Goal: Geometric OptimizAtion Libraries

Goal (Geometric OptimizAtion Libraries) is a collection of Haskell libraries for numerical optimization and machine learning. Expanding on vectors with static sizes, Goal furnishes vectors with additional type-level structure based on ideas from differential geometry. The goals of Goal are to provide types, classes, and functions that are:

• practical, and provide a safe and effective means of expressing and applying efficient optimization algorithms.
• intuitive, such that types and classes can be easily read and understood, and meaningfully describe their values and functions.
• evocative, such that the correspondence between Goal types and mathematical constructs promotes an appreciation and understanding of mathematical optimization and geometry.

For more detailed explanations of the Goal libraries, visit the individual package pages. At my blog you may find examples and tutorials for Goal.

The central packages of the Goal libraries are:

Core

goal-core re-exports a number of other libraries, and provides a set of additional utility functions useful for scientific computing. In particular, implementations of Mealy Automata (Circuits), tools for working with CSV files and gnuplot, and a module which combines vector-sized vectors with hmatrix.

Geometry

goal-geometry provides the basic types and classes which drive the manifold/geometry based approach of Goal. Points and manifolds, dual and multilinear spaces, function spaces and multilayer neural networks, and generic optimization routines are defined here.

Probability

goal-probability provides tools for implementing and applying basic statistical models. The core concept of goal-probability are statistical manifolds, i.e. manifold of probability distributions, with a focus on exponential family distributions.

Graphical

goal-graphical provides tools for with dynamical and graphical models. Various graphical models are defined here, e.g. mixture models and restricted Boltzmann machines, dynamical models such as HMMs and Kalman filters, and in both cases algorithms for fitting them e.g. expectation maximization and contrastive divergence minimization.