Notation

Summary

Notation keeps formulas readable across mathematical foundations, probability, machine learning, forecasting, and evaluation. Pages may introduce local symbols, but these conventions are the default. Use acronyms for short names and glossary for prose definitions.

Common symbols

Symbol	Typical meaning
$x$	Feature vector, observation, or input.
$X$	Data matrix or random variable, depending on context.
$y$	Target label or observed outcome.
$haty$	Prediction.
$theta$	Model parameters.
$w,b$	Linear-model weights and bias.
$$\begin{gathered} p(y \\ midx) \end{gathered}$$	Conditional probability of outcome $y$ given input $x$.
$mathcalD$	Dataset or data-generating distribution.
$Omega$	Observed entries in a sparse matrix.
$lambda$	Regularization strength or generic rate parameter.
$nabla$	Gradient operator.
$mathbbE$	Expectation.
$eta$	Learning rate or step size.
$sigma$	Sigmoid function, or a standard deviation by context.
$gamma$	Discount factor in reinforcement learning.
$pi$	Policy in reinforcement learning.

Matrix notation

Vectors are usually lowercase bold or plain lowercase depending on page style. Matrices are uppercase. In recommender systems, $R$ often denotes a user-item matrix, $p_u$ a user factor, and $q_i$ an item factor.

Evaluation notation

Use $k$ for a cutoff in ranked retrieval, $n$ for sample size, and $t$ for time index. When a metric has a specialized definition, link to the metric page or references instead of redefining it inline.

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