High-Dimensional Space and the Law of Large Numbers | Data Science | BCA Notes | #ipumusings
High-Dimensional Space and the Law of Large Numbers
Data Science (BCA Notes)
In Data Science, two important ideas are High-Dimensional Space and the Law of Large Numbers. Let’s understand these concepts in simple terms:
High-Dimensional Space
Imagine you’re measuring different features of something, like the height, weight, and age of a person.
Each feature is like a dimension. For example:
- Height = 1 dimension
- Height + Weight = 2 dimensions
- Height + Weight + Age = 3 dimensions
A high-dimensional space is very different from the two and three-dimensional spaces we are familiar with. Now, imagine increasing the number of features to 10, 20, or even 100! This creates a high-dimensional space.
Why is it important?
In high-dimensional space, data points (like objects or people) can look very far apart, making it harder to analyse relationships.
Data scientists use special techniques to handle this, like reducing the dimensions to focus on what matters most.
Law of Large Numbers
This is a concept in statistics that says:
"The more data you collect, the closer your results will be to the actual truth.
Example:
If you toss a coin 10 times, you might get heads 7 times (70%).
But if you toss the coin 1,000 times, the result will be closer to 50% heads and 50% tails.
In probability theory, the law of large numbers (LLN) is a mathematical law that states that the average of the results obtained from a large number of independent random samples converges to the true value if it exists. It means if you repeat an experiment independently a large number of times and average the result, what you obtain should be close to the expected value.
Why is it important?
In Data Science, having more data often leads to more accurate predictions and better insights.
How They Work Together
High-dimensional space helps us work with complex data (like images or text with many features).
The Law of Large Numbers ensures that when we analyse a lot of data, we get results that are reliable and meaningful.
Together, these concepts form the foundation for solving big problems in Data Science!
