Selecting thresholding and shrinking parameters with generalized SURE for low rank matrix estimation - implementation -

Selecting thresholding and shrinking parameters with generalized SURE for low rank matrix estimation by Julie Josse, Sylvain Sardy

To estimate a low rank matrix from noisy observations, truncated singular value decomposition has been extensively used and studied: empirical singular values are hard thresholded and empirical singular vectors remain untouched. Recent estimators not only truncate but also shrink the singular values. In the same vein, we propose a continuum of thresholding and shrinking functions that encompasses hard and soft thresholding. To avoid an unstable and costly cross-validation search of their thresholding and shrinking parameters, we propose new rules to select these two regularization parameters from the data. In particular we propose a generalized Stein unbiased risk estimation criterion that does not require knowledge of the variance of the noise and that is computationally fast. In addition, it automatically selects the rank of the matrix. A Monte Carlo simulation reveals that our estimator outperforms the tested methods in terms of mean squared error and rank estimation.

The attendant R implementation of the algorithm is on Julie Josses's site.


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Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization - implementation -

Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization by Jian Zhang, Chen Zhao, Debin Zhao, Wen Gao

From many fewer acquired measurements than suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that, a signal can be reconstructed with high probability when it exhibits sparsity in some domain. Most of the conventional CS recovery approaches, however, exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are irrespective of the non-stationarity of natural signals and cannot achieve high enough degree of sparsity, thus resulting in poor CS recovery performance. In this paper, we propose a new framework for image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization. The intrinsic sparsity of natural images is enforced substantially by sparsely representing overlapped image patches using the adaptively learned sparsifying basis in the form of L0 norm, greatly reducing blocking artifacts and confining the CS solution space. To make our proposed scheme tractable and robust, a split Bregman iteration based technique is developed to solve the non-convex L0 minimization problem efficiently. Experimental results on a wide range of natural images for CS recovery have shown that our proposed algorithm achieves significant performance improvements over many current state-of-the-art schemes and exhibits good convergence property.

The implementation can be found here on Jian Zhang's page.

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WESNR : Mixed Noise Removal by Weighted Encoding with Sparse Nonlocal Regularization

Mixed Noise Removal by Weighted Encoding withSparse Nonlocal Regularization by Jielin Jiang, Lei Zhang, and Jian Yang

Abstract—Mixed noise removal from natural images is a challenging task since the noise distribution usually does nothave a parametric model and has a heavy tail. One typical kind of mixed noise is additive white Gaussian noise (AWGN) coupledwith impulse noise (IN). Many mixed noise removal methods are detection based methods. They first detect the locations of impulsenoise pixels and then remove the mixed noise. However, such methods tend to generate many artifacts when the mixed noise is strong. In this paper, we propose a simple yet eff ective method,namely weighted encoding with sparse nonlocal regularization (WESNR), for mixed noise removal. In WESNR, there is not an explicit step of impulse pixel detection; instead, soft impulse pixel detection via weighted encoding is used to deal with IN and AWGN simultaneously. Meanwhile, the image sparsity prior and nonlocal self-similarity prior are integrated into a regularization term and introduced into the variational encoding framework. Experimental results show that the proposed WESNR method achieves leading mixed noise removal performance in terms ofboth quantitative measures and visual quality.

The attendant implementation is on Lei Zhang's page.

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Fast Tracking via Spatio-Temporal Context Learning - implementation -

Fast Tracking via Spatio-Temporal Context Learning by Kaihua Zhang, Lei Zhang, Ming-Hsuan Yang, David Zhang

In this paper, we present a simple yet fast and robust algorithm which exploits the spatio-temporal context for visual tracking. Our approach formulates the spatio-temporal relationships between the object of interest and its local context based on a Bayesian framework, which models the statistical correlation between the low-level features (i.e., image intensity and position) from the target and its surrounding regions. The tracking problem is posed by computing a confidence map, and obtaining the best target location by maximizing an object location likelihood function. The Fast Fourier Transform is adopted for fast learning and detection in this work. Implemented in MATLAB without code optimization, the proposed tracker runs at 350 frames per second on an i7 machine. Extensive experimental results show that the proposed algorithm performs favorably against state-of-the-art methods in terms of efficiency, accuracy and robustness.

The attendant implementation is here.

