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Income and wealth allocation are foundational components of how economies operate. These are complex distributions, and it is hard to get a real sense for their dynamics using simplifications like average or median. One metric that…
We give the first sample complexity characterizations for outcome indistinguishability, a theoretical framework of machine learning recently introduced by Dwork, Kim, Reingold, Rothblum, and Yona (STOC 2021). In outcome…
This paper identifies the salient factors that characterize the inequality income distribution for Romania. Data analysis is rigorously carried out using sophisticated techniques borrowed from classical statistics (Theil). Decomposition of…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…
A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…
The ability to quantify distinctness of a cluster structure is fundamental for certain simulation studies, in particular for those comparing performance of different classification algorithms. The intrinsic integral measure based on the…
With the growing use of ML in highly consequential domains, quantifying disparity with respect to protected attributes, e.g., gender, race, etc., is important. While quantifying disparity is essential, sometimes the needs of an occupation…
Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…
In the spirit of recent asymptotic works on the General Poverty Index (GPI) in the field of Welfare Analysis, the asymptotic representation of the non-decomposable Takayama's index, which has failed to be incorporated in the unified GPI…
Many researchers have identified distribution shift as a likely contributor to the reproducibility crisis in behavioral and biomedical sciences. The idea is that if treatment effects vary across individual characteristics and experimental…
In this paper, I study the nonparametric identification and estimation of the marginal effect of an endogenous variable $X$ on the outcome variable $Y$, given a potentially mismeasured instrument variable $W^*$, without assuming linearity…
We propose a framework to analyze how multivariate representations disentangle ground-truth generative factors. A quantitative analysis of disentanglement has been based on metrics designed to compare how one variable explains each…
Recent years have seen growing interest in learning disentangled representations, in which distinct features, such as size or shape, are represented by distinct neurons. Quantifying the extent to which a given representation is disentangled…
In this paper, we extend the framework of Brezis--Van Schaftingen--Yung type inequalities in metric measure spaces by exploring several novel directions. First, we establish finite difference characterizations and fractional Sobolev-type…
This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and M\"obius inversion, where algebraic identities are realised by taking homotopy cardinality of equivalences…
We present a conceptual model to measure disparity--the target study--where social groups may be similarly situated (i.e., balanced) on allowable covariates. Our model, based on a sampling design, does not intervene to assign social group…
We set in this paper a coherent theory based on functional empirical processes to consider both the poverty and the inequality indices in one Gaussian field enabling to study the influence of the one on the other. We use the General Poverty…
The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or…
This note records a common threshold/surplus decomposition for single-threshold stopping rules in the classical prophet inequality. The same decomposition is used to certify several deterministic thresholds, including the median, half-mean,…