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 ...

This post is about using minimax estimation for robust learning when the test data distribution is expected to be different from the training data distribution, i.e learning that is robust to data drift. Cost Sensitive Loss Functions Given a training data set $latex D = \{x_i, y_i\}_{i=1,\ldots,N}$, most learning algorithms learn a classifier $latex \phi$ that is parametrized by a vector $latex w$ by minimizing a loss function where $latex l(x_i, y_i, w)$ is the loss on example $latex i$ and $latex f(w)$ is some function that penalizes complexity. For example for logistic regression the loss function looks like for some $latex \lambda > 0$. If, in addition, the examples came with costs $latex c_i$ (that somehow specify the importance of minimizing the loss on that particular example), we can perform cost sensitive learning by over/under-sampling the training data or minimize a cost-weighted loss function (see this paper by Zadrozny et. al. ) We further constrain $latex \sum_i^N c_i...