Consistent Polyhedral Surrogates for Top-k Classification and Variants

Jessie Finocchiaro, Rafael Frongillo, Emma Goodwill, Anish Thilagar

Published in International Conference on Machine Learning 2022, 2022


Abstract: Top-k classification is a generalization of multiclass classification used widely in information retrieval, image classification, and other extreme classification settings. Several hinge-like (piecewise-linear) surrogates have been proposed for the problem, yet all are either non-convex or inconsistent. For the proposed hinge-like surrogates that are convex (i.e., polyhedral), we apply the embedding framework Finocchiaro et al. (2019) to determine the prediction problem for which the surrogate is consistent. These problems can all be interpreted as variants of top-k classification, which may be better aligned with some applications. We leverage this analysis to derive constraints on the conditional label distributions under which these proposed surrogates become consistent for top-k. It has been further suggested that every convex hinge-like surrogate must be inconsistent for top-k. Yet, we use the same embedding framework to give the first consistent polyhedral surrogate for this problem.

The Structured Abstain Problem and the Lovász Hinge

Jessie Finocchiaro, Rafael Frongillo, Enrique Nueve

Published in Conference on Learning Theory 2022, 2022


Abstract: The Lovász hinge is a convex surrogate recently proposed for structured binary classification, in which k binary predictions are made simultaneously and the error is judged by a submodular set function. Despite its wide usage in image segmentation and related problems, its consistency has remained open. We resolve this open question, showing that the Lovász hinge is inconsistent for its desired target unless the set function is modular. Leveraging a recent embedding framework, we instead derive the target loss for which the Lovász hinge is consistent. This target, which we call the structured abstain problem, allows one to abstain on any subset of the k predictions. We derive two link functions, each of which are consistent for all submodular set functions simultaneously.

Online Platforms and the Fair Exposure Problem Under Homophily

Jakob Schoeffer, Alexander Ritchie, Keziah Naggita, Faidra Monachou, Jessie Finocchiaro, Marc Juarez

Published in In submission, 2022


Abstract: In the wake of increasing political extremism, online platforms have been criticized for contributing to polarization. One line of criticism has focused on echo chambers and the recommended content served to users by these platforms. In this work, we introduce the fair exposure problem: given limited intervention power of the platform, the goal is to enforce balance in the spread of content (e.g., news articles) among two groups of users through constraints similar to those imposed by the Fairness Doctrine in the United States in the past. Groups are characterized by different affiliations (e.g., political views) and have different preferences for content. We develop a stylized framework that models intra- and inter-group content propagation under homophily, and we formulate the platform’s decision as an optimization problem that aims at maximizing user engagement, potentially under fairness constraints. Our main notion of fairness requires that each group see a mixture of their preferred and non-preferred content, encouraging information diversity. Promoting such information diversity is often viewed as desirable and a potential means for breaking out of harmful echo chambers. We study the solutions to both the fairness-agnostic and fairness-aware problems. We prove that a fairness-agnostic approach inevitably leads to group-homogeneous targeting by the platform. This is only partially mitigated by imposing fairness constraints: we show that there exist optimal fairness-aware solutions which target one group with different types of content and the other group with only one type that is not necessarily the group’s most preferred. Finally, using simulations with real-world data, we study the system dynamics and quantify the price of fairness.

Unifying Lower Bounds on Prediction Dimension of Consistent Convex Surrogates

Jessie Finocchiaro, Rafael Frongillo, Bo Waggoner

Published in Neural Information Processing Systems (NeurIPS) 2021, 2021


Abstract: Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as a target loss, as in classification and structured prediction, or simply as a (conditional) statistic of the data, as in risk measure estimation. These two scenarios typically involve different techniques for designing and analyzing surrogate losses. We unify these settings using tools from property elicitation, and give a general lower bound on prediction dimension. Our lower bound tightens existing results in the case of discrete predictions, showing that previous calibration-based bounds can largely be recovered via property elicitation. For continuous estimation, our lower bound resolves on open problem on estimating measures of risk and uncertainty.

