In an era where generative AI and large language models (LLMs) dominate headlines, it’s easy to forget that beneath the surface of every smart algorithm lies a surprisingly old-school foundation: statistics. From how LLMs predict your next word to how banks assess credit risk, statistical principles like sampling, averages, variance, and dimensionality reduction quietly power the digital tools shaping our future.
Let’s explore how fundamental statistical methods like descriptive and inferential statistics play a vital role in building LLMs, while also drawing parallels to how financial institutions use these same concepts in everyday decision-making.
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Sampling: When You Can’t Ask Everyone, Ask a Few
Statisticians and machine learning engineers face the same practical problem: you can’t measure everything. Instead of analyzing the entire population, both turn to sampling.
Take a pharmaceutical company testing a new drug. They can’t administer it to every patient in the world. Instead, they test a sample, 100 patients, for example, and record how long it takes each to recover. The results might range from 2 to 20 days. That range reveals a critical truth: the wider the spread, the harder it is to draw strong conclusions about the drug’s average effectiveness.
This same challenge applies when training language models. Engineers use massive datasets, but even those are still just samples of human language. From that sample, the model must infer how the broader “population” of language behaves.
Descriptive vs. Inferential Statistics: What You Know vs. What You Guess
Descriptive statistics help us summarize what we see in our sample. In the drug trial, we might say the average recovery time was 8 days. But that’s not the same as saying the average patient in the world would recover in 8 days.
That leap, from sample to population, requires inferential statistics. Inferential statistics involve estimating how confident we are that our findings generalize. If our sample shows wide variation (2 to 20 days), we may only be 60% confident in the 8-day average. The less variation we observe, the more confident we become.
In financial services, inferential statistics are used in similar ways. Suppose a bank wants to predict the likelihood that a borrower will default. Rather than analyze every borrower, it studies a sample. From this, it makes an inference: a 5% default probability. But confidence depends on sample size and consistency. The smaller or noisier the sample, the less trustworthy the estimate.
Outliers and Averages: When One Number Skews Everything
Let’s revisit our drug trial. If most patients recover in 6 to 10 days, but one takes 30 days, that outlier skews the average upwards. The new mean might suggest the drug is less effective than it really is.
Imagine a fintech where six employees earn an average of $45,000. A newly hired CEO earns $150,000. The mean salary rises to $60,000, painting a misleading picture. This is why companies often report the median instead. Medians are less sensitive to extreme values, offering a more accurate picture of typical outcomes.
In LLMs, outliers can be anomalous words or sentence structures that mislead the model if not handled carefully. This is why training often involves regularization and normalization techniques, methods rooted in statistical theory to prevent overfitting based on rare examples.
Distribution, Standard Deviation, and Confidence
Variation matters as much as averages. A drug with recovery times from 2 to 20 days might have the same average as one with recovery times from 7 to 9 days, but the second drug inspires more confidence. This spread is measured by standard deviation.
Banks care deeply about standard deviation too. Two portfolios may have the same expected return, but one might have much greater risk (i.e., variability of returns). Understanding this volatility helps portfolio managers make better investment decisions.
In LLMs, variance helps explain uncertainty in predictions. When a model generates multiple potential outputs, standard deviation across those results may guide whether the model is confident in its answer or just guessing.
Skewed Distributions: Not All Data Is Symmetrical
A perfectly symmetrical dataset means the mean, median, and mode are identical. But data is rarely perfect. A right-skewed distribution (e.g., salaries with one very high outlier) pulls the mean upward. A left-skewed curve (e.g., many small losses and one big gain) pulls it down.
Understanding skew is critical in both AI and finance. In credit scoring, a few extremely risky borrowers can distort average risk metrics. In LLMs, highly repetitive data might skew the model toward certain words or phrases unless balanced properly.
Dimensionality Reduction: Cutting Complexity Without Losing Meaning
LLMs work with enormous datasets. The more attributes or features (think columns in a spreadsheet), the more complex the training becomes. Each column introduces new relationships, making it harder to draw meaningful patterns.
In finance, analysts face the same problem when evaluating hundreds of customer attributes. Not every data point matters. Techniques like principal component analysis (PCA) and feature selection help reduce data to its most important dimensions.
The same is true for LLMs. Engineers remove redundant or irrelevant data to simplify learning and improve accuracy. This is especially important when processing unstructured data like text, images, or audio, all of which must be converted into structured formats like matrices before being fed to the model.
Why This Matters to Financial Services
While the inner workings of LLMs might feel abstract, the underlying math has direct parallels in financial services:
- Sampling: Used in market surveys and product testing
- Mean and Median: Used in compensation benchmarking, pricing strategies
- Standard Deviation: Used in risk management and volatility assessments
- Inferential Statistics: Used to project trends from sample data
- Dimensionality Reduction: Used in KYC and AML systems to prioritize signals
In both worlds, the goal is the same: make smart predictions based on incomplete information.
Behind the scenes of every intelligent AI system lies a backbone of statistical reasoning. As financial institutions deploy LLMs to enhance customer service, automate underwriting, or detect fraud, it’s critical that decision-makers understand the statistical mechanics involved.
Because at the end of the day, whether you’re interpreting language or balancing a portfolio, it’s not just about big data. It’s about smart data, and the statistics that make sense of it.
If you want to learn more about this, consider the ‘No Code AI and Machine Learning: Building Data Science Solutions Program’ delivered by MIT through the Great Learning platform, use this link for $100 off.
For more on this topic, check out: Understanding Basic Probability Is The First Step To Better Models or AI’s Growing Role In Financial Security And Fraud Prevention.
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