TreeExtensions.Gam メソッド
定義
重要
一部の情報は、リリース前に大きく変更される可能性があるプレリリースされた製品に関するものです。 Microsoft は、ここに記載されている情報について、明示または黙示を問わず、一切保証しません。
オーバーロード
| Gam(BinaryClassificationCatalog+BinaryClassificationTrainers, String, String, String, Int32, Int32, Double) |
Create GamBinaryTrainer。 一般化加算モデル (GAM) を使用してターゲットを予測します。 |
| Gam(BinaryClassificationCatalog+BinaryClassificationTrainers, GamBinaryTrainer+Options) |
高度なオプションを使用して作成 GamBinaryTrainer します。これは、一般化された加算モデル (GAM) を使用してターゲットを予測します。 |
| Gam(RegressionCatalog+RegressionTrainers, GamRegressionTrainer+Options) |
高度なオプションを使用して作成 GamRegressionTrainer します。これは、一般化された加算モデル (GAM) を使用してターゲットを予測します。 |
| Gam(RegressionCatalog+RegressionTrainers, String, String, String, Int32, Int32, Double) |
Create GamRegressionTrainer。 一般化加算モデル (GAM) を使用してターゲットを予測します。 |
Gam(BinaryClassificationCatalog+BinaryClassificationTrainers, String, String, String, Int32, Int32, Double)
Create GamBinaryTrainer。 一般化加算モデル (GAM) を使用してターゲットを予測します。
public static Microsoft.ML.Trainers.FastTree.GamBinaryTrainer Gam (this Microsoft.ML.BinaryClassificationCatalog.BinaryClassificationTrainers catalog, string labelColumnName = "Label", string featureColumnName = "Features", string exampleWeightColumnName = default, int numberOfIterations = 9500, int maximumBinCountPerFeature = 255, double learningRate = 0.002);static member Gam : Microsoft.ML.BinaryClassificationCatalog.BinaryClassificationTrainers * string * string * string * int * int * double -> Microsoft.ML.Trainers.FastTree.GamBinaryTrainer<Extension()>
Public Function Gam (catalog As BinaryClassificationCatalog.BinaryClassificationTrainers, Optional labelColumnName As String = "Label", Optional featureColumnName As String = "Features", Optional exampleWeightColumnName As String = Nothing, Optional numberOfIterations As Integer = 9500, Optional maximumBinCountPerFeature As Integer = 255, Optional learningRate As Double = 0.002) As GamBinaryTrainerパラメーター
- exampleWeightColumnName
- String
重み列の例の名前 (省略可能)。
- numberOfIterations
- Int32
機能の学習に使用するイテレーションの数。
- maximumBinCountPerFeature
- Int32
フィーチャの概算に使用するビンの最大数。
- learningRate
- Double
学習率。 GAM は、学習率が小さい場合に最適です。
戻り値
例
using System;
using System.Collections.Generic;
using Microsoft.ML;
using Microsoft.ML.Data;
namespace Samples.Dynamic.Trainers.BinaryClassification
{
public static class Gam
{
// This example requires installation of additional NuGet package for
// Microsoft.ML.FastTree at
// https://www.nuget.org/packages/Microsoft.ML.FastTree/
public static void Example()
{
// Create a new context for ML.NET operations. It can be used for
// exception tracking and logging, as a catalog of available operations
// and as the source of randomness.
var mlContext = new MLContext();
// Create the dataset.
var samples = GenerateData();
// Convert the dataset to an IDataView.
var data = mlContext.Data.LoadFromEnumerable(samples);
// Create training and validation sets.
var dataSets = mlContext.Data.TrainTestSplit(data);
var trainSet = dataSets.TrainSet;
var validSet = dataSets.TestSet;
// Create a GAM trainer.
// Use a small number of bins for this example. The setting below means
// for each feature, we divide its range into 16 discrete regions for
// the training process. Note that these regions are not evenly spaced,
// and that the final model may contain fewer bins, as neighboring bins
// with identical values will be combined. In general, we recommend
// using at least the default number of bins, as a small number of bins
// limits the capacity of the model.
var trainer = mlContext.BinaryClassification.Trainers
.Gam(maximumBinCountPerFeature: 16);
// Fit the model using both of training and validation sets. GAM can use
// a technique called pruning to tune the model to the validation set
// after training to improve generalization.
var model = trainer.Fit(trainSet, validSet);
// Extract the model parameters.
var gam = model.Model.SubModel;
// Now we can inspect the parameters of the Generalized Additive Model
// to understand the fit and potentially learn about our dataset. First,
// we will look at the bias; the bias represents the average prediction
// for the training data.
