Nuit Blanche in Review (July 2014)

We have had quite a few new items, including my first paper published in the realm of compressive sensing since the last Nuit Blanche in Review (June 2014). We also had 11 implementations made available by their respective authors:

• GreBsmo: Greedy Bilateral Sketch, Completion & Smoothing - implementation -
• Adaptive-Rate Compressive Sensing Using Side Information - implementation -
• Tight convex relaxations for sparse matrix factorization - implementation -
• Mondrian Forests: Efficient Online Random Forests - implementation -
• Fast matrix completion without the condition number - implementation -
• Dynamic MR image reconstruction–separation from undersampled (k,t)-space via low-rank plus sparse prior - implementation -
• Understanding Random Forests: From Theory to Practice - implementation -
• Phase Retrieval via Wirtinger Flow: Theory and Algorithms - implementation -
• Randomized Numerical Linear Algebra for Large Scale Data Analysis ( libSkylark: Sketching based Matrix computations for Machine Learning )
• SASIR: LOFAR Sparse Image Reconstruction - implementation -
• Stable, Robust and Super Fast Reconstruction of Tensors Using Multi-Way Projections - implementation -

My paper also resulted in a few blog entries:

• Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium
• The Post Publication Peer Review of "Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium"
• Additional Photos and Video to "Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium"
• Follow up on "Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium"

I also featured a certain number of related papers 

• Speckle suppression via sparse representation for wide-field imaging through turbid media
• Random Matrices Are Too Damn Large !
• Another Comment on " Random Matrices Are Too Damn Large ! "
• Compressed Sensing via Universal Denoising and Approximate Message Passing
• Transmission of quantum entanglement through a random medium / Terahertz compressive imaging with metamaterial spatial light modulators

It also had me to be more focused about certain publishing options. More on that later:

• Does a lack of affiliation mean I cannot publish ?
• How To Cite Nuit Blanche and related pages

Other papers and notes were also featured:

• Compressed Subspace Matching on the Continuum / Subspace Learning From Bits
• Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed $\ell_1/ell_2$ Regularization
• Complexity-Matching Universal Signal Estimation in Compressed Sensing
• Tensor Networks for Big Data Analytics and Large-Scale Optimization Problems
• Rows vs Columns for Linear Systems of Equations - Randomized Kaczmarz or Coordinate Descent ?
• Context Aware Recommendation Systems ( Lei Tang, Xavier Amatriain)
• The Gamification Design Problem
• The 200 Million Dollar Assumption

A discussion on Uncertainty Relations with compressive sensing led to a few posts:

• Simultaneous Measurement of Complementary Observables with Compressive Sensing
• Entropic Uncertainty Relations in Quantum Physics / On asymptotic structure in compressed sensing
• Some Comments: Universal Compressed Sensing of Markov Sources, A survey of uncertainty principles and some signal processing applications, Refined support and entropic uncertainty inequalities

I also did a presentation at the Paris Context Aware Meetup:

• It's not as random as it seems, Paris Context Aware Meetup #1

Sunday Morning Insight: 

• Sunday Morning Insight: Zero Knowledge Sensor Design / Data Driven Sensor Design
• Sunday Morning Insight: Note By Note Cooking
• Sunday Morning Insight: Mathematical and Algorithmic Analysis of Network and Biological Data & Open problems from the 2014 Bertinoro Workshop on Sublinear Algorithms

Meetings (CfP, Slides, Videos)

• GdR ISIS: Acquisition/Echantillonnage comprimé : quelles réalisations/applications pratiques ?
• Saturday Morning Videos: 27th Annual Conference on Learning Theory (COLT), Barcelona 2014
• Last Call for Contributions - TCMM 2014 International Workshop on Technical Computing for Machine Learning and Mathematical Engineering, 8 - 12 September, 2014 - Leuven, Belgium
• Slides: Summer School on Hashing: Theory and Applications, 2014
• Video Stream: GraphLab Conference 2014
• Slides: Science on the Sphere
• It's not as random as it seems, Paris Context Aware Meetup #1
• Saturday Morning Videos: 27th Annual Conference on Learning Theory (COLT), Barcelona 
• Saturday Morning Videos: Machine Learning Summer School Pittsburgh 2014, Muthu Muthukrishnan
• Saturday Morning Videos: Paris-Saclay Center for Data Science kick-off meeting

Other Videos

• Saturday Morning Video: A simple heart rate monitor, Fireworks filmed with a drone, Thermal Touch - A New Augmented Reality Interface for Wearables

Hamming's time

• It's Friday afternoon, it's Hamming's time: Higher Order Antipode Maps ?

