FaiREE: Fair Classification with Finite-Sample and Distribution-Free Guarantee

Algorithmic fairness plays an increasingly critical role in machine learning research. Several group fairness notions and algorithms have been proposed. However, the fairness guarantee of existing fair classification methods mainly depends on specific data distributional assumptions, often requiring large sample sizes, and fairness could be violated when there is a modest number of samples, which is often the case in practice. In this paper, we propose FaiREE, a fair classification algorithm that can satisfy group fairness constraints with finite-sample and distribution-free theoretical guarantees. FaiREE can be adapted to satisfy various group fairness notions (e.g., Equality of Opportunity, Equalized Odds, Demographic Parity, etc.) and achieve the optimal accuracy. These theoretical guarantees are further supported by experiments on both synthetic and real data. FaiREE is shown to have favorable performance over state-of-the-art algorithms.Comment: 45 pages, 9 figure

Anderson-Bernoulli Localization On 2d And 3d Lattice

The Anderson model describes the behaviour of electrons inside a piece of metal with uniform impurity.The Anderson-Bernoulli model is a special case of the Anderson model where the potential has Bernoulli distribution. We consider Anderson-Bernoulli localization on d dimensional lattice for d=2,3. For d=2, we prove that, if the potential has symmetric Bernoulli distribution and the disorder is large, then localization happens outside a small neighborhood of finitely many energies. For d=3, we prove that localization happens at the bottom of the spectrum

Spin gap and magnetic resonance in superconducting BaFe1.9_{1.9}Ni%_{0.1}As2_{2}

We use neutron spectroscopy to determine the nature of the magnetic excitations in superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_{c}=20$ K). Above $T_{c}$ the excitations are gapless and centered at the commensurate antiferromagnetic wave vector of the parent compound, while the intensity exhibits a sinusoidal modulation along the c-axis. As the superconducting state is entered a spin gap gradually opens, whose magnitude tracks the $T$-dependence of the superconducting gap observed by angle resolved photoemission. Both the spin gap and magnetic resonance energies are temperature \textit{and} wave vector dependent, but their ratio is the same within uncertainties. These results suggest that the spin resonance is a singlet-triplet excitation related to electron pairing and superconductivity.Comment: 4 pages, 4 figure

Effect of Zn doping on magnetic order and superconductivity in LaFeAsO

We report Zn-doping effect in the parent and F-doped LaFeAsO oxy-arsenides. Slight Zn doping in LaFe$_{1-x}$Zn$_{x}$AsO drastically suppresses the resistivity anomaly around 150 K associated with the antiferromagnetic (AFM) spin density wave (SDW) in the parent compound. The measurements of magnetic susceptibility and thermopower confirm further the effect of Zn doping on AFM order. Meanwhile Zn doping does not affect or even enhances the $T_c$ of LaFe$_{1-x}$Zn$_{x}$AsO$_{0.9}$F$_{0.1}$, in contrast to the effect of Zn doping in high-$T_c$ cuprates. We found that the solubility of Zn content ($x$) is limited to less than 0.1 in both systems and further Zn doping (i.e., $x$ $\geq$ 0.1) causes phase separation. Our study clearly indicates that the non-magnetic impurity of Zn$^{2+}$ ions doped in the Fe$_2$As$_2$ layers affects selectively the AFM order, and superconductivity remains robust against the Zn doping in the F-doped superconductors.Comment: 7 figures, 13 pages; revised version with more dat