Console.WriteLine($"Average prediction: {gam.Bias:0.00}");
// Now look at the shape functions that the model has learned. Similar
// to a linear model, we have one response per feature, and they are
// independent. Unlike a linear model, this response is a generic
// function instead of a line. Because we have included a bias term,
// each feature response represents the deviation from the average
// prediction as a function of the feature value.
for (int i = 0; i < gam.NumberOfShapeFunctions; i++)
{
// Break a line.
Console.WriteLine();
// Get the bin upper bounds for the feature.
var binUpperBounds = gam.GetBinUpperBounds(i);
// Get the bin effects; these are the function values for each bin.
var binEffects = gam.GetBinEffects(i);
// Now, write the function to the console. The function is a set of
// bins, and the corresponding function values. You can think of
// GAMs as building a bar-chart or lookup table for each feature.
Console.WriteLine($"Feature{i}");
for (int j = 0; j < binUpperBounds.Count; j++)
Console.WriteLine(
$"x < {binUpperBounds[j]:0.00} => {binEffects[j]:0.000}");
}
// Expected output:
// Average prediction: 0.82
//
// Feature0
// x < -0.44 => 0.286
// x < -0.38 => 0.225
// x < -0.32 => 0.048
// x < -0.26 => -0.110
// x < -0.20 => -0.116
// x < 0.18 => -0.143
// x < 0.25 => -0.115
// x < 0.31 => -0.005
// x < 0.37 => 0.097
// x < 0.44 => 0.263
// x < ∞ => 0.284
//
// Feature1
// x < 0.00 => -0.350
// x < 0.24 => 0.875
// x < 0.31 => -0.138
// x < ∞ => -0.188
// Let's consider this output. To score a given example, we look up the
// first bin where the inequality is satisfied for the feature value.
// We can look at the whole function to get a sense for how the model
// responds to the variable on a global level.The model can be seen to
// reconstruct the parabolic and step-wise function, shifted with
// respect to the average expected output over the training set.
// Very few bins are used to model the second feature because the GAM
// model discards unchanged bins to create smaller models. One last
// thing to notice is that these feature functions can be noisy. While
// we know that Feature1 should be symmetric, this is not captured in
// the model. This is due to noise in the data. Common practice is to
// use resampling methods to estimate a confidence interval at each bin.
// This will help to determine if the effect is real or just sampling
// noise. See for example: Tan, Caruana, Hooker, and Lou.
// "Distill-and-Compare: Auditing Black-Box Models Using Transparent
// Model Distillation."
// <a href='https://arxiv.org/abs/1710.06169'>arXiv:1710.06169</a>."
}
private class Data
{
public bool Label { get; set; }
[VectorType(2)]
public float[] Features { get; set; }
}
/// <summary>
/// Creates a dataset, an IEnumerable of Data objects, for a GAM sample.
/// Feature1 is a parabola centered around 0, while Feature2 is a simple
/// piecewise function.
/// </summary>
/// <param name="numExamples">The number of examples to generate.</param>
/// <param name="seed">The seed for the random number generator used to
/// produce data.</param>
/// <returns></returns>
private static IEnumerable<Data> GenerateData(int numExamples = 25000,
int seed = 1)
{
var rng = new Random(seed);
float centeredFloat() => (float)(rng.NextDouble() - 0.5);
for (int i = 0; i < numExamples; i++)
{
// Generate random, uncoupled features.
var data = new Data
{
Features = new float[2] { centeredFloat(), centeredFloat() }
};
// Compute the label from the shape functions and add noise.
