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.
Proposes a weaker faithfulness assumption for causal discovery.
New algorithm estimates causal effects for non-Gaussian data.
In recent years the possibility of relaxing the so-called Faithfulness assumption in automated causal discovery has been investigated. The investigation showed (1) that the Faithfulness assumption can be weakened in various ways that in an important sense preserve its power, and (2) that weakening of Faithfulness may h…
Paper relaxes faithfulness assumption for causal discovery using interventions.
Directed graphical models provide a useful framework for modeling causal or directional relationships for multivariate data. Prior work has largely focused on identifiability and search algorithms for directed acyclic graphical (DAG) models. In many applications, feedback naturally arises and directed graphical models …
The paper defines conditions for learning causal graphs from data with unobserved variables.
This paper deals with chain graphs under the alternative Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. We also show that the extension of Meek's conjecture to AMP chain graphs does n…
Improved causal discovery methods for large graphs without strict assumptions.
We tackle causal discovery in linear systems with measurement error and unobserved causes.
Bayesian networks are typically faithful, with implications for causal inference.
This thesis relaxes assumptions for causal discovery, making methods applicable to more complex systems.
This work addresses the following question: Under what assumptions on the data generating process can one infer the causal graph from the joint distribution? The approach taken by conditional independence-based causal discovery methods is based on two assumptions: the Markov condition and faithfulness. It has been show…
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables. Our approach is a two-stage quadratic programming method that…
Consider the problem of learning, from non-experimental data, the causal (Markov equivalence) structure of the true, unknown causal Bayesian network (CBN) on a given, fixed set of (categorical) variables. This learning problem is known to be so hard that there is no learning algorithm that converges to the truth for al…
Causal effect estimation from observational data is an important and much studied research topic. The instrumental variable (IV) and local causal discovery (LCD) patterns are canonical examples of settings where a closed-form expression exists for the causal effect of one variable on another, given the presence of a th…
This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover, we show that the extension of Meek's conjecture to AMP chain graphs does not hold…
Study on faithfulness of Burau representation for Artin-Tits groups.
Improves decision-making by correcting feature selection bias.
Proves Burau representation is faithful for 4-strand braids.
We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal relationships among the observed variables. Under faithfulness assumption, we propos…
Two new metrics assess LLM faithfulness and entropy, improving model reliability.
We prove asymptotic faithfulness for the quantum mapping class group representation. This provides the first example of asymptotic faithfulness lying outside of the family. The methods used are generalized from the proof of asymptotic faithfulness for skein mapping class group represent…
Efficiently learns linear non-Gaussian DAGs with noisy nodes.
New method learns dependencies in high-dimensional data without graph assumptions.
Study evaluates feature ranking methods' faithfulness in ML models, improving with dimensionality reduction.
The main goal of this paper is to compute $μ(\g)$ and $μ_{nil}(\g)$ for each nilpotent Lie algebra $\g$ of dimension 6 over a field of characteristic zero $\k$. Here $μ(\g)$ and $μ_{nil}(\g)$ is the minimal dimension of a faithful representation of $\g$ and the minimal dimension of a faithful nilrepresentation of $\g$,…
The Burau representation is a natural action of the braid group B_n on the free Z[t,t^{-1}]-module of rank n-1. It is a longstanding open problem to determine for which values of n this representation is faithful. It is known to be faithful for n=3. Moody has shown that it is not faithful for n>8 and Long and Paton imp…
In this article we study the space of left- and bi-invariant orderings on a torsion-free nilpotent group . We will show that generally the set of such orderings is equipped with a faithful action of the automorphism group of . We prove a result which allows us to establish the same conclusion when is assumed …
We show the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the PSL(2,K) representation variety, where K is the field of real or complex numbers, answering a question of W. Goldman. We also prove the existence of faithful representations into PU…
The Burau representation of 3-strand braid group modulo p is determined and shown to be faithful for small p.
Skein algebra action is faithful if quantum parameter isn't a root of 1.
The study evaluates how well local explanations align with model predictions.
The paper proposes new interpretability paradigms to improve model faithfulness.
Measures faithfulness of LLM explanations to reveal hidden biases and misleading claims.
Detect hidden confounding in observational data using multiple environments.
Paper shows identifiability of causal models with unobserved variables.
We give a direct proof for the asymptotic faithfulness of the quantum representations of the mapping class groups using peak sections in Kodaira embedding. We give also estimates on the norm of the parallell transport of the projective connection on the Verlinde bundle. The faithfulness has been proved earlier …
We analyze two braid group representations and their reductions modulo p.
Counterexamples show Salter's question on Burau image is negative for n=4.
Proposes generating virtual data points to overcome the curse of dimensionality.
In this paper we investigate the spectral problem in Finsler geometry. Due to the nonlinearity of the Finsler-Laplacian operator, we introduce \textit{faithful dimension pairs} by means of which the spectrum of a compact reversible Finsler metric measure manifold is defined. Various upper and lower bounds of such eigen…
Based on a normal form for braid group elements suggested by Dehornoy, we prove several representations of braid groups by automorphisms of a free group to be faithful. This includes a simple proof of the standard Artin's representation being faithful.
We show that a certain linear representation of the singular braid monoid on three strands is faithful. Furthermore we will give a second - group theoretically motivated - solution to the word problem in this monoid.
This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the regular Gaussian distributions that factorize with respect to a chain graph with parameters have positive Lebesgue measure with respect to , whereas those that factorize with respect…
ID-ExpO fine-tunes neural networks for more faithful explanations.
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error va…
We prove that a free group F_2 admits a faithful discrete representation into Diff_{+}(I). We also prove that F_2 admits a faithful discrete representation into Homeo_{+}(I). Some properties of these representations have been studied. In the last section we raise several questions.
The faithfulness of the orthogonal group case of Brauer's representation of the Brauer centralizer algebras restricted to their Temperley-Lieb subalgebras, which was established by Vaughan Jones, is here proved in a new, elementary and self-contained, manner.