Gradient Scan Gibbs Sampler: an efficient algorithm for high-dimensional Gaussian distributions

This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set of directions. The algorithm is proved to converge, i.e. the drawn samples are asymptotically distributed according to the target distribution. Our main motivation is in inverse problems related to general linear observation models and their solution in a hierarchical Bayesian framework implemented through sampling algorithms. It finds direct applications in semi-blind/unsupervised methods as well as in some non-Gaussian methods. The paper provides an illustration focused on the unsupervised estimation for super-resolution methods.Comment: 18 page

Beyond actions : exploring the discovery of tactics from user logs

Search log analysis has become a common practice to gain insights into user search behaviour; it helps gain an understanding of user needs and preferences, as well as an insight into how well a system supports such needs. Currently, log analysis is typically focused on low-level user actions, i.e. logged events such as issued queries and clicked results, and often only a selection of such events are logged and analysed. However, types of logged events may differ widely from interface to interface, making comparison between systems difficult. Further, the interpretation of the meaning of and subsequent analysis of a selection of events may lead to conclusions out of context—e.g. the statistics of observed query reformulations may be influenced by the existence of a relevance feedback component. Alternatively, in lab studies user activities can be analysed at a higher level, such as search tactics and strategies, abstracted away from detailed interface implementation. Unfortunately, until now the required manual codings that map logged events to higher-level interpretations have prevented large-scale use of this type of analysis. In this paper, we propose a new method for analysing search logs by (semi-)automatically identifying user search tactics from logged events, allowing large-scale analysis that is comparable across search systems. In addition, as the resulting analysis is at a tactical level we reduce potential issues surrounding the need for interpretation of low-level user actions for log analysis. We validate the efficiency and effectiveness of the proposed tactic identification method using logs of two reference search systems of different natures: a product search system and a video search system. With the identified tactics, we perform a series of novel log analyses in terms of entropy rate of user search tactic sequences, demonstrating how this type of analysis allows comparisons of user search behaviours across systems of different nature and design. This analysis provides insights not achievable with traditional log analysis

Generative Image Modeling Using Spatial LSTMs

Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a number of problems but only recently have found their way into generative image models. We here introduce a recurrent image model based on multi-dimensional long short-term memory units which are particularly suited for image modeling due to their spatial structure. Our model scales to images of arbitrary size and its likelihood is computationally tractable. We find that it outperforms the state of the art in quantitative comparisons on several image datasets and produces promising results when used for texture synthesis and inpainting

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

Making use of partial knowledge about hidden states in HMMs : an approach based on belief functions.

International audienceThis paper addresses the problem of parameter estimation and state prediction in Hidden Markov Models (HMMs) based on observed outputs and partial knowledge of hidden states expressed in the belief function framework. The usual HMM model is recovered when the belief functions are vacuous. Parameters are learnt using the Evidential Expectation- Maximization algorithm, a recently introduced variant of the Expectation-Maximization algorithm for maximum likelihood estimation based on uncertain data. The inference problem, i.e., finding the most probable sequence of states based on observed outputs and partial knowledge of states, is also addressed. Experimental results demonstrate that partial information about hidden states, when available, may substantially improve the estimation and prediction performances

How to Solve Classification and Regression Problems on High-Dimensional Data with a Supervised Extension of Slow Feature Analysis

Supervised learning from high-dimensional data, e.g., multimedia data, is a challenging task. We propose an extension of slow feature analysis (SFA) for supervised dimensionality reduction called graph-based SFA (GSFA). The algorithm extracts a label-predictive low-dimensional set of features that can be post-processed by typical supervised algorithms to generate the final label or class estimation. GSFA is trained with a so-called training graph, in which the vertices are the samples and the edges represent similarities of the corresponding labels. A new weighted SFA optimization problem is introduced, generalizing the notion of slowness from sequences of samples to such training graphs. We show that GSFA computes an optimal solution to this problem in the considered function space, and propose several types of training graphs. For classification, the most straightforward graph yields features equivalent to those of (nonlinear) Fisher discriminant analysis. Emphasis is on regression, where four different graphs were evaluated experimentally with a subproblem of face detection on photographs. The method proposed is promising particularly when linear models are insufficient, as well as when feature selection is difficult

Estimating the granularity coefficient of a Potts-Markov random field within an MCMC algorithm

This paper addresses the problem of estimating the Potts parameter B jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on B requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method the estimation of B is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating B jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of B. On the other hand, assuming that the value of B is known can degrade estimation performance significantly if this value is incorrect. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images