Machine learning has become one of the first choices for most newbies and IT professionals. But to enter this field, one must have specific predetermined skills, and one of those skills is mathematics. Mathematics is essential for learning ML technology and developing practical business applications. When we talk about mathematics for machine learning, it mainly focuses on probability and statistics, the primary topics for getting started with ML. Probability and statistics are fundamental to ML and data science for developing ML algorithms and building decision-making capabilities. Probability and statistics are also primary prerequisites for studying ML.
This blog will discuss the probability that will help you simplify the ML process and implement the algorithms in machine learning.
Probability in Machine Learning
Probability is the cornerstone of ML, which tells how likely an event is to occur. The probability value is always between 0 and 1. It is a fundamental concept and a primary prerequisite for understanding ML models and their applications.
How Does This Relate to Machine Learning?
So we've learned probability theory basics, but we're still confused about how it relates to machine learning. It's not so? We use probability when we have to make predictions. Once we have a model in ML and data, we can use it to make predictions based on the trained model. Consider the case where we have a data set for different temperatures in an area for other dates. Here we can use the model to predict how many water bottles need to be stored in a given area.
Distributions
A probability distribution can be defined as a function that explains each possible value and possibility that a variable can occur in a given range for any particular experiment.
Continuous Distribution
A continuous distribution explains the probability of occurrence of all values in a given range in a particular experiment. Only the range of values has a non-zero probability. In a continuous distribution, the probability of a continuous random variable equaling some value is always 0. It is often represented by the area under the curve.
Discrete Distribution
The discrete distribution explains the probability of occurrence of each value of a discrete arbitrary variable. In a discrete probability distribution, every possible value of a discrete random variable has a non-zero probability. Henceforth, the discrete probability distribution is mainly shown in tabular form.
To better understand probability, it can be further categorized into different types as follows:
Empirical Probability:
Empirical probability can be calculated as the number of occurrences of an event divided by the total number of observed incidents.
Theoretical Probability:
Theoretical probability can be calculated as the number of ways a particular event can occur divided by the total number of possible outcomes.
Joint probability: Tells about the possibility of the simultaneous occurrence of two random events.
P(A ∩ B) = P(A). P(B)
Where;
P(A ∩ B) = Probability of events A and B both occurring.
P (A) = Probability of event A
P (B) = probability of event B
Conditional Probability:
Can be explained as the probability of an event occurring relative to one or more other events.
E.g., Let's say Event A – Today, you read this blog.
Action B – You will drink a drink today.
Conditional probability would look at these two different events, event A and event B, about each other and calculate both events A and B such that you would be drinking a drink while reading this article today.
For another example, suppose event A – It will rain today.
Event B – You have to go out today
The conditional probability would be the probability that both A and B will occur, i.e., If it rains today, you have to go outside. This could predict how likely you are to carry an umbrella today.
Why Do We Need Probability for ML and Data Science?
Machine learning is a subpart of artificial intelligence (AI). Although AI and Data Science are two different fields, many things overlap. We need to understand the mathematics behind the models we use for AI and Data Science. We learned math Statistics and probability are widely used in data science. Similarly, artificial intelligence uses linear algebra, calculus, and probability extensively to determine linear regression. Introductory algebra is the backbone for all these different areas of mathematics that are then used by artificial intelligence and data science.
Application of Probability in Machine Learning
With this background, let's explore how probability can be applied to Machine Learning.
Sampling – solving non-deterministic processes
Probability forms the basis of sampling. In machine learning, uncertainty can arise in many ways – for example – noise in the data. Likelihood provides a toolkit for modeling uncertainty. Noise could occur from observational variabilities, such as measurement errors or other sources. Noise affects both inputs and outputs.
In addition to the noise in the sample data, we should also consider the effects of bias. Even if the observations are sampled uniformly, i.e., no sampling bias is assumed – other constraints can introduce bias. For example, if we select a set of participants from a specific region of the country., by definition. The sample is biased for this area. We could expand the sample size and variance in the data by including more regions in the country. We must balance variance and bias so that the selected sample represents the task we are trying to model.
We are usually given a dataset, i.e., we have no control over the process of creating and sampling the dataset. To deal with this lack of control over sampling, we split the data into train and test sets or use resampling techniques. Thus, probability (via sampling) is included when we have incomplete coverage of the problem domain.
Pattern recognition is a key part of machine learning. We can approach machine learning as a pattern recognition problem from a Bayesian perspective. In Pattern Recognition – Christopher Bishop takes a Bayesian perspective and presents approximate inference algorithms for situations where exact answers are impossible. For the same reasons mentioned above, probability theory is vital to pattern recognition. It helps to satisfy noise/uncertainty and finite sample size and apply Bayesian principles to machine learning.
Training – use in maximum likelihood estimation
Many iterative machine learning techniques, such as maximum likelihood estimation (MLE), are based on probability theory. MLE is used for training in models such as linear regression, logistic regression, and artificial neural networks.
Development of specific algorithms
Probability forms the basis of specific algorithms such as the Naive Bayes classifier.
Optimization of hyperparameters
In machine learning models such as neural networks, hyperparameters are tuned using techniques such as grid search. Bayesian optimization can also be used to optimize hyperparameters.
Model evaluation
In binary classification tasks, we predict a single probability score. Model evaluation techniques require us to summarize model performance based on predicted probabilities. For example, aggregation measures such as log loss require an understanding of probability theory.
Conclusion
In this blog, we learned about probabilities. We knew what probabilities are and how they are used in real life and understood the different types of conditional probabilities. One of the key things to note is the difference between likelihood and probability. Many engineers confuse probability with probability, so every individual working in the field should learn these essential tools to help them create solutions as efficiently as possible.
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