　
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RCoS : Image Compressive Sensing Recovery via Collaborative Sparsity - implementation -

Image Compressive Sensing Recovery via Collaborative Sparsity by Jian Zhang, Debin Zhao, Chen Zhao, Ruiqin Xiong, Siwei Ma, Wen Gao.

Compressed Sensing (CS) has drawn quite an amount of attention as a joint sampling and compression approach. Its theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. So one of the most significant challenges in CS is to seek a domain where a signal can exhibit a high degree of sparsity and hence be recovered faithfully. Most of conventional CS recovery approaches, however, exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are irrespective of the nonstationarity of natural signals and cannot achieve high enough degree of sparsity, thus resulting in poor rate-distortion performance. In this paper, we propose a new framework for compressed sensing recovery via collaborative sparsity (RCoS), which enforces local two-dimensional sparsity and nonlocal three-dimensional sparsity simultaneously in an adaptive hybrid space-transform domain, thus substantially utilizing intrinsic sparsities of natural images and greatly confining the CS solution space. In addition, an efficient augmented Lagrangian based technique is developed to solve the above optimization problem. Experimental results on a wide range of natural images are presented to demonstrate the efficacy of the new CS recovery strategy.

The attendant implementation is here on Jian Zhang's site.

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Sunday Morning Insights: The Power of Zero

From Wikipedia, Cursive hieroglyphs from thePapyrus of Ani

Triggered by the discussion we had with Brenda McCowan on Unraveling Dolphin Communication Complexity, Past approaches and next steps (video is here) at the Paris Machine Learning Meetup #10, I was fascinated by the potentiality of machine learning algorithms focused on exploration when there is no obvious prior knowledge. Something along the lines of the zero-knowledge proofs where one wants to know more, while knowing nothing [1]. I went ahead and asked several interweb communities about learning without training samples. Here is the initial request I sent out:

Dumb Question: Unsupervised Learning in Science ? 

The vast majority of ML related work and investigation revolves on some amount of supervised learning where there are examples of known meanings. Does anybody know of an example where the learning was unsupervised. For instance someone (re-)learning the Egyptian hieroglyphs without the Rosetta stone or somebody (re-)discovering the Mayan alphabet using strictly machine learning techniques ? The example does not have to be about human languages.

I obviously received good answers on unsupervised learning such as dictionary learning in image processing but I wanted to see what else was out there. On Google+ (here), John Taylor mentioned the following:

In your Rosetta/Maya examples decoding was done by people who already knew several languages. That definitely helped, as opposite to the case if discoverers of Rosetta stone would had no clue about existence of languages. And yes there are papers about such things, so called "zero shot learning". Basically ML systems were trained and "knew" something already, but were given something they never saw with a task of figuring what it could be. And they did good, well at least one system guesses were orders of magnitude better ones then a random guess. If that is something that you are looking for - go Google Scholar and search for zero shot learning papers. 

From Zero-Shot Learning by Convex Combination of Semantic Embeddings by Mohammad Norouzi, Tomas Mikolov, Samy Bengio, Yoram Singer, Jonathon Shlens, Andrea Frome, Greg S. Corrado, Jeffrey Dean, one can read that "zero-shot learning" is defined as "annotation of images with new labels corresponding to previously unseen object categories". That seems pretty close because in effect we are not starting from nothing and we all know from compressive sensing that with additional prior, one can go much farther. In the case of Dolphin communication, Brenda and colleagues are asking whether there are discussions and /or dialects. If one assume that there are discussions, the question becomes, how do we learn that language/dialect.  Here are the most recent papers that mention zero-shot learning, a subject I will probably come back to every once in a while. Here is an example that involve animals yet is centered on imagery. On Reddit, I received three answers   micro_cam

Biologists use a lot of unsupervised learning to look for subtypes in diseases etc:

http://cancergenome.nih.gov/researchhighlights/researchbriefs/foursubtypes

alfonsoeromero

Another application of clustering, in biology too, is the clustering of protein-protein interaction networks to figure out what protein complexes exist in the organism

teamnano

I've used unsupervised learning to downselect candidate ligands from a much larger pool of materials that would have been economically prohibitive to procure. Each ligand had a set of descriptors associated with it, and once a good ligand had been identified from experiments additional ligands could be identified using a nearest neighbors search....you can get a general idea of some of the methods I used if you read some of the cheminformatics publications by Alexander Tropsha. His publications page is here. https://pharmacy.unc.edu/Directory/tropsha/publications

and on LinkedIn, Bill Winkler mentioned the following:

Various forms of unsupervised learning (clustering), semi-supervised learning (moderate or small amounts of 'truth' data are combined with unlabelled data where 'truth' is not known), and supervised learning have been around for 30+ years.

