Discrimination via algorithmic decision making has received considerable attention. Prior work largely focuses on defining conditions for fairness, but does not define satisfactory measures of algorithmic unfairness. In this paper, we focus on the following question: Given two unfair algorithms, how should we determine which of the two is more unfair? Our core idea is to use existing inequality indices from economics to measure how unequally the outcomes of an algorithm benefit different individuals or groups in a population. Our work offers a justified and general framework to compare and contrast the (un)fairness of algorithmic predictors. This unifying approach enables us to quantify unfairness both at the individual and the group level. Further, our work reveals overlooked tradeoffs between different fairness notions: using our proposed measures, the overall individual-level unfairness of an algorithm can be decomposed into a between-group and a within-group component. Earlier methods are typically designed to tackle only between-group unfairness, which may be justified for legal or other reasons. However, we demonstrate that minimizing exclusively the between-group component may, in fact, increase the within-group, and hence the overall unfairness. We characterize and illustrate the tradeoffs between our measures of (un)fairness and the prediction accuracy.
We introduce a novel approach for building language models based on a systematic, recursive exploration of skip n-gram models which are interpolated using modified Kneser-Ney smoothing. Our approach generalizes language models as it contains the classical interpolation with lower order models as a special case. In this paper we motivate, formalize and present our approach. In an extensive empirical experiment over English text corpora we demonstrate that our generalized language models lead to a substantial reduction of perplexity between 3.1% and 12.7% in comparison to traditional language models using modified Kneser-Ney smoothing. Furthermore, we investigate the behaviour over three other languages and a domain specific corpus where we observed consistent improvements. Finally, we also show that the strength of our approach lies in its ability to cope in particular with sparse training data. Using a very small training data set of only 736 KB text we yield improvements of even 25.7% reduction of perplexity.
A major challenge in studying robustness in deep learning is defining the set of "meaningless" perturbations to which a given Neural Network (NN) should be invariant. Most work on robustness implicitly uses a human as the reference model to define such perturbations. Our work offers a new view on robustness by using another reference NN to define the set of perturbations a given NN should be invariant to, thus generalizing the reliance on a reference "human NN" to any NN. This makes measuring robustness equivalent to measuring the extent to which two NNs share invariances, for which we propose a measure called STIR. STIR re-purposes existing representation similarity measures to make them suitable for measuring shared invariances. Using our measure, we are able to gain insights into how shared invariances vary with changes in weight initialization, architecture, loss functions, and training dataset. Our implementation is available at: https:// github.com/nvedant07/STIR.
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