The problem we address in this paper is to label datapoints when the information about them is provided primarily in terms of their subsets or groups. The knowledge we have for a group is a numerical weight or likelihood value for each group member to belong to same class. These likelihood values are computed given a class specific model, either explicit or implicit, of the pattern we wish to l...

An unsupervised multiresolution conditional random field (CRF) approach to texture segmentation problems is introduced. This approach involves local and long-range information in the CRF neighbourhood to determine the classes of image blocks. Like most Markov random field (MRF) approaches, the proposed method treats the image as an array of random variables and attempts to assign an optimal cla...

In this paper, we study a challenging problem of mining data generating rules and state transforming rules (i.e., semantics) underneath multiple correlated time series streams. A novel Correlation field-based Semantics Learning Framework (CfSLF) is proposed to learn the semantic. In the framework, we use Hidden Markov Random Field (HMRF) method to model relationship between latent states and ob...

Random eld models are able to synthesize a large variety of complex patterns with a small number of parameters. This paper discusses the use of a Gibbs random eld model as part of an image coding system. In particular, some semantic and perceptual attributes of this model are addressed.

We propose variational bounds on the log-likelihood of an undirected probabilistic graphical model p that are parametrized by flexible approximating distributions q. These bounds are tight when q = p, are convex in the parameters of q for interesting classes of q, and may be further parametrized by an arbitrarily complex neural network. When optimized jointly over q and p, our bounds enable us ...

The Gaussian process latent variable model (GPLVM) is an unsupervised probabilistic model for nonlinear dimensionality reduction. A supervised extension, called discriminative GPLVM (DGPLVM), incorporates supervisory information into GPLVM to enhance the classification performance. However, its limitation of the latent space dimensionality to at most C − 1 (C is the number of classes) leads to ...

We introduce a class of multi-scale models for random fields. The novel framework couples standard Markov models for the random field stochastic process at different levels of resolution, and links them via error models to induce a new and rich class of structured linear models reconciling modelling and information at different levels of resolution. Jeffrey’s rule of conditioning is used to rev...

The Curve Indicator Random Field

Random field theory is used in the statistical analysis of SPM’s whenever there is a spatial component to the inference. Most important is the question of detecting an effect or activation at an unknown spatial location. Very often we do not know in advance where to look for an effect, and we are interested in searching the whole brain, or part of it. This presents special statistical problems ...

Herein, we propose generating CAPTCHAs through random field simulation and give a novel, effective and efficient algorithm to do so. Indeed, we demonstrate that sufficient information about word tests for easy human recognition is contained in the site marginal probabilities and the site-to-nearby-site covariances and these quantities can be embedded into KNW conditional probabilities, designed...