3,657 research outputs found
Advancing Subgroup Fairness via Sleeping Experts
We study methods for improving fairness to subgroups in settings with overlapping populations and sequential predictions. Classical notions of fairness focus on the balance of some property across different populations. However, in many applications the goal of the different groups is not to be predicted equally but rather to be predicted well. We demonstrate that the task of satisfying this guarantee for multiple overlapping groups is not straightforward and show that for the simple objective of unweighted average of false negative and false positive rate, satisfying this for overlapping populations can be statistically impossible even when we are provided predictors that perform well separately on each subgroup. On the positive side, we show that when individuals are equally important to the different groups they belong to, this goal is achievable; to do so, we draw a connection to the sleeping experts literature in online learning. Motivated by the one-sided feedback in natural settings of interest, we extend our results to such a feedback model. We also provide a game-theoretic interpretation of our results, examining the incentives of participants to join the system and to provide the system full information about predictors they may possess. We end with several interesting open problems concerning the strength of guarantees that can be achieved in a computationally efficient manner
Online Isotonic Regression
We consider the online version of the isotonic regression problem. Given a
set of linearly ordered points (e.g., on the real line), the learner must
predict labels sequentially at adversarially chosen positions and is evaluated
by her total squared loss compared against the best isotonic (non-decreasing)
function in hindsight. We survey several standard online learning algorithms
and show that none of them achieve the optimal regret exponent; in fact, most
of them (including Online Gradient Descent, Follow the Leader and Exponential
Weights) incur linear regret. We then prove that the Exponential Weights
algorithm played over a covering net of isotonic functions has a regret bounded
by and present a matching
lower bound on regret. We provide a computationally efficient version of this
algorithm. We also analyze the noise-free case, in which the revealed labels
are isotonic, and show that the bound can be improved to or even to
(when the labels are revealed in isotonic order). Finally, we extend the
analysis beyond squared loss and give bounds for entropic loss and absolute
loss.Comment: 25 page
On the Bayes-optimality of F-measure maximizers
The F-measure, which has originally been introduced in information retrieval,
is nowadays routinely used as a performance metric for problems such as binary
classification, multi-label classification, and structured output prediction.
Optimizing this measure is a statistically and computationally challenging
problem, since no closed-form solution exists. Adopting a decision-theoretic
perspective, this article provides a formal and experimental analysis of
different approaches for maximizing the F-measure. We start with a Bayes-risk
analysis of related loss functions, such as Hamming loss and subset zero-one
loss, showing that optimizing such losses as a surrogate of the F-measure leads
to a high worst-case regret. Subsequently, we perform a similar type of
analysis for F-measure maximizing algorithms, showing that such algorithms are
approximate, while relying on additional assumptions regarding the statistical
distribution of the binary response variables. Furthermore, we present a new
algorithm which is not only computationally efficient but also Bayes-optimal,
regardless of the underlying distribution. To this end, the algorithm requires
only a quadratic (with respect to the number of binary responses) number of
parameters of the joint distribution. We illustrate the practical performance
of all analyzed methods by means of experiments with multi-label classification
problems
RELEAF: An Algorithm for Learning and Exploiting Relevance
Recommender systems, medical diagnosis, network security, etc., require
on-going learning and decision-making in real time. These -- and many others --
represent perfect examples of the opportunities and difficulties presented by
Big Data: the available information often arrives from a variety of sources and
has diverse features so that learning from all the sources may be valuable but
integrating what is learned is subject to the curse of dimensionality. This
paper develops and analyzes algorithms that allow efficient learning and
decision-making while avoiding the curse of dimensionality. We formalize the
information available to the learner/decision-maker at a particular time as a
context vector which the learner should consider when taking actions. In
general the context vector is very high dimensional, but in many settings, the
most relevant information is embedded into only a few relevant dimensions. If
these relevant dimensions were known in advance, the problem would be simple --
but they are not. Moreover, the relevant dimensions may be different for
different actions. Our algorithm learns the relevant dimensions for each
action, and makes decisions based in what it has learned. Formally, we build on
the structure of a contextual multi-armed bandit by adding and exploiting a
relevance relation. We prove a general regret bound for our algorithm whose
time order depends only on the maximum number of relevant dimensions among all
the actions, which in the special case where the relevance relation is
single-valued (a function), reduces to ; in the
absence of a relevance relation, the best known contextual bandit algorithms
achieve regret , where is the full dimension of
the context vector.Comment: to appear in IEEE Journal of Selected Topics in Signal Processing,
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