Random notes:

• More Than 20 Artificially Intelligent Space Probes Were Already Not Contained in the Frame of this Picture
• 1250 posts on the CompressiveSensing Subreddit.
• A Second Inflection Point in Genome Sequencing ? and then ...
• Being a child of Moore's Law

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GreBsmo: Greedy Bilateral Sketch, Completion & Smoothing - implementation -

In CAI: Cable And Igor's Adventures in Matrix Factorization, Cable and I used the GoDec algorithm of Tianyi Zhou to play with several Youtube videos. There are all here. Kyle Kastner did a similar undertaking using Python and IPython. it is all here.

Today, we have an even faster version of GoDecin GreBsmo as featured in Greedy Bilateral Sketch, Completion & Smoothing by Tianyi Zhou, Dacheng Tao

Recovering a large low-rank matrix from highly corrupted, incomplete or sparse outlier overwhelmed observations is the crux of various intriguing statistical problems. We explore the power of “greedy bilateral (GreB)” paradigm in reducing both time and sample complexities for solving these problems. GreB models a lowrank variable as a bilateral factorization, and updates the left and right factors in a mutually adaptive and greedy incremental manner. We detail how to model and solve low-rank approximation, matrix completion and robust PCA in GreB’s paradigm. On their MATLAB implementations, approximating a noisy 104 × 104 matrix of rank 500 with SVD accuracy takes 6s; MovieLens10M matrix of size 69878 × 10677 can be completed in 10s from 30% of 107 ratings with RMSE 0.86 on the rest 70%; the low-rank background and sparse moving outliers in a 120×160 video of 500 frames are accurately separated in 1s. This brings 30 to 100 times acceleration in solving these popular statistical problems.

The attendant code is here.

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GdR ISIS: Acquisition/Echantillonnage comprimé : quelles réalisations/applications pratiques ?

One of my co-author, Laurent Daudet, asked me to feature this French centered CfP (speakers do not need to be presenting in French). Here it is:

Réunion du GdR ISIS

• Titre : Acquisition/Echantillonnage comprimé : quelles réalisations/applications pratiques ?
• Dates : 2014-09-12
• Lieu : Télécom ParisTech, PARIS

Nous vous rappelons que, afin de garantir l'accès de tous les inscrits aux salles de réunion, l'inscription aux réunions est gratuite mais obligatoire.

Annonce :

« Acquisition/Echantillonnage comprimé : quelles réalisations/applications pratiques ? »

Journée thématique conjointe GDR/ISIS et GDR/SoC-SiP

Organisateurs :

Patricia Desgreys (LTCI/IMT/Télécom ParisTech,patricia.desgreys@telecom-paristech.fr) et Laurent Daudet (Institut Langevin / Université Paris Diderot, laurent.daudet@espci.fr )

Objectifs :

Cette journée thématique organisée conjointement par les GdR ISIS et SoC-SiP est consacrée aux applications concrètes des travaux dans le domaine de l’acquisition comprimée (ou Compressed Sensing, CS) depuis que le concept a été défini par E. Candes et D. Donoho en 2004. Cette théorie montre que la plupart des signaux (à représentation parcimonieuse dans une base élémentaire) peuvent être échantillonnés linéairement avec un taux d’échantillonnage très faible (proportionnel à leur parcimonie). Ainsi le CS permet d’acquérir une information avec un nombre réduit d’observations, potentiellement bien moindre que selon les critères de Shannon-Nyquist.

Depuis ces publications fondatrices, l’acquisition comprimée a été très étudiée, particulièrement pour le choix des bases de projection et l’optimisation des algorithmes de reconstruction. Concrètement le CS peut être utilisé pour réduire la complexité et la consommation dans un grand nombre de domaine d’applications : radio-intelligente, acquisition d’ondes acoustiques ou optiques, acquisition de signaux médicaux. Plus récemment, des réalisations physiques illustrant les principes de l’acquisition comprimée ont été publiées pour la conversion analogique à information (A2I), l’acquisition de signaux radio, ou l’imagerie.

Nous proposons, lors de cette journée, de faire un bilan des applications concrètes visées par le CS, des premières réalisations et de leurs performances.

La matinée sera consacrée à deux exposés tutoriels, de 1h chacun (45’ + 15’ de questions) :

• C. Studer (Cornell University) and Qiuting Huang (ETH Zurich): Analog-to-Information Converters: From Applications to Circuits
• Laurent Jacques (UC Louvain) : Optique et acquisition comprimée : déflectométrie schlieren compressive et reconstruction de cartes d'indice de réfraction

L’après-midi sera consacré à des exposés courts (20’ + 10’ de questions), selon l’appel à contributions ci-dessous.

Les membres du GdR ISIS sont priés de s’inscrire sur le sitehttp://www.gdr-isis.fr/.

Toute autre personne intéressée par cette journée est invitée à contacter les organisateurs.

Appel à contribution :

Les personnes souhaitant présenter leurs travaux sont invitées à faire part de leur intention (titre + résumé 1/2 page) aux organisateurs avant le 20 août.
Le programme définitif sera communiqué le 30 août.

