Related papers: Approximations and bounds for binary Markov random…
An important part of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov Random Field. The belief propagation algorithm, which is an exact procedure to compute…
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…
We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…
Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…
We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…
The complete framework for the $\epsilon$-machine construction of the one dimensional Ising model is presented correcting previous mistakes on the subject. The approach follows the known treatment of the Ising model as a Markov random…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
Undirected graphical models have been successfully used to jointly model the spatial and the spectral dependencies in earth observing hyperspectral images. They produce less noisy, smooth, and spatially coherent land cover maps and give top…
Inference for doubly intractable distributions is challenging because the intractable normalizing functions of these models include parameters of interest. Previous auxiliary variable MCMC algorithms are infeasible for multi-dimensional…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…
The softmax representation of probabilities for categorical variables plays a prominent role in modern machine learning with numerous applications in areas such as large scale classification, neural language modeling and recommendation…
With recent advances in structural biology, including experimental techniques and deep learning-enabled high-precision structure predictions, molecular dynamics methods that scale up to large biomolecular systems are required. Current…
Two methods to approximate infinitely divisible random fields are presented. The methods are based on approximating the kernel function in the spectral representation of such fields, leading to numerical integration of the respective…
Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general.…