We describe random walk boundaries (in particular, the Poisson--Furstenberg, or PF-boundary) for a vast family of groups in terms of the hyperbolic boundary of a special free subgroup. We prove that almost all trajectories of the random walk (with respect to an arbitrary nondegenerate measure on the group) converge to …
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48 results for “Markov boundary”
Markov boundary improves tabular prediction but not as expected.
problem Improving tabular prediction using the Markov boundary.
method Evaluation on a synthetic SCM benchmark with feature counts from 40 to 1000.
result Restricting a regressor to the Markov boundary often improves prediction, but existing discovery and training pipelines do not fully exploit this.
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…
Solves optimal stopping for Gauss-Markov bridges using time-space transformation.
problem Optimal stopping problem of a Gauss-Markov bridge.
method Time-space transformation approach, Picard iteration algorithm.
result Lipschitz continuity of the optimal stopping boundary and its characterization.
Algorithm learns Bayesian network structure efficiently from data.
problem Learning directed acyclic graphical models from observational data.
method Local Markov boundary search procedure to recursively construct ancestral sets.
result Simple greedy search algorithm learns Markov boundary of each node efficiently.
Simulation of Multidimensional Diffusions with Sticky Boundaries via Markov Chain Approximationmath.PR
New method simulates sticky boundaries in multidimensional diffusions.
problem Simulating sticky boundaries in multidimensional diffusions.
method Approximate sticky diffusion by a Markov chain, using either finite difference or matching local moments.
result Validates both construction methods for first-order simulation schemes.
We prove Feynman-Kac formulas for solutions to elliptic and parabolic boundary value and obstacle problems associated with a general Markov diffusion process. Our diffusion model covers several popular stochastic volatility models, such as the Heston model, the CEV model and the SABR model, which are widely used as ass…
Fast algorithm solves BVPs in linear time with probabilistic uncertainty.
problem Solving boundary value problems efficiently and accurately.
method Gauss--Markov prior tailored to BVPs, linear-time computation.
result Probabilistic solution with linear time complexity and comparable quality.
Characterizes slopes for Markov ordering on prime pairs.
problem Investigating the Markov ordering on relatively prime integer pairs.
method Employing the stable norm on modular torus homology.
result Characterizes slopes for monotonicity of Markov ordering.
Causal Markov Boundariesstat.ML
Paper improves feature selection for predicting outcomes from observational data.
problem Feature selection for post-intervention outcome prediction from pre-intervention variables in healthcare settings.
method Extends Markov boundary concept to treatment-outcome pairs, uses observational and experimental data.
result Combining observational and experimental data improves feature selection and effect estimation.
Deriving option prices from operational-time Markov lattices
problem Option pricing
method Operational-time Markov lattice
result Derives option-pricing equations from an operational-time Markov lattice
A new method reduces CI tests for causal structure learning.
problem Exponential CI tests in constraint-based methods.
method Recursive Markov boundary-based approach.
result Significantly reduces CI tests compared to existing methods.
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm for hidden Markov models, in a sequential data setting. Given a collapsed hidden Markov Model, we break its long M…
New findings on hyperbolic groups and their boundaries.
problem Understanding the structure of cubulated hyperbolic groups with specific boundary conditions.
method Utilizing ideas from Markovic's work on Cannon's conjecture, focusing on quasi-convex subgroups and limit sets.
result Cubulated hyperbolic groups with certain boundary conditions are virtually fundamental groups of specific manifolds.
Detecting topological properties of Markov compacta with combinatorial properties of their diagramsmath.GT
We develop a formalism that allows us to describe Markov compacta with finite sets of diagrams that are building blocks of the entire sequence. This encodes complex, continuous spaces with discrete collections of combinatorial objects. We show that topological properties of the limit (such as -connectedness, local $…
We give a criterion in terms of the boundary for the existence of a proper cocompact action of a word-hyperbolic group on a CAT(0) cube complex. We describe applications towards lattices and hyperbolic 3-manifold groups. In particular, by combining the theory of special cube complexes, the surface subgroup result of Ka…
We show that the nearest point retraction is a uniform quasi-isometry from the Thurston metric on a hyperbolic domain in the Riemann sphere to the boundary of the convex hull of its complement. As a corollary, one obtains explicit bounds on the quasi-isometry constant of the nearest point retraction with respect to the…
We develop continuous time Markov chain (CTMC) approximation of one-dimensional diffusions with a lower sticky boundary. Approximate solutions to the action of the Feynman-Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matri…
New Markov chains defined on simplicial complexes for understanding their topology.
