Building cost functions minimizing to some summary statistics

Building cost functions minimizing to some summary statistics

A learning machine--or a model--is usually trained by minimizing a given criterion (the expectation of the cost function), measuring the discrepancy between the model output and the desired output. As is already well known, the choice of the cost function has a profound impact on the probabilistic interpretation of the output of the model, after training. In this work, we use the calculus of va...

Polynomial Time Summary Statistics for Two general Classes of Functions

In previous work we showed, by Walsh analysis, that summary statistics such as mean, variance, skew, and higher order statistics can be computed in polynomial time for embedded landscapes. We then used these statistics to study the epistatic structure of MAXSAT problems. These results were dependent on two facts: these functions have a polynomial number of nonzero Walsh coe cients and the coe c...

Influence functions of some depth functions, and application to depth-weighted L-statistics

Depth functions are increasingly being used in building nonparametric outlier detectors and in constructing useful nonparametric statistics such as depth-weighted L-statistics. Robustness of a depth function is an essential property for such applications. Here, robustness of three key depth functions, the spatial, simplicial, and generalized Tukey, is explored via the influence function (IF) ap...

Summary statistics in vision

Minimizing Total Calibration Cost

Bender et al. (SPAA 2013) have proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be often calibrated. Given that calibration costs, it is important to study policies minimizing the calibration cost while performing all the necessary tests. We focus on the single-machine setting and we extend...