Machine Learning & Statistical Learning

Several add-on packages implement ideas and methods developed at the borderline between computer science and statistics - this field of research is usually referred to as machine learning. The packages can be roughly structured into the following topics:

*Neural Networks and Deep Learning*: Single-hidden-layer neural network are implemented in package nnet (shipped with base R). Package RSNNS offers an interface to the Stuttgart Neural Network Simulator (SNNS). Packages implementing deep learning flavours of neural networks include deepnet (feed-forward neural network, restricted Boltzmann machine, deep belief network, stacked autoencoders), RcppDL (denoising autoencoder, stacked denoising autoencoder, restricted Boltzmann machine, deep belief network) and h2o (feed-forward neural network, deep autoencoders). An interface to tensorflow is available in tensorflow.*Recursive Partitioning*: Tree-structured models for regression, classification and survival analysis, following the ideas in the CART book, are implemented in rpart (shipped with base R) and tree. Package rpart is recommended for computing CART-like trees. A rich toolbox of partitioning algorithms is available in Weka, package RWeka provides an interface to this implementation, including the J4.8-variant of C4.5 and M5. The Cubist package fits rule-based models (similar to trees) with linear regression models in the terminal leaves, instance-based corrections and boosting. The C50 package can fit C5.0 classification trees, rule-based models, and boosted versions of these.

Two recursive partitioning algorithms with unbiased variable selection and statistical stopping criterion are implemented in package party and partykit. Function`ctree()`

is based on non-parametric conditional inference procedures for testing independence between response and each input variable whereas`mob()`

can be used to partition parametric models. Package model4you can be used to build trees based on more complex models, for example models featuring a treatment effect to be partitioned. Transformation trees for estimating discrete and continuous predictive distributions based on transformation models, also allowing censoring and truncation, are available from package trtf. Extensible tools for visualizing binary trees and node distributions of the response are available in package party and partykit as well.

Tree-structured varying coefficient models are implemented in package vcrpart.

For problems with binary input variables the package LogicReg implements logic regression. Graphical tools for the visualization of trees are available in package maptree.

Trees for modelling longitudinal data by means of random effects is offered by package REEMtree. Partitioning of mixture models is performed by RPMM.

Computational infrastructure for representing trees and unified methods for prediction and visualization is implemented in partykit. This infrastructure is used by package evtree to implement evolutionary learning of globally optimal trees. Survival trees are available in various package, LTRCtrees allows for left-truncation and interval-censoring in addition to right-censoring.*Random Forests*: The reference implementation of the random forest algorithm for regression and classification is available in package randomForest. Package ipred has bagging for regression, classification and survival analysis as well as bundling, a combination of multiple models via ensemble learning. In addition, a random forest variant for response variables measured at arbitrary scales based on conditional inference trees is implemented in package party. randomForestSRC implements a unified treatment of Breiman's random forests for survival, regression and classification problems. Quantile regression forests quantregForest allow to regress quantiles of a numeric response on exploratory variables via a random forest approach. For binary data, The varSelRF and Boruta packages focus on variable selection by means for random forest algorithms. In addition, packages ranger and Rborist offer R interfaces to fast C++ implementations of random forests. Reinforcement Learning Trees, featuring splits in variables which will be important down the tree, are implemented in package RLT. wsrf implements an alternative variable weighting method for variable subspace selection in place of the traditional random variable sampling. Package RGF is an interface to a Python implementation of a procedure called regularized greedy forests. Random forests for parametric models, including forests for the estimation of predictive distributions, are available in packages trtf (predictive transformation forests, possibly under censoring and trunction), model4you (featuring a simple user interface for building forests based on arbitrary parametric models fitted in R), and grf (an implementation of generalised random forests).*Regularized and Shrinkage Methods*: Regression models with some constraint on the parameter estimates can be fitted with the lasso2 and lars packages. Lasso with simultaneous updates for groups of parameters (groupwise lasso) is available in package grplasso; the grpreg package implements a number of other group penalization models, such as group MCP and group SCAD. The L1 regularization path for generalized linear models and Cox models can be obtained from functions available in package glmpath, the entire lasso or elastic-net regularization path (also in elasticnet) for linear regression, logistic and multinomial regression models can be obtained from package glmnet. The penalized package provides an alternative implementation of lasso (L1) and ridge (L2) penalized regression models (both GLM and Cox models). Package biglasso fits Gaussian and logistic linear models under L1 penalty when the data can't be stored in RAM. Package RXshrink can be used to identify and display TRACEs for a specified shrinkage path and to determine the appropriate extent of shrinkage. Semiparametric additive hazards models under lasso penalties are offered by package ahaz. A generalisation of the Lasso shrinkage technique for linear regression is called relaxed lasso and is available in package relaxo. Fisher's LDA projection with an optional LASSO penalty to produce sparse solutions is implemented in package penalizedLDA. The shrunken centroids classifier and utilities for gene expression analyses are implemented in package pamr. An implementation of multivariate adaptive regression splines is available in package earth. Various forms of penalized discriminant analysis are implemented in packages hda and sda. Package LiblineaR offers an interface to the LIBLINEAR library. The ncvreg package fits linear and logistic regression models under the the SCAD and MCP regression penalties using a coordinate descent algorithm. The same penalties are also implemented in the picasso package. An implementation of bundle methods for regularized risk minimization is available form package bmrm. The Lasso under non-Gaussian and heteroscedastic errors is estimated by hdm, inference on low-dimensional components of Lasso regression and of estimated treatment effects in a high-dimensional setting are also contained. Package SIS implements sure independence screening in generalised linear and Cox models. Normal and binary logistic linear models under various penalties (or mixtures of those) can be estimated using package oem.*Boosting and Gradient Descent*: Various forms of gradient boosting are implemented in package gbm (tree-based functional gradient descent boosting). Package xgboost implements tree-based boosting using efficient trees as base learners for several and also user-defined objective functions. The Hinge-loss is optimized by the boosting implementation in package bst. Package GAMBoost can be used to fit generalized additive models by a boosting algorithm. An extensible boosting framework for generalized linear, additive and nonparametric models is available in package mboost. Likelihood-based boosting for Cox models is implemented in CoxBoost and for mixed models in GMMBoost. GAMLSS models can be fitted using boosting by gamboostLSS. An implementation of various learning algorithms based on Gradient Descent for dealing with regression tasks is available in package gradDescent.*Support Vector Machines and Kernel Methods*: The function`svm()`

