# Symbolic vs Numeric Representations

So far we've looked symbolic (discrete) representations of data and hypotheses, but often there are tasks that are naturally represented as a *prediction of numeric values*.

In a symbolic representation, machine learning takes the form of a *hypothesis space search* - represented using formal hypothesis language (Trees, Rules, Logic, etc).

However for numeric representations, machine learning takes the form of a *function space "search"* - represented using mathematical models (Linear Equations, Neural Networks, etc).

# Methods for Numeric Representation

Some methods we use for this are:

- Linear Regression (from statistics) - the process of computing an expression that predicts a numeric quantity (from data we have).
- Perceptron (from machine learning) - a biologically-inspired linear prediction method (artificial neural network).
- Multi-Layer Neural Networks - learning non-linear predictors, based on hidden nodes between the input and output
- Regression Trees - each leaf predicts a numeric quantity (the average value of training instances that reach the leaf), and each internal node can test discrete or continuous attributes.
- Model Trees - regression tree with linear regression models at the leaf nodes. These can fit with non-axis-orthogonal slopes, and have a smoothing operation at the internal

nodes to approximate continuous fractions.

# Regression

Regression is the process of determining the weights for the regression equation, which is the linear sum of attribute values (with appropriate weights) to determine a numeric quantity.