Search

Conditional demographic parity (CDP) is a measure of the demographic parity of a predictive model or decision process when conditioning on an additional feature or set of features. Many algorithmic fairness techniques exist to target demographic parity, but CDP is much harder to achieve, particularly when the conditioning variable has many levels and/or when the model outputs are continuous. The problem of auditing and enforcing CDP is understudied in the literature. In light of this, we propose novel measures of {conditional demographic disparity (CDD)} which rely on statistical distances borrowed from the optimal transport literature. We further design and evaluate regularization-based approaches based on these CDD measures. Our methods, \fairbit{} and \fairlp{}, allow us to target CDP even when the conditioning variable has many levels. When model outputs are continuous, our methods target full equality of the conditional distributions, unlike other methods that only consider first moments or related proxy quantities. We validate the efficacy of our approaches on real-world datasets.

In this paper we introduce the John-Nirenberg's type spaces $\text{JN}_p$ associated with the Gaussian measure $d\gamma(x) = \pi^{-d/2}e^{-|x|^2}dx$ in $\mathbb{R}^d$ where $1

We propose a test of the significance of a variable appearing on the Lasso path and use it in a procedure for selecting one of the models of the Lasso path, controlling the Family-Wise Error Rate. Our null hypothesis depends on a set A of already selected variables and states that it contains all the active variables. We focus on the regularization parameter value from which a first variable outside A is selected. As the test statistic, we use this quantity's conditional p-value, which we define conditional on the non-penalized estimated coefficients of the model restricted to A. We estimate this by simulating outcome vectors and then calibrating them on the observed outcome's estimated coefficients. We adapt the calibration heuristically to the case of generalized linear models in which it turns into an iterative stochastic procedure. We prove that the test controls the risk of selecting a false positive in linear models, both under the null hypothesis and, under a correlation condition, when A does not contain all active variables. We assess the performance of our procedure through extensive simulation studies. We also illustrate it in the detection of exposures associated with drug-induced liver injuries in the French pharmacovigilance database.

We present an analysis of the galaxy merger rate in the redshift range $4.0

We report measurements of the galaxy two-point correlation function at cosmic dawn, using photometrically-selected sources from the JWST Advanced Deep Extragalactic Survey (JADES). The JWST/NIRCam dataset comprises approximately $N_g \simeq 7000$ photometrically-selected Lyman Break Galaxies (LBGs), spanning in the redshift range $5\leq z<11$. The primary objective of this study is to extend clustering measurements beyond redshift $z>10$, finding a galaxy bias $b=9.6\pm1.7$ for the sample at $\overline{z} = 10.6$. The result suggests that the observed sources are hosted by dark matter halos of approximately $M_{h}\sim 10^{10.6}~\mathrm{M_{\odot}}$, in broad agreement with theoretical and numerical modelling of early galaxy formation during the epoch of reionization. Furthermore, the JWST JADES dataset enables an unprecedented investigation of clustering of dwarf galaxies two orders of magnitude fainter than the characteristic $L_*$ luminosity (i.e. with $M_{F200W}\simeq-15.8$) during the late stages of the epoch of reionization at $z\sim 6$. By analyzing clustering as a function of luminosity, we find that $b(M_{F200W})$ aligns with previous results for brighter galaxies and then decreases with $M_{F200W}$, as theoretically expected for fainter candidates. These initial results demonstrate the potential for further quantitative characterisation of the interplay between assembly of dark matter and light during cosmic dawn that the growing samples of JWST observations are enabling., Comment: MNRAS accepted; 8 pages, 4 figures

We will show that, contrary to the behavior of the higher order Riesz transforms studied so far on the atomic Hardy space $\mathcal{H}^1(\mathbb R^n, \gamma)$, associated with the Ornstein-Uhlenbeck operator with respect to the $n$-dimensional Gaussian measure $\gamma$, the new Gaussian Riesz transforms are bounded from $\mathcal{H}^1(\mathbb R^n, \gamma)$ to $L^1(\mathbb R^n, \gamma)$, for any order and dimension $n$. We will also prove that the classical Gaussian Riesz transforms of higher order are bounded from an adequate subspace of $\mathcal{H}^1(\mathbb R^n, \gamma)$ into $L^1(\mathbb R^n, \gamma)$, extending Bruno's result (J. Fourier Anal. Appl. 25, 4 (2019), 1609--1631) for the first order case., Comment: 15 pages

