Category: Data Science

Gabriel Vasconcelos explains the bagging technique:

The name bagging comes from boostrap aggregating. It is a machine learning technique proposed by Breiman (1996) to increase stability in potentially unstable estimators. For example, suppose you want to run a regression with a few variables in two steps. First, you run the regression with all the variables in your data and select the significant ones. Second, you run a new regression using only the selected variables and compute the predictions.

This procedure is not wrong if your problem is forecasting. However, this two step estimation may result in highly unstable models. If many variables are important but individually their importance is small, you will probably leave some of them out, and small perturbations on the data may drastically change the results.

Read on to see how bootstrap aggregation works and how it solves this solution instability problem.

Steph Locke explains what beta values on parameters in a regression actually signify:

When we read the list of coefficients, here is how we interpret them:

• The intercept is the starting point – so if you knew no other information it would be the best guess.

• Each coefficient multiplies the corresponding column to refine the prediction from the estimate. It tells us how much one unit in each column shifts the prediction.

• When you use a categorical variable, in R the intercept represents the default position for a given value in the categorical column. Every other value then gets a modifier to the base prediction.

Linear regression is easy, but the real value here is Steph’s explanation of logistic regression coefficients.

David Smith links to a video describing an application of Bayes’s Theorem and gives the example of medical tests:

If you get a blood test to diagnose a rare disease, and the test (which is very accurate) comes back positive, what’s the chance you have the disease? Well if “rare” means only 1 in a thousand people have the disease, and “very accurate” means the test returns the correct result 99% of the time, the answer is … just 9%. There’s less than a 1 in 10 chance you actually have the disease (which is why doctor will likely have you tested a second time).

Now that result might seem surprising, but it makes sense if you apply Bayes Theorem. (A simple way to think of it is that in a population of 1000 people, 10 people will have a positive test result, plus the one who actually has the disease. One in eleven of the positive results, or 9%, actually detect a true disease.)

This goes to sensitivity/recall (in the medical field, they call it sensitivity; in the documents world and in the Microsoft ML space, they call it recall):  True positives / (True positives + False negatives).  Supposing a million people, 1000 will have the disease.  Of those 1000, we expect the test to find 990 (99%).  Of the 999,000 people who don’t have the disease, we expect the test to produce 9990 false negatives (1%).  990 / (990 + 9990) = 9%.