Stochastic Simulation

BioSimulator.jl

Stochastic simulation of Markov chains representing discrete dynamical systems using the Julia language. It provides an easy-to-use model building system and implements commonly used Gillespie-like algorithms as well as $\tau$-leaping methods.

In collaboration with Tim Stutz, I also implemented support for simulating stochastic processes with a spatial component using interacting particle systems.

Related

• BioSimualtorPetriNets.jl: Draw petri nets from well-mixed models in BioSimulator.jl.

Optimization

ProximalDistanceAlgorithms.jl

Implements proximal distance algorithms for

• metric nearness problems,
• convex regression,
• sparse convex clustering,
• image denoising, and
• improving a matrix’s condition number

as examples that illustrate the flexibility of the proximal distance principle.

Classification

SparseMVDA.jl

Implements algorithms for fitting sparse classifiers based on vertex discriminant analysis. Fitting a single classifier to predict multiple classes improves prediction, lends interpretability to selected features, and reduces computational burden.

SparseSVM.jl

Implements algorithms for fitting sparse $L_{2}$ support vector machines (SVM) using distance majorization. By constructing a quadratic surrogate for the original loss, we can quickly fit a SVM with no more than $k$ active features. Model stability can be assessed with repeated cross validation. Both binary and multiclass problems are supported.