By Christer Holloman, Contributor

Statistics and probability are foundational pillars that support much of modern technology, particularly in the realms of artificial intelligence and finance. One of the most significant concepts that has emerged from statistical theory is Bayes Theorem, which plays a crucial role in making sense of uncertainty and calculating combined outcomes. Just as conditional probability equips us with the tools to make informed decisions as new information becomes available, it also forms the backbone of the sophisticated algorithms that drive large language models (LLMs) like ChatGPT.

Before delving into the complexities of these models, it's essential to recognize that their development is rooted in basic statistical principles. While the media often attributes advancements in AI to artificial intelligence and deep learning, the unsung hero behind these breakthroughs is actually foundational statistics. In this article, I aim to demystify the relationship between conditional probability and LLMs, while also illustrating its applicability in other fields such as financial fraud detection and customer behavior analysis.

At the heart of a large language model is its mechanism to predict the next most probable word in a sentence. This process mirrors the work of a financial analyst who assesses the likelihood of a customer defaulting on a loan. For LLMs, the task is to determine the probability of the next word in a sentence based on the preceding context. This is where conditional probability comes into play, represented by the notation P(A|B), which translates to the probability of A given B. In financial contexts, this could mean assessing the probability that a transaction is fraudulent based on specific unusual characteristics, like occurring at 3 AM or originating from a location that the user has never visited. In natural language processing, a similar question might arise: Whats the probability that the next word is bank, given that the current phrase is She walked into the?

To answer these questions effectively, both finance and language processing rely heavily on joint probabilities and Bayes Theorem, which serve to update our understanding as new data becomes available. For instance, consider a hypothetical classroom scenario where 60% of students passed the first test. Among those who passed, 80% performed well on the second test. However, for those who failed the first test, only 30% were able to pass the second. This information allows us to calculate both joint probabilitieslike the likelihood of a student passing both tests (0.6 0.8 = 0.48)and conditional probabilities, such as the chance of passing Test 1, given that a student has already passed Test 2.

Now, lets draw a parallel between these tests and the tokens that form the foundation of language models. Large language models operate on complex probabilistic trees akin to the classroom example, continuously calculating and adjusting the likelihood of various word combinations based on extensive training data.

Bayes Theorem becomes particularly valuable when we know the outcome but need to deduce the underlying cause. This reverse inference is instrumental in both natural language processing (NLP) and finance. Take, for example, streaming giant Netflix. If 65% of users who watched Star Wars also viewed Return of the Jedi, and only 45% of non-Star Wars viewers watched the same sequel, Bayes Theorem can help us calculate the probability that a user who has watched Return of the Jedi has also seen Star Wars.

This reverse reasoning mirrors the logic financial institutions use when flagging potentially suspicious transactions. If, for instance, the bank identifies that only 1% of transactions are fraudulent, Bayes Theorem can assist in determining the updated likelihood of fraud when certain risk conditions are met, such as high transaction value or an unusual geographical location. The formula to calculate this conditional probability takes the following shape: P(Fraud|RiskConditions) = (P(RiskConditions|Fraud) * P(Fraud)) / P(RiskConditions). Even when the base fraud rate is low, a significant rise in the conditional likelihoodtriggered by new informationcan lead to alerts for potentially fraudulent transactions.

Financial services don't merely observe the developments in machine learning; they actively engage with these technologies to enhance credit scoring, detect fraud, segment customers, and personalize products. Traditional credit assessment methods often rely on static credit bureau information and rigid guidelines, which can be inadequate for gig workers, immigrants, or small businesses that lack comprehensive credit histories. By incorporating conditional probabilities to evaluate repayment likelihood based on unconventional income sources, models can become more inclusive and predictive.

Moreover, the ability to utilize conditional probability enables companies to adjust risk assessments in real time. An unusual transaction alone might not trigger an alert; however, if it occurs at an odd hour in a foreign country, particularly if the cardholder has never traveled there before, the combined joint probability could surpass a critical threshold, prompting further investigation.

Similarly, telecommunications and banking industries utilize these predictive models to identify customer churn. If 4% of users typically discontinue services each month, this rate can soar to 20% among users who contact customer service multiple times in a short period and reduce their spending. Conditional models provide essential insights to flag these high-risk customers, allowing firms to implement retention strategies proactively.

So, how do large language models scale these foundational principles to accommodate billions of parameters? Training an LLM requires feeding it extensive datasetseffectively entire libraries of textand calculating the probabilities of individual words based on their preceding context. Through this process, these models construct probabilistic mappings between tokens (which can be words or characters) and refine their predictions using techniques like gradient descent and backpropagation. Yet, irrespective of the complexity, the core mechanism remains consistent: Given X, whats the probability of Y?

Just as financial institutions draw on structured data (like transaction logs) and unstructured data (such as customer service transcripts or emails) to make predictions, LLMs integrate grammar, syntax, and semantics to forecast human-like text. Whether the goal is to train an LLM for drafting SEC filings or to develop a fraud detection model for a digital bank, the underlying mathematics is the same. Bayes Theorem assists us in reverse-engineering causality from effects, while joint probability enables the calculation of combined outcomes. Furthermore, conditional probability empowers businesses to make informed decisions as new information emerges.

In an era increasingly defined by data and algorithm-driven insights, understanding these fundamental principles is crucial not just for data scientists but for any executive steering digital transformation. In essence, whether predicting credit defaults or chatbot responses, the future remains firmly rooted in the mathematical concepts learned in high school. If youre interested in further exploring these ideas, consider the No Code AI and Machine Learning: Building Data Science Solutions Program offered by MIT via the Great Learning platform, where you can access a $100 discount. For additional insights on this topic, check out articles like How AI, Data Science, And Machine Learning Are Shaping The Future or AIs Growing Role In Financial Security And Fraud Prevention on Forbes.