Synthetic data has made tremendous strides in various commercial settings including finance, healthcare, and virtual reality. We present a broad overview of prototypical applications of synthetic data in the financial sector and in particular provide richer details for a few select ones. These cover a wide variety of data modalities including tabular, time-series, event-series, and unstructured arising from both markets and retail financial applications. Since finance is a highly regulated industry, synthetic data is a potential approach for dealing with issues related to privacy, fairness, and explainability. Various metrics are utilized in evaluating the quality and effectiveness of our approaches in these applications. We conclude with open directions in synthetic data in the context of the financial domain., Comment: 50 pages, journal submission; updated 6 privacy levels

We present a novel approach for measuring the two-point correlation function of galaxies in narrow pencil beam surveys with varying depths. Our methodology is utilized to expand high-redshift galaxy clustering investigations up to $z \sim 8$ by analyzing a comprehensive sample consisting of $N_g = 160$ Lyman break galaxy candidates obtained through optical and near-infrared photometric data within the CANDELS GOODS datasets from the Hubble Space Telescope Legacy Fields. For bright sources with $M_{UV} < -19.8$, we determine a galaxy bias of $b = 9.33\pm4.90$ at $\overline{z} = 7.7$ and a correlation length of $r_0 = 10.74\pm7.06$ $h^{-1}Mpc$. We obtain similar results for the XDF, with a galaxy bias measurement of $b = 8.26\pm3.41$ at the same redshift for a slightly fainter sample with a median luminosity of $M_{UV} = -18.4$. By comparing with dark-matter halo bias and employing abundance matching, we deduce a characteristic halo mass of $M_h \sim 10^{11.5} M_{\odot}$ and a duty cycle close to unity. To validate our approach for variable-depth datasets, we replicate the analysis in a region with near-uniform depth using a standard two-point correlation function estimator, yielding consistent outcomes. Our study not only provides a valuable tool for future utilization in JWST datasets but also suggests that the clustering of early galaxies continues to increase with redshift beyond $z \gtrsim 8$, potentially contributing to the existence of protocluster structures observed in early JWST imaging and spectroscopic surveys at $z \gtrsim 8$.

We construct indefinite Einstein solvmanifolds that are standard, but not of pseudo-Iwasawa type. Thus, the underlying Lie algebras take the form $\mathfrak{g}\rtimes_D\mathbb{R}$, where $\mathfrak{g}$ is a nilpotent Lie algebra and $D$ is a nonsymmetric derivation. Considering nonsymmetric derivations has the consequence that $\mathfrak{g}$ is not a nilsoliton, but satisfies a more general condition. Our construction is based on the notion of nondiagonal triple on a nice diagram. We present an algorithm to classify nondiagonal triples and the associated Einstein metrics. With the use of a computer, we obtain all solutions up to dimension $5$, and all solutions in dimension $\leq9$ that satisfy an additional technical restriction. By comparing curvatures, we show that the Einstein solvmanifolds of dimension $\leq 5$ that we obtain by our construction are not isometric to a standard extension of a nilsoliton., Comment: 23 pages, 1 figure, 1 ancillary file. Presentation improved and bibliography updated

Data distillation and coresets have emerged as popular approaches to generate a smaller representative set of samples for downstream learning tasks to handle large-scale datasets. At the same time, machine learning is being increasingly applied to decision-making processes at a societal level, making it imperative for modelers to address inherent biases towards subgroups present in the data. While current approaches focus on creating fair synthetic representative samples by optimizing local properties relative to the original samples, their impact on downstream learning processes has yet to be explored. In this work, we present fair Wasserstein coresets (FWC), a novel coreset approach which generates fair synthetic representative samples along with sample-level weights to be used in downstream learning tasks. FWC uses an efficient majority minimization algorithm to minimize the Wasserstein distance between the original dataset and the weighted synthetic samples while enforcing demographic parity. We show that an unconstrained version of FWC is equivalent to Lloyd's algorithm for k-medians and k-means clustering. Experiments conducted on both synthetic and real datasets show that FWC: (i) achieves a competitive fairness-utility tradeoff in downstream models compared to existing approaches, (ii) improves downstream fairness when added to the existing training data and (iii) can be used to reduce biases in predictions from large language models (GPT-3.5 and GPT-4)., Comment: Accepted at NeurIPS 2024, 30 pages, 7 figures, 8 tables

