# Glossary¶

- Common Time
\(4/4\) time-signature, also denoted \(\mathcal{C}\).

- Cost Function
- Loss Function
A mapping between an outcome and a real number that signifies the

*loss*or*cost*of that outcome. The*outcome*variable may be an event like dropping hot cup of tea, in which case the cost is some numerical value representing how terrible that is. More commonly the*outcome*variable is a vector representing, for example, the probability mass a function (like a neural network) assigned to an input.- Enharmonic Equivalence
Two notes, intervals, scales or chords are enharmonic equivalents if they have different names but contain the exact same notes. Imagine a building. The ceiling of the first floor and the floor of the second floor are the same thing, but the naming is different depending on your point of view.

- Hessian Matrix
A square matrix of the second-order partial derivatives of a function. On the diagional are the partial derivatives in a single direction, and the other spots are taken up by all the mixed-partial derivatives. Example in 2D:

\[\mathbf{H}f(x,y) = \begin{bmatrix} \frac{\partial^2 f}{\partial x^2} & \frac{\partial^2 f}{\partial xy}\\ \frac{\partial^2 f}{\partial yx} & \frac{\partial^2 f}{\partial y^2} \end{bmatrix}\]- Iverson Bracket
Notation that converts logical propositions inside the brackets to a \(1\) if true and \(0\) if false. One application is to mathematically include or exclude elements of vectors or sets in a summation or product:

\[\v x = \begin{bmatrix}1&3&7&9\end{bmatrix}\\ \sum_{i=1}^n \left[x_i > 5 \right] = 2\]- Jacobian Matrix
Matrix of first-order partial derivatives of a vector-valued function. If \(f\) is a function that maps some vector \(\mathbf{x}\) in \(\mathbb{R}^n\) to \(\mathbf{f(x)}\) in \(\mathbb{R}^m\), its Jacobian is:

\[\mathbf{J} f = \begin{bmatrix} \frac{\partial \mathbf{f}}{\partial x_1} & \dots & \frac{\partial \mathbf{f}}{\partial x_n} \end{bmatrix} = \begin{bmatrix} \frac{\partial f_1}{\partial x_1} & \dots & \frac{\partial f_1}{\partial x_n}\\ \dots & \ddots & \vdots\\ \frac{\partial f_m}{\partial x_1} & \dots & \frac{\partial f_m}{\partial x_n}\\ \end{bmatrix}\]- Observed Variable
- Unobserved Variable
A factor that is a part of a statistical relationship like a correlation or causation, and is (not) recorded in the data at hand.

- Operator Overloading
Having an operator do different things depending on the type of the arguments. For example, we are familiar with

`+`

adding numbers, but the operator is often extended to support adding images, dates and other datatypes.- RANSAC
Random Sample Consensus. Iterative method of fitting a model.

Draw \(s\) samples from the data.

Fit the model to these samples.

Check how many points from the full dataset fall within an acceptable range \(d\) around the model - these are inliers.

Do this for \(N\) iterations.

Choose the model with the most inliers and refit it to all inliers.

- Signed Distance
The distance of a point to some surface, with the sign signifying on which side of the surface the point is located.

- TOML
Tom’s Obvious, Minimal Language. A readable configuration file format. Example:

title = "TOML Example" [author] name = "Stefan Wijnja" website = "https://stfwn.com" [database] server = "192.168.8.1" ports = [ 8001, 8001, 8002 ]

- Trace
The sum of the components on the main diagonal of a square matrix. The trace has the property that for three matrices \(A, B, C\): \(\mathrm{Tr}(ABC) = \mathrm{Tr}(BCA)\)

- Unit Vector
A vector with norm of \(1\), i.e.: \(\sqrt{x \cdot x} = 1\).