A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We establish that over a C^{2,1} manifold the exponential map of any Lipschitz connection or spray determines a local Lipeomophism and that, furthermore, reversible convex normal neighborhoods do exist. To that end we use the method of Picard-Lindelof approximation to prove the strong differentiability of the exponenti…
By using Stationary-to-Randers correspondence (SRC), a characterization of light and time-convexity of the boundary of a region of a standard stationary (n+1)-spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler n or (n+1)-space of Randers type. The latter convexity is analyzed in d…
It is shown that the space of null geodesics of a star-shaped causally simple subset of Minkowski space is contactomorphic to the canonical contact structure in the spherical cotangent bundle of Rn. In the 3-dimensional case we prove a similar result for a large class of causally simple contractible subse…
While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to inconsistent estimation of Granger causal interactions. We propose a class of non…
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as products of coefficients. However, it …
We prove that the topology, smooth structure, and metric of a compact Lorentzian manifold with boundary is uniquely determined by data at the boundary. The data consists of the lengths and directions of future-directed once-broken geodesics connecting points on the boundary, which are first timelike and then lightlike.…
PULSE estimator improves prediction in causal inference with bounded interventions.
problem Optimizing causal models for bounded interventions.
method Relates K-class estimators to anchor regression, introduces PULSE estimator for minimization of mean squared prediction error with bounded constraints.
result PULSE estimator outperforms other estimators in real data and simulation experiments, especially in weak instrument settings.
Defines new metrics for Lorentzian spaces and their convergence.
problem Defining metrics for Lorentzian spaces and their convergence.
method Abstract approach to Lorentzian Gromov-Hausdorff distance and convergence, defining bounded Lorentzian-metric spaces, and proving stability under GH limits.
result GH limits of Lorentzian-metric spaces are isometric and homeomorphic.
We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropic causality that works in a very general functional model but makes the assumption that the unobserved exogenous variable has small entropy in t…
New findings on lightconvex boundaries in Finslerian spacetimes.
problem Understanding causal structures in Finslerian spacetimes.
method General results for indefinite Finslerian manifolds with boundary, and equivalence among boundary lightconvexity, causally simple interior, and Hausdorff space of cone geodesics.
result Equivalence among boundary lightconvexity, causally simple interior, and Hausdorff space of cone geodesics in globally hyperbolic spacetimes.
Unified framework for clustering and learning causal graphs across subjects.
problem Bias and obscured subpopulation-specific dependencies in multivariate systems.
method Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM) integrated with Structural Equation Modeling (SEM).
result Unified framework recovers cluster-specific causal dependency structures with high true positive rate and low false discovery rate.
This paper presents a novel data-driven technique based on the spatiotemporal pattern network (STPN) for energy/power prediction for complex dynamical systems. Built on symbolic dynamic filtering, the STPN framework is used to capture not only the individual system characteristics but also the pair-wise causal dependen…
Ridge regularized linear models (RRLMs), such as ridge regression and the SVM, are a popular group of methods that are used in conjunction with coefficient hypothesis testing to discover explanatory variables with a significant multivariate association to a response. However, many investigators are reluctant to draw ca…
The minimization of convex objectives coming from linear supervised learning problems, such as penalized generalized linear models, can be formulated as finite sums of convex functions. For such problems, a large set of stochastic first-order solvers based on the idea of variance reduction are available and combine bot…
We quantify causal bias in continuous treatment settings.
problem Identifying and quantifying causal bias in continuous treatment scenarios.
method Developed a novel characterization of causal bias in structural causal models, proving conditions for zero bias and efficient estimation.
result Causal bias can be estimated efficiently under certain structural equation restrictions, allowing for causal regularization of predictive models.