Induced Model Matching: How Restricted Models Can Help Larger Ones

We consider scenarios where a very accurate predictive model using restricted features is available at the time of training of a larger, full-featured, model. This restricted model may be thought of as "side-information", derived either from an auxiliary exhaustive dataset or on the same dataset, by forcing the restriction. How can the restricted model be useful to the full model? We propose an approach for transferring the knowledge of the restricted model to the full model, by aligning the full model's context-restricted performance with that of the restricted model's. We call this methodology Induced Model Matching (IMM) and first illustrate its general applicability by using logistic regression as a toy example. We then explore IMM's use in language modeling, the application that initially inspired it, and where it offers an explicit foundation in contrast to the implicit use of restricted models in techniques such as noising. We demonstrate the methodology on both LSTM and transformer full models, using $N$-grams as restricted models. To further illustrate the potential of the principle whenever it is much cheaper to collect restricted rather than full information, we conclude with a simple RL example where POMDP policies can improve learned MDP policies via IMM.

Fair Learning with Private Demographic Data

Sensitive attributes such as race are rarely available to learners in real world settings as their collection is often restricted by laws and regulations. We give a scheme that allows individuals to release their sensitive information privately while still allowing any downstream entity to learn non-discriminatory predictors. We show how to adapt non-discriminatory learners to work with privatized protected attributes giving theoretical guarantees on performance. Finally, we highlight how the methodology could apply to learning fair predictors in settings where protected attributes are only available for a subset of the data.

From Fair Decision Making to Social Equality

The study of fairness in intelligent decision systems has mostly ignored long-term influence on the underlying population. Yet fairness considerations (e.g. affirmative action) have often the implicit goal of achieving balance among groups within the population. The most basic notion of balance is eventual equality between the qualifications of the groups. How can we incorporate influence dynamics in decision making? How well do dynamics-oblivious fairness policies fare in terms of reaching equality? In this paper, we propose a simple yet revealing model that encompasses (1) a selection process where an institution chooses from multiple groups according to their qualifications so as to maximize an institutional utility and (2) dynamics that govern the evolution of the groups' qualifications according to the imposed policies. We focus on demographic parity as the formalism of affirmative action. We then give conditions under which an unconstrained policy reaches equality on its own. In this case, surprisingly, imposing demographic parity may break equality. When it doesn't, one would expect the additional constraint to reduce utility, however, we show that utility may in fact increase. In more realistic scenarios, unconstrained policies do not lead to equality. In such cases, we show that although imposing demographic parity may remedy it, there is a danger that groups settle at a worse set of qualifications. As a silver lining, we also identify when the constraint not only leads to equality, but also improves all groups. This gives quantifiable insight into both sides of the mismatch hypothesis. These cases and trade-offs are instrumental in determining when and how imposing demographic parity can be beneficial in selection processes, both for the institution and for society on the long run.

Learning Non-Discriminatory Predictors

We consider learning a predictor which is non-discriminatory with respect to a "protected attribute" according to the notion of "equalized odds" proposed by Hardt et al. [2016]. We study the problem of learning such a non-discriminatory predictor from a finite training set, both statistically and computationally. We show that a post-hoc correction approach, as suggested by Hardt et al, can be highly suboptimal, present a nearly-optimal statistical procedure, argue that the associated computational problem is intractable, and suggest a second moment relaxation of the non-discrimination definition for which learning is tractable.

Tradeoffs for Space, Time, Data and Risk in Unsupervised Learning

Faced with massive data, is it possible to trade off (statistical) risk, and (computational) space and time? This challenge lies at the heart of large-scale machine learning. Using k-means clustering as a prototypical unsupervised learning problem, we show how we can strategically summarize the data (control space) in order to trade off risk and time when data is generated by a probabilistic model. Our summarization is based on coreset constructions from computational geometry. We also develop an algorithm, TRAM, to navigate the space/time/data/risk tradeoff in practice. In particular, we show that for a fixed risk (or data size), as the data size increases (resp. risk increases) the running time of TRAM decreases. Our extensive experiments on real data sets demonstrate the existence and practical utility of such tradeoffs, not only for k-means but also for Gaussian Mixture Models.

On the Impossibility of Learning the Missing Mass

This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete distribution. The probability of this event is referred to as the "missing mass". The impossibility result can then be stated as: the missing mass is not distribution-free PAC-learnable in relative error. The proof is semi-constructive and relies on a coupling argument using a dithered geometric distribution. This result formalizes the folklore that in order to predict rare events, one necessarily needs distributions with "heavy tails".