Supervised learning is the standard machine learning method where training data are available.

The semi-supervised learning is where a moderate amount of labelled ('truth') data is combined with unlabelled data. In active learning (a variant of semi-supervised), 'truth' data may be gradually obtained until sufficient 'truth' is available for training a classifier.

For a naive Bayes classifiers, Nigam et al. provide an approach for semi-supervised learning.

Nigam, K., A. K. McCallum, S. Thrun, and T. Mitchell (2000), “Text Classification from Labeled and Unlabelled Documents using EM, Machine Learning, 39, 103-134.

The methods can extended (via a variant of boosting) where both better parameters and better models are obtained simulltaneously. The models/software hold for unsupervised, semi-supervised, and supervised learning.

Winkler, W. E. (2000), “Machine Learning, Information Retrieval, and Record Linkage,” American Statistical Association, Proceedings of the Section on Survey Research Methods, 20-29. (also available at http://nisla05.niss.org/affiliates/dqworkshop/papers/winkler.pdf ).

The following provides a method of unsupervised learning that automatically finds optimal parameters in ~500 subareas of the U.S. The methods outperform an active learning approach (semi-supervised learning) that is widely used for computer matching (record linkage). I presented the following paper in the session "Best from Wiley Interdisciplinary Reviews" at the 2011 Conference on the Interface Between Computing Science and Statistics.

Herzog, T. N., Scheuren, F., and Winkler, W.E., (2010), “Record Linkage,” in (D. W. Scott, Y. Said, and E. Wegman, eds.) Wiley Interdisciplinary Reviews: Computational Statistics, New York, N. Y.: Wiley, 2 (5), September/October, 535-543 .

The unsupervised learning methods were first applied for production software for the U.S. Decennial Censuses.

Winkler, W. E. (1988), "Using the EM Algorithm for Weight Computation in the Fellegi-Sunter Model of Record Linkage," Proceedings of the Section on Survey Research Methods, American Statistical Association, 667-671, also at http://www.census.gov/srd/papers/pdf/rr2000-05.pdf .

The methods were rediscovered using a method where Generalized Additive Models are used for getting the best naive Bayes (conditional independence) approximation of a general Bayes network model but use far less efficient algorithms than the earlier algorithms of Winkler (1988).

Larsen, K. (2005), Generalized Naïve Bayes Classifiers, SIGKDD Explorations, 7 (1), 76-81, doi, 10.1145/1089815.1089826.

Thank you to all who contributed to this post. [1] The Security of Knowing Nothing, B. Chazelle, Nature 446 (26 April 2007), 992-993.and also Zero proof knowledge explained to your kids or on MathOverFlow or one based on Sudoku.




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Registration: 2014 Workshop on Algorithms for Modern Massive Data Sets (MMDS 2014)

We have covered these excellent MMDS meetings before. Mike Mahoney just sent me the following:

Hi Igor,

Hope all is well.... I wanted to ask you to distribute the announcement to anyone in your circles who you think might be interested.

The announcement is below, and note that early registration has been extended by a week.

Thanks!

Michael

Sure Mike. 

Registration for the 2014 Workshop on Algorithms for Modern Massive Data Sets (MMDS 2014) is now available at: 

http://mmds-data.org/home/registration2014 

Early registration has been extended until May 7, 2014.
In addition to four days of talks on algorithmic and statistical aspects of modern large-scale data analysis, MMDS 2014 will have a contributed poster session one evening. The registration fee is waived for student poster presenters. You may apply to present a poster at the link above.
Event: MMDS 2014: Workshop on Algorithms for Modern Massive Data Sets
Dates: June 17-20, 2014
Location: UC Berkeley, Berkeley, CA
Website: http://mmds-data.orgContact: organizers@mmds-data.org
Synopsis: The 2014 Workshop on Algorithms for Modern Massive Data Sets (MMDS 2014) will address algorithmic, mathematical, and statistical challenges in modern statistical data analysis. The goals of MMDS 2014 are to explore novel techniques for modeling and analyzing massive, high-dimensional, and nonlinearly-structured scientific and internet data sets, and to bring together computer scientists, statisticians,
mathematicians, and data analysis practitioners to promote cross-fertilization of ideas.

