Independent and Identically Distributed Data (IDD)

IID is the most common type of random data you’ll come across in everyday settings. Flipping a (fair) coin is the most powerful and straightforward example of this. All of the flips are “independent” because the coin doesn’t remember what it displayed yesterday.

The variables are identically distributed because you have a 50% – 50% probability of getting heads or tails every time you flip it – resulting in an identical and even distribution.

  • Independent and Identically Distributed Data – A property of a sequence of random variables in which each element has the same probability distribution as the other values and is mutually independent.

Simply put, a distribution that is both independent and identical means that the values at any point in the random process are random variables. If these variables have the same distribution and are independent of one another, then they are independently and identically distributed.

If the random variables X1 and X2 are independent, it means that the value of X1 has no effect on the value of X2, that the value of X2 has no effect on the value of X1, and that the random variables X1 and X2 follow the same distribution.

As a result, X1 and X2 are both in the same boat. The same distribution function The same distribution, the same probability for idd random variables, the same expectation, and variance are all shared by the same distribution shape and distribution parameters.

IDD and Machine Learning

ML is the process of learning and training from current data in order to forecast and simulate data in the future. Therefore, all of them are based on past data, with models being employed to suit future data. As a result, we must rely on historical data that is broadly representative.

To make decisions based on unknown facts, we must summarize the rules from current data (experience). If the training data obtained is not typical of the entire scenario, or if it is a specific case, the rules will be summarized incorrectly. These laws do not have a promotion effect because they are based on individual instances.

Individual cases in the training sample can be considerably reduced by assuming independent and identical distribution.

How can you know if your data is spread uniformly and independently? Here are some helpful hints!

Consider how you gathered your data for independence. Did you take a convenience sample or did you employ random sampling? Do you feel that consecutive observations are related or impact each other if you employ easily available subjects?


Recognizing your data collection method, as well as the subject area, might assist you in determining whether or not your conclusions are objective. Random sampling is a fantastic approach to ensure that your observations are independent!

Determine whether there are any trends in the data for the identically distributed section. Graphs can assist you in this area. Look for trends in your data by graphing it in the order you measured each item.

  • IDD assumption in machine learning is central to one of the most widely used data science theorems, the central limit theorem (CLT), which is at the heart of hypothesis testing. According to CLT, if we take large enough random samples from a population, the sample means will be approximately normally distributed. As you can see, the random samples taken cannot be dependent, and the random variable distribution cannot change over time.
  • The IID assumption is also at the heart of the law of big numbers, which holds that an observed sample average from a large sample population will be close to the true population average, and will get closer as the sample size grows.

In some ways, the assumption of independent and identically distributed machine learning data aids in the training of algorithms by assuming that the data distribution will not change across time or space and that samples will not be reliant on one another.

However, machine learning does not necessarily need an even distribution of data and IDD process. Samples (data) from the same distribution are required in many problems since it is believed that the model developed using the training data set may be reasonably employed in the test set.

This method can be made more logical by assuming the same distribution. Many machine learning issues do not require the same distribution of samples because the present machine learning direction’s content has become quite broad. Some online algorithms developed in the machine learning field, for example, do not require data distribution.