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Computational Core Module

Computational Core Module contains libraries the implement Algorithm/Computation Support, Function Analysis, Model Validation, Numerical Analysis, Numerical Optimizer, Spline Builder, and Statistical Learning.

Component Libraries

  • Function Analysis => Special Function and their Analysis.

  • Graph Algorithms => Graph Representation and Path Traversal.

  • Model Validation => Functionality for Statistical Hypotheses Validation and Testing.

  • Numerical Analysis => Functionality for Numerical Methods - including Rx Solvers, Linear Algebra, and Statistical Measure Distributions.

  • Numerical Optimizer => Functionality for Numerical Optimization - including Constrained and Mixed Integer Non-Linear Optimizers.

  • Spline Builder => Functionality for constructing Spline Based Curves and Surfaces.

  • Statistical Learning => Statistical Learning Analyzers and Machine Learning Schemes.

Function Analysis Coverage

  • Gamma Function
  • Stirling's Approximation
  • Lanczos Approximation
  • Incomplete Gamma Function
  • Digamma Function
  • Beta Function
  • Hypergeometric Function
  • Bessel Function
  • Stretched Exponential Function
  • Error Function

Graph Algorithm Coverage

  • Priority Queue
  • Binary Heap
  • Binomial Heap
  • Soft Heap
  • The Soft Heap: An Approximate Priority Queue with Optimal Error Rate
  • A Simpler Implementation and Analysis of Chazelle’s Soft Heaps
  • Spanning Tree
  • Minimum Spanning Tree
  • Prim's Algorithm
  • Kruskal's Algorithm
  • Boruvka's Algorithm
  • Reverse-Delete Algorithm
  • Breadth-first Search
  • Depth-first Search
  • Dijkstra's Algorithm
  • Bellman-Ford Algorithm
  • Johnson's Algorithm
  • A* Search Algorithm
  • Floyd-Warshall Algorithm
  • Selection Algorithm
  • Quickselect
  • Median Of Medians
  • Floyd-Rivest Algorithm
  • Introselect
  • Order Statistics Tree
  • Maximum Sub-array Problem
  • Subset Sum Problem
  • 3SUM

Model Validation Coverage

  • Probability Integral Transform
  • t-Statistic
  • p-value
  • Q-Q Plot
  • Basel III Framework for Backtesting Exposure Models
  • Initial Margin Backtesting Framework
  • Model Risk Management Framework

Numerical Analysis Coverage

  • Introduction
  • Framework
  • Search Initialization
  • Numerical Challenges in Search
  • Variate Iteration
  • Open Search Method: Newton Method
  • Closed Search Methods
  • Polynomial Root Search
  • Meta-heuristics
  • Multivariate Distribution
  • Linear Systems Analysis and Transformation
  • Rayleigh Quotient Iteration
  • Power Iteration
  • Sylvester's Formula
  • Numerical Integration
  • Gaussian Quadrature
  • Gauss-Kronrod Quadrature
  • Gamma Distribution
  • Chi Square Distribution
  • Non-central Chi-Square Distribution

Numerical Optimizer Coverage

  • Convex Optimization - Introduction and Overview
  • Newton’s Method in Optimization
  • Constrained Optimization
  • Lagrange Multipliers
  • Spline Optimizer
  • Karush-Kuhn-Tucker Conditions
  • Interior Point Method
  • Portfolio Selection with Cardinality and Bound Constraints
  • Simplex Algorithm

Spline Builder Coverage

  • Overview
  • Calibration Framework
  • Spline Builder Setup
  • B Splines
  • Polynomial Spline Basis Function
  • Local Spline Stretches
  • Spline Stretch Calibration
  • Spline Jacobian
  • Shape Preserving Spline
  • Koch Lyche Kvasov Tension Splines
  • Smoothing Splines
  • Multi Dimensional Splines

Statistical Learning Coverage

  • Probabilistic Bounds
  • Efron-Stein Bounds
  • Entropy Methods
  • Concentration of Measure
  • Standard SLT Framework
  • Generalization and Consistency
  • Empirical Risk Minimization
  • Symmetrization
  • Generalization Bounds
  • Rademacher Complexity
  • Local Rademacher Averages
  • Normalized ERM
  • Noise Conditions
  • VC Theory and VC Dimension
  • Sauer Lemma and VC Classifier Framework
  • Covering and Entropy Numbers
  • Covering Numbers for Real-Valued Function Classes
  • Operator Theory Methods for Entropy Numbers
  • Generalization Bounds via Uniform Convergence
  • Kernel Machines
  • Entropy Numbers for Kernel Machines
  • Discrete Spectra of Convolution Operators
  • Covering Numbers for Given Decay Rates
  • Kernels for High Dimensional Data
  • Regularization Networks Entropy Numbers Determination - Practice
  • Minimum Description Length Approach
  • Bayesian Methods
  • Knowledge Based Bounds
  • Approximation Error and Bayes’ Consistency
  • No Free Lunch Theorem
  • Generative and Discriminative Models
  • Supervised Learning
  • Unsupervised Learning
  • Machine Learning
  • Pattern Recognition
  • Statistical Classification
  • Linear Discriminant Analysis
  • Logistic Regression
  • Multinomial Logistic Regression
  • Decision Trees and Decision Lists
  • Variable Bandwidth Kernel Density Estimation
  • k-Nearest Neighbors Algorithm
  • Perceptron
  • Support Vector Machines (SVM)
  • Gene Expression Programming (GEP)
  • Cluster Analysis
  • Mixture Model
  • Deep Learning
  • Hierarchical Clustering
  • k-Means Clustering
  • Correlation Clustering
  • Kernel Principal Component Analysis (Kernel PCA)
  • Ensemble Learning
  • ANN Ensemble Averaging
  • Boosting
  • Bootstrap Aggregating
  • Tensors and Multi-linear Subspace Learning
  • Kalman Filtering
  • Particle Filtering
  • Regression Analysis
  • Component Analysis
  • Kriging
  • Hidden Markov Models
  • Markov Chain Models
  • Markov Random and Condition Random Fields
  • Maximum Entropy Markov Models (MEMM)
  • Probabilistic Grammar and Parsing
  • Bayesian Analysis: Concepts, Formulation, Usage, and Application

Algorithm Support Coverage

Computation Support Coverage

DROP Specifications