Organizers: Michael Mahoney (UC Berkeley), Alexander Shkolnik (Stanford), Petros Drineas (RPI), Reza Zadeh (Stanford), Fernando Perez (UC Berkeley)

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Multiple Regularizers: Multi-View Learning and Hyperspectral Imagery

I came across the following two papers which have in common the utilization of several regularizers in learning and inverse problems, an issue of on-going interest in semi-supervised learning, see also previously

• Multiple regularizers, Robust NMF and a simple question
• Multiple Regularizers For the Reconstruction of Natural Objects ?
• Optimization with multiple non-standard regularizers

I wonder how those approaches will eventually be comparable. The only way we have been able to see this in compressive sensing is through their performance in phase transition type of problems. We all know that using prior information will help in making polynomial-time algorithms go further (i.e. for instance less sampling is required for block sparse signals than sparse-only signals), but the question for this multi-regularizer issue is: should we go for simple metrics one at a time (and hence with multiple regularizers) or should we go for specifically designed metrics (see Francis Bach's course at slide 99 and up Structured sparsity through convex optimization , where he mentions the use of submodularity to find new regularizers) ? To avoid fragmentation between fields which will be unavoidable, we need to make sure that multi regularizers or simple more effective regularizers are put to the test through the simple phase transition acid test.

Without further due, here are today's papers:

Overlapping Trace Norms in Multi-View Learning by Behrouz Behmardi, Cedric Archambeau, Guillaume Bouchard

Multi-view learning leverages correlations between different sources of data to make predic- tions in one view based on observations in another view. A popular approach is to assume that, both, the correlations between the views and the view-specific covariances have a low- rank structure, leading to inter-battery factor analysis, a model closely related to canonical correlation analysis. We propose a convex relaxation of this model using structured norm regularization. Further, we extend the convex formulation to a robust version by adding an l1-penalized matrix to our estimator, similarly to convex robust PCA. We develop and compare scalable algorithms for several convex multi-view models. We show experimentally that the view-specific correlations are improving data imputation performances, as well as labeling accuracy in real-world multi-label prediction tasks.

Reconstructing Hyperspectral Images from Compressive Sensors by Exploiting the Prior Knowledge by Yingbiao Jia, Yan Feng

Compressive Sensing (CS) indicates new mechanism for hyperspectral imaging and practical hyperspectral compressive sensors have been designed to acquire fewer compressive measurements. However the numerical reconstruction of the hyperspectral data from the compressive measurements requires solving an ill-posed inverse problem and additional constraints are needed to seek a better solution. Based on the observation that in CS reconstruction quality can be improved from intelligent use of prior knowledge of the original data, we proposed an efficient new method to reconstruct Hyperspectral Images (HSI) in this paper. Our method, which exploit the HSI data structure characters of spatial 2D piecewise smoothness, low-rank property and adjacent spectrum correlation, have allowed to reconstruct HSI with compound regularizers. Moreover, an efficient numerical algorithm is developed for our method. The experimental results show that our method exhibits its superiority over other known state-of-the-art methods with higher reconstruction quality at the same measurement rates.

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CSJob: PhD Studentship, Sparse Representation and Learning in Pattern Recognition at Computer Science Department, Laval University, Canada

Brahim Chaib-draa just sent me the following:

Hello Igor,  

Thanks for the very nice and inspiring blog
Would you please (if it is possible) advertise the following Proposal for PhD Thesis at Laval University, Québec (Canada)
Thanks a lot

Pr. B. Chaib-draa

Directeur des études gradués

Dépt IFT/GLO, Université Laval, Québec, Canada

Sure Brahim ! here it is:

Proposal for PhD Thesis

Sparse Representation and Learning in Pattern Recognition
at Computer Science Department, Laval University, Canada

Keywords:  Sparse Representation, Structured Sparsity, Sparse Subspace Learning, Visual Recognition, Feature Selection, Sparse Coding, Sparsity Induced Similarity,

Background:  Sparse representation and learning have been extensively used recently in machine learning, computer vision, pattern recognition, etc. Generally speaking, sparse representation and learning aim to find the sparsest linear combination of basis functions from a complete dictionary. A rational behind this lies in the fact that there is a sparse connectivity between nodes in human brain.

