Class QuantileRegressionOptions<T>

Namespace

AiDotNet.Models.Options

Assembly

AiDotNet.dll

Configuration options for Quantile Regression, a technique that enables prediction of specific quantiles of the conditional distribution rather than just the conditional mean.

public class QuantileRegressionOptions<T> : RegressionOptions<T>

Type Parameters

T

Inheritance

object

ModelOptions

RegressionOptions<T>

QuantileRegressionOptions<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

Quantile Regression extends traditional regression methods by estimating conditional quantiles of the response variable. While standard regression estimates the conditional mean E(Y|X), Quantile Regression can estimate any conditional quantile Q(a|X) for a ? (0,1), including medians (a = 0.5) and other percentiles. This technique provides a more comprehensive view of the relationship between variables, allowing for the analysis of the full conditional distribution. It is particularly valuable when the conditional distribution is non-Gaussian, skewed, or when outliers are present. Quantile Regression is also robust to heteroscedasticity (non-constant variance) and can reveal how different parts of the distribution respond differently to predictor variables.

For Beginners: Quantile Regression helps predict specific percentiles of possible outcomes, not just the average outcome.

Think about salary predictions:

• Regular regression might tell you "the average salary for this job is $75,000"
• But Quantile Regression could tell you:
  • "10% of people in this job earn less than $50,000" (10th percentile)
  • "Half of people in this job earn less than $70,000" (median or 50th percentile)
  • "90% of people in this job earn less than $120,000" (90th percentile)

What this technique does:

• It focuses on specific slices of the data distribution
• Instead of minimizing squared errors (as in mean regression)
• It minimizes a different loss function that depends on which quantile you want
• This gives you insight into different parts of the outcome distribution

This is especially useful when:

• The outcomes aren't evenly distributed around the average
• You're interested in extreme cases (very high or low values)
• Different factors might affect different parts of the distribution differently
• You want to understand risk or uncertainty better

For example, in healthcare, knowing that a treatment reduces the risk of severe complications (the high quantile) is different information than knowing it reduces the average symptom severity.

This class lets you configure how the quantile regression algorithm operates.

Properties

LearningRate

Gets or sets the learning rate for the optimization algorithm.

public double LearningRate { get; set; }

Property Value

double

The learning rate, defaulting to 0.01.

Remarks

The learning rate controls the step size in the gradient-based optimization process used to estimate the quantile regression model. A smaller learning rate leads to more precise but slower convergence, while a larger learning rate can speed up learning but risks overshooting the optimal solution or causing instability. The appropriate learning rate depends on the scale and characteristics of the data. If the algorithm fails to converge or produces poor results, adjusting this parameter may help. For quantile regression, the optimization landscape can sometimes be less smooth than for mean regression, potentially requiring a smaller learning rate for stable convergence.

For Beginners: This setting controls how quickly the algorithm adjusts its predictions during training.

The default value of 0.01 means:

• The algorithm takes moderate-sized steps when improving its model
• It's a balance between learning speed and learning stability

Think of it like walking down a hill blindfolded:

• A small learning rate (like 0.001) means taking tiny, cautious steps
  • Safer but takes much longer to reach the bottom
• A large learning rate (like 0.1) means taking big, bold steps
  • Faster but you might trip or miss the lowest point entirely

You might want a smaller learning rate (like 0.001):

• When your model is unstable or oscillating during training
• When you need very precise results and have time for longer training
• When working with data that has very large or varied scales

You might want a larger learning rate (like 0.05):

• When training is taking too long
• When you're doing initial exploration
• When you have a lot of data and want faster convergence

Finding the right learning rate often requires experimentation - too small and training takes forever, too large and the model might never find the best solution.

MaxIterations

Gets or sets the maximum number of iterations for the optimization algorithm.

public int MaxIterations { get; set; }

Property Value

int

The maximum number of iterations, defaulting to 1000.

Remarks

This parameter limits the number of iterations the optimization algorithm will perform when fitting the quantile regression model. It serves as a stopping criterion to prevent excessive computation time in cases where convergence is slow or not achieved. The algorithm may terminate earlier if convergence is detected before reaching this limit. For simpler datasets or higher learning rates, fewer iterations may be sufficient, while complex relationships or lower learning rates might require more iterations to reach convergence. Monitoring the convergence behavior can help in determining an appropriate value for this parameter.

For Beginners: This setting controls how many times the algorithm will try to improve its predictions before stopping.

The default value of 1000 means:

• The algorithm will make up to 1000 attempts to refine its model
• It might stop earlier if it determines the model isn't improving anymore

Think of it like a game where you're trying to guess a number:

• Each iteration is one guess
• After each guess, you get feedback to improve your next guess
• MaxIterations is like setting a limit: "I'll stop after 1000 guesses even if I haven't found the exact answer"

You might want more iterations (like 5000 or 10000):

• When your data is complex or has subtle patterns
• When using a very small learning rate
• When you need high precision and have the computational resources

You might want fewer iterations (like 500 or 100):

• When you need faster training times
• When you have simpler data relationships
• When you're doing exploratory analysis and don't need perfect results
• When you notice the model stops improving well before 1000 iterations

This setting helps prevent the model from training indefinitely, ensuring it eventually completes even if it hasn't reached perfect convergence.

Quantile

Gets or sets the quantile to be estimated by the regression model.

public double Quantile { get; set; }

Property Value

double

The quantile value between 0 and 1, defaulting to 0.5 (median regression).

Remarks

This parameter determines which quantile of the conditional distribution the model will estimate. The quantile must be a value between 0 and 1, where 0.5 represents the median (50th percentile), 0.9 represents the 90th percentile, 0.1 represents the 10th percentile, and so on. Setting this value to 0.5 (the default) results in median regression, which is more robust to outliers than mean regression. Lower values (e.g., 0.1) focus on the lower tail of the distribution, while higher values (e.g., 0.9) focus on the upper tail. Different quantiles can reveal how the relationship between predictors and the response variable changes across the distribution.

For Beginners: This setting controls which percentile of the data you want to predict.

The default value of 0.5 means:

• You're trying to predict the median (middle value)
• Half of outcomes will likely be above your prediction
• Half of outcomes will likely be below your prediction

Think of it like height predictions:

• Quantile 0.5 (median): The height where half of people are taller and half are shorter
• Quantile 0.9 (90th percentile): The height where only 10% of people are taller
• Quantile 0.1 (10th percentile): The height where 90% of people are taller

You might choose different quantiles for different purposes:

• 0.5 for a typical or central prediction (median)
• 0.9 or higher when you're concerned about upper limits or worst-case scenarios
• 0.1 or lower when you're concerned about lower limits or best-case scenarios
• Multiple quantiles (running the model multiple times) to get a full picture of possibilities

For example, in flood risk modeling, the 0.99 quantile might tell you the water level that has only a 1% chance of being exceeded - critical information for safety planning.