This paper presents an analysis of importance weighting for learning from finite samples and gives a series of theoretical and algorithmic results. We point out simple cases where importance weighting can fail, which suggests the need for an analysis of the properties of this technique. We then give both upper and lower bounds for generalization with bounded importance weights and, more signifi...

Importance weighting is a convenient general way to adjust for draws from the wrong distribution, but the resulting ratio estimate can be noisy when the importance weights have a heavy right tail, as routinely occurs when there are aspects of the target distribution not well captured by the approximating distribution. More stable estimates can be obtained by truncating the importance ratios. He...

Importance sampling is widely used in machine learning and statistics, but its power is limited by the restriction of using simple proposals for which the importance weights can be tractably calculated. We address this problem by studying black-box importance sampling methods that calculate importance weights for samples generated from any unknown proposal or black-box mechanism. Our method all...

Abstract Vendor Selection Problem (VSP) has been considered in this paper as an integrated method of Fuzzy Analytic Hierarchy Process (FAHP) and Quality Function Deployment (QFD) in the pharmaceutical company. In QFD method, determining the importance of the "weights" for the customer requirements is an essential and crucial issue. FAHP has been used to determine the importance of the "we...

This article advocates for the wider use of relative importance indices as a supplement to multiple regression analyses. The goal of such analyses is to partition explained variance among multiple predictors to better understand the role played by each predictor in a regression equation. Unfortunately, when predictors are correlated, typically relied upon metrics are flawed indicators of variab...

‎‎In the Data Envelopment Analysis (DEA) the efficiency of the units‎ ‎can be obtained by identifying the degree of the importance of the‎ ‎criteria (inputs-outputs).In DEA basic models‎, ‎challenges are zero‎ ‎and unequal weights of the criteria when decision‎- ‎making units are‎ ‎evaluated‎. ‎One of the strategies applied to deal with these problems‎ ‎is using common weights of the each input...

We discuss methods for calculating statistics for weighted samples using software that does not support weights. Such samples arise in survey sampling with unequal probabilities, importance sampling, and bootstrap tilting. The software might not support weights for reasons of eeciency, simplicity, or because it was quicker to write the software without supporting weights. We discuss several tec...