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 CAT(0) groups show superexponential subgroup Dehn functions.
Finite quotients of braid groups have large sizes.
The study shows exponential distortion in virtually special groups containing free subgroups.
We prove a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) metric spaces. For random walks with finite superexponential moment, we show that the equality is achieved if and only if the Gibbs density is…
Optimal data-driven formulations are found for learning and decision-making with historical data.
Let (X,g) be a metrically complete, simply connected Riemannian manifold with bounded geometry and pinched negative curvature, i.e. there are constants a>b>0 such that -a^2<K<-b^2 for all sectional curvatures K. Here bounded geometry is used in the sense that all covariant derivatives of the Riemannian curvature tensor…
There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis. A…
Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In th…
Dealing with uncertainty in Bayesian Network structures using maximum a posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often intractable due to the superexponential number of possible directed, acyclic graphs. When the prior is decomposable, two classes of graphs where efficient learning can take plac…
Measures of wealth and production have been found to scale superlinearly with the population of a city. Therefore, it makes economic sense for humans to congregate together in dense settlements. A recent model of population dynamics showed that population growth can become superexponential due to the superlinear scalin…
We study a family of regularized score-based estimators for learning the structure of a directed acyclic graph (DAG) for a multivariate normal distribution from high-dimensional data with . Our main results establish support recovery guarantees and deviation bounds for a family of penalized least-squares estima…
Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the f…
Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough formulates the problem as a continuous optimization with a structural constraint that e…
Quantifies polynomial approximation rates for smooth functions under various distributions.