6. Basic Statistical Concepts for Machine Learning
When we talk about Machine Learning (ML) and Deep Learning (DL), we enter a territory where statistics plays a crucial role. Understanding basic statistical concepts is essential for developing models that are not only efficient but also reliable. In this chapter, we will cover some of the fundamental statistical concepts that every ML and DL practitioner should know.
Random Variables and Probability Distributions
A random variable is a variable whose possible values are the result of a random phenomenon. There are two types of random variables: discrete, which take on a countable number of values, and continuous, which take on any value in an interval or collection of intervals. Understanding random variables is important for modeling uncertainty and making predictions in ML.
Associated with each random variable, there is a probability distribution that describes how the probabilities are distributed among the possible values of the variable. Some of the most common distributions include the normal (or Gaussian) distribution, binomial distribution, and Poisson distribution, among others. Choosing the correct distribution is essential for properly modeling the data and making correct statistical inferences.
Measures of Central Tendency and Dispersion
Measures of central tendency include the mean, median and mode. They are used to identify the center of the data. The average is the sum of all values divided by the number of values. The median is the middle value when the data is ordered, and the mode is the most frequent value. These measurements help you understand where your data is, but they don't tell the whole story.
Measures of dispersion, such as standard deviation, variance, range and interquartile range, provide information about the variation or dispersion of data around the central tendency. Standard deviation and variance are particularly important as they quantify the degree of data dispersion and are fundamental in training and evaluating ML models.
Central Limit Theorem and Law of Large Numbers
The Central Limit Theorem (TLC) is one of the pillars of statistics. It states that for a large enough sample, the distribution of sample means will approximate a normal distribution, regardless of the distribution of the original data. This is extremely useful in ML as many statistical methods assume that data follows a normal distribution.
The Law of Large Numbers (LGN) says that as the sample size increases, the sample mean approaches the population mean. This means we can get more accurate estimates as we collect more data. In ML, this is relevant for model training, as the more data we have, the more robust the model will be.
Statistical Inference
Statistical inference is the process of drawing conclusions about a population based on a sample of data. This includes estimating parameters, performing hypothesis testing, and constructing confidence intervals. In ML, statistical inference is used to validate models and make predictions.
Hypothesis testing is used to determine whether a result is statistically significant or occurred by chance. This is crucial to avoid overinterpreting patterns in the data that may not be meaningful.
Confidence intervals provide a range within which we expect the true value of the population parameter to lie, with a certain level of confidence. This is important to understand the accuracy of our estimates.
Correlation and Causality
Correlation measures the strength and direction of the linear relationship between two variables. The correlation coefficient ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation. In ML, correlation analysis is used for feature selection and to understand relationships between variables.
However, it is crucial to understand that correlation does not imply causation. causality indicates that one variable directly influences another, which is a stronger concept than simple correlation. In ML, it is important not to confuse the two, as this can lead to erroneous conclusions about the influence of features on predicted results.
Regression and Analysis of Variance (ANOVA)
Regression is a statistical technique used to model and analyze relationships between variables. In ML, regression is often used to predictcontinuous values. Regression analysis helps you understand how the value of the dependent variable changes when any of the independent variables are varied.
The Analysis of Variance (ANOVA) is a technique used to compare the means of three or more groups to see if at least one of them is statistically different from the others. ANOVA is particularly useful in ML situations where we need to test the effectiveness of different algorithms or parameters.
In summary, basic statistical concepts are the backbone of Machine Learning and Deep Learning. They provide the tools necessary to collect, analyze and interpret data, allowing models to learn from the data and make accurate predictions. Therefore, a solid understanding of these concepts is indispensable for anyone who wants to work with ML and DL using Python.