data.Label = Sigmoid(Parabola(data.Features[0])
+ SimplePiecewise(data.Features[1]) + centeredFloat()) > 0.5;
yield return data;
}
}
private static float Parabola(float x) => x * x;
private static float SimplePiecewise(float x)
{
if (x < 0)
return 0;
else if (x < 0.25)
return 1;
else
return 0;
}
private static double Sigmoid(double x) => 1.0 / (1.0 + Math.Exp(-1 * x));
}
}
適用対象
Gam(BinaryClassificationCatalog+BinaryClassificationTrainers, GamBinaryTrainer+Options)
高度なオプションを使用して作成 GamBinaryTrainer します。これは、一般化された加算モデル (GAM) を使用してターゲットを予測します。
public static Microsoft.ML.Trainers.FastTree.GamBinaryTrainer Gam (this Microsoft.ML.BinaryClassificationCatalog.BinaryClassificationTrainers catalog, Microsoft.ML.Trainers.FastTree.GamBinaryTrainer.Options options);static member Gam : Microsoft.ML.BinaryClassificationCatalog.BinaryClassificationTrainers * Microsoft.ML.Trainers.FastTree.GamBinaryTrainer.Options -> Microsoft.ML.Trainers.FastTree.GamBinaryTrainer<Extension()>
Public Function Gam (catalog As BinaryClassificationCatalog.BinaryClassificationTrainers, options As GamBinaryTrainer.Options) As GamBinaryTrainerパラメーター
- options
- GamBinaryTrainer.Options
トレーナー オプション。
戻り値
例
using System;
using System.Collections.Generic;
using Microsoft.ML;
using Microsoft.ML.Data;
using Microsoft.ML.Trainers.FastTree;
namespace Samples.Dynamic.Trainers.BinaryClassification
{
public static class GamWithOptions
{
// This example requires installation of additional NuGet package for
// Microsoft.ML.FastTree at
// https://www.nuget.org/packages/Microsoft.ML.FastTree/
public static void Example()
{
// Create a new context for ML.NET operations. It can be used for
// exception tracking and logging, as a catalog of available operations
// and as the source of randomness.
var mlContext = new MLContext();
// Create the dataset.
var samples = GenerateData();
// Convert the dataset to an IDataView.
var data = mlContext.Data.LoadFromEnumerable(samples);
// Create training and validation datasets.
var dataSets = mlContext.Data.TrainTestSplit(data);
var trainSet = dataSets.TrainSet;
var validSet = dataSets.TestSet;
// Create a GAM trainer.
// Use a small number of bins for this example. The setting below means
// for each feature, we divide its range into 16 discrete regions for
// the training process. Note that these regions are not evenly spaced,
// and that the final model may contain fewer bins, as neighboring bins
// with identical values will be combined. In general, we recommend
// using at least the default number of bins, as a small number of bins
// limits the capacity of the model. Also, set the learning rate to half
// the default to slow down the gradient descent, and double the number
// of iterations to compensate.
var trainer = mlContext.BinaryClassification.Trainers.Gam(
new GamBinaryTrainer.Options
{
NumberOfIterations = 19000,
MaximumBinCountPerFeature = 16,
LearningRate = 0.001
});
// Fit the model using both of training and validation sets. GAM can use
// a technique called pruning to tune the model to the validation set
// after training to improve generalization.
var model = trainer.Fit(trainSet, validSet);
// Extract the model parameters.
var gam = model.Model.SubModel;
// Now we can inspect the parameters of the Generalized Additive Model
// to understand the fit and potentially learn about our dataset. First,
// we will look at the bias; the bias represents the average prediction
// for the training data.
Console.WriteLine($"Average prediction: {gam.Bias:0.00}");
// Now look at the shape functions that the model has learned. Similar
// to a linear model, we have one response per feature, and they are
// independent. Unlike a linear model, this response is a generic
// function instead of a line. Because we have included a bias term,
// each feature response represents the deviation from the average
// prediction as a function of the feature value.
for (int i = 0; i < gam.NumberOfShapeFunctions; i++)
{
// Break a line.
Console.WriteLine();
// Get the bin upper bounds for the feature.
var binUpperBounds = gam.GetBinUpperBounds(i);
// Get the bin effects; these are the function values for each bin.
var binEffects = gam.GetBinEffects(i);
// Now, write the function to the console. The function is a set of
// bins, and the corresponding function values. You can think of
// GAMs as building a bar-chart or lookup table for each feature.