Recent years have seen a surge of machine learning approaches aimed at reducing disparities in model outputs across different subgroups. In many settings, training data may be used in multiple downstream applications by different users, which means it may be most effective to intervene on the training data itself. In this work, we present FairWASP, a novel pre-processing approach designed to reduce disparities in classification datasets without modifying the original data. FairWASP returns sample-level weights such that the reweighted dataset minimizes the Wasserstein distance to the original dataset while satisfying (an empirical version of) demographic parity, a popular fairness criterion. We show theoretically that integer weights are optimal, which means our method can be equivalently understood as duplicating or eliminating samples. FairWASP can therefore be used to construct datasets which can be fed into any classification method, not just methods which accept sample weights. Our work is based on reformulating the pre-processing task as a large-scale mixed-integer program (MIP), for which we propose a highly efficient algorithm based on the cutting plane method. Experiments demonstrate that our proposed optimization algorithm significantly outperforms state-of-the-art commercial solvers in solving both the MIP and its linear program relaxation. Further experiments highlight the competitive performance of FairWASP in reducing disparities while preserving accuracy in downstream classification settings., Comment: AAAI 2024, 15 pages, 4 figures, 1 table

We represent by $\{W_{\lambda, t}^\alpha\}_{t>0}$ the semigroup generated by $-\mathbb L^{\alpha}_\lambda$, where $\mathbb L^{\alpha}_\lambda$ is a Hardy operator on a half space. The operator $\mathbb L^{\alpha}_\lambda$ includes a fractional Laplacian and it is defined by \[\mathbb L^{\alpha}_\lambda=(-\Delta)^{\alpha/2}_{\mathbb{R}^d_+}+\lambda x_d^{-\alpha}, \quad \alpha\in (0,2], \lambda \geq 0.\] We prove that, for every $k\in \mathbb N$, the $\rho$-variation operator $\mathcal{V}_\rho\left(\left\{t^k\partial_t^k W_{\lambda,t}^\alpha\right\}\right)$ is bounded on $L^p(\mathbb{R}^d_+, w)$ for each $1

The Sendov conjecture asserts that if $p(z) = \prod_{j=1}^{N}(z-z_j)$ is a polynomial with zeros $|z_j| \leq 1$, then each disk $|z-z_j| \leq 1$ contains a zero of $p'$. Our purpose is the following: Given a zero $z_j$ of order $n \geq 2$, determine whether there exists $\zeta \not= z_j$ such that $p'(\zeta) = 0$ and $|z_j - \zeta| \leq 1$. In this paper we present some partial results on the problem., Comment: Annales Polonici Mathematici, 2023

This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process follows that of a Gaussian mixture, DGMEs are capable of approximating complex probability distributions, such as heavy-tailed or multimodal distributions. Our contributions include the derivation of an expectation-maximization (EM) algorithm used for learning the model parameters, which results in an upper-bound on the log-likelihood of training data over that of standard deep ensembles. Additionally, the proposed EM training procedure allows for learning of mixture weights, which is not commonly done in ensembles. Our experimental results demonstrate that DGMEs outperform state-of-the-art uncertainty quantifying deep learning models in handling complex predictive densities., Comment: Accepted at Uncertainty in Artificial Intelligence (UAI) 2023 Conference, 7 figures, 11 tables

JWST observations confirm the existence of galaxies as early as 300Myr and at a higher number density than expected based on galaxy formation models and HST observations. Yet, sources confirmed spectroscopically in the first 500Myr have estimated stellar masses $<5\times10^8M_\odot$, limiting the signal to noise ratio (SNR) for investigating substructure. We present a high-resolution spectroscopic and spatially resolved study of a rare bright galaxy at $z=9.3127\pm0.0002$ with a stellar mass of $(2.5^{+0.7}_{-0.5})\times10^9M_\odot$, forming $25^{+3}_{-4}M_\odot/yr$ and with a metallicity of $\sim0.1Z_\odot$- lower than in the local universe for the stellar mass but in line with expectations of chemical enrichment in galaxies 1-2Gyr after the Big Bang. The system has a morphology typically associated to two interacting galaxies, with a two-component main clump of very young stars (age$<10$Myr) surrounded by an extended stellar population ($130\pm20$Myr old, identified by modeling the NIRSpec spectrum) and an elongated clumpy tidal tail. The spectroscopic observations identify O, Ne and H emission lines, and the Lyman break, where there is evidence of substantial Ly$\alpha$ absorption. The [OII] doublet is resolved spectrally, enabling an estimate of the electron number density and ionization parameter of the interstellar medium and showing higher densities and ionization than in lower redshift analogs. For the first time at $z>8$, we identify evidence of absorption lines (Si, C and Fe), with low confidence individual detections but SNR$>6$ when stacked. The absorption features suggest that Ly$\alpha$ is damped by the interstellar and circumgalactic medium. Our observations provide evidence of rapid efficient build-up of mass and metals in the immediate aftermath of the Big Bang through mergers, demonstrating that massive galaxies with several billion stars exist earlier than expected., Comment: 52 pages, 10 figures This version of the article has been accepted for publication, after peer review and is subject to Springer Nature's AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1038/s41550-024-02218-7