In many signal processing applications (video, image processing, speech recognition, etc.)  the data sets are usually high dimensional and very large. In this context, sparse representation and learning have shown to be promising techniques for addressing them.

Recently, many important theoretical results enriched this area as for instance [1]: (i) the sparsest representation in a general dictionary is unique and can be found by using L1 minimisation [2]; (ii) the sparse representation can be covered by solving the convex programming, if the dictionary has a restricted isometry property [3,4]. Thanks to these important results and their corollaries, sparse representation and learning have extensively been used in many areas including signal processing and applications as speech recognition, machine learning, computer vision, digital multimedia, robotics, etc. A complete review on sparse representation and learning from both theory and applications sides appeared recently [1].

Goal and Objectives:

The goal of this PhD research is to strive to address the following issues:

• Is the sparsity assumption always supported by the data? Nowadays, compressive sensing has become one of the standard techniques of object recognition. If the sparsity is however not supported by the data, it is not guarantee to recover the exact signal and therefore sparse approximations may not deliver the robustness or performance desired [5]. In this case what sort of acceptable (in terms of computation load) robust method can be?   
• When the Sparse Representation is Relevant? It is important here to perform an in-depth analysis of sparse representation in pattern recognition and see empirically if this sparse representation improves recognition performance compared to non-sparse representations [6]. To this end, it would be important to take into consideration the way to extract features and to refine them as well as the computational load induced by the all process of sparse representation. 
• Sparse Representation or Collaborative Representation, which one is the best?Similarly to Zhang’s work [7], it would be appropriate to see if the use of all training samples to collaboratively represent a query sample is much more crucial to sparse representation based classification (SRC). Taking into consideration the fact that the collaborative representation based classification (CRC) plays a more important role than L1-regularization as shown by Zhang et al. [7], it would be opportune to see what new instantiations of CRC (with less computational load than usual SRC) can be proposed.
• Is sparse representation and learning usefulness in the context of video-based action modeling and recognition? Are ideas from this application fairly general and applicable to other recognition problems? One should here explore the usefulness of sparse representation and learning in the context of video classification, looking particularly at the problem of recognizing human actions-both physical actions and facial expressions [8]. This can be achieved by constructing an overcomplete dictionary using a set of spatio-temporal descriptors (extracted from the video sequences) in such a way that each of these descriptors is represented by some linear combination of a small number of dictionary elements. By doing so, one can achieve a more compact and richer representation than classical methods using clustering and vector quantization. It is also important to see which representation (sparse vs collaborative) is the more convenient for human-action recognition.  Experiments and validation of generalization to other recognition problems can be done on several data sets containing various physical actions, facial expressions and object recognition.

Job Description:

The PhD candidate will focus on signal processing and machine learning. In this context, she will first acquire expertise in different topics such as clustering and classification, Bayesian and generative modelling, signal separation, parameter and state estimation,  time series and space state methods, compression and coding. Then, the PhD candidate is expected to contribute to the advancement of the literature on sparse representation and learning along many different lines: methodological, theoretical, algorithmic and experimental.

Profile:

The applicant must have a Master of Science in Computer Science or Computer Engineering, Statistics, or related fields, possibly with background in Signal Processing and optimization. Good written and oral communication skills in English are required.

Application:

The application should include a brief description of research interests and past experience, a CV, degrees and grades, a copy of Master thesis (or a draft thereof), motivation letter (short but pertinent to this call), relevant publications (if any), and other relevant documents. Candidates are encouraged to provide letter(s) of recommendation and contact information to reference persons. Please send your application to chaib@ift.ulaval.ca. The deadline for the application is June15th, 2014, but we encourage the applicants to contact me as soon as possible. 

• Supervisors:  Pr. Brahim Chaib-draa
• Place: Department Computer Science and software Engineering, Laval University,Québec

Working Environment:

• The PhD candidate will work at Damas lab part of the Department Computer Science and software Engineering in collaboration with researchers from REPARTI center of which Chaib-draa is affiliated (http://reparti.gel.ulaval.ca/). REPARTI provides several advantages, including a human infrastructure to help with some management aspects for research, and access to a wide network of other researchers in areas closely related to the topic of this PhD proposal.