A Decomposition of a Complete Graph with a Hole

Roxanne Back, Alejandra Brewer Castano, Rachel Galindo, Jessie Finocchiaro

Published in Open Journal of Discrete Mathematics, 2021


Abstract: In the field of design theory, the most well-known design is a Steiner Triple System. In general, a G-design on H is an edge-disjoint decomposition of H into isomorphic copies of G. In a Steiner Triple system, a complete graph is decomposed into triangles. In this paper we let H be a complete graph with ahole and G be a complete graph on four vertices minus one edge, also referred to as a K_4-e. A complete graph with a hole, K_d + v, consists of acomplete graph ond vertices,K_d, and a set of independent vertices of size v, V, where each vertex in V is adjacent to each vertex in K_d. Whend is even,we give two constructions for the decomposition of a complete graph with ahole into copies of K_4 -e: the Alpha-Delta Construction, and the Alpha-Beta-Delta Construction. By restricting d and v so that v = 2(d-1) - 5a, we are able to resolve both of these cases for a subset of K_d + v using difference methods and 1-factors.

Bridging Machine Learning and Mechanism Design Towards Algorithmic Fairness

Jessie Finocchiaro, Roland Maio, Faidra Monachou, Gourab Patro, Manish Raghavan, Ana-Andreea Stoica, Stratis Tsirtis

Published in ACM Conference on Fairness, Accountability and Transparency (FAccT) 2021. Originally appeared at AI for Social Good (AI4SG) Workshop at Harvard CRCS., 2020


Abstract: As fairness and discrimination concerns permeate the design of both machine learning algorithms and mechanism design problems, we discuss differences in approaches between these two fields. We aim to bridge these two communities into a cohesive narrative that encompasses both the large-scale capabilities of machine learning and group-focused fairness as well as the strategic incentives and utility-based notions of fairness from mechanism de-sign, showing their necessity in designing a fair pipeline.

Evolutionary Optimization of Cooperative Strategies for the Iterated Prisoner’s Dilemma

Jessie Finocchiaro, H. David Mathias

Published in IEEE Transactions on Games 2020, 2020


Abstract: The Iterated Prisoner’s Dilemma (IPD) has been studied in fields as diverse as economics, computer science, psychology, politics, and environmental studies. This is due, in part, to the intriguing property that its Nash Equilibrium is not globally optimal. Typically treated as a single-objective problem, a player’s goal is to maximize their own score. In some work, minimizing the opponent’s score is an additional objective. Here, we explore the role of explicitly optimizing for mutual cooperation in IPD player performance. We implement a genetic algorithm in which each member of the population evolves using one of four multi-objective fitness functions: selfish, communal, cooperative, and selfless, the last three of which use a cooperative metric as an objective. As a control, we also consider two single-objective fitness functions. We explore the role of representation in evolving cooperation by implementing four representations for evolving players. Finally, we evaluate the effect of noise on the evolution of cooperative behaviors. Testing our evolved players in tournaments in which a player’s own score is the sole metric, we find that players evolved with mutual cooperation as an objective are very competitive. Thus, learning to play nicely with others is a successful strategy for maximizing personal reward.

Embedding Dimension of Polyhedral Losses

Jessie Finocchiaro, Rafael Frongillo, Bo Waggoner

Published in Conference on Learning Theory (COLT) 2020, 2020


Abstract: A common technique in supervised learning with discrete losses, such as 0-1 loss, is to optimize a convex surrogate loss over R^d, calibrated with respect to the original loss. In particular, recent work has investigated embedding the original predictions (e.g. labels) as points in R^d, showing an equivalence to using polyhedral surrogates. In this work, we study the notion of the embedding dimension of a given discrete loss: the minimum dimension d such that an embedding exists. We characterize d-embeddability for all d, with a particularly tight characterization for d=1 (embedding into the real line), and useful necessary conditions for d>1 in the form of a quadratic feasibility program. We illustrate our results with novel lower bounds for abstain loss.

