Fairness criteria through the lens of directed acyclic graphical models

A substantial portion of the literature on fairness in algorithms proposes, analyzes, and operationalizes simple formulaic criteria for assessing fairness. Two of these criteria, Equalized Odds and Calibration by Group, have gained significant attention for their simplicity and intuitive appeal, but also for their incompatibility. This chapter provides a perspective on the meaning and consequences of these and other fairness criteria using graphical models which reveals Equalized Odds and related criteria to be ultimately misleading. An assessment of various graphical models suggests that fairness criteria should ultimately be case-specific and sensitive to the nature of the information the algorithm processes

A proof‐of‐concept pilot randomized comparative trial of brief Internet‐based compassionate mind training and cognitive‐behavioral therapy for perinatal and intending to become pregnant women

Depression is a prevalent and costly mental health problem that affects women as well as their larger communities, with substantial impacts on mother and infant during childbearing years. Face‐to‐face care has not adequately addressed this global concern due to difficulties in scaling these resources. Internet interventions, which can provide psychological tools to those lacking adequate access, show promise in filling this void. We conducted a 2‐condition proof‐of‐concept pilot randomized trial comparing brief Internet‐based cognitive behavioural therapy (CBT) and brief Internet‐based compassionate mind training (CMT) for women who are currently pregnant, became pregnant within the last year, and intend to become pregnant in the future. We found that, although CMT and CBT demonstrated near equivalence in improving affect, self‐reassurance, self‐criticism, and self‐compassion, CMT showed superiority to CBT in reducing depression and anxiety symptoms. These findings provide a compelling initial argument for the use of CMT as an avenue for addressing problems associated with negative affect. Implications, limitations, and future directions along this line of research will also be discussed.Campus Research Board at Palo Alto University Elton C and Joan R Waelde Meditation Fellowshi

The Panchromatic Hubble Andromeda Treasury II. Tracing the Inner M31 Halo with Blue Horizontal Branch Stars

We attempt to constrain the shape of M31's inner stellar halo by tracing the surface density of blue horizontal branch (BHB) stars at galactocentric distances ranging from 2 kpc to 35 kpc. Our measurements make use of resolved stellar photometry from a section of the Panchromatic Hubble Andromeda Treasury (PHAT) survey, supplemented by several archival Hubble Space Telescope observations. We find that the ratio of BHB to red giant stars is relatively constant outside of 10 kpc, suggesting that the BHB is as reliable a tracer of the halo population as the red giant branch. In the inner halo, we do not expect BHB stars to be produced by the high metallicity bulge and disk, making BHB stars a good candidate to be a reliable tracer of the stellar halo to much smaller galactocentric distances. If we assume a power-law profile r^(-\alpha) for the 2-D projected surface density BHB distribution, we obtain a high-quality fit with a 2-D power-law index of \alpha=2.6^{+0.3}_{-0.2} outside of 3 kpc, which flattens to \alpha<1.2 inside of 3 kpc. This slope is consistent with previous measurements but is anchored to a radial baseline that extends much farther inward. Finally, assuming azimuthal symmetry and a constant mass-to-light ratio, the best-fitting profile yields a total halo stellar mass of 2.1^{+1.7}_{-0.4} x 10^9 M_sun. These properties are comparable with both simulations of stellar halo formation formed by satellite disruption alone, and with simulations that include some in situ formation of halo stars.Comment: 15 pages, 1 table, 5 figures, accepted for publication in Ap