Let $f$ be a nonnegative function of class $C^k$ ($k \geq 2$) such that $f^{(k)}$ is H\''older continuous with exponent $\alpha$ in $(0,1]$. If $f'(x) = \cdots = f^{(k)}(x) = 0$ when $f(x) = 0$, we show that $f^{\mu}$ is differentiable for $\mu \in (1/(k+\alpha), 1)$ and under an additional condition we show that $(f^\mu)'$ is H\''older continuous with exponent $\beta = \mu(1+\alpha) - 1$ (if $\beta \leq 1$) at $x \in [0,T]$ when $f(x) = 0$. $(f^\mu)'$ is Lipschitz continuous at $x$ if $f(x) > 0$.

In this paper we introduce spaces of $\textup{BLO}$-type related to Laguerre polynomial expansions. We consider the probability measure on $(0,\infty)$ defined by $d\gamma_\alpha(x)=\frac{2}{\Gamma(\alpha+1)}e^{-x^2}x^{2\alpha+1}dx$ with $\alpha>-\frac12$. For every $a>0$, the space $\textup{BLO}_a((0,\infty),\gamma_\alpha)$ consists of all those measurable functions defined on $(0,\infty)$ having bounded lower oscillation with respect to $\gamma_\alpha$ over an admissible family $\mathcal{B}_a$ of intervals in $(0,\infty)$. The space $\textup{BLO}_a((0,\infty),\gamma_\alpha)$ is a subspace of the space $\textup{BMO}_a((0,\infty),\gamma_\alpha)$ of bounded mean oscillation functions with respect to $\gamma_\alpha$ and $\mathcal{B}_a$. The natural $a$-local centered maximal function defined by $\gamma_\alpha$ is bounded from $\textup{BMO}_a((0,\infty),\gamma_\alpha)$ into $\textup{BLO}_a((0,\infty),\gamma_\alpha)$. We prove that the maximal operator, the $\rho$-variation and the oscillation operators associated with local truncations of the Riesz transforms in the Laguerre setting are bounded from $L^\infty((0,\infty),\gamma_\alpha)$ into $\textup{BLO}_a((0,\infty),\gamma_\alpha)$. Also, we obtain a similar result for the maximal operator of local truncations for spectral Laplace transform type multipliers.

Hawkes processes have recently risen to the forefront of tools when it comes to modeling and generating sequential events data. Multidimensional Hawkes processes model both the self and cross-excitation between different types of events and have been applied successfully in various domain such as finance, epidemiology and personalized recommendations, among others. In this work we present an adaptation of the Frank-Wolfe algorithm for learning multidimensional Hawkes processes. Experimental results show that our approach has better or on par accuracy in terms of parameter estimation than other first order methods, while enjoying a significantly faster runtime., Comment: Presented at the NeurIPS 2022 Workshop on Synthetic Data for Empowering ML Research. 9 pages, 3 figures, 4 tables

In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),\gamma_\alpha)$ to $L^1((0,\infty),\gamma_\alpha)$ and also from $L^\infty((0,\infty),\gamma_\alpha)$ to $\BMO((0,\infty),\gamma_\alpha)$, with respect to the probability measure $d\gamma_\alpha (x)=\frac{2}{\Gamma(\alpha+1)} x^{2\alpha+1} e^{-x^2} dx$ on $(0,\infty)$ when ${\alpha>-\frac12}$. We shall apply it to establish endpoint estimates for Riesz transforms, maximal operators, Littlewood-Paley functions, multipliers of Laplace transform type, fractional integrals and variation operators in the Laguerre setting., Comment: 22 pages