An Embedding Framework for Consistent Polyhedral Surrogates

Jessie Finocchiaro, Rafael Frongillo, Bo Waggoner

Published in Neural Information Processing Systems (NeurIPS) 2019, 2019


Abstract: We formalize and study the natural approach of designing convex surrogate loss functions via embeddings for problems such as classification or ranking. In this approach, one embeds each of the finitely many predictions (e.g. classes) as a point in Rd, assigns the original loss values to these points, and convexifies the loss in between to obtain a surrogate. We prove that this approach is equivalent, in a strong sense, to working with polyhedral (piecewise linear convex) losses. Moreover, given any polyhedral loss L, we give a construction of a link function through which L is a consistent surrogate for the loss it embeds. We go on to illustrate the power of this embedding framework with succinct proofs of consistency or inconsistency of various polyhedral surrogates in the literature.

Convex Elicitation of Continuous Properties

Jessie Finocchiaro, Rafael Frongillo

Published in Neural Information Processing Systems (NeurIPS) 2018, 2018


A property or statistic of a distribution is said to be elicitable if it can be expressed as the minimizer of some loss function in expectation. Recent work shows that continuous real-valued properties are elicitable if and only if they are identifiable, meaning the set of distributions with the same property value can be described by linear constraints. From a practical standpoint, one may ask for which such properties do there exist convex loss functions. In this paper, in a finite-outcome setting, we show that in fact every elicitable real-valued property can be elicited by a convex loss function. Our proof is constructive, and leads to convex loss functions for new properties.

Social Trends in the Iterated Prisoner’s Dilemma (Extended Abstract)

Published in Genetic and Evolutionary Computation Conference (GECCO) 2017, 2017


Abstract: In this paper, we utilize a multi-objective genetic algorithm (GA) to investigate the Iterated Prisoner’s Dilemma problem with a population of players that don’t have uniform objectives. Each of the members of our population has one of four objective pairs. We simulate a tournament similar to those in previous work to investigate patterns of convergence in objective pairs when they are free to change. We also consider the most successful objective pair within a population when members’ objective pairs are fixed.

Investigating Social Trends in the Iterated Prisoner’s Dilemma

Jessie Finocchiaro

Published in Florida Southern College Archives, 2017


Abstract: In ethics, many academics make the assumption that all people want to be good. Evil comes in where there is a conflict of good decisions; where a decision that is good for one person contradicts the good of another. In this case, a person will make a different decision depending on their definition of the good they want to accomplish. In a society that starts with an equal proportion of selfishly good and selfessly good people, we aim to investigate the convergence of behavior through simulating the Iterated Prisoner’s Dilemma over time.

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Egocentric Height Estimation

Jessie Finocchiaro, Aisha Urooj Khan, Ali Borji

Published in Winter Conference on Applications in Computer Vision (WACV), 2017


Abstract: Egocentric, or first-person, vision which became popular in recent years with an emerge in wearable technology,is different than exocentric (third-person) vision in some distinguishable ways, one of which being that the camera-wearer is generally not visible in the video frames. Recent work has been done on action and object recognition in egocentric videos, as well as work on biometric extraction from first-person videos. Height estimation can be a useful feature for both soft-biometrics and object tracking. Here, we propose a method of estimating the height of an egocentric camera without any calibration or reference points. We used both traditional computer vision approaches and deep learning in order to determine the visual cues that results in best height estimation. Here, we introduce a framework inspired by two stream networks comprising of two Convolutional Neural Networks, one based on spatial information, and one based on information given by optical flow in a frame. Given an egocentric video as an input to the framework, our model yields a height estimate as an output. We also incorporate late fusion to learn a combination of temporal and spatial cues. Comparing our model with other methods we used as baselines, we achieve height estimates for videos with a Mean Average Error of 14.04 cm over a range of 103 cm of data, and classification accuracy for relative height (tall, medium or short) up to 93.75% where chance level is 33%.