General number crunching/data analysis packages. (Specialist software is dealt with elsewhere. See machine vision, machine listening, gesture recognition, scientific workflow etc.)
R is a galaxy of statistical packages.
Sundry deep learning packages are on their own page.
Scala’s ecosystem is growing here
so is julia’s.
SHARK is a fast, modular, feature-rich open-source C++ machine learning library. It provides methods for linear and nonlinear optimization, kernel-based learning algorithms, neural networks, and various other machine learning techniques (see the feature list below). It serves as a powerful toolbox for real world applications as well as research. Shark depends on Boost and CMake.
ELL is Microsoft’s open source thing targetting tiny processors and embedded devices
Vowpal Rabbit despite its abstruse project description, seems to be a good library for out-of-core linear learning (i.e. regression or classification from non-stupendously large machine using a stupendously large data set). Approaches include various online (that is, out-of-core) optimisations. L1/L2 regularisation. Linear or logistic models. (i.e. linear models). Squared, hinge, logistic, or quantiles losses. (Has a python binding btw, doesn’t everything?)
bash data science command line.