Console.WriteLine($"Feature{i}");
for (int j = 0; j < binUpperBounds.Count; j++)
Console.WriteLine(
$"x < {binUpperBounds[j]:0.00} => {binEffects[j]:0.000}");
}
// Expected output:
// Average prediction: 0.82
//
// Feature0
// x < -0.44 => 0.286
// x < -0.38 => 0.225
// x < -0.32 => 0.048
// x < -0.26 => -0.110
// x < -0.20 => -0.116
// x < 0.18 => -0.143
// x < 0.25 => -0.115
// x < 0.31 => -0.005
// x < 0.37 => 0.097
// x < 0.44 => 0.263
// x < ∞ => 0.284
//
// Feature1
// x < 0.00 => -0.350
// x < 0.24 => 0.875
// x < 0.31 => -0.138
// x < ∞ => -0.188
// Let's consider this output. To score a given example, we look up the
// first bin where the inequality is satisfied for the feature value.
// We can look at the whole function to get a sense for how the model
// responds to the variable on a global level. The model can be seen to
// reconstruct the parabolic and step-wise function, shifted with
// respect to the average expected output over the training set. Very
// few bins are used to model the second feature because the GAM model
// discards unchanged bins to create smaller models.One last thing to
// notice is that these feature functions can be noisy. While we know
// that Feature1 should be symmetric, this is not captured in the model.
// This is due to noise in the data. Common practice is to use
// resampling methods to estimate a confidence interval at each bin.
// This will help to determine if the effect is real or just sampling
// noise. See for example: Tan, Caruana, Hooker, and Lou.
// "Distill-and-Compare: Auditing Black-Box Models Using Transparent
// Model Distillation."
// <a href='https://arxiv.org/abs/1710.06169'>arXiv:1710.06169</a>."
}
private class Data
{
public bool Label { get; set; }
[VectorType(2)]
public float[] Features { get; set; }
}
/// <summary>
/// Creates a dataset, an IEnumerable of Data objects, for a GAM sample.
/// Feature1 is a parabola centered around 0, while Feature2 is a simple
/// piecewise function.
/// </summary>
/// <param name="numExamples">The number of examples to generate.</param>
/// <param name="seed">The seed for the random number generator used to
/// produce data.</param>
/// <returns></returns>
private static IEnumerable<Data> GenerateData(int numExamples = 25000,
int seed = 1)
{
var rng = new Random(seed);
float centeredFloat() => (float)(rng.NextDouble() - 0.5);
for (int i = 0; i < numExamples; i++)
{
// Generate random, uncoupled features.
var data = new Data
{
Features = new float[2] { centeredFloat(), centeredFloat() }
};
// Compute the label from the shape functions and add noise.
data.Label = Sigmoid(Parabola(data.Features[0]) +
SimplePiecewise(data.Features[1]) + centeredFloat()) > 0.5;
yield return data;
}
}
private static float Parabola(float x) => x * x;
private static float SimplePiecewise(float x)
{
if (x < 0)
return 0;
else if (x < 0.25)
return 1;
else
return 0;
}
private static double Sigmoid(double x) => 1.0 / (1.0 + Math.Exp(-1 * x));
}
}
適用対象
Gam(RegressionCatalog+RegressionTrainers, GamRegressionTrainer+Options)
高度なオプションを使用して作成 GamRegressionTrainer します。これは、一般化された加算モデル (GAM) を使用してターゲットを予測します。
public static Microsoft.ML.Trainers.FastTree.GamRegressionTrainer Gam (this Microsoft.ML.RegressionCatalog.RegressionTrainers catalog, Microsoft.ML.Trainers.FastTree.GamRegressionTrainer.Options options);static member Gam : Microsoft.ML.RegressionCatalog.RegressionTrainers * Microsoft.ML.Trainers.FastTree.GamRegressionTrainer.Options -> Microsoft.ML.Trainers.FastTree.GamRegressionTrainer<Extension()>
Public Function Gam (catalog As RegressionCatalog.RegressionTrainers, options As GamRegressionTrainer.Options) As GamRegressionTrainerパラメーター
- options
- GamRegressionTrainer.Options
トレーナー オプション。
戻り値
例
using System;
using System.Collections.Generic;
using System.Linq;
using Microsoft.ML;
using Microsoft.ML.Data;
using Microsoft.ML.Trainers.FastTree;
namespace Samples.Dynamic.Trainers.Regression
{
public static class GamWithOptions
{
// This example requires installation of additional NuGet
// package for Microsoft.ML.FastTree found at
// https://www.nuget.org/packages/Microsoft.ML.FastTree/
public static void Example()
{
// Create a new context for ML.NET operations. It can be used for
// exception tracking and logging, as a catalog of available operations
// and as the source of randomness. Setting the seed to a fixed number
// in this example to make outputs deterministic.
