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Stochasta

Stochasta is a fast, lightweight, and dependency-free Crystal shard providing modular implementations of stochastic, optimization, and unsupervised learning algorithms.

What Stochasta Offers

Stochasta brings powerful stochastic models, nature-inspired search metaheuristics, and unsupervised data science algorithms to the Crystal ecosystem. It offers:

1. Metaheuristic Global Optimization: Find global extrema for complex continuous or discrete functions where traditional mathematical optimization fails, using Genetic Algorithms, PSO, Differential Evolution, Artificial Bee Colony, and Simulated Annealing.
2. Combinatorial Optimization: Solve routing and sequence-based discrete problems like the Traveling Salesperson Problem (TSP) using Ant Colony Optimization.
3. Advanced Clustering Suite: Group data structures using diverse paradigms—centroid partition (K-Means), density reachability (DBSCAN, Mean Shift), representative cluster medoids (K-Medoids), or bottom-up merge trees (Hierarchical Agglomerative Clustering).
4. Probabilistic & Bayesian Reasoning: Evaluate Bayes' theorem posterior probability updates and classify multi-class categorical texts using Laplace-smoothed Naive Bayes.
5. Dimensionality Reduction: Project complex multi-dimensional datasets to lower dimensions (e.g. for visualization or preprocessing) via Principal Component Analysis (PCA) using a built-in Jacobi eigenvalue decomposition.
6. Association Mining: Discover hidden relationships in transactional/shopping databases with the Apriori association rule mining algorithm.
7. Stochastic Simulations: Run Monte Carlo sample simulations and numerical multi-dimensional integration.
8. Quantitative Finance Suite: Optimize asset weights for minimum variance or maximum Sharpe ratio (solved via built-in PSO), estimate returns with Black-Litterman, measure VaR/CVaR risk, and simulate asset prices using Geometric Brownian Motion.

Features

• Genetic Algorithms (Stochasta::Genetic): Flexible evolutionary engine with customizable selection (tournament), crossover, mutation, and support for elitism.
• Monte Carlo Simulation (Stochasta::MonteCarlo): Stochastic simulation trials, 1D and multi-dimensional numerical integration.
• Particle Swarm Optimization (PSO) (Stochasta::PSO): Continuous optimization in bounded spaces.
• Bayesian Statistics (Stochasta::Bayes): Categorical Naive Bayes classifiers with Laplace smoothing and Bayesian updating calculators.
• K-Means Clustering (Stochasta::KMeans): Standard iterative K-Means clustering algorithm.
• Gaussian Mixture Models (GMM) (Stochasta::GMM): Soft probability-based clustering trained via Expectation-Maximization.
• Hierarchical Clustering (Stochasta::Hierarchical): Agglomerative clustering supporting Single, Complete, and Average linkages.
• K-Medoids (PAM) (Stochasta::KMedoids): Partitioning Around Medoids using actual dataset points as centroids.
• Mean Shift (Stochasta::MeanShift): Density-based clustering to automatically discover cluster centers.
• DBSCAN Clustering (Stochasta::DBSCAN): Density-based spatial clustering for arbitrary shapes and noise extraction.
• Principal Component Analysis (PCA) (Stochasta::PCA): Unsupervised dimensionality reduction powered by a pure Crystal symmetric Jacobi eigenvalue solver.
• Apriori Algorithm (Stochasta::Apriori): Association rule mining and frequent itemsets locator.
• Differential Evolution (DE) (Stochasta::DifferentialEvolution): Global vector population optimizer for continuous spaces.
• Ant Colony Optimization (ACO) (Stochasta::AntColony): Combinatorial Traveling Salesperson Problem (TSP) solver.
• Artificial Bee Colony (ABC) (Stochasta::ArtificialBeeColony): Swarm-based global optimizer modeled after honey bee foraging.
• Simulated Annealing (Stochasta::SimulatedAnnealing): Probabilistic optimization technique for finding global extrema.
• Portfolio Optimization & Quant Finance (Stochasta::Portfolio): Minimum variance/maximum Sharpe allocation (utilizing built-in PSO), Black-Litterman returns updating, VaR & CVaR risk estimators, and Geometric Brownian Motion path generators.

Installation

1. Add the dependency to your shard.yml:

   dependencies:
     stochasta:
       github: eltony81/stochasta

2. Run shards install

Usage Examples

Complete, well-commented execution files are available in the examples/ directory:

• genetic_example.cr: Solve a OneMax bitstring optimization problem using Genetic Algorithms.
• monte_carlo_example.cr: Estimate Pi and run 1D/2D numerical integrals.
• pso_example.cr: Find the global minimum of the Rosenbrock function.
• de_example.cr: Optimize continuous dimensions using Differential Evolution.
• aco_example.cr: Solve the Traveling Salesperson Problem (TSP) using Ant Colony System.
• abc_example.cr: Find global minimums using Artificial Bee Colony.
• bayes_example.cr: Run Bayesian inference and classify spam/ham messages.
• clustering_example.cr: Combine PCA dimension reduction, K-Means partitioning, and DBSCAN noise detection.
• gmm_example.cr: Run soft probabilistic clustering with Gaussian Mixture Models.
• hierarchical_example.cr: Cluster data using bottom-up Hierarchical Agglomerative Clustering.
• kmedoids_example.cr: Partition data around medoids chosen from actual points.
• mean_shift_example.cr: Run density-based cluster centroid discovery.
• apriori_example.cr: Mine shopping transaction databases for association rules (Support, Confidence, Lift).
• annealing_example.cr: Probabilistic optimization on continuous mathematical functions.
• portfolio_optimization_example.cr: Perform Markowitz portfolio optimization using PSO.
• black_litterman_example.cr: Estimate adjusted asset returns using the Black-Litterman model.
• risk_metrics_example.cr: Calculate Value at Risk (VaR) and Conditional Value at Risk (CVaR).
• gbm_example.cr: Simulate future stock price paths using Geometric Brownian Motion.

Quick Sample: Naive Bayes Classification

require "stochasta"

# Initialize a Naive Bayes classifier
classifier = Stochasta::Bayes::NaiveClassifier(String, String).new

# Train the model
classifier.train(["buy", "cheap", "deal"], "spam")
classifier.train(["meeting", "project", "deadline"], "ham")

# Predict on new unseen features
label = classifier.predict(["cheap", "deadline"])
puts "Classified as: #{label}"

Running Tests

Stochasta has a comprehensive spec suite. To run the tests, execute:

crystal spec

Contributors

• tony - creator and maintainer