Models and Algorithms are the most fundamental concepts in mathematics and the applied sciences that use them and in modern information technology. However, the places occupied by these concepts are quite different. This is particularly clear in computational mathematics: while the Model is used only as a formal description of the computational object, the Algorithm is the basis for the very organization of the computer process.

Algorithms are all around us. The animal world, humans, computers, and machines are based on their principles. Some of them are obvious, while others are hidden from view, but that doesn’t mean they don’t exist. But what is the difference between a model and an algorithm? Let’s find out.

## Key Takeaways

- A model represents the relationship between variables in a system, while an algorithm is a step-by-step procedure to solve a problem or perform a task.
- Models can be static or dynamic and provide predictions or insights, while algorithms provide instructions for achieving a specific goal.
- Algorithms can be used to create or optimize models, while models can be used as input for various algorithms.

## Model vs Algorithm

A model defines patterns. A model can be used to make predictions using previous data. Algorithms can be created using models. A model can be a computer program. An algorithm is a sequence of instructions followed to solve a particular problem. Algorithms can be based on mathematical calculations. Algorithms can be used in different fields, including IT.

Algorithm properties:

- Universality (massiveness) – algorithm applicability to different input data sets.
- Discreteness – the process of solving the problem according to the algorithm is divided into separate actions.
- Finiteness – each of the actions and the entire algorithm as a whole is necessarily completed.
- Results – on termination of the algorithm’s execution, the final result is obtained without fail.
- Executability (effectiveness) – the result of the algorithm is achieved for a finite number of steps.
- Determinism (certainty) – the algorithm should not contain any prescriptions, the meaning of which can be perceived ambiguously. I.e. the same precept after execution must give the same result.
- Consistency – the order of execution of commands must be clear to the executor and must not allow ambiguity.

A model acts as a program and can make predictions based on the functionality already built into the algorithm. Thus, models are the algorithms working on data. A model is a representation of what the algorithm has already learned.

The following properties of models are distinguished:

- Adequacy
- Detail
- Value

Adequacy is the degree to which a model corresponds to a real object or process. Adequacy is one of the most important properties that determine the value of a model.

## Comparison Table

Parameters of Comparison | Model | Algorithm |
---|---|---|

Definition | Model is an expression of an algorithm that identifies hidden patterns. | An algorithm is a set of well-defined instructions used for solving a complex problem. |

Meaning | A model is a representation of what has already been learned by an algorithm. | Algorithms are the engines of machine learning that convert a dataset into a mode. |

Concept | A model is a computer program with specific instructions and data structures. | Algorithms are based on statistics, calculus, and linear algebra. |

Where is used | can find patterns or make decisions from a previously unseen dataset | Algorithms are used in all areas of IT and many other industries |

Type | Binary classification, multiclass classification, and regression | Supervised, semi-supervised, unsupervised and reinforcement |

## What is Model?

The model stores the output of the “algorithm”. It represents what has been extracted from the algorithm “learning” from the data and contains a specific set of functions from the algorithm. A model is a representation of real or imaginary world objects and their properties.

Models are widely used in scientific research (with the purpose of acquiring new knowledge about the world around us), in engineering and in practical human activities. No model can reproduce with absolute accuracy all properties and behaviour of its prototype, and therefore numerical or other results obtained on the basis of a model correspond to reality only approximately, with a certain degree of accuracy. Sometimes accuracy of a model can be expressed in some units, and sometimes we have to be limited to “qualitative” estimates or just common sense.

## What is an Algorithm?

An algorithm is a clear sequence of actions, the execution of which gives some predetermined result. Simply put, it is a set of instructions for a particular task. The term is best known in computer science, where it refers to instructions for solving a problem in an efficient way. Algorithms now refer to any sequence of actions that can be clearly described and divided into simple steps which lead to a goal.

The word “algorithm” comes from the name of the Central Asian mathematician al-Khwarizmi.

(IX century) and was used in mathematics to denote the rules of performing four arithmetic operations: addition, subtraction, multiplication and division. Nowadays, the concept of algorithms is used not only in mathematics but also in many areas of human activity,

## Main Differences Between Model and Algorithm

### Algorithm

- Algorithms are procedures performed on data to find patterns and learn.
- Algorithms are a type of automatic programming in which machine learning models represent the program itself.
- The algorithms are based on statistics, calculus, and linear algebra.
- Algorithm-a clear and precise prescription (instruction) to the performer to perform a certain sequence of actions to achieve a specified goal or solve a given problem.
- The algorithm has a number of input quantities – arguments, which are set before the start of work. The goal of the algorithm is to get a result.

### Model

- A model is some object, a system of objects, processes or phenomena, in one sense or another similar to other objects, systems of objects, processes or phenomena.
- The linear regression model stores the vector of coefficients and constants that best fit the data.
- Models are the result of algorithms and consist of data and a prediction algorithm.
- A decision tree template stores the set of if-then statements corresponding to individual branches.
- The model can be saved for later and acts as a program, using the previously saved functions of the algorithm to make new predictions.