var mlContext = new MLContext(seed: 0);
// Create a list of training data points.
var dataPoints = GenerateRandomDataPoints(1000);
// Convert the list of data points to an IDataView object, which is
// consumable by ML.NET API.
var trainingData = mlContext.Data.LoadFromEnumerable(dataPoints);
// Define trainer options.
var options = new GamRegressionTrainer.Options
{
LabelColumnName = nameof(DataPoint.Label),
FeatureColumnName = nameof(DataPoint.Features),
// The entropy (regularization) coefficient.
EntropyCoefficient = 0.3,
// Reduce the number of iterations to 50.
NumberOfIterations = 50
};
// Define the trainer.
var pipeline =
mlContext.Regression.Trainers.Gam(options);
// Train the model.
var model = pipeline.Fit(trainingData);
// Create testing data. Use different random seed to make it different
// from training data.
var testData = mlContext.Data.LoadFromEnumerable(
GenerateRandomDataPoints(5, seed: 123));
// Run the model on test data set.
var transformedTestData = model.Transform(testData);
// Convert IDataView object to a list.
var predictions = mlContext.Data.CreateEnumerable<Prediction>(
transformedTestData, reuseRowObject: false).ToList();
// Look at 5 predictions for the Label, side by side with the actual
// Label for comparison.
foreach (var p in predictions)
Console.WriteLine($"Label: {p.Label:F3}, Prediction: {p.Score:F3}");
// Expected output:
// Label: 0.985, Prediction: 0.841
// Label: 0.155, Prediction: 0.187
// Label: 0.515, Prediction: 0.496
// Label: 0.566, Prediction: 0.467
// Label: 0.096, Prediction: 0.144
// Evaluate the overall metrics
var metrics = mlContext.Regression.Evaluate(transformedTestData);
PrintMetrics(metrics);
// Expected output:
// Mean Absolute Error: 0.04
// Mean Squared Error: 0.01
// Root Mean Squared Error: 0.05
// RSquared: 0.98 (closer to 1 is better. The worst case is 0)
}
private static IEnumerable<DataPoint> GenerateRandomDataPoints(int count,
int seed = 0)
{
var random = new Random(seed);
for (int i = 0; i < count; i++)
{
float label = (float)random.NextDouble();
yield return new DataPoint
{
Label = label,
// Create random features that are correlated with the label.
Features = Enumerable.Repeat(label, 50).Select(
x => x + (float)random.NextDouble()).ToArray()
};
}
}
// Example with label and 50 feature values. A data set is a collection of
// such examples.
private class DataPoint
{
public float Label { get; set; }
[VectorType(50)]
public float[] Features { get; set; }
}
// Class used to capture predictions.
private class Prediction
{
// Original label.
public float Label { get; set; }
// Predicted score from the trainer.
public float Score { get; set; }
}
// Print some evaluation metrics to regression problems.
private static void PrintMetrics(RegressionMetrics metrics)
{
Console.WriteLine("Mean Absolute Error: " + metrics.MeanAbsoluteError);
Console.WriteLine("Mean Squared Error: " + metrics.MeanSquaredError);
Console.WriteLine(
"Root Mean Squared Error: " + metrics.RootMeanSquaredError);
Console.WriteLine("RSquared: " + metrics.RSquared);
}
}
}
適用対象
Gam(RegressionCatalog+RegressionTrainers, String, String, String, Int32, Int32, Double)
Create GamRegressionTrainer。 一般化加算モデル (GAM) を使用してターゲットを予測します。
public static Microsoft.ML.Trainers.FastTree.GamRegressionTrainer Gam (this Microsoft.ML.RegressionCatalog.RegressionTrainers catalog, string labelColumnName = "Label", string featureColumnName = "Features", string exampleWeightColumnName = default, int numberOfIterations = 9500, int maximumBinCountPerFeature = 255, double learningRate = 0.002);static member Gam : Microsoft.ML.RegressionCatalog.RegressionTrainers * string * string * string * int * int * double -> Microsoft.ML.Trainers.FastTree.GamRegressionTrainer<Extension()>
Public Function Gam (catalog As RegressionCatalog.RegressionTrainers, Optional labelColumnName As String = "Label", Optional featureColumnName As String = "Features", Optional exampleWeightColumnName As String = Nothing, Optional numberOfIterations As Integer = 9500, Optional maximumBinCountPerFeature As Integer = 255, Optional learningRate As Double = 0.002) As GamRegressionTrainerパラメーター
- exampleWeightColumnName
- String
重み列の例の名前 (省略可能)。
- numberOfIterations
- Int32
機能の学習に使用するイテレーションの数。
- maximumBinCountPerFeature
- Int32
フィーチャの概算に使用するビンの最大数。
- learningRate
- Double
学習率。 GAM は、学習率が小さい場合に最適です。
戻り値
例
using System;
using System.Collections.Generic;
using System.Linq;
using Microsoft.ML;
using Microsoft.ML.Data;
namespace Samples.Dynamic.Trainers.Regression
{
public static class Gam
{
// This example requires installation of additional NuGet
// package for Microsoft.ML.FastTree found at
// https://www.nuget.org/packages/Microsoft.ML.FastTree/
public static void Example()
{
// Create a new context for ML.NET operations. It can be used for
// exception tracking and logging, as a catalog of available operations
// and as the source of randomness. Setting the seed to a fixed number
// in this example to make outputs deterministic.
