# Glossary¶

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.

Hessian Matrix

A square matrix of 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:

$\begin{bmatrix} \frac{\partial^2 f}{\partial x^2} & \frac{\partial^2 f}{\partial xy}\\ \frac{\partial^2 f}{\partial yx} & \frac{\partial^2}{\partial y^2} \end{bmatrix}$
Observed Variable

A factor that is a part of a statistical relationship like a correlation or causation, and is recorded in the data at hand.

RANSAC

Random Sample Consensus. Iterative method of fitting a model.

1. Draw $$s$$ samples from the data.

2. Fit the model to these samples.

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

4. Do this for $$N$$ iterations.

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

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.: $$\sqrt{x \cdot x} = 1$$.

Unobserved Variable

A factor that is a part of a statistical relationship like a correlation or causation, but is not recorded in the data at hand.