Innuo

First I would like to mention that, since my last post , I came across the paper from 2005 on Robust Supervised Learning by J. Andrew Bagnell that proposed almost exactly the same regularized minimax algorithm as the one I derived. He motivates the problem slightly differently and weights each example separately and not based on types, but the details are essentially identical. Experiments on Synthetic Data I tried the algorithm on some synthetic data and a linear logistic regression model. The results are shown in the figures below. In both examples, there are examples from two classes (red and blue). Each class is a drawn from a  mixture of two normal distributions (i.e., there are two types per class). The types are shown as red squares and red circles, and blue diamonds and blue triangles. Class-conditionally the types have a skewed distribution. There are 9 times as many red squares as red circles, and 9 times as many blue diamonds as triangles. We would expect a plain logistic ...

As opposed to the traditional supervised learning setting where the labeled training data is generated (we hope) independently and identically, in active learning the learner is allowed to select points for which labels are requested. Because it is often impossible to construct the equivalent real-world object from its feature values, almost universally, active learning is pool-based . That is we start with a large pool of unlabeled data and the learner (usually sequentially) picks the objects from the pool for which the labels are requested. One unavoidable effect of active learning is that we end up with a biased training data set. If the true data distribution is $latex P(x,y)$, we have data drawn from some distribution $latex \hat{P}(x,y)$ (as always $latex x$ is the feature vector and $latex y$ is the class label). We would like to correct for this bias so it does not lead to learning an incorrect classifier. And furthermore we want to use this biased data set to accurately evalu...