Dimensionality reduction: Simplifying experiment data

If you've ever tried to analyze experiment data with hundreds of variables, you know the feeling. Your spreadsheet looks like a wall of numbers, your models take forever to run, and you can't even visualize what's happening. It's like trying to understand a city by looking at every single street address instead of just checking out a map.

That's where dimensionality reduction comes in. Think of it as a way to zoom out and see the forest instead of getting lost in the trees. By focusing on what really matters in your data, you can actually start making sense of your experiments.

Introduction to dimensionality reduction in experiment data

Let's be honest - dimensionality reduction sounds way more complicated than it actually is. At its core, you're just simplifying your data while keeping the important stuff. Instead of tracking 500 features about each user, maybe you really only need to understand 10 key behaviors that capture 90% of what's going on.

The real magic happens when you apply this to experimental data. Suddenly, you can:

• Actually visualize your results (try plotting 50 dimensions on a graph)

• Train models that don't take three days to run

• Avoid overfitting because you're not drowning in noise

There are basically two ways to go about this. You can either pick the features that matter most (feature selection) or create new super-features that combine the old ones (feature extraction). Both have their place, and honestly, the Reddit debates about which is better can get pretty heated.

The catch? Sometimes you lose important information in the process. And if your data has outliers, some techniques will freak out and give you wonky results. But hey, no tool is perfect.

Key techniques for dimensionality reduction

Principal component analysis (PCA)

PCA is like the Swiss Army knife of dimensionality reduction. It finds the directions where your data varies the most and keeps those. The machine learning community loves it because it's fast, reliable, and works great when your data relationships are roughly linear.

Here's the thing about PCA - it's not trying to be clever. It just looks for where the action is in your data and preserves that. If most of your user behavior variation comes from two main patterns (say, "power users" vs "casual browsers"), PCA will find those patterns and let you work with them directly.

Non-linear methods: t-SNE and UMAP

Sometimes your data doesn't play nice with straight lines. That's where t-SNE and UMAP come to the rescue. These techniques are phenomenal at preserving the "neighborhoods" in your data - keeping similar things close together even after reducing dimensions.

The ML community can't stop talking about these, especially for visualization. Got customer segments that cluster in weird, non-linear ways? UMAP will help you see them. Trying to understand how different experiment variants relate to each other? t-SNE can create beautiful 2D maps that actually make sense.

The downside? They're slower than PCA and can be a bit finicky to tune. But when you need to capture complex patterns in your experiment data, they're often worth the extra effort.

Benefits and limitations in experimental data analysis

Let me tell you what dimensionality reduction can actually do for your experiments. First off, visualization becomes possible. David Robinson's analysis of handwritten digits shows this beautifully - you can actually see patterns that were invisible in the raw data.

It also helps you avoid the classic trap of overfitting. When you've got more features than data points (which happens all the time in experiments), your model starts memorizing noise instead of learning patterns. Dimensionality reduction forces you to focus on the signal.

But here's what the skeptics on Reddit will tell you - and they're not wrong:

• You will lose some information. Period.

• Outliers can completely mess up your results

• Sometimes the original features are exactly what you need

The key is knowing when to use it. Small dataset with clear, interpretable features? Maybe skip the fancy reduction. Massive experimental data with hundreds of metrics? Now we're talking.

Best practices for applying dimensionality reduction to experiments

Before you jump into any dimensionality reduction, get your data house in order. Clean it, scale it, and actually look at it. David Robinson's approach to tidying genomics data shows how much this matters - you can't reduce dimensions effectively if you don't understand what you're starting with.

Choosing the right technique isn't rocket science, but it does require some thought:

• Got mostly linear relationships? Start with PCA

• Dealing with complex, clustered data? Try UMAP or t-SNE

• Need to maintain interpretability? Stick with simpler methods

Here's something people don't talk about enough - you need to balance simplicity with information preservation. Sure, reducing 1000 dimensions to 2 looks great on a plot, but did you just throw away the insights that would've helped you understand why your experiment failed?

When you're working with experiments specifically, context matters. As Tom Cunningham points out, the dimensions you keep should align with what you're trying to learn. Are you looking for user segments? Treatment effects? Long-term behavior changes? Each goal might need a different approach.

The teams at Statsig have found that iterative experimentation works best. Try a technique, validate that you haven't lost critical information, then proceed. It's not glamorous, but it works.

Closing thoughts

Dimensionality reduction isn't magic - it's just a practical tool for making sense of complex experimental data. Start simple with PCA, explore non-linear methods when needed, and always validate that you're not throwing away the insights you actually care about.

The best approach? Experiment with your experiments. Try different techniques, see what patterns emerge, and trust your domain knowledge to guide you. Your data will tell you what it needs if you listen.

Want to dig deeper? Check out:

• Feature engineering techniques for improving your input data

• The classic Elements of Statistical Learning for the mathematical foundations

• Your favorite ML community forums where practitioners share what actually works

Hope you find this useful! Now go forth and reduce those dimensions - your future self will thank you when you're not staring at a 500-column spreadsheet at 2 AM.