The invisible power of fairness. How machine learning shapes democracy

Many machine learning systems make extensive use of large amounts of data regarding human behaviors. Several researchers have found various discriminatory practices related to the use of human-related machine learning systems, for example in the field of criminal justice, credit scoring and advertising. Fair machine learning is therefore emerging as a new field of study to mitigate biases that are inadvertently incorporated into algorithms. Data scientists and computer engineers are making various efforts to provide definitions of fairness. In this paper, we provide an overview of the most widespread definitions of fairness in the field of machine learning, arguing that the ideas highlighting each formalization are closely related to different ideas of justice and to different interpretations of democracy embedded in our culture. This work intends to analyze the definitions of fairness that have been proposed to date to interpret the underlying criteria and to relate them to different ideas of democracy.Comment: 12 pages, 1 figure, preprint version, submitted to The 32nd Canadian Conference on Artificial Intelligence that will take place in Kingston, Ontario, May 28 to May 31, 201

Three-dimensional carrier-dynamics simulation of terahertz emission from photoconductive switches

A semi-classical Monte Carlo model for studying three-dimensional carrier dynamics in photoconductive switches is presented. The model was used to simulate the process of photoexcitation in GaAs-based photoconductive antennas illuminated with pulses typical of mode-locked Ti:Sapphire lasers. We analyzed the power and frequency bandwidth of THz radiation emitted from these devices as a function of bias voltage, pump pulse duration and pump pulse location. We show that the mechanisms limiting the THz power emitted from photoconductive switches fall into two regimes: when illuminated with short duration (<40 fs) laser pulses the energy distribution of the Gaussian pulses constrains the emitted power, while for long (>40 fs) pulses, screening is the primary power-limiting mechanism. A discussion of the dynamics of bias field screening in the gap region is presented. The emitted terahertz power was found to be enhanced when the exciting laser pulse was in close proximity to the anode of the photoconductive emitter, in agreement with experimental results. We show that this enhancement arises from the electric field distribution within the emitter combined with a difference in the mobilities of electrons and holes.Comment: 7 pages, 7 figure

On the Number of Iterations for Dantzig-Wolfe Optimization and Packing-Covering Approximation Algorithms

We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$ variables, with high probability, any such algorithm requires $\Omega(\rho \log(m)/\epsilon^2)$ iterations to compute a $(1+\epsilon)$-approximate solution, where $\rho$ is the width of the input. The bound is tight for a range of the parameters $(m,n,\rho,\epsilon)$. The algorithms in the class include Dantzig-Wolfe decomposition, Benders' decomposition, Lagrangean relaxation as developed by Held and Karp [1971] for lower-bounding TSP, and many others (e.g. by Plotkin, Shmoys, and Tardos [1988] and Grigoriadis and Khachiyan [1996]). To prove the bound, we use a discrepancy argument to show an analogous lower bound on the support size of $(1+\epsilon)$-approximate mixed strategies for random two-player zero-sum 0/1-matrix games

The elusive old population of the dwarf spheroidal galaxy Leo I

We report the discovery of a significant old population in the dwarf spheroidal (dSph) galaxy Leo I as a result of a wide-area search with the ESO New Technology Telescope. Studies of the stellar content of Local Group dwarf galaxies have shown the presence of an old stellar population in almost all of the dwarf spheroidals. The only exception was Leo I, which alone appeared to have delayed its initial star formation episode until just a few Gyr ago. The color-magnitude diagram of Leo I now reveals an extended horizontal branch, unambiguously indicating the presence of an old, metal-poor population in the outer regions of this galaxy. Yet we find little evidence for a stellar population gradient, at least outside R > 2' (0.16 kpc), since the old horizontal branch stars of Leo I are radially distributed as their more numerous intermediate-age helium-burning counterparts. The discovery of a definitely old population in the predominantly young dwarf spheroidal galaxy Leo I points to a sharply defined first epoch of star formation common to all of the Local Group dSph's as well as to the halo of the Milky Way.Comment: 4 pages, 3 postscript figures, uses apjfonts.sty, emulateapj.sty. Accepted for publication in ApJ Letter

NiO: Correlated Bandstructure of a Charge-Transfer Insulator

The bandstructure of the prototypical charge-transfer insulator NiO is computed by using a combination of an {\it ab initio} bandstructure method and the dynamical mean-field theory with a quantum Monte-Carlo impurity solver. Employing a Hamiltonian which includes both Ni-d and O-p orbitals we find excellent agreement with the energy bands determined from angle-resolved photoemission spectroscopy. This solves a long-standing problem in solid state theory. Most notably we obtain the low-energy Zhang-Rice bands with strongly k-dependent orbital character discussed previously in the context of low-energy model theories.Comment: 4 pages, 3 figur

