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In this paper we consider the problem of combining multiple probabilistic causal models, provided by different experts, under the requirement that the aggregated model satisfy the criterion of counterfactual fairness. We build upon the work…
Composites are amongst the most important materials manufactured today, as evidenced by their use in countless applications. In order to establish the suitability of composites in specific applications, finite element (FE) modelling, a…
We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros
It is frequently possible to produce new Calabi-Yau threefolds from old ones by a process of allowing the complex structure to degenerate to a singular one, and then performing a resolution of singularities. (Some care is needed to ensure…
In this paper we propose a hypothesis about how different uses of maintaining dragging, either as a physical tool in a dynamic geometry environment or as a psychological tool for generating conjectures can influence subsequent processes of…
Combining evidence from different sources can be achieved with Bayesian or Dempster-Shafer methods. The first requires an estimate of the priors and likelihoods while the second only needs an estimate of the posterior probabilities and…
This is a technical report, containing all the theorem proofs in paper "Link Identifiability in Communication Networks with Two Monitors" by Liang Ma, Ting He, Kin K. Leung, Ananthram Swami, and Don Towsley, published in IEEE Globecom,…
This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy…
Here we prove some conjectures on the monotony of combinatorial sequences from the recent preprint of Zhi--Wei Sun.
Gallai's path decomposition conjecture states that the edges of any connected graph on n vertices can be decomposed into at most (n+1)/2 paths. We confirm that conjecture for all graphs with maximum degree at most five.
We study fairness in Machine Learning (FairML) through the lens of attribute-based explanations generated for machine learning models. Our hypothesis is: Biased Models have Biased Explanations. To establish that, we first translate existing…
Unobserved confounding is a major hurdle for causal inference from observational data. Confounders---the variables that affect both the causes and the outcome---induce spurious non-causal correlations between the two. Wang & Blei (2018)…
This note has been updated (April, 2020) to respond to "Towards Clarifying the Theory of the Deconfounder" by Yixin Wang, David M. Blei (arXiv:2003.04948). This original note, posted in January, 2020, is meant to complement our previous…
With the advent of online networks, societies are substantially more connected with individual members able to easily modify and maintain their own social links. Here, we show that active network maintenance exposes agents to confirmation…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…
Vision-language models can encode societal biases and stereotypes, but there are challenges to measuring and mitigating these multimodal harms due to lacking measurement robustness and feature degradation. To address these challenges, we…
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
This article is a survey about applications of bi-quantization theory in Lie theory. We focus on a conjecture of M. Duflo. Most of the applications are coming from our article with Alberto Cattaneo and some extensions are relating…
In 1993 Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank $1$ boolean intervals whose minimal faces together form a subcomplex. Stanley further conjectured that…