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Law of Averages

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In this article at OpenGenus, we will explore the Law of Averages in Machine Learning.

Table of content

  1. Law of Averages
  2. The Law of Large Numbers
  3. The Central Limit Theorem
  4. Gambler's Fallacy
  5. Examples in Everyday Life

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Law of Averages

The Law of Averages is a statistical concept that suggests that if a large enough sample is taken from a population, the mean of the sample will be close to the mean of the population. In the context of machine learning, this means that as the size of the training data increases, the performance of the model will converge towards its true performance on the underlying population.

The Law of Averages is important in machine learning because it implies that with enough data, we can train a model that is capable of generalizing well to new, unseen data. This is because the more data we have, the more representative it is of the underlying population, and the more accurate the model's estimates will be.

However, it's important to note that the Law of Averages only holds when the data is randomly sampled from the population and is independent and identically distributed (i.i.d). If the data is biased or non-i.i.d, the Law of Averages may not apply, and the model's performance may not improve with additional data.

Therefore, when working with machine learning models, it's important to carefully consider the quality and diversity of the data and ensure that it is representative of the underlying population. It's also important to use appropriate evaluation metrics and validation techniques to measure the performance of the model and ensure that it generalizes well to new data.

The Law of Averages is also known by several other names in statistics and machine learning, including the Law of Large Numbers and the Central Limit Theorem. These concepts are related to the Law of Averages and are often used in combination to make predictions and inferences about data.

The Law of Large Numbers

The Law of Large Numbers states that as the sample size increases, the sample mean will converge towards the true population mean. Specifically, it states that for any given level of precision, there exists a sample size large enough such that the difference between the sample mean and the population mean will be less than the specified level of precision with a high probability.

The Central Limit Theorem

The Central Limit Theorem, for example, states that if a large number of independent and identically distributed random variables are added together, their sum will be approximately normally distributed. This means that as the sample size increases, the distribution of the sample means will approach a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Gambler's Fallacy

The Gambler's Fallacy, also known as the Monte Carlo Fallacy, is a cognitive bias in which an individual believes that if a certain event has occurred repeatedly in the past, it is less likely to occur again in the future. In other words, the individual believes that past outcomes can influence the probability of future outcomes, even when the events are independent.

The Gambler's Fallacy is particularly prevalent in games of chance, such as roulette or coin tosses. For example, a person who has seen the roulette ball land on black for several consecutive spins may believe that it is due to land on red soon, as they believe the odds of it landing on black so many times in a row are low. In reality, the odds of the ball landing on black or red on any given spin are always the same, regardless of past outcomes.

In machine learning, the Gambler's Fallacy can manifest in several ways. For example, a model may overfit the training data by assuming that patterns in the data will continue to hold true in the future, even when there is no reason to believe that they will. Alternatively, a model may underfit the data by assuming that past outcomes have no influence on future outcomes, even when they do.

To avoid the Gambler's Fallacy in machine learning, it's important to ensure that the model is trained on a representative sample of data and that the data is independent and identically distributed. It's also important to use appropriate validation techniques to evaluate the model's performance and ensure that it generalizes well to new data. Additionally, it's important to avoid making assumptions about the data based solely on past outcomes and to carefully consider the underlying probability distributions and dependencies in the data.

Examples in Everyday Life

Numerous examples of the Law of Averages can be observed and applied in real life. Here are some instances:

  1. Weather Forecasting : Meteorologists use historical data to make weather predictions, assuming that the patterns observed in the past will continue into the future. The Law of Averages suggests that over time, the predictions will tend to be accurate, as long as the weather patterns remain consistent.
  2. Coin Tossing : If you flip a fair coin repeatedly, the Law of Averages states that the number of heads and tails will tend towards being equal. For example, if you flip a coin 10 times, you might not get exactly 5 heads and 5 tails, but as you keep flipping the coin more and more times, the number of heads and tails will get closer and closer to being equal.
  3. Stock Market : Investors often use historical data to predict future stock prices, assuming that trends observed in the past will continue into the future. The Law of Averages suggests that over time, the stock market will tend to produce an average rate of return, but individual stocks may have more extreme fluctuations in the short term.
  4. Population Growth : Demographers use the Law of Averages to make predictions about population growth over time. Assuming a consistent birth rate and mortality rate, the Law of Averages suggests that the population will tend to grow at a relatively constant rate, although there may be fluctuations due to external factors like migration or disease outbreaks.
  5. Sports : In sports like basketball, players often have shooting streaks where they make several shots in a row. While it might seem like the player is "on fire" and more likely to make the next shot, the Law of Averages suggests that the player's shooting percentage will eventually return to their average over time.

With this article at OpenGenus, you must have the complete idea of Law of Averages.

Law of Averages
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