problem Understanding the topology of simplicial complexes and hypergraphs.
method Defining new Markov chains on simplicial complexes and studying their properties.
result The generator of the new Markov chain is the upper Laplacian, and the Markov chain is positive recurrent.
Revisits life insurance surplus models with new technical bases.
problem Classifying and extending life insurance surplus models.
method Using Markov models and classifying technical bases in Thiele's equation.
result Introduces a `canonical' model with three technical bases.
Let N be an irreducible, compact 3-manifold with empty or toroidal boundary which is not a closed graph manifold. Using recent work of Agol, Kahn-Markovic and Przytycki-Wise we will show that pi_1(N) admits a cofinal filtration with `fast' growth of Betti numbers as well as a cofinal filtration of pi_1(N) with `slow' g…
We prove that the Gromov boundary of every hyperbolic group is homeomorphic to some Markov compactum. Our reasoning is based on constructing a sequence of covers of , which is quasi--invariant wrt. the ball -type (defined by Cannon) for sufficiently large. We also ensure certain additional propert…
This paper includes an original self contained proof of well-posedness of an initial-boundary value problem involving a non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. We call this market model a semi-Markov modulated market. Although a wellposedness resu…
Given a hyperbolic domain, the nearest point retraction is a conformally natural homotopy equivalence from the domain to the boundary of the convex core of its complement. Marden and Markovic showed that if the domain is uniformly perfect, then there exists a conformally natural quasiconformal map which admits a bounde…
Path-connectivity of thick laminations on high-genus surfaces.
problem Path-connectivity of thick laminations on high-genus surfaces.
method Teichmüller ray analysis and subshift of finite type construction.
result Path-connectedness of the Morse boundary of the mapping class group.
Schrödinger bridge solved with Weyl calculus for quadratic state cost.
problem Optimal control policy to steer joint state statistics.
method Weyl calculus in quantum mechanics for reaction-diffusion PDEs.
result Explicit Markov kernel for quadratic state cost found.
A new clustering method estimates non-linear boundaries and automatically selects the number of clusters.
problem Discriminative clustering with non-linear boundaries and data abnormalities.
method Regularized mutual information objective function with a mixture of Gaussian and uniform distributions.
result Automatic selection of the number of components and estimation of non-linear boundaries.
In this paper, we will show that the projection does not have a section; i.e. the braid group cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary point-wise and marked points in the interior as a set. We also give a new proof of a result o…
Sullivan showed that there exists such that if is a simply connected hyperbolic domain, then there exists a conformally natural -quasiconformal map from to the boundary of the convex hull of its complement which extends to the identity on . Explicit …
Markov switching models (MSMs) are probabilistic models that employ multiple sets of parameters to describe different dynamic regimes that a time series may exhibit at different periods of time. The switching mechanism between regimes is controlled by unobserved random variables that form a first-order Markov chain. Ex…
Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundariescs.LG
New method learns diffusion transition density for Bayesian inference.
problem Bayesian inference on diffusions with inaccessible boundaries.
method Neural Galerkin framework to solve FP equation with Dirac mass.
result Approximates likelihood function for efficient posterior sampling.
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. The benchmark information-theoretic results in the case of d-regular graphs require the number of samples to be at least proportional to the logarithm of the number of vertices to allow consistent graph recovery. When…
Study no-arbitrage conditions in 1D diffusion markets with interest rates.
problem Determining no-arbitrage conditions in 1D diffusion markets with interest rates.
method Established deterministic criteria for no-arbitrage notions in terms of scale function and speed measure.
result Revealed various effects, e.g., NIP not excluded by reflecting boundaries.
