A contiguous area cartogram is a geographic map in which the area of each region is proportional to numerical data (e.g., population size) while keeping neighboring regions connected. In this study, we investigated whether value-to-area legends (square symbols next to the values represented by the squares' areas) and grid lines aid map readers in making better area judgments. We conducted an experiment to determine the accuracy, speed, and confidence with which readers infer numerical data values for the mapped regions. We found that, when only informed about the total numerical value represented by the whole cartogram without any legend, the distribution of estimates for individual regions was centered near the true value with substantial spread. Legends with grid lines significantly reduced the spread but led to a tendency to underestimate the values. Comparing differences between regions or between cartograms revealed that legends and grid lines slowed the estimation without improving accuracy. However, participants were more likely to complete the tasks when legends and grid lines were present, particularly when the area units represented by these features could be interactively selected. We recommend considering the cartogram's use case and purpose before deciding whether to include grid lines or an interactive legend.
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Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigenvectors of the graph Laplacian. One attractive application of ER is to point clouds, i.e. graphs whose vertices correspond to IID samples from a distribution over a metric space. Unfortunately, it was shown that the ER between any two points converges to a trivial quantity that holds no information about the graph's structure as the size of the sample increases to infinity. In this study, we show that this trivial solution can be circumvented by considering a region-based ER between pairs of small regions rather than pairs of points and by scaling the edge weights appropriately with respect to the underlying density in each region. By keeping the regions fixed, we show analytically that the region-based ER converges to a non-trivial limit as the number of points increases to infinity. Namely the ER on a metric space. We support our theoretical findings with numerical experiments.
This paper addresses a mathematically tractable model of the Prisoner's Dilemma using the framework of active inference. In this work, we design pairs of Bayesian agents that are tracking the joint game state of their and their opponent's choices in an Iterated Prisoner's Dilemma game. The specification of the agents' belief architecture in the form of a partially-observed Markov decision process allows careful and rigourous investigation into the dynamics of two-player gameplay, including the derivation of optimal conditions for phase transitions that are required to achieve certain game-theoretic steady states. We show that the critical time points governing the phase transition are linearly related to each other as a function of learning rate and the reward function. We then investigate the patterns that emerge when varying the agents' learning rates, as well as the relationship between the stochastic and deterministic solutions to the two-agent system.
Context. Algorithmic racism is the term used to describe the behavior of technological solutions that constrains users based on their ethnicity. Lately, various data-driven software systems have been reported to discriminate against Black people, either for the use of biased data sets or due to the prejudice propagated by software professionals in their code. As a result, Black people are experiencing disadvantages in accessing technology-based services, such as housing, banking, and law enforcement. Goal. This study aims to explore algorithmic racism from the perspective of software professionals. Method. A survey questionnaire was applied to explore the understanding of software practitioners on algorithmic racism, and data analysis was conducted using descriptive statistics and coding techniques. Results. We obtained answers from a sample of 73 software professionals discussing their understanding and perspectives on algorithmic racism in software development. Our results demonstrate that the effects of algorithmic racism are well-known among practitioners. However, there is no consensus on how the problem can be effectively addressed in software engineering. In this paper, some solutions to the problem are proposed based on the professionals' narratives. Conclusion. Combining technical and social strategies, including training on structural racism for software professionals, is the most promising way to address the algorithmic racism problem and its effects on the software solutions delivered to our society.
We study the problem of fair sequential decision making given voter preferences. In each round, a decision rule must choose a decision from a set of alternatives where each voter reports which of these alternatives they approve. Instead of going with the most popular choice in each round, we aim for proportional representation. We formalize this aim using axioms based on Proportional Justified Representation (PJR), which were proposed in the literature on multi-winner voting and were recently adapted to multi-issue decision making. The axioms require that every group of $\alpha\%$ of the voters, if it agrees in every round (i.e., approves a common alternative), then those voters must approve at least $\alpha\%$ of the decisions. A stronger version of the axioms requires that every group of $\alpha\%$ of the voters that agrees in a $\beta$ fraction of rounds must approve $\beta\cdot\alpha\%$ of the decisions. We show that three attractive voting rules satisfy axioms of this style. One of them (Sequential Phragm\'en) makes its decisions online, and the other two satisfy strengthened versions of the axioms but make decisions semi-online (Method of Equal Shares) or fully offline (Proportional Approval Voting). The first two are polynomial-time computable, and the latter is based on an NP-hard optimization, but it admits a polynomial-time local search algorithm that satisfies the same axiomatic properties. We present empirical results about the performance of these rules based on synthetic data and U.S. political elections. We also run experiments where votes are cast by preference models trained on user responses from the moral machine dataset about ethical dilemmas.
Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response. However, for large systems this procedure can quickly become computationally overwhelming, especially in three-dimensions when the microstructure is locally complex. In such settings multi-scale modeling offers a route to a more efficient model by holding out the promise of a framework with fewer degrees of freedom, which at the same time faithfully represents, up to a certain scale, the behavior of the system. In this paper, we present a methodology that produces such models for inelastic systems upon the basis of a variational scheme. The essence of the scheme is the construction of a variational statement for the free energy as well as the dissipation potential for a coarse scale model in terms of the free energy and dissipation functions of the fine scale model. From the coarse scale energy and dissipation we can then generate coarse scale material models that are computationally far more efficient than either directly solving the fine scale model or by resorting to FE-square type modeling. Moreover, the coarse scale model preserves the essential mathematical structure of the fine scale model. An essential feature for such schemes is the proper definition of the coarse scale inelastic variables. By way of concrete examples, we illustrate the needed steps to generate successful models via application to problems in classical plasticity, included are comparisons to direct numerical simulations of the microstructure to illustrate the accuracy of the proposed methodology.
Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical scenarios. Without additional assumptions about the unobserved variables, it is not possible to recover any causal relationships from observational data. Fortunately, in many applied settings, additional structure among the confounders can be expected. In particular, pervasive confounding is commonly encountered and has been utilized for consistent causal estimation in linear causal models. In this paper, we present a provably consistent method to estimate causal relationships in the non-linear, pervasive confounding setting. The core of our procedure relies on the ability to estimate the confounding variation through a simple spectral decomposition of the observed data matrix. We derive a DAG score function based on this insight, prove its consistency in recovering a correct ordering of the DAG, and empirically compare it to previous approaches. We demonstrate improved performance on both simulated and real datasets by explicitly accounting for both confounders and non-linear effects.
We study a dynamic allocation problem in which $T$ sequentially arriving divisible resources are to be allocated to a number of agents with linear utilities. The marginal utilities of each resource to the agents are drawn stochastically from a known joint distribution, independently and identically across time, and the central planner makes immediate and irrevocable allocation decisions. Most works on dynamic resource allocation aim to maximize the utilitarian welfare, i.e., the efficiency of the allocation, which may result in unfair concentration of resources on certain high-utility agents while leaving others' demands under-fulfilled. In this paper, aiming at balancing efficiency and fairness, we instead consider a broad collection of welfare metrics, the H\"older means, which includes the Nash social welfare and the egalitarian welfare. To this end, we first study a fluid-based policy derived from a deterministic surrogate to the underlying problem and show that for all smooth H\"older mean welfare metrics it attains an $O(1)$ regret over the time horizon length $T$ against the hindsight optimum, i.e., the optimal welfare if all utilities were known in advance of deciding on allocations. However, when evaluated under the non-smooth egalitarian welfare, the fluid-based policy attains a regret of order $\Theta(\sqrt{T})$. We then propose a new policy built thereupon, called Backward Infrequent Re-solving with Thresholding ($\mathsf{BIRT}$), which consists of re-solving the deterministic surrogate problem at most $O(\log\log T)$ times. We prove the $\mathsf{BIRT}$ policy attains an $O(1)$ regret against the hindsight optimal egalitarian welfare, independently of the time horizon length $T$. We conclude by presenting numerical experiments to corroborate our theoretical claims and to illustrate the significant performance improvement against several benchmark policies.
Wearable health devices are ushering in a new age of continuous and noninvasive remote monitoring. One application of this technology is in anxiety detection. Many advancements in anxiety detection have happened in controlled lab settings, but noise prevents these advancements from generalizing to real-world conditions. We seek to progress the field by studying how noise impacts model performance and developing models that are robust to noisy, real-world conditions and, hence, attuned to the commotion of everyday life. In this study we look to investigate why and how previous methods have failed. Using the wearable stress and affect detection (WESAD) dataset, we compare the effect of various intensities of noise on machine learning models classifying levels of physiological arousal in the three-class classification problem: baseline vs. stress vs. amusement. Before introducing noise, our baseline model performance reaches 98.7%, compared to Schmidt 2018's 80.3%. We discuss potential sources of this discrepancy in results through a careful evaluation of feature extraction and model architecture choices. Finally, after the introduction of noise, we provide a thorough analysis of the effect of noise on each model architecture.
The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic estimation variance and derived an optimal set for the case without hidden variables. For the case with hidden variables there can be settings where no optimal set exists and currently only a sufficient graphical optimality criterion of limited applicability has been derived. In the present work optimality is characterized as maximizing a certain adjustment information which allows to derive a necessary and sufficient graphical criterion for the existence of an optimal adjustment set and a definition and algorithm to construct it. Further, the optimal set is valid if and only if a valid adjustment set exists and has higher (or equal) adjustment information than the Adjust-set proposed in Perkovi{\'c} et al. [Journal of Machine Learning Research, 18: 1--62, 2018] for any graph. The results translate to minimal asymptotic estimation variance for a class of estimators whose asymptotic variance follows a certain information-theoretic relation. Numerical experiments indicate that the asymptotic results also hold for relatively small sample sizes and that the optimal adjustment set or minimized variants thereof often yield better variance also beyond that estimator class. Surprisingly, among the randomly created setups more than 90\% fulfill the optimality conditions indicating that also in many real-world scenarios graphical optimality may hold. Code is available as part of the python package \url{//github.com/jakobrunge/tigramite}.
We consider the problem of online allocation subject to a long-term fairness penalty. Contrary to existing works, however, we do not assume that the decision-maker observes the protected attributes -- which is often unrealistic in practice. Instead they can purchase data that help estimate them from sources of different quality; and hence reduce the fairness penalty at some cost. We model this problem as a multi-armed bandit problem where each arm corresponds to the choice of a data source, coupled with the online allocation problem. We propose an algorithm that jointly solves both problems and show that it has a regret bounded by $\mathcal{O}(\sqrt{T})$. A key difficulty is that the rewards received by selecting a source are correlated by the fairness penalty, which leads to a need for randomization (despite a stochastic setting). Our algorithm takes into account contextual information available before the source selection, and can adapt to many different fairness notions. We also show that in some instances, the estimates used can be learned on the fly.
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