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4. GTApprox

This part of the pSeven Core manual is a guide to the Generic Tool for Approximation (GTApprox).

• 4.1. Introduction
  • 4.1.1. Overview
  • 4.1.2. Problem Statement
  • 4.1.3. Sample Size Requirements
• 4.2. General Usage
  • 4.2.1. Smart Training
    • 4.2.1.1. Additional Data Properties
    • 4.2.1.2. Model Features
    • 4.2.1.3. Training Features
  • 4.2.2. Manual Training
• 4.3. Approximation Modes
  • 4.3.1. Exact Fit
  • 4.3.2. Noisy Problems
    • 4.3.2.1. Heteroscedastic data
    • 4.3.2.2. Data with Errorbars
  • 4.3.3. Output Dependency Modes
  • 4.3.4. Sample Weighting
  • 4.3.5. Categorical Variables
    • 4.3.5.1. Building a Model with Categorical Variables
    • 4.3.5.2. Model with Categorical Variables
    • 4.3.5.3. Categorical Variables for TA, iTA and TGP techniques
  • 4.3.6. Categorical Outputs
  • 4.3.7. Submodels and Parallel Training
• 4.4. Quality Assessment
  • 4.4.1. Model Validation
    • 4.4.1.1. Error metrics
      • 4.4.1.1.1. Componentwise errors
      • 4.4.1.1.2. Aggregated errors
    • 4.4.1.2. Accuracy on train set
    • 4.4.1.3. Internal Validation
      • 4.4.1.3.1. Cross-validation procedure details
    • 4.4.1.4. Validation on test set
  • 4.4.2. Evaluation of accuracy in given point
    • 4.4.2.1. Example
• 4.5. Techniques
  • 4.5.1. Gradient Boosted Regression Trees
    • 4.5.1.1. Overview
    • 4.5.1.2. Configuration
      • 4.5.1.2.1. Shrinkage
      • 4.5.1.2.2. Stochastic Boosting
      • 4.5.1.2.3. Model Complexity
      • 4.5.1.2.4. Leaf Weighting
      • 4.5.1.2.5. Incremental Training
    • 4.5.1.3. Algorithm
      • 4.5.1.3.1. Initial Training
      • 4.5.1.3.2. Train Sample Filtering
      • 4.5.1.3.3. Incremental Training
  • 4.5.2. Gaussian Processes
    • 4.5.2.1. Overview
    • 4.5.2.2. Algorithm Details
      • 4.5.2.2.1. Used class of GPs
      • 4.5.2.2.2. Tuning of covariance function parameters
  • 4.5.3. High Dimensional Approximation
    • 4.5.3.1. Overview
    • 4.5.3.2. Algorithm description
  • 4.5.4. High Dimensional Approximation combined with Gaussian Processes
    • 4.5.4.1. Overview
    • 4.5.4.2. Algorithm description
  • 4.5.5. Incomplete Tensor Products of Approximations
    • 4.5.5.1. Overview
    • 4.5.5.2. The overall workflow
    • 4.5.5.3. Smoothing
    • 4.5.5.4. Model Complexity Reduction
  • 4.5.6. Mixture of Approximators
    • 4.5.6.1. Overview
    • 4.5.6.2. Algorithm Details
    • 4.5.6.3. Design Space Decomposition
    • 4.5.6.4. Calculating Model Output
    • 4.5.6.5. Initial Model
    • 4.5.6.6. Artificial Example: Discontinuous Function
  • 4.5.7. Piecewise Linear Approximation
    • 4.5.7.1. Overview
    • 4.5.7.2. Algorithm Details
    • 4.5.7.3. Delaunay Triangulation
  • 4.5.8. Response Surface Model
    • 4.5.8.1. Overview
    • 4.5.8.2. Description
    • 4.5.8.3. Parameters Estimation
    • 4.5.8.4. Regression Model Structure
  • 4.5.9. Sparse Gaussian Process
    • 4.5.9.1. Overview
  • 4.5.10. 1D Splines with tension
    • 4.5.10.1. Overview
  • 4.5.11. Tensor Products of Approximations
    • 4.5.11.1. Overview
    • 4.5.11.2. Discrete/categorical variables
    • 4.5.11.3. The overall workflow
    • 4.5.11.4. Factorization of the training set
    • 4.5.11.5. Approximation in single factors
    • 4.5.11.6. Smoothing
    • 4.5.11.7. Model Complexity Reduction
    • 4.5.11.8. Examples
  • 4.5.12. Tensored Gaussian Processes
    • 4.5.12.1. Overview
  • 4.5.13. Table Function
    • 4.5.13.1. Overview
• 4.6. Details
  • 4.6.1. Sample Cleanup
    • 4.6.1.1. Input Rounding
  • 4.6.2. Automatic Technique Selection
  • 4.6.3. Deterministic and Randomized Training
  • 4.6.4. Training Time and Accuracy Tradeoffs
    • 4.6.4.1. Accelerator
  • 4.6.5. Multi-core Scalability
  • 4.6.6. Using Clusters
  • 4.6.7. Model Smoothing
    • 4.6.7.1. Anisotropic Smoothing
    • 4.6.7.2. Error-Based Smoothing
    • 4.6.7.3. Notes on Smoothing Methods
  • 4.6.8. Model Metainformation
  • 4.6.9. Model Details
    • 4.6.9.1. Input and Output Descriptions
    • 4.6.9.2. Training Dataset Information
      • 4.6.9.2.1. Accuracy
      • 4.6.9.2.2. Sample Statistics
    • 4.6.9.3. Training Time
    • 4.6.9.4. Regression Model Information
    • 4.6.9.5. Input Constraints
    • 4.6.9.6. Output Constraints
    • 4.6.9.7. Constraints Formula
    • 4.6.9.8. Model Decomposition
    • 4.6.9.9. Structure Reference
  • 4.6.10. Model Gradients and AE Gradients
  • 4.6.11. Model Export
  • 4.6.12. Approximation Model Structure
• 4.7. Option Reference
• 4.8. Hint Reference
• 4.9. References