Develops a smooth operator framework for analyzing neural network representations.
problem Analyzing the geometry of feedforward neural network representations.
method Introduces a smooth operator-theoretic approach based on diffusion Markov operators derived from feature clouds.
result Establishes a stable operator-geometric framework for tracking training, width, and perturbation stability.
New approach infers object type from physical data and functional requirements.
problem Classical design theory treats object type as a given, but this paper argues it should be inferred.
method C-DMBD, a constrained extension of Dynamic Markov Blanket Detection algorithm, models product surface as a Markov blanket.
result Requirement-steered inference is computationally tractable and models different object types with different parameterizations.
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
problem Optimal stopping in multi-dimensional processes with non-exponential discounting.
method Probabilistic potential theory to establish existence of optimal equilibria.
result Existence of optimal equilibria for multi-dimensional stopping problems.
In this paper we discuss four problems regarding Markov equivalences for subclasses of loopless mixed graphs. We classify these four problems as finding conditions for internal Markov equivalence, which is Markov equivalence within a subclass, for external Markov equivalence, which is Markov equivalence between subclas…
Improves TTS accuracy by correcting context-dependent units.
problem Improves text-to-speech accuracy through speaker adaptation.
method Statistical model predicting context-dependent phonetic unit classes and their mean error values.
result Corrected boundaries of units improve TTS accuracy compared to HMM segmentation.
The paper estimates key metrics for linear models with Markov or hidden Markov sources.
problem Estimating free energy, mutual information, and MMSE for linear models with specific signal priors.
method Replica analysis in statistical physics, focusing on Markov and hidden Markov sources.
result The linear model with Markov or hidden Markov sources can be simplified into decoupled AWGN channels.
Markov Observation Modelsstat.ML
Expands Hidden Markov Model to include Markov chain observations.
problem Handling Markov chain observations in Hidden Markov Models.
method Developed Expectation-Maximization algorithm and Viterbi algorithm analogs.
result Estimates transition probabilities for hidden states and observations.
Discrete-time weak approximation of a Black-Scholes model with drift and volatility Markov switchingmath.PR
Study approximates financial market with discrete-time models.
problem Approximating continuous-time financial market models with discrete-time.
method Constructs discrete-time market models with Markov switching and proves convergence.
result Discrete-time models converge to continuous-time Black-Scholes model with Markov switching.
New neural processes use stacked Markov operators to improve flexibility.
problem Improving flexibility in neural processes.
method Stacking neural parameterized Markov transition operators in function space.
result MNPs outperform baseline models on various tasks.
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading strategies, we analyze the timings and sequences of the investor's market participation,…
New algorithms for RL in Markov games with independent linear function approximation, breaking the curse of multiagents.
problem Tackles the challenge of learning Markov equilibria in large state space Markov games with multiple agents.
method Proposes independent linear Markov games and designs new algorithms for learning Markov coarse correlated equilibria and Markov correlated equilibria with polynomial sample complexity.
result Breaks the curse of multiagents by achieving sample complexity bounds that scale polynomially with each agent's function class complexity.
The paper bounds generalization errors for deep neural networks with Markov datasets.
problem Bounding generalization errors for deep learning with Markov datasets.
method Developed new symmetrization inequalities for Markov chains, using spectral gap of the infinitesimal generator.
result Derived upper bounds on generalization errors for deep neural networks with Markov datasets.
Markov partitions for the geodesic flow on compact Riemann surfaces of constant negative curvaturemath.DG
The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.
problem Understanding Markov partitions for general hyperbolic flows.
method Rigorous construction of Markov partitions for geodesic flow on Riemann surfaces of constant negative curvature.
result Explicit forms of rectangles and local cross sections provided for the geodesic flow.
We rephrase Gromov's definition of Markov compacta, introduce a subclass of Markov compacta defined by one building block and study cohomological dimensions of these compacta. We show that for a Markov compactum , $\dim_{\Z_{(p)}}X=\dim_{\Q}X$ for all but finitely many primes where is the localization…