252 research outputs found
Moduli Spaces of Embedded Constant Mean Curvature Surfaces with Few Ends and Special Symmetry
We give necessary conditions on complete embedded \cmc surfaces with three or
four ends subject to reflection symmetries. The respective submoduli spaces are
two-dimensional varieties in the moduli spaces of general \cmc surfaces. We
characterize fundamental domains of our \cmc surfaces by associated great
circle polygons in the three-sphere.Comment: latex2e, AMS-latex, 24 page
Causal Reasoning for Algorithmic Fairness
In this work, we argue for the importance of causal reasoning in creating fair algorithms for decision making. We give a review of existing approaches to fairness, describe work in causality necessary for the understanding of causal approaches, argue why causality is necessary for any approach that wishes to be fair, and give a detailed analysis of the many recent approaches to causality-based fairness
Operationalizing Complex Causes: A Pragmatic View of Mediation
We examine the problem of causal response estimation for complex objects (e.g., text, images, genomics). In this setting, classical \emph{atomic} interventions are often not available (e.g., changes to characters, pixels, DNA base-pairs). Instead, we only have access to indirect or \emph{crude} interventions (e.g., enrolling in a writing program, modifying a scene, applying a gene therapy). In this work, we formalize this problem and provide an initial solution. Given a collection of candidate mediators, we propose (a) a two-step method for predicting the causal responses of crude interventions; and (b) a testing procedure to identify mediators of crude interventions. We demonstrate, on a range of simulated and real-world-inspired examples, that our approach allows us to efficiently estimate the effect of crude interventions with limited data from new treatment regimes
Making Decisions that Reduce Discriminatory Impacts
As machine learning algorithms move into realworld settings, it is crucial to ensure they are
aligned with societal values. There has been
much work on one aspect of this, namely the
discriminatory prediction problem: How can
we reduce discrimination in the predictions themselves? While an important question, solutions to
this problem only apply in a restricted setting, as
we have full control over the predictions. Often
we care about the non-discrimination of quantities we do not have full control over. Thus, we
describe another key aspect of this challenge, the
discriminatory impact problem: How can we
reduce discrimination arising from the real-world
impact of decisions? To address this, we describe
causal methods that model the relevant parts of
the real-world system in which the decisions are
made. Unlike previous approaches, these models not only allow us to map the causal pathway
of a single decision, but also to model the effect
of interference–how the impact on an individual
depends on decisions made about other people.
Often, the goal of decision policies is to maximize a beneficial impact overall. To reduce the
discrimination of these benefits, we devise a constraint inspired by recent work in counterfactual
fairness (Kusner et al., 2017), and give an efficient
procedure to solve the constrained optimization
problem. We demonstrate our approach with an
example: how to increase students taking college
entrance exams in New York City public schools
Causal Reasoning for Algorithmic Fairness
In this work, we argue for the importance of causal reasoning in creating
fair algorithms for decision making. We give a review of existing approaches to
fairness, describe work in causality necessary for the understanding of causal
approaches, argue why causality is necessary for any approach that wishes to be
fair, and give a detailed analysis of the many recent approaches to
causality-based fairness
The Sensitivity of Counterfactual Fairness to Unmeasured Confounding
Causal approaches to fairness have seen substantial recent interest, both from the machine
learning community and from wider parties interested in ethical prediction algorithms. In
no small part, this has been due to the fact
that causal models allow one to simultaneously
leverage data and expert knowledge to remove
discriminatory effects from predictions. However, one of the primary assumptions in causal
modeling is that you know the causal graph.
This introduces a new opportunity for bias,
caused by misspecifying the causal model.
One common way for misspecification to occur is via unmeasured confounding: the true
causal effect between variables is partially described by unobserved quantities. In this work
we design tools to assess the sensitivity of fairness measures to this confounding for the popular class of non-linear additive noise models (ANMs). Specifically, we give a procedure for computing the maximum difference
between two counterfactually fair predictors,
where one has become biased due to confounding. For the case of bivariate confounding our
technique can be swiftly computed via a sequence of closed-form updates. For multivariate confounding we give an algorithm that can
be efficiently solved via automatic differentiation. We demonstrate our new sensitivity analysis tools in real-world fairness scenarios to assess the bias arising from confounding
Causal Effect Inference for Structured Treatments
We address the estimation of conditional average treatment effects (CATEs) for structured treatments (e.g., graphs, images, texts). Given a weak condition on the effect, we propose the generalized Robinson decomposition, which (i) isolates the causal estimand (reducing regularization bias), (ii) allows one to plug in arbitrary models for learning, and (iii) possesses a quasi-oracle convergence guarantee under mild assumptions. In experiments with small-world and molecular graphs we demonstrate that our approach outperforms prior work in CATE estimation
Premi\`ere valeur propre du laplacien, volume conforme et chirurgies
We define a new differential invariant a compact manifold by , where is the conformal volume of for
the conformal class , and prove that it is uniformly bounded above. The
main motivation is that this bound provides a upper bound of the
Friedlander-Nadirashvili invariant defined by \inf_g\sup_{\tilde
g\in[g]}\lambda_1(M,\tilde g)\Vol(M,\tilde g)^{\frac 2n}.
The proof relies on the study of the behaviour of when
one performs surgeries on .Comment: 11 pages, 5 figures, in Frenc
- …