from e1071 offers an interface to the LIBSVM library and package kernlab implements a flexible framework for kernel learning (including SVMs, RVMs and other kernel learning algorithms). An interface to the SVMlight implementation (only for one-against-all classification) is provided in package klaR. The relevant dimension in kernel feature spaces can be estimated using rdetools which also offers procedures for model selection and prediction.*Bayesian Methods*: Bayesian Additive Regression Trees (BART), where the final model is defined in terms of the sum over many weak learners (not unlike ensemble methods), are implemented in packages BayesTree, BART, and bartMachine. Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian processes including Bayesian CART and treed linear models are made available by package tgp. MXM implements variable selection based on Bayesian networks. Bayesian structure learning in undirected graphical models for multivariate continuous, discrete, and mixed data is implemented in package BDgraph; corresponding methods relying on spike-and-slab priors are available from package ssgraph. Naive Bayes classifiers are available in naivebayes.*Optimization using Genetic Algorithms*: Package rgenoud offers optimization routines based on genetic algorithms. The package Rmalschains implements memetic algorithms with local search chains, which are a special type of evolutionary algorithms, combining a steady state genetic algorithm with local search for real-valued parameter optimization.*Association Rules*: Package arules provides both data structures for efficient handling of sparse binary data as well as interfaces to implementations of Apriori and Eclat for mining frequent itemsets, maximal frequent itemsets, closed frequent itemsets and association rules. Package opusminer provides an interface to the OPUS Miner algorithm (implemented in C++) for finding the key associations in transaction data efficiently, in the form of self-sufficient itemsets, using either leverage or lift.*Fuzzy Rule-based Systems*: Package frbs implements a host of standard methods for learning fuzzy rule-based systems from data for regression and classification. Package RoughSets provides comprehensive implementations of the rough set theory (RST) and the fuzzy rough set theory (FRST) in a single package.*Model selection and validation*: Package e1071 has function`tune()`

for hyper parameter tuning and function`errorest()`

(ipred) can be used for error rate estimation. The cost parameter C for support vector machines can be chosen utilizing the functionality of package svmpath. Functions for ROC analysis and other visualisation techniques for comparing candidate classifiers are available from package ROCR. Packages hdi and stabs implement stability selection for a range of models, hdi also offers other inference procedures in high-dimensional models.*Other procedures*: Evidential classifiers quantify the uncertainty about the class of a test pattern using a Dempster-Shafer mass function in package evclass. The OneR (One Rule) package offers a classification algorithm with enhancements for sophisticated handling of missing values and numeric data together with extensive diagnostic functions.*Meta packages*: Package caret provides miscellaneous functions for building predictive models, including parameter tuning and variable importance measures. The package can be used with various parallel implementations (e.g. MPI, NWS etc). In a similar spirit, package mlr offers a high-level interface to various statistical and machine learning packages. Package SuperLearner implements a similar toolbox. The h2o package implements a general purpose machine learning platform that has scalable implementations of many popular algorithms such as random forest, GBM, GLM (with elastic net regularization), and deep learning (feedforward multilayer networks), among others.*Elements of Statistical Learning*: Data sets, functions and examples from the book The Elements of Statistical Learning: Data Mining, Inference, and Prediction by Trevor Hastie, Robert Tibshirani and Jerome Friedman have been packaged and are available as ElemStatLearn.*GUI*rattle is a graphical user interface for data mining in R.*Visualisation (initially contributed by Brandon Greenwell)*The`stats::termplot()`

function package can be used to plot the terms in a model whose predict method supports`type="terms"`

. The effects package provides graphical and tabular effect displays for models with a linear predictor (e.g., linear and generalized linear models). Friedman’s partial dependence plots (PDPs), that are low dimensional graphical renderings of the prediction function, are implemented in a few packages. gbm, randomForest and randomForestSRC provide their own functions for displaying PDPs, but are limited to the models fit with those packages (the function`partialPlot`

from randomForest is more limited since it only allows for one predictor at a time). Packages pdp, plotmo, and ICEbox are more general and allow for the creation of PDPs for a wide variety of machine learning models (e.g., random forests, support vector machines, etc.); both pdp and plotmo support multivariate displays (plotmo is limited to two predictors while pdp uses trellis graphics to display PDPs involving three predictors). By default, plotmo fixes the background variables at their medians (or first level for factors) which is faster than constructing PDPs but incorporates less information. ICEbox focuses on constructing individual conditional expectation (ICE) curves, a refinement over Friedman's PDPs. ICE curves, as well as centered ICE curves can also be constructed with the`partial()`

function from the pdp package. ggRandomForests provides ggplot2-based tools for the graphical exploration of random forest models (e.g., variable importance plots and PDPs) from the randomForest and randomForestSRC packages.

10 days ago

Torsten Hothorn

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