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.
New invariant from non-acyclic flat connections.
We prove that Thompson's group is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman-Thompson groups with the homology of the zeroth component of the infinite loop space of the mod Moore spectrum. As , we can deduce that t…
The paper studies 4-charts with three crossings and their equivalence to a specific knot.
We explore non-acyclic GFlowNets in discrete settings.
COSMO learns DAG structure without acyclicity constraints.
Acyclicity proven for curve complex on surfaces.
We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a lambda-regular SU(2) or SL(2, C)-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate…
New method learns DAGs from data without acyclicity constraint.
CDFD analyzes circularity and directionality in weighted directed networks.
New method estimates causal structure from sparse data.
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of such models is a well-studied problem. However, existing methods have significant …
ALIAS uses RL to learn DAGs without acyclicity constraints.
We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then…
Develops a new method for learning non-parametric DAGs using RKHS.
The construction of invariants of three-dimensional manifolds with a triangulated boundary, proposed earlier by the author for the case when the boundary consists of not more than one connected component, is generalized to any number of components. These invariants are based on the torsion of acyclic complexes of geome…
Two extremal classes of acyclic groups are discussed. For an arbitrary group G, there is always a homomorphism from an acyclic group of cohomological dimension 2 onto the maximum perfect subgroup of G, and there is always an embedding of G in a binate (hence acyclic) group. In the other direction, there are no nontrivi…
In this note we derive enumerative formulas for several types of labelled acyclic directed graphs by slight modifications of the familiar recursive formula for simple acyclic digraphs. These considerations are motivated by, and based upon, recent combinatorial results in geometric topology obtained by S.Choi, who estab…
ENCOD learns causal graphs efficiently without acyclicity constraints.
We give a Dehn-Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free group. Then we construct an additive invariant of those homology cylinders which act on the acyclic closure trivially. We also describe some…
New results on relative simplicial volume using bounded acyclicity.
The paper explores conditions for homology spheres to bound acyclic smooth manifolds and symplectic fillings.
Proposes an approach to ensure acyclic graphs in Bayesian structure learning.
We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analo…
We determine which 3-manifolds admit a unitary representation such that the corresponding twisted chain complex is acyclic.
Proposes an evolutionary approach to fitting acyclic VAR models.
Solves linearity problem for acyclic groups, bounds Cheeger-Gromov ρ-invariants.
In terms of Turaev's shadows, we provide a sufficient condition for a compact, smooth, acyclic 4-manifold with boundary the 3-sphere to be diffeomorphic to the standard 4-ball. As a consequence, we prove that if a compact, smooth, acyclic 4-manifold with boundary the 3-sphere has shadow-complexity at most 2, then it is…
We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph on vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with vertice…
DAGMA learns DAGs faster and more accurately using log-determinant acyclicity.
Identifies causal effects in LiNGAM models with latent variables.
We describe computationally efficient methods for learning mixtures in which each component is a directed acyclic graphical model (mixtures of DAGs or MDAGs). We argue that simple search-and-score algorithms are infeasible for a variety of problems, and introduce a feasible approach in which parameter and structure sea…
What discuss the problem of obtaining new manifold invariants via different analogues of 6j-symbols and the torsion of acyclic complexes.
The paper tackles learning varying DAG structures based on contextual features.
Let X be a compactum such that dim_Q X < n+1, n>1. We prove that there is a Q-acyclic resolution r: Z-->X from a compactum Z of dim < n+1. This allows us to give a complete description of all the cases when for a compactum X and an abelian group G such that dim_G X < n+1, n>1 there is a G-acyclic resolution r: Z-->X fr…
ProDAG uses variational inference to learn DAGs with uncertainty quantification.
Study counterfactuals in cyclic systems with shifts and scales.
DAGgr aggregates multiple DAGs to stabilize causal structure learning.
We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30 (2002) 1414-1440] and discuss how to evaluate the score efficiently.
We show that standard cyclic actions on Brieskorn homology 3-spheres with non-empty fixed set do not extend smoothly to any contractible smooth 4-manifold it may bound. The quotient of any such extension would be an acyclic -manifold with boundary a related Brieskorn homology sphere. We briefly discuss well known in…
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges between nodes represent the influence of components of the system on each other.…
We show that there can be no algorithm to decide whether infinite recursively described acyclic aspherical 2-complexes are contractible. We construct such a complex that is contractible if and only if the Collatz conjecture holds.
Study identifies parameters in causal models with latent confounding.
A combination of Bestvina--Brady Morse theory and an acyclic reflection group trick produces a torsion-free finitely presented Q-Poincaré duality group which is not the fundamental group of an aspherical closed ANR Q-homology manifold. The acyclic construction suggests asking which Q-Poincaré duality groups act freely …
This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs".
Study non-acyclic SL2-representations of twist knots and their L-functions.
Proves conditions for separating regions in homogeneous spaces without trivial topology.
Neural networks with DAGs show linearity as width increases.
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of t…