Using state space differential geometry for nonlinear blind source separation

Given a time series of multicomponent measurements of an evolving stimulus, nonlinear blind source separation (BSS) seeks to find a "source" time series, comprised of statistically independent combinations of the measured components. In this paper, we seek a source time series with local velocity cross correlations that vanish everywhere in stimulus state space. However, in an earlier paper the local velocity correlation matrix was shown to constitute a metric on state space. Therefore, nonlinear BSS maps onto a problem of differential geometry: given the metric observed in the measurement coordinate system, find another coordinate system in which the metric is diagonal everywhere. We show how to determine if the observed data are separable in this way, and, if they are, we show how to construct the required transformation to the source coordinate system, which is essentially unique except for an unknown rotation that can be found by applying the methods of linear BSS. Thus, the proposed technique solves nonlinear BSS in many situations or, at least, reduces it to linear BSS, without the use of probabilistic, parametric, or iterative procedures. This paper also describes a generalization of this methodology that performs nonlinear independent subspace separation. In every case, the resulting decomposition of the observed data is an intrinsic property of the stimulus' evolution in the sense that it does not depend on the way the observer chooses to view it (e.g., the choice of the observing machine's sensors). In other words, the decomposition is a property of the evolution of the "real" stimulus that is "out there" broadcasting energy to the observer. The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see http://www.geocities.com/dlevin2001/ . New version is identical to original version except for URL in the bylin

Normalized power priors always discount historical data

Power priors are used for incorporating historical data in Bayesian analyses by taking the likelihood of the historical data raised to the power α as the prior distribution for the model parameters. The power parameter α is typically unknown and assigned a prior distribution, most commonly a beta distribution. Here, we give a novel theoretical result on the resulting marginal posterior distribution of α in case of the normal and binomial model. Counterintuitively, when the current data perfectly mirror the historical data and the sample sizes from both data sets become arbitrarily large, the marginal posterior of α does not converge to a point mass at α=1 but approaches a distribution that hardly differs from the prior. The result implies that a complete pooling of historical and current data is impossible if a power prior with beta prior for α is used

Atomic and itinerant effects at the transition metal x-ray absorption K-pre-edge exemplified in the case of V2_2O3_3

X-ray absorption spectroscopy is a well established tool for obtaining information about orbital and spin degrees of freedom in transition metal- and rare earth-compounds. For this purpose usually the dipole transitions of the L- (2p to 3d) and M- (3d to 4f) edges are employed, whereas higher order transitions such as quadrupolar 1s to 3d in the K-edge are rarely studied in that respect. This is due to the fact that usually such quadrupolar transitions are overshadowed by dipole allowed 1s to 4p transitions and, hence, are visible only as minor features in the pre-edge region. Nonetheless, these features carry a lot of valuable information, similar to the dipole L-edge transition, which is not accessible in experiments under pressure due to the absorption of the diamond anvil pressurecell. We recently performed a theoretical and experimental analysis of such a situation for the metal insulator transition of (V(1-x)Crx)2O3. Since the importance of the orbital degrees of freedom in this transition is widely accepted, a thorough understanding of quadrupole transitions of the vanadium K-pre-edge provides crucial information about the underlying physics. Moreover, the lack of inversion symetry at the vanadium site leads to onsite mixing of vanadium 3d- and 4p- states and related quantum mechanical interferences between dipole and quadrupole transitions. Here we present a theoretical analysis of experimental high resolution x-ray absorption spectroscopy at the V pre-K edge measured in partial fluorescence yield mode for single crystals. We carried out density functional as well as configuration interaction calculations in order to capture effects coming from both, itinerant and atomic limits

First principles investigations of the electronic, magnetic and chemical bonding properties of CeTSn (T=Rh,Ru)

The electronic structures of CeRhSn and CeRuSn are self-consistently calculated within density functional theory using the local spin density approximation for exchange and correlation. In agreement with experimental findings, the analyses of the electronic structures and of the chemical bonding properties point to the absence of magnetization within the mixed valent Rh based system while a finite magnetic moment is observed for trivalent cerium within the Ru-based stannide, which contains both trivalent and intermediate valent Ce.Comment: 6 pages, 7 figures, for more information see http://www.physik.uni-augsburg.de/~eyert