Related papers: The CS decomposition and conditional negative corr…
The standard formulation of quantum theory assumes that events are ordered is a background global causal structure. Recently in Ref.[$\href{http://www.nature.com/ncomms/journal/v3/n10/full/ncomms2076.html}{Nat. Commun. {\bf3}, 1092…
Causal decomposition has provided a powerful tool to analyze health disparity problems, by assessing the proportion of disparity caused by each mediator. However, most of these methods lack \emph{policy implications}, as they fail to…
Conformal prediction (CP) offers distribution-free uncertainty quantification for machine learning models, yet its interplay with fairness in downstream decision-making remains underexplored. Moving beyond CP as a standalone operation…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
Causal decomposition analysis (CDA) is an approach for modeling the impact of hypothetical interventions to reduce disparities. It is useful for identifying foci that future interventions, including multilevel and multimodal interventions,…
In distributed multi-agent systems, correctness is often entangled with operational policies such as scheduling, batching, or routing, which makes systems brittle since performance-driven policy evolution may break integrity guarantees.…
For a measure preserving dynamical system $(\mathcal{X},f, \mu)$, we consider the time series of maxima $M_n=\max\{X_1,\ldots,X_n\}$ associated to the process $X_n=\phi(f^{n-1}(x))$ generated by the dynamical system for some observable…
Classical correlations without predefined causal order arise from processes where parties manipulate random variables, and where the order of these interactions is not predefined. No assumption on the causal order of the parties is made,…
Deep learning based image compressed sensing (CS) has achieved great success. However, existing CS systems mainly adopt a fixed measurement matrix to images, ignoring the fact the optimal measurement numbers and bases are different for…
When a financial institution declines an application for credit, an adverse action (AA) is said to occur. The applicant is then entitled to an explanation for the negative decision. This paper focuses on credit decisions based on a…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
Causal inference is fundamental across scientific disciplines, yet existing methods struggle to capture instantaneous, time-evolving causal relationships in complex, high-dimensional systems. In this paper, assimilative causal inference…
A new determinant inequality of positive semidefinite matrices is discovered and proved by us. This new inequality is useful for attacking and solving a variety of optimization problems arising from the design of wireless communication…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
Aligning the decision-making process of machine learning algorithms with that of experienced radiologists is crucial for reliable diagnosis. While existing methods have attempted to align their diagnosis behaviors to those of radiologists…
Suppose we want to build a system that answers a natural language question by representing its semantics as a logical form and computing the answer given a structured database of facts. The core part of such a system is the semantic parser…
Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. In this paper, we study the limiting process of L-ensembles based on…
Conformal prediction (CP) is widely presented as distribution-free predictive inference with finite-sample marginal coverage under exchangeability. We argue that CP is best understood as a rank-calibrated descendant of the…