iFair: Learning Individually Fair Data Representations for Algorithmic Decision Making

People are rated and ranked, towards algorithmic decision making in an increasing number of applications, typically based on machine learning. Research on how to incorporate fairness into such tasks has prevalently pursued the paradigm of group fairness: giving adequate success rates to specifically protected groups. In contrast, the alternative paradigm of individual fairness has received relatively little attention, and this paper advances this less explored direction. The paper introduces a method for probabilistically mapping user records into a low-rank representation that reconciles individual fairness and the utility of classifiers and rankings in downstream applications. Our notion of individual fairness requires that users who are similar in all task-relevant attributes such as job qualification, and disregarding all potentially discriminating attributes such as gender, should have similar outcomes. We demonstrate the versatility of our method by applying it to classification and learning-to-rank tasks on a variety of real-world datasets. Our experiments show substantial improvements over the best prior work for this setting.Comment: Accepted at ICDE 2019. Please cite the ICDE 2019 proceedings versio

Large-Scale Model of the Milky Way: Stellar Kinematics and Microlensing Event Timescale Distribution in the Galactic Bulge

We build a stellar-dynamical model of the Milky Way barred bulge and disk, using a newly implemented adaptive particle method. The underlying mass model has been previously shown to match the Galactic near-infrared surface brightness as well as gas-kinematic observations. Here we show that the new stellar-dynamical model also matches the observed stellar kinematics in several bulge fields, and that its distribution of microlensing event timescales reproduces the observed timescale distribution of the {\it MACHO} experiment with a reasonable stellar mass function. The model is therefore an excellent basis for further studies of the Milky Way. We also predict the observational consequences of this mass function for parallax shifted events.Comment: 13 pages, 3 figures. Accepted to ApJ

Spatial and Dynamical Biases in Velocity Statistics of Galaxies

We present velocity statistics of galaxies and their biases inferred from the statistics of the underlying dark matter using a cosmological hydrodynamic simulation of galaxy formation in low-density and spatially flat cold dark matter cosmogony. We find that the pairwise velocity dispersion (PVD) of all galaxies is significantly lower than that of the dark matter particles, and that the PVD of the young galaxies is lower than that of the old types, and even of all galaxies together, especially at small separations. These results are in reasonable agreement with the recent measurements of PVDs in the Las Campanas redshift survey, the PSCz catalogue and the SDSS data. We also find that the low PVD of young galaxies is due to the effects of dynamical friction as well as the different spatial distribution. We also consider the mean infall velocity and the POTENT density reconstruction that are often used to measure the cosmological parameters, and investigate the effects of spatial bias and dynamical friction. In our simulation, the mean infall velocity of young galaxies is significantly lower than that of all the galaxies or of the old galaxies, and the dynamical bias becomes important on scales less than 3Mpc/h. The mass density field reconstructed from the velocity field of young galaxies using the POTENT-style method suffers in accuracy both from the spatial bias and the dynamical friction on the smoothing scale of R_s=8Mpc/h. On the other hand, in the case of R_s=12Mpc/h, which is typically adopted in the actual POTENT analysis, the density reconstruction based on various tracers of galaxies is reasonably accurate.Comment: 29 pages, 11 figures, accepted for publication in the Ap

Steady state sedimentation of ultrasoft colloids

The structural and dynamical properties of ultra-soft colloids - star polymers - exposed to a uniform external force field are analyzed applying the multiparticle collision dynamics approach, a hybrid coarse-grain mesoscale simulation approach, which captures thermal fluctuations and long-range hydrodynamic interactions. In the weak field limit, the structure of the star polymer is nearly unchanged, however in an intermediate regime, the radius of gyration decreases, in particular transverse to the sedimentation direction. In the limit of a strong field, the radius of gyration increases with field strength. Correspondingly, the sedimentation coefficient increases with increasing field strength, passes through a maximum and decreases again at high field strengths. The maximum value depends on the functionality of the star polymer. High field strengths lead to symmetry breaking with trailing, strongly stretched polymer arms and a compact star polymer body. In the weak field linear response regime, the sedimentation coefficient follows the scaling relation of a star polymer in terms of functionality and arm length

Equity of Attention: Amortizing Individual Fairness in Rankings

Rankings of people and items are at the heart of selection-making, match-making, and recommender systems, ranging from employment sites to sharing economy platforms. As ranking positions influence the amount of attention the ranked subjects receive, biases in rankings can lead to unfair distribution of opportunities and resources, such as jobs or income. This paper proposes new measures and mechanisms to quantify and mitigate unfairness from a bias inherent to all rankings, namely, the position bias, which leads to disproportionately less attention being paid to low-ranked subjects. Our approach differs from recent fair ranking approaches in two important ways. First, existing works measure unfairness at the level of subject groups while our measures capture unfairness at the level of individual subjects, and as such subsume group unfairness. Second, as no single ranking can achieve individual attention fairness, we propose a novel mechanism that achieves amortized fairness, where attention accumulated across a series of rankings is proportional to accumulated relevance. We formulate the challenge of achieving amortized individual fairness subject to constraints on ranking quality as an online optimization problem and show that it can be solved as an integer linear program. Our experimental evaluation reveals that unfair attention distribution in rankings can be substantial, and demonstrates that our method can improve individual fairness while retaining high ranking quality.Comment: Accepted to SIGIR 201

Free energy and extension of a semiflexible polymer in cylindrical confining geometries

We consider a long, semiflexible polymer, with persistence length $P$ and contour length $L$, fluctuating in a narrow cylindrical channel of diameter $D$. In the regime $D\ll P\ll L$ the free energy of confinement $\Delta F$ and the length of the channel $R_\parallel$ occupied by the polymer are given by Odijk's relations $\Delta F/R_\parallel=A_\circ k_BTP^{-1/3}D^{-2/3}$ and $R_\parallel=L[1-\alpha_\circ(D/P)^{2/3}]$, where $A_\circ$ and $\alpha_\circ$ are dimensionless amplitudes. Using a simulation algorithm inspired by PERM (Pruned Enriched Rosenbluth Method), which yields results for very long polymers, we determine $A_\circ$ and $\alpha_\circ$ and the analogous amplitudes for a channel with a rectangular cross section. For a semiflexible polymer confined to the surface of a cylinder, the corresponding amplitudes are derived with an exact analytic approach. The results are relevant for interpreting experiments on biopolymers in microchannels or microfluidic devices.Comment: 15 pages without figures, 5 figure

Commutators as Powers in Free Products of Groups

The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified.Comment: AMS-LaTex, 6 pages, no figure