What is a feature?

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\def\rvw{\vec{W}} \def\rvx{\vec{X}} \def\rvy{\vec{Y}} \def\rvz{\vec{Z}} \def\seta{A} \def\setb{B} \def\setc{C} \def\setd{D} \def\sete{E} \def\setf{F} \def\setg{G} \def\seth{H} \def\seti{I} \def\setj{J} \def\setk{K} \def\setl{L} \def\setm{M} \def\setn{N} \def\seto{O} \def\setp{P} \def\setq{Q} \def\setr{R} \def\sets{S} \def\sett{T} \def\setu{U} \def\setv{V} \def\setw{W} \def\setx{X} \def\sety{Y} \def\setz{Z} \def\fa{a} \def\fb{b} \def\fc{c} \def\fd{d} \def\fe{e} \def\ff{f} \def\fg{g} \def\fh{h} \def\fi{i} \def\fj{j} \def\fk{k} \def\fl{l} \def\fm{m} \def\fn{n} \def\fo{o} \def\fp{p} \def\fq{q} \def\fr{r} \def\fs{s} \def\ft{t} \def\fu{u} \def\fv{v} \def\fw{w} \def\fx{x} \def\fy{y} \def\fz{z} \def\fA{A} \def\fB{B} \def\fC{C} \def\fD{D} \def\fE{E} \def\fF{F} \def\fG{G} \def\fH{H} \def\fI{I} \def\fJ{J} \def\fK{K} \def\fL{L} \def\fM{M} \def\fN{N} \def\fO{O} \def\fP{P} \def\fQ{Q} \def\fR{R} \def\fS{S} \def\fT{T} \def\fU{U} \def\fV{V} \def\fW{W} \def\fX{X} \def\fY{Y} \def\fZ{Z} \def\ma{A} \def\mb{B} \def\mc{C} \def\md{D} \def\me{E} \def\mf{F} \def\mg{G} \def\mh{H} \def\mi{I} \def\mj{J} \def\mk{K} \def\ml{L} \def\mm{M} \def\mn{N} \def\mo{O} \def\mp{P} \def\mq{Q} \def\mr{R} \def\ms{S} \def\mt{T} \def\matu{U} \def\mv{V} \def\mw{W} \def\mx{X} \def\my{Y} \def\mz{Z} \def\loss{\mathcal{L}} \newcommand{\dkl}[2]{D_{\text{KL}}\mathopen{}\paren{#1\,||\,#2}} \newcommand{\dataset}{S} \newcommand{\ndataset}{N} \newcommand{\idataset}{n} \newcommand{\inputRV}{\mathcal{X}} \newcommand{\inputvec}{\vec{x}} \newcommand{\ninputvec}[1]{\vec{x}_{#1}} \newcommand{\iinputvec}[1]{x_{#1}} \newcommand{\niinputvec}[2]{x_{#1, #2}} \newcommand{\icpnt}{i} \newcommand{\inputmatrix}{X} \newcommand{\inputdim}{D} \newcommand{\outputval}{y} \newcommand{\ioutputval}[1]{y_{#1}} \newcommand{\outputvec}{\vec{y}} \newcommand{\trainset}{S_{\text{train}}} \newcommand{\testset}{S_{\text{test}}} \newcommand{\truemodel}{f_{\text{true}}} \newcommand{\trainedmodel}{f_{\trainset}} \newcommand{\linmodel}[1]{f_{#1}} 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In machine-learning, a feature is an input variable to a supervised learning problem.

In typical scenarios, the dataset ( $\dataset$ ) consists of pairs $(\vec{\iinputvec{\idataset}}, \ioutputval{\idataset})$ where $\vec{\iinputvec{\idataset}}$ is a $\inputdim$ -dimensional vector of inputs and $\ioutputval{\idataset}$ is called the output value.

$\dataset = \{(\ninputvec{\idataset}, \ioutputval{\idataset}) \mid \idataset \leq \ndataset\}$

The component $\sx_{\si\sj}$ is-called the $\sj$ -th feature. The $\sj$ -th feature vector is the vector:

$\vf_{\sj} = \begin{pmatrix} \sx_{1\sj} \\ \sx_{2\sj} \\ \vdots \\ \sx_{\sn\sj} \end{pmatrix}$

Other names for the features are:

covariates,
independent variables,
explanatory variables,
exogenous variables,
predictors,
regressors