arXiv research

New neural processes use stacked Markov operators to improve flexibility.

Paper proposes a new method for training diffusion models using Markov operators.

Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with curren…

Neural networks parameterize time-varying Markov dynamics in financial time series.

A new sampler improves the inference of causal structures from observational data.

Alexander's and Markov's theorems state that any link type in $R^3$ is represented by a closed braid and that such representations are related by some elementary operations called Markov moves. We generalize the notion of a braid to that in 4-dimensional space and establish an analogue of these theorems.

The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert's projective metric or to a related family of seminorms (Hopf's oscillation or Hilbert's seminorm). We generalize these properties to abstract consensus operators over normal cones, w…

Extended Gauss-Markov theorem for linear estimation with bounded bias.

Deriving option prices from operational-time Markov lattices

Model predicts operational risk using HMMs with economic covariates.

Study of $q$-rationals and their geometric properties, including deformed Farey triangulation and Springborn operations.

Banded matrices can be used as precision matrices in several models including linear state-space models, some Gaussian processes, and Gaussian Markov random fields. The aim of the paper is to make modern inference methods (such as variational inference or gradient-based sampling) available for Gaussian models with band…

Develops a smooth operator framework for analyzing neural network representations.

We show that, for generative classifiers, conditional independence corresponds to linear constraints for the induced discrimination functions. Discrimination functions of undirected Markov network classifiers can thus be characterized by sets of linear constraints. These constraints are represented by a second order fi…

The time to converge to the steady state of a finite Markov chain can be greatly reduced by a lifting operation, which creates a new Markov chain on an expanded state space. For a class of quadratic objectives, we show an analogous behavior where a distributed ADMM algorithm can be seen as a lifting of Gradient Descent…

Study on gradient descent in Hilbert spaces with Markov chains, focusing on mixing coefficients.

Extended elliptical slice sampling for infinite-dimensional spaces, proving reversibility.

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic programming algorithms for solving Markov decision problems. These recursive stochastic a…

New algorithms reduce complexity for learning in MDPs with entropy regularization.

Modified Metropolis algorithm ensures convergence for multivariate binary distributions with fixed-order updates.

Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distributio…

We use elementary methods to compute the L2-dimension of the eigenspaces of the Markov operator on the lamplighter group and of generalizations of this operator on other groups. In particular, we give a transparent explanation of the spectral measure of the Markov operator on the lamplighter group found by Grigorchuk-Z…

Study variance-reduced method for estimating fixed points in Banach spaces.

Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general framework for pricing both discretely and continuously monitored Asian options under one-dimensional Markov processes. In …

Researchers approximate conditional expectation operators using kernel methods.

RILA learns HQMMs robustly against adversarial corruption.

Identity testing for reversible Markov chains without symmetry assumption.

In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a Hamiltonian Monte Carlo algorithm using a continuous time Markov jump process, and ar…

The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with latent variables imply independence constraints in the distribution resulting from a…

Study of Markov-modulated affine processes for richer models in finance.

Data balancing reduces variance in machine learning models.

This paper investigates the large-time asymptotic behavior of the sensitivities of cash flows. In quantitative finance, the price of a cash flow is expressed in terms of a pricing operator of a Markov diffusion process. We study the extent to which the pricing operator is affected by small changes of the underlying Mar…

The paper proposes a method to improve Koopman operator estimation using indicator functions.

Kernel-based methods improve policy evaluation in MRP models.

Intertwining curvature bounds for graphs and quantum Markov semigroups verified.

Unified framework for analyzing convergence of RSAs using Wasserstein divergence.

Survey of mathematical foundations for reinforcement learning.

Specialized knot theory theorems for strongly involutive links.

Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targ…

We introduce a general framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and behavioral economics. Within the framework, applying weighted norm spaces to incorporate …

New measures generalize existing ones, linking information and risk.

The paper parallelizes HMM inference for efficient long-term computations.

We introduce a new algorithm for approximate inference that combines reparametrization, Markov chain Monte Carlo and variational methods. We construct a very flexible implicit variational distribution synthesized by an arbitrary Markov chain Monte Carlo operation and a deterministic transformation that can be optimized…

HOPE improves SSMs for long-memory tasks with robust initialization and training.

New method speeds up Bayesian inverse problem solving with neural operators.

New framework for efficient optimal transport distances between Markov chains.

Recently, \citet{SuttonMW15} introduced the emphatic temporal differences (ETD) algorithm for off-policy evaluation in Markov decision processes. In this short note, we show that the projected fixed-point equation that underlies ETD involves a contraction operator, with a $\sqrtγ$-contraction modulus (where $γ$ is the …

Unified view of federated learning and distributed RL using local stochastic approximation.