Learning Active Vision

What to measure next to improve decision making? On top-down task driven feature saliency

“…We follow Kappen et al [3] and consider the sequential measurement process as a two-stage process. We represent the signal detection problem by probability distribution over a set of C signal groups or classes indexed by the discrete variable c, (c = 1, ..., C).…”

“…log p(c, z|x)p(c, z|x)dz (3) As z j is unknown at this stage in the process we are forced to average ΔS j (x, z j ) with respect to this variable given the information we have access to, i.e., with respect to the distribution of z j conditioned on the initial measurement x.…”

“…(4) The information gain can be used to rank features in importance [8], [3]. Note, the second term does not depend on j, hence, can be neglected in the saliency estimate.…”

“…On the remaining N test data points we simulate an incomplete measurement situation in which only D 0 < D features are available for the estimation (a) Error rates in the training set of complete data (N train = 200) and the test set (Ntest = 95) using complete data, the test error using the initial feature set (3,4), and the test error using (3,4) were estimated with a simple Wishart prior with a diagonal mean covariance matrix of unit variance. Prior to training all variables were normalized to zero mean and unit variance.…”

“…While not as well studied as the basic missing data problem, the sequential measurement problem has been studied in several application areas including active vision [3], [4], petrophysics and medical diagnosis [5], geophysics [6], and robot navigation [7]. These previous efforts all use an information theoretic approach but implemented in specialized domain dependent representations, hence, less general than the present approach.…”