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Category Archives: Modeling
Continuous Bayes’ Theorem
Bayes’ Rule is one of the fundamental Theorems of statistics, but up until recently, I have to admit, I was never very impressed with it. Bayes’ gives you a way of determining the probability that a given event will occur, or … Continue reading
Posted in Modeling
2 Comments
Genetic algorithms and symbolic regression
A few months ago, I wrote a post about optimization using gradient descent, which involves searching for a model that best meets certain criteria by repeatedly making adjustments that improve things a little bit at a time. In many situations, this works … Continue reading
Posted in Modeling, Regression
1 Comment
Configuration Spaces and the Meaning of Probability
I recently finished reading Nate Silver’s book The Signal and the Noise, which has gotten me thinking about how exactly one should interpret models/probability distributions, and the predictions they make. (If you’ve read this book or plan to read it, … Continue reading
Posted in Modeling
8 Comments
Kmeans
The subject of this weeks post is probably one of the most polarizing algorithms in the data world: It seems that most experts either swear by Kmeans or absolutely hate it. The difference of opinion boils down to one of … Continue reading
Posted in Modeling, Unsupervised learning
8 Comments
Mixture models
In the last few posts, we’ve been looking at algorithms that combine a number of simple models/distributions to form a single more complex and sophisticated model. With both neural networks and decision trees/random forests, we were interested in the classification … Continue reading
Posted in Modeling
7 Comments
Principal Component Analysis
Now that we’ve gotten a taste of the curse of dimensionality, lets look at another potential problem with the basic form of regression we discussed a few posts back. Notice that linear/least squares regression always gives you an answer, whether or … Continue reading
Posted in Modeling
22 Comments
The curse of dimensionality
Now that we’ve had a glimpse of what it means to analyze data sets in different dimensions, we should take a little detour to consider really high dimensional data. In the discussion of regression, I suggested using your intuition about … Continue reading
Posted in Modeling
10 Comments
General regression and over fitting
In the last post, I discussed the statistical tool called linear regression for different dimensions/numbers of variables and described how it boils down to looking for a distribution concentrated near a hyperplane of dimension one less than the total number … Continue reading
Posted in Modeling, Regression
14 Comments
The geometry of linear regression
In this post, we’ll warm up our geometry muscles by looking at one of the most basic data analysis techniques: linear regression. You’ve probably encountered it elsewhere, but I want to think about it from the point of view of … Continue reading
Posted in Modeling, Regression
28 Comments