Encyclopedia_Discrete vs Continuous

Discrete vs. Continuous

A discrete variable is one with a well defined finite set of possible values, called states. Examples are: the number of dimes in a purse, a statement which is either “true” or “false”, which party will win the election, the country of origin, voltage output of a digital device, and the place a roulette wheel stops.

A continuous variable is one which can take on a value between any other two values, such as: indoor temperature, time spent waiting, water consumed, color wavelength, and direction of travel. A discrete variable corresponds to a digital quantity, while a continuous variable corresponds to an analog quantity.

With Netica you can choose whether you want a node to represent a discrete or continuous variable.

Often a variable will be continuous at one scale, but discrete on another. For instance the amount of water consumed might be discrete if you count individual water molecules, but it is continuous at the scale you are concerned with. Likewise, the voltage output of a digital device might be discrete at the scale you are concerned with (“high” & “low”), but continuous on a finer scale (0.7 - 3.5V), and then discrete on a very fine scale (corresponding to the number of electrons on a capacitor). You only need consider the scale of interest when setting whether a node is continuous or discrete.

Sometimes you want a continuous variable to behave like a discrete one. To do this, you break up the total range of the continuous variable into a number of intervals by supplying numbers showing where one interval ends and the next begins. This is known as discretizing the variable, and the numbers are called thresholds. Each interval corresponds to one state of the discrete version of the variable. A discretized variable is sometimes known as an interval variable, since its domain is composed of intervals. In Netica, a single node represents both the continuous and discrete versions of the variable, and Netica will convert a value of the continuous variable into a discrete state when appropriate. Netica allows you to discretize any continuous node, by choosing Modify → Discretize Nodes. (If the variable is discrete then the menu won't have a "Discretization" choice).

Conversely, a discrete node may have numeric quantities attached to each state, so that each state can represent a number, but the variable is incapable of representing numbers between those of each state (more info).