Transfer learning

Changes at test time

Ex. Google Flu Trends

Training \(x\sim p^*\), test \(x\sim q^*\).

Instance weighting: upweight examples underrepresented at test time \[ \wh L(\te) = \rc n \sumo in \wh w(x) \ell((x,y);\te). \]

Problems: have to estimate \(\wh w\), have to assume \(q^*\) is absolutely continuous wrt \(p^*\).

Domain adaptation/multi-task learning

Even \(p^*(y|x)\) can be different.

Solve joint ERM problem assuming weight vectors are close.

Regularize by e.g. \(\sum_{i\ne j}\ve{w_i-w_j}^2\), \(\ve{W}_*\), or \(\ve{W}_{2,1}\) (sum of \(L^2\) norms of rows - for sparse set of features).

NN: share same hidden layer.

Deep NN non-robust: perturbation \[ \min_{r\in \R^d} (f(x+r) - y_{\text{wrong}})^2 + \la\ve{r}^2. \]

Robust optimization: \(K\) features zeroed out at test time.