var mlContext = new MLContext(seed: 0);
// Create a list of training data points.
var dataPoints = GenerateRandomDataPoints(1000);
// Convert the list of data points to an IDataView object, which is
// consumable by ML.NET API.
var trainingData = mlContext.Data.LoadFromEnumerable(dataPoints);
// Define the trainer.
var pipeline = mlContext.Regression.Trainers.Gam(
labelColumnName: nameof(DataPoint.Label),
featureColumnName: nameof(DataPoint.Features));
// Train the model.
var model = pipeline.Fit(trainingData);
// Create testing data. Use different random seed to make it different
// from training data.
var testData = mlContext.Data.LoadFromEnumerable(
GenerateRandomDataPoints(5, seed: 123));
// Run the model on test data set.
var transformedTestData = model.Transform(testData);
// Convert IDataView object to a list.
var predictions = mlContext.Data.CreateEnumerable<Prediction>(
transformedTestData, reuseRowObject: false).ToList();
// Look at 5 predictions for the Label, side by side with the actual
// Label for comparison.
foreach (var p in predictions)
Console.WriteLine($"Label: {p.Label:F3}, Prediction: {p.Score:F3}");
// Expected output:
// Label: 0.985, Prediction: 0.948
// Label: 0.155, Prediction: 0.089
// Label: 0.515, Prediction: 0.463
// Label: 0.566, Prediction: 0.509
// Label: 0.096, Prediction: 0.106
// Evaluate the overall metrics
var metrics = mlContext.Regression.Evaluate(transformedTestData);
PrintMetrics(metrics);
// Expected output:
// Mean Absolute Error: 0.03
// Mean Squared Error: 0.00
// Root Mean Squared Error: 0.03
// RSquared: 0.99 (closer to 1 is better. The worst case is 0)
}
private static IEnumerable<DataPoint> GenerateRandomDataPoints(int count,
int seed = 0)
{
var random = new Random(seed);
for (int i = 0; i < count; i++)
{
float label = (float)random.NextDouble();
yield return new DataPoint
{
Label = label,
// Create random features that are correlated with the label.
Features = Enumerable.Repeat(label, 50).Select(
x => x + (float)random.NextDouble()).ToArray()
};
}
}
// Example with label and 50 feature values. A data set is a collection of
// such examples.
private class DataPoint
{
public float Label { get; set; }
[VectorType(50)]
public float[] Features { get; set; }
}
// Class used to capture predictions.
private class Prediction
{
// Original label.
public float Label { get; set; }
// Predicted score from the trainer.
public float Score { get; set; }
}
// Print some evaluation metrics to regression problems.
private static void PrintMetrics(RegressionMetrics metrics)
{
Console.WriteLine("Mean Absolute Error: " + metrics.MeanAbsoluteError);
Console.WriteLine("Mean Squared Error: " + metrics.MeanSquaredError);
Console.WriteLine(
"Root Mean Squared Error: " + metrics.RootMeanSquaredError);
Console.WriteLine("RSquared: " + metrics.RSquared);
}
}
}