Online learning of Hawkes processes has received increasing attention in the last couple of years especially for modeling a network of actors. However, these works typically either model the rich interaction between the events or the latent cluster of the actors or the network structure between the actors. We propose to model the latent structure of the network of actors as well as their rich interaction across events for real-world settings of medical and financial applications. Experimental results on both synthetic and real-world data showcase the efficacy of our approach., Comment: 12 pages, 6 figures, 3 tables

In this paper we introduce the atomic Hardy space $\mathcal{H}^1((0,\infty),\gamma_\alpha)$ associated with the non-doubling probability measure $d\gamma_\alpha(x)=\frac{2x^{2\alpha+1}}{\Gamma(\alpha+1)}e^{-x^2}dx$ on $(0,\infty)$, for ${\alpha>-\frac12}$. We obtain characterizations of $\mathcal{H}^1((0,\infty),\gamma_\alpha)$ by using two local maximal functions. We also prove that the truncated maximal function defined through the heat semigroup generated by the Laguerre differential operator is bounded from $\mathcal{H}^1((0,\infty),\gamma_\alpha)$ into $L^1((0,\infty),\gamma_\alpha)$., Comment: 27 pages

Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as sample complexity for learning the parameters and releasing differentially private versions, are yet to be thoroughly analyzed. In this work, we study standard Hawkes processes with background intensity $\mu$ and excitation function $\alpha e^{-\beta t}$. We provide both non-private and differentially private estimators of $\mu$ and $\alpha$, and obtain sample complexity results in both settings to quantify the cost of privacy. Our analysis exploits the strong mixing property of Hawkes processes and classical central limit theorem results for weakly dependent random variables. We validate our theoretical findings on both synthetic and real datasets., Comment: 30 pages, 4 figures

The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $2n+3$, which are in one-to-one correspondence with pseudo-K\"ahler nilpotent Lie algebras of dimension $2n$ endowed with a compatible derivation, in a suitable sense. We characterize the pseudo-K\"ahler structures and derivations giving rise to Sasaki-Einstein metrics. We classify $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $\leq 7$ and those whose pseudo-K\"ahler reduction is an abelian Lie algebra. The Einstein metrics we obtain are standard, but not of pseudo-Iwasawa type., Comment: 26 pages, 2 figures; v2: corrected Proposition 4.3 and Theorem 4.4 to account for the sign ambiguity; v3: improved notation and presentation; introduction and Section 1 expanded to illustrate the geometric meaning of the construction; Examples 3.9 and 4.6 expanded; title changed for clarity; added Example 2.6 and two figures

Because geostationary satellite (Geo) imagery provides a high temporal resolution window into tropical cyclone (TC) behavior, we investigate the viability of its application to short-term probabilistic forecasts of TC convective structure to subsequently predict TC intensity. Here, we present a prototype model which is trained solely on two inputs: Geo infrared imagery leading up to the synoptic time of interest and intensity estimates up to 6 hours prior to that time. To estimate future TC structure, we compute cloud-top temperature radial profiles from infrared imagery and then simulate the evolution of an ensemble of those profiles over the subsequent 12 hours by applying a Deep Autoregressive Generative Model (PixelSNAIL). To forecast TC intensities at hours 6 and 12, we input operational intensity estimates up to the current time (0 h) and simulated future radial profiles up to +12 h into a ``nowcasting'' convolutional neural network. We limit our inputs to demonstrate the viability of our approach and to enable quantification of value added by the observed and simulated future radial profiles beyond operational intensity estimates alone. Our prototype model achieves a marginally higher error than the National Hurricane Center's official forecasts despite excluding environmental factors, such as vertical wind shear and sea surface temperature. We also demonstrate that it is possible to reasonably predict short-term evolution of TC convective structure via radial profiles from Geo infrared imagery, resulting in interpretable structural forecasts that may be valuable for TC operational guidance.

We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-K\"ahler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension $5$ and those of dimension $7$ whose K\"ahler reduction in the above sense is abelian., Comment: 25 pages, 1 table. v2: corrected the Lie algebras appearing in Theorem 5.7 and Table 1; added Remark 5.9 concerning isomorphisms between Lie algebras in Table 1; typos corrected; presentation improved