Regression

Learn how to predict continuous values using AiDotNet’s regression algorithms.

What is Regression?

Regression is a supervised learning task where the goal is to predict continuous numeric values from input features. Examples include:

• House price prediction
• Temperature forecasting
• Stock price estimation
• Sales revenue prediction

Types of Regression

Simple Regression

One input feature predicts one output. Example: Predict house price from square footage.

Multiple Regression

Multiple input features predict one output. Example: Predict house price from square footage, bedrooms, and location.

Polynomial Regression

Non-linear relationships using polynomial features.

Quick Start

using AiDotNet;
using AiDotNet.Data.Loaders;
using AiDotNet.Regression;
using AiDotNet.Tensors.LinearAlgebra;

// House features: sqft, bedrooms, bathrooms, age
double[][] features =
{
    new[] { 1400.0, 3.0, 2.0, 15.0 }, new[] { 1600.0, 3.0, 2.0, 10.0 },
    new[] { 1700.0, 3.0, 2.5, 5.0 },  new[] { 1875.0, 4.0, 3.0, 8.0 },
    new[] { 1100.0, 2.0, 1.0, 25.0 }, new[] { 2200.0, 4.0, 3.0, 2.0 }
};
double[] prices = { 245000, 312000, 279000, 308000, 199000, 425000 };

var X = ToMatrix(features);
var y = new Vector<double>(prices);

var result = await new AiModelBuilder<double, Matrix<double>, Vector<double>>()
    .ConfigureModel(new RandomForestRegression<double>())
    .ConfigureDataLoader(DataLoaders.FromMatrixVector(X, y))
    .BuildAsync();

var newHome = new Matrix<double>(1, 4);
foreach (var (v, j) in new[] { 1500.0, 3.0, 2.0, 12.0 }.Select((v, j) => (v, j)))
    newHome[0, j] = v;
Console.WriteLine($"Predicted price: ${result.Predict(newHome)[0]:N0}");

// Metrics come off the result — no hand-rolled math.
var stats = result.GetDataSetStats(X, y);
Console.WriteLine($"R²: {stats.PredictionStats.R2:F4}, RMSE: {stats.ErrorStats.RMSE:N0}");

static Matrix<double> ToMatrix(double[][] rows)
{
    var m = new Matrix<double>(rows.Length, rows[0].Length);
    for (int i = 0; i < rows.Length; i++)
        for (int j = 0; j < rows[0].Length; j++)
            m[i, j] = rows[i][j];
    return m;
}

Available Regressors

Swap the ConfigureModel(...) argument to change algorithm — everything else stays the same.

Tree-Based Methods

Linear Methods

Distance-Based & Neural

Neural Network Regression

using AiDotNet;
using AiDotNet.Data.Loaders;
using AiDotNet.Regression;
using AiDotNet.Tensors.LinearAlgebra;

double[][] features =
{
    new[] { 1400.0, 3.0 }, new[] { 1600.0, 3.0 }, new[] { 1700.0, 3.0 },
    new[] { 1875.0, 4.0 }, new[] { 1100.0, 2.0 }, new[] { 2200.0, 4.0 }
};
double[] targets = { 245000, 312000, 279000, 308000, 199000, 425000 };

var result = await new AiModelBuilder<double, Matrix<double>, Vector<double>>()
    .ConfigureModel(new NeuralNetworkRegression<double>())
    .ConfigureDataLoader(DataLoaders.FromArrays(features, targets))
    .BuildAsync();

Console.WriteLine($"Trained: {result.TotalTrainableParameters:N0} parameters");

Data Preprocessing

Pass a preprocessing pipeline to ConfigurePreprocessing(...) to scale or impute features before training — useful for linear and distance-based models. Regularized linear models like RidgeRegression pair well with feature scaling.

using AiDotNet;
using AiDotNet.Data.Loaders;
using AiDotNet.Regression;
using AiDotNet.Tensors.LinearAlgebra;

double[][] features =
{
    new[] { 1400.0, 3.0 }, new[] { 1600.0, 3.0 }, new[] { 1700.0, 3.0 }, new[] { 1875.0, 4.0 }
};
double[] targets = { 245000, 312000, 279000, 308000 };

var result = await new AiModelBuilder<double, Matrix<double>, Vector<double>>()
    .ConfigureModel(new RidgeRegression<double>())
    .ConfigureDataLoader(DataLoaders.FromArrays(features, targets))
    .BuildAsync();

Console.WriteLine("Trained a regularized linear model.");

Evaluation Metrics

Every regression metric is computed for you and lives under result.GetDataSetStats(X, y).

using AiDotNet;
using AiDotNet.Data.Loaders;
using AiDotNet.Regression;
using AiDotNet.Tensors.LinearAlgebra;

double[][] data =
{
    new[] { 1400.0, 3.0 }, new[] { 1600.0, 3.0 }, new[] { 1700.0, 3.0 },
    new[] { 1875.0, 4.0 }, new[] { 1100.0, 2.0 }, new[] { 2200.0, 4.0 }
};
double[] targets = { 245000, 312000, 279000, 308000, 199000, 425000 };

var X = ToMatrix(data);
var y = new Vector<double>(targets);

var result = await new AiModelBuilder<double, Matrix<double>, Vector<double>>()
    .ConfigureModel(new GradientBoostingRegression<double>())
    .ConfigureDataLoader(DataLoaders.FromMatrixVector(X, y))
    .BuildAsync();

var stats = result.GetDataSetStats(X, y);
Console.WriteLine($"MAE:  {stats.ErrorStats.MAE:F4}");
Console.WriteLine($"MSE:  {stats.ErrorStats.MSE:F4}");
Console.WriteLine($"RMSE: {stats.ErrorStats.RMSE:F4}");
Console.WriteLine($"R²:   {stats.PredictionStats.R2:F4}");

static Matrix<double> ToMatrix(double[][] rows)
{
    var m = new Matrix<double>(rows.Length, rows[0].Length);
    for (int i = 0; i < rows.Length; i++)
        for (int j = 0; j < rows[0].Length; j++)
            m[i, j] = rows[i][j];
    return m;
}

Best Practices

1. Start simple: Use MultipleRegression as a baseline.
2. Check for outliers: Outliers heavily influence linear models.
3. Feature scaling: Most algorithms benefit from ConfigurePreprocessing().
4. Regularize: Use RidgeRegression or LassoRegression to prevent overfitting.
5. Validate: Add ConfigureCrossValidation(...) for robust evaluation.

Next Steps

• Classification Tutorial - For predicting discrete labels
• Time Series Tutorial - For temporal data