses a logarithmic link function to ensure predictions are always positive. Poisson regression is widely used in fields such as epidemiology, insurance (claim counts), ecology (species counts), and marketing (number of purchases).

For Beginners: Poisson Regression is a technique specially designed for predicting counts of things.

Imagine you want to predict:

• How many customers will visit a store each hour
• How many calls a support center will receive each day
• How many defects will appear in manufactured products

When working with counts:

• You never have negative numbers (you can't have -3 customers)
• You often have small whole numbers (0, 1, 2, 3, etc.)
• The data often clusters near zero with a "long tail" of occasional higher values

Regular regression methods can give nonsensical results for this kind of data (like predicting -2.5 customers). Poisson regression specifically handles count data by:

• Always predicting non-negative values
• Understanding the special patterns common in count data
• Properly handling the case when counts are zero

This class lets you configure how the algorithm searches for the best model to fit your count data.

Properties

DecompositionType

Gets or sets the matrix decomposition type to use when solving the weighted least squares problem.

public MatrixDecompositionType DecompositionType { get; set; }

Property Value

MatrixDecompositionType

The matrix decomposition type, defaulting to QR decomposition.

Remarks

The decomposition type determines how the system of linear equations is solved during each iteration of the IRLS algorithm. QR decomposition is a numerically stable choice suitable for most problems.

For Beginners: This setting controls the mathematical method used to solve equations during model fitting. The default QR method works well for most cases - you typically don't need to change this unless you have specific performance or numerical stability requirements.

MaxIterations

Gets or sets the maximum number of iterations allowed in the model fitting process.

public int MaxIterations { get; set; }

Property Value

int

The maximum number of iterations, defaulting to 100.

Remarks

This parameter controls how many times the algorithm will attempt to refine the model coefficients during the fitting process. Poisson regression typically uses iterative methods like Iteratively Reweighted Least Squares (IRLS) to maximize the likelihood function. The algorithm iteratively updates the model parameters until convergence is reached or the maximum number of iterations is exceeded. Setting this value too low might prevent the model from converging to an optimal solution, while setting it too high might waste computational resources if the model has already converged.

For Beginners: This setting controls how many attempts the algorithm makes to find the best model.

The default value of 100 means:

• The algorithm will try up to 100 times to improve its predictions
• It stops earlier if it finds a solution that's good enough (based on the Tolerance setting)
• It stops after 100 attempts even if it hasn't found an ideal solution

Think of it like finding the lowest point in a valley while blindfolded:

• You take a step in what seems like the downward direction
• You check if you're lower than before
• You repeat this process, gradually getting closer to the bottom
• MaxIterations is like saying "I'll take at most 100 steps, then stop wherever I am"

You might want more iterations (like 500 or 1000):

• For complex datasets where finding the best model is difficult
• When high precision is critical for your application
• If you notice the model isn't converging with the default setting

You might want fewer iterations (like 50 or 20):

• For simpler datasets where solutions are found quickly
• When you need faster training times
• In exploratory analysis where approximate solutions are acceptable

Tolerance

Gets or sets the convergence tolerance threshold for the model fitting process.

public double Tolerance { get; set; }

Property Value

double

The convergence tolerance, defaulting to 1e-6 (0.000001).

Remarks

This parameter determines how precise the solution needs to be before the algorithm considers the model to have converged. Specifically, it defines the threshold for the change in model parameters or log-likelihood between consecutive iterations. When the change falls below this tolerance level, the iterative process terminates, as further improvements would be negligible. A smaller tolerance value requires more precision and potentially more iterations, while a larger value allows for earlier termination with a less precise solution. The optimal setting depends on the specific application's requirements for precision versus computational efficiency.

For Beginners: This setting determines how precise the model solution needs to be before the algorithm stops refining it.

The default value of 0.000001 (1e-6) means:

• The algorithm will stop when changes between iterations become very small (less than one millionth)
• It's considered "close enough" to the perfect solution at this point
• Further refinements would make negligible difference to predictions

Think of it like adjusting the focus on a camera:

• At first, turning the focus ring makes a big difference to clarity
• As you get closer to perfect focus, small adjustments make less noticeable improvements
• Eventually, you reach a point where further adjustments don't visibly improve the image
• Tolerance is like deciding "this is sharp enough" and stopping

You might want a smaller tolerance (like 1e-8 or 1e-10):

• For applications requiring extremely precise results
• When using the model for scientific research or critical decisions
• If you have the computational resources to support more iterations

You might want a larger tolerance (like 1e-4 or 1e-3):

• When approximate solutions are sufficient
• To speed up model training, especially with large datasets
• For preliminary analysis or when building many models