We study causal subset selection with Directed Information as the measure of prediction causality. Two typical tasks, causal sensor placement and covariate selection, are correspondingly formulated into cardinality constrained directed information maximizations. To attack the NP-hard problems, we show that the first problem is submodular while not necessarily monotonic.

Nevertheless, we show that under certain minimal and realistic distributional settings, it is possible to obtain a (1+ null)-approximation with a nearly linear running time and poly (k/null) + O ( k log n) columns. Namely, we show that if the input matrix A has the form A = B + E, where B is an arbitrary rank-k matrix, and E is a matrix with i.i.d.

Neural Information Processing Systems http://nips.cc/

The recent success of deep learning frameworks in applications such as image classification [9], speech recognition [20], and object detection [13] stems primarily from the availability of large amounts of labeled data.

Neural Information Processing Systems http://nips.cc/

Many recent approaches to learn submodular functions suffer from limited expressiveness.

Intuitively, there is a tradeoff between the amount of weakly-labeled dataandtheprecision oftheweaklabels.