Last edit: Thanks everybody for participating, it’s been a very interesting workshop. Please find the slides below, and here’s the dinner pic.
The workshop will take place at Ecole centrale de Lille, Cité scientifique, Villeneuve d’Ascq. It’s a 200m walk from subway station “4 cantons”, at the very end of Line 1 (the yellow line on subway maps). Once there, you can ask for directions at the entrance desk.
- 9.45-10.15 : Welcome
- 10.15-10.40 : Hong-Phuong Dang (Lille), BNP dictionary learning and inverse problems in image processing, slides
- 10.40-11.05 : Jessica Sodjo (Bordeaux), Image segmentation combining Markov random fields and Dirichlet processes, slides
- 11.05-11.30 : Clément Elvira (Lille), BNP and unmixing of hyperspectral images, slides
- 11.30-11.45 : coffee break
- 11.45-12.10 : Jorge Prendes (Toulouse), Change detection for remote sensing multi-sensor images, slides
- 12.10-12.50 : internal discussions about the ANR project
- 12.50-14.20 : lunch break at University restaurant Barrois
- 14.20-14.45 : Mohanad Albughdadi (Toulouse), Hemodynamic Brain Parcellation using a Non-parametric Bayesian Approach, slides
- 14.45-15.20 : Rémi Bardenet (Lille), On determinantal point processes, slides
- 15.20-15.50 : coffee break
- 15.50-16.25 : Balaji Lakshminarayanan (UCL, UK), Mondrian Forests, slides
- 16.25-17.00 : Yarin Gal (Cambridge, UK), Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference, slides
- 17.00-17.35 : Neil Spencer/Sean Jewell (UBC, Canada), Atomic spatial processes, slides
- 17.35-18.15 : Discussions / debrief
- Hong-Phuong Dang (Lille), BNP dictionary learning and inverse problems in image processing
Learning redundant dictionaries for sparse representation from sets of patches has proven its efficiency in solving inverse problems. In many methods, the size of the dictionary is fixed in advance. Moreover the optimization process often calls for the prior knowledge of the noise level to tune parameters. We propose a Bayesian non parametric approach which is able to learn a dictionary of adapted size : the adequate number of atoms is inferred thanks to an Indian Buffet Process (IBP) prior. Moreover the noise level is also accurately estimated so that nearly no parameter tuning is needed. To go further, we focus on power laws that establish a relationship between the number of atoms used in the dictionary and the rank of those atoms in an ordered sequence. Caron (2012) proposed a Bayesian Non Parametric model where each data has its own characteristic and each feature its own popularity. The set of associations between customers and dishes forms a bipartite graph. This allows the model to capture the power law behavior of real world bipartite graph. This model will studied instead of IBP in future work.
- Clément Elvira (Lille), BNP and unmixing of hyperspectral images
In a hyperspectral image, a pixel is often composed of thousands of bands. Each macroscopic object is characterized by its spectral signature, called endmember, and each pixel is a convex combination of endmembers. This common assumption is known as the linear mixing model. The operation that consists of finding the proportion of endmembers in each pixel is called unmixing. In this talk, we describe a new Bayesian algorithm that jointly extracts endmembers and finds their respectives proportions in the convex combination. Most unmixing algorithms proposed in the literature consider the amount of endmembers fixed in advance. We propose a Bayesian non parametric approach to infer the number of spectra using an Indian Buffet Process prior. Moreover, in our model, the dimensionality reduction, which is intimately bound to the amount of endmember in hyperspectral analysis, is integrated to the Bayesian framework. A uniform distribution on the Stiefel manifold allows us to sample an orthogonal basis. We believe that unmixing performance can be increased when the dimensionality reduction is driven by the task. We will then discuss a more simple task where we expect our algorithm will be relevant.
- Jorge Prendes (Toulouse), Change detection for remote sensing multi-sensor images
Remote sensing images are images of the Earth acquired from planes or satellites. Many different sensors have been developed to measure different properties of the earth surface, including optical images, SAR images and hyperspectral images. One of the interest of this images is the detection of changes on datasets of multitemporal images. Change detection has been thoroughly studied on the case where the dataset consist of images acquired by the same sensor. However, having to deal with datasets containing images acquired from different sensors (heterogeneous images) is becoming very common nowadays. We proposed a statistical model to deal with heterogeneous images which describe the joint distribution of the pixel intensity of the images, more precisely a non parametric mixture model. On unchanged areas, we expect the parameter vector of the model to belong to a manifold related to the physical properties of the objects present on the image. The distance of the model parameter to the manifold can be thus be used as a similarity measure. The model parameters are estimated through a collapsed Gibbs sampler using a Bayesian non parametric approach combined with a Markov random field.
- Mohanad Albughdadi (Toulouse), Hemodynamic Brain Parcellation using a Non-parametric Bayesian Approach
One of the most challenging issues in fMRI data analysis is the functional parcellation of the brain into a number of hemodynamically homogenous regions called parcels. The joint parcellation detection estimation (JPDE) model addresses this issue through an automatic inference of the parcels directly from the fMRI data. However, to do so, the number of parcels needs to be fixed a priori, which is a difficult task that generally depends on the subject or on the population this subject belongs to. An automatic model selection approach is proposed to overcome this issue. This approach relies on a non- parametric Bayesian approach estimating online the number of parcels using a Dirichlet process mixture model combined with a hidden Markov random field.
- Rémi Bardenet (Lille), On determinantal point processes
Determinantal point processes (DPPs) are point process models that encode repulsiveness through algebraic arguments. This talk will be a short tutorial on DPPs from a user point of view, and I’ll finish by browsing some DPP projects I’m involved in.
Yarin Gal (Cambridge, UK), Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference
We offer insights into why recent state-of-the-art models in image processing work so well, and rely on the Gaussian process to obtain state-of-the-art results for the CIFAR-10 dataset.
- Neil Spencer/Sean Jewell (UBC, Canada), Atomic spatial processes
The emergence of compact GPS systems and the establishment of open data initiatives has resulted in widespread availability of spatial data for many urban centres. These data can be leveraged to develop data-driven intelligent resource allocation systems for urban issues such as policing, sanitation, and transportation. We employ techniques from Bayesian non-parametric statistics to develop a process which captures a common characteristic of urban spatial datasets. Specifically, our new spatial process framework models events which occur repeatedly at discrete spatial points, the number and locations of which are unknown a priori. We develop a representation of our spatial process which facilitates posterior simulation, resulting in an interpretable and computationally tractable model. The framework’s superiority over both empirical grid-based models and Dirichlet process mixture models is demonstrated by fitting, interpreting, and comparing models of graffiti prevalence for both downtown Vancouver and Manhattan.