Benefits:

• Duration: 36 months – starting date: September 2014, 1^st
• Salary: 19 000$/Year + 3 000$/year (from University)

References:

1. Cheng, H.; Liu, Z.; Yang, L.; and Chen, X. Sparse Representation and Learning in Visual Recognition: Theory and Applications, Signal Processing, 93, 2013.
2. Donoho, D. and Elad, M. Optimally Sparse Representation in General (non-orthogonal) Dictionaries via L1 minimization. Proc. Of the National Academy of Sciences, 100(5), 2003.
3. Candes, E.J.; Romberg, J. K. and Tao, T. Stable Signal Recovery from Incomplete and Inaccurate Measurements. Communications on Pure and Applied Mathematics, 59(8), 2006.
4. Candes, E. J. and Tao, T. Near optimal Signal Recovery from random Projection: Universal Encoding Strategies? IEEE Transaction on Information Theory, 52(12), 2006.
5. Shi, Q,; Erikson, A.,; Hengel, A. and Shen, C. Is Face Recognition really a Compressive Sensing Problem? In Proc. of CVPR’11, 2011.
6. Rigamonti, R.; Brown, M. A. and Lepetit, V.  Are Sparse Representations Really Relevant for Image Classification? In Proc. of CVPR’11, 2011.
7. Zhang, L.; Yang, M.; and Feng X. Sparse Representation or Collaborative Representations: which Helps Face Recognition? IEEE Int. Conf on Computer Vision, 2011.
8. Guha, T. and Ward, R. K. Learning Sparse Representations for Human Action Recognition, IEEE Transaction on PAMI, 34(8), 2012.

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CSJob: Data Scientist Position. Chaire "Economie et gestion des nouvelles données"

Gabriel Peyre sent me the following three weeks ago but it slipped through the many things that happened this past month:

Dear Igor,

If you think it is interesting for your readership, would it be possible that you post some advertisement for the following position ?

All the best

Gabriel

Here is the announcement:

Position as data scientist

Chaire "Economie et gestion des nouvelles données"

• Location: within one of the lab of the chaire (Paris-Dauphine, ENS Ulm, Ecole Polytechnique or ENSAE).
• Duration: 1 year renewable at least once.
• Salary: to be discussed depending on the applicant’s profile.
• Start: as early as May 2014, and no later than September 2014.
• Application process: send a resume and a motivation letter to:
  Stephane Gaiffas <stephane.gaiffas@cmap.polytechnique.fr>
  Robin Ryder <ryder@ceremade.dauphine.fr>
  Gabriel Peyré <peyre@ceremade.dauphine.fr>

Job description

The chaire "Economie et gestion des nouvelles données" is recruiting a talented young engineer specialized in large scale computing and data processing. The targeted applications include machine learning, imaging sciences and finance. This is a unique opportunity to join a newly created research group between the best Parisian labs in applied mathematics and computer science (Paris-Dauphine, ENS Ulm, Ecole Polytechnique and ENSAE) working hand in hand with major industrial companies (Havas, BNP Paribas, Warner Bros.). The proposed position consists in helping researchers of the group to develop and implement large-scale data processing methods, and applying these methods on real-life problems in collaboration with the industrial partners.

A non-exhaustive list of methods that are currently investigated by researchers of the group, and that will play a key role in the computational framework developed by the recruited engineer, includes :

• Large scale non-smooth optimization methods (proximal schemes, interior points, optimization on manifolds).
• Machine learning problems (kernelized methods, Lasso, collaborative filtering, deep learning, learning for graphs, learning for time-dependent systems), with a particular focus on large-scale problems and stochastic methods.
• Imaging problems (compressed sensing, super-resolution).
• Approximate Bayesian Computation (ABC) methods.
• Particle and Sequential Monte Carlo methods

Candidate profile

The candidate should have a very good background in computer science with various programming environments (e.g. Matlab, Python, C++) and knowledge of high performance computing methods (e.g. GPU, parallelization, cloud computing). He/she should adhere to the open source philosophy and possibly be able to interact with the relevant communities (e.g. scikitlearn initiative). Typical curriculum includes engineering school or Master studies in computer science / applied maths / physics, and possibly a PhD (not required).

Working environment

The recruited engineer will work within one of the labs of the chaire. He will benefit from a very stimulating working environment and all required computing resources. He will work in close interaction with the 4 research labs of the chaire, and will also have regular meetings with the industrial partners. More information about the chaire can be found online at

http://www.di.ens.fr/~aspremon/chaire/

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