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We consider scenarios where a very accurate (often small) predictive model using restricted features is available when training a full-featured (often larger) model. This restricted model may be thought of as "side-information", and can come either from an auxiliary dataset or from the same dataset by forcing the restriction. How can the restricted model be useful to the full model? To answer this, we introduce a methodology called Induced Model Matching (IMM). IMM aligns the context-restricted, or induced, version of the large model with the restricted model. We relate IMM to approaches such as noising, which is implicit in addressing the problem, and reverse knowledge distillation from weak teachers, which is explicit but does not exploit restriction being the nature of the weakness. We show that these prior methods can be thought of as approximations to IMM and can be problematic in terms of consistency. Experimentally, we first motivate IMM using logistic regression as a toy example. We then explore it in language modeling, the application that initially inspired it, and demonstrate it on both LSTM and transformer full models, using bigrams as restricted models. We lastly give a simple RL example, which shows that POMDP policies can help learn better MDP policies. The IMM principle is thus generally applicable in common scenarios where restricted data is cheaper to collect or restricted models are easier to learn. 

Ranking algorithms in online platforms serve not only users on the demand side, but also items on the supply side. While ranking has traditionally presented items in an order that maximizes their utility to users, the uneven interactions that different items receive as a result of such a ranking can pose item fairness concerns. Moreover, interaction is affected by various forms of bias, two of which have received considerable attention: position bias and selection bias. Position bias occurs due to lower likelihood of observation for items in lower ranked positions. Selection bias occurs because interaction is not possible with items below an arbitrary cutoff position chosen by the front-end application at deployment time (i.e., showing only the top-kitems). A less studied, third form of bias, trust bias, is equally important, as it makes interaction dependent on rank even after observation, by influencing the item’s perceived relevance. To capture interaction disparity in the presence of all three biases, in this paper we introduce a flexible fairness metric. Using this metric, we develop a post-processing algorithm that optimizes fairness in ranking through greedy exploration and allows a tradeoff between fairness and utility. Our algorithm outperforms state-of-the-art fair ranking algorithms on several datasets.