Lien : http://gdr-isis.fr/index.php?page=reunion&idreunion=253

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Adaptive-Rate Compressive Sensing Using Side Information - implementation -

Adaptive-Rate Compressive Sensing Using Side Information by Garrett Warnell, Sourabh Bhattacharya, Rama Chellappa, Tamer Basar

We provide two novel adaptive-rate compressive sensing (CS) strategies for sparse, time-varying signals using side information. Our first method utilizes extra cross-validation measurements, and the second one exploits extra low-resolution measurements. Unlike the majority of current CS techniques, we do not assume that we know an upper bound on the number of significant coefficients that comprise the images in the video sequence. Instead, we use the side information to predict the number of significant coefficients in the signal at the next time instant. For each image in the video sequence, our techniques specify a fixed number of spatially-multiplexed CS measurements to acquire, and adjust this quantity from image to image. Our strategies are developed in the specific context of background subtraction for surveillance video, and we experimentally validate the proposed methods on real video sequences.

The attendant code is on Garrett Warnell's project page.

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Tight convex relaxations for sparse matrix factorization - implementation -

Tight convex relaxations for sparse matrix factorization by Emile Richard, Guillaume Obozinski, Jean-Philippe Vert 

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and low-rank sparse bilinear regression as potential applications. We compute slow rates and an upper bound on the statistical dimension of the suggested norm for rank 1 matrices, showing that its statistical dimension is an order of magnitude smaller than the usual ℓ1-norm, trace norm and their combinations. Even though our convex formulation is in theory hard and does not lead to provably polynomial time algorithmic schemes, we propose an active set algorithm leveraging the structure of the convex problem to solve it and show promising numerical results.

The implementation of the Sparse PCA using various methods and some sparsely factorized matrices using the (k,q)-trace norm as penalty are on Emile Richard's software page. They will be added to the Advanced Matrix Factorization Jungle page shortly.

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Compressed Subspace Matching on the Continuum / Subspace Learning From Bits

Two different techniques to learn more about the subspace you're in.

Compressed Subspace Matching on the Continuum by William Mantzel, Justin Romberg

We consider the general problem of matching a subspace to a signal in R^N that has been observed indirectly (compressed) through a random projection. We are interested in the case where the collection of K-dimensional subspaces is continuously parameterized, i.e. naturally indexed by an interval from the real line, or more generally a region of R^D. Our main results show that if the dimension of the random projection is on the order of K times a geometrical constant that describes the complexity of the collection, then the match obtained from the compressed observation is nearly as good as one obtained from a full observation of the signal. We give multiple concrete examples of collections of subspaces for which this geometrical constant can be estimated, and discuss the relevance of the results to the general problems of template matching and source localization.

Subspace Learning From Bits by Yuejie Chi

This paper proposes a simple sensing and estimation framework to faithfully recover the principal subspace of high-dimensional datasets or data streams from a collection of one-bit measurements from distributed sensors based on comparing accumulated energy projections of their data samples of dimension n over pairs of randomly selected directions. By leveraging low-dimensional structures, the top eigenvectors of a properly designed surrogate matrix is shown to recover the principal subspace of rank $r$ as soon as the number of bit measurements exceeds the order of $nr^2 \log n$, which can be much smaller than the ambient dimension of the covariance matrix. The sample complexity to obtain reliable comparison outcomes is also obtained. Furthermore, we develop a low-complexity online algorithm to track the principal subspace that allows new bit measurements arrive sequentially. Numerical examples are provided to validate the proposed approach.

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Mondrian Forests: Efficient Online Random Forests - implementation -

It looks Mondrian inspired a few images in the mind of people ( CS: The Boogie Woogie Grid ). Here is different version of a random forest, only online this time:  

Mondrian Forests: Efficient Online Random Forests by Balaji Lakshminarayanan, Daniel M. Roy, Yee Whye Teh

Ensembles of randomized decision trees, usually referred to as random forests, are widely used for classification and regression tasks in machine learning and statistics. Random forests achieve competitive predictive performance and are computationally efficient to train and test, making them excellent candidates for real-world prediction tasks. The most popular random forest variants (such as Breiman's random forest and extremely randomized trees) operate on batches of training data. Online methods are now in greater demand. Existing online random forests, however, require more training data than their batch counterpart to achieve comparable predictive performance. In this work, we use Mondrian processes (Roy and Teh, 2009) to construct ensembles of random decision trees we call Mondrian forests. Mondrian forests can be grown in an incremental/online fashion and remarkably, the distribution of online Mondrian forests is the same as that of batch Mondrian forests. Mondrian forests achieve competitive predictive performance comparable with existing online random forests and periodically re-trained batch random forests, while being more than an order of magnitude faster, thus representing a better computation vs accuracy tradeoff.

The GitHub repository for the implementation of the Mondrian Forest  is here.

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Saturday Morning Videos: 27th Annual Conference on Learning Theory (COLT), Barcelona 2014

 All the videos of the 27th Annual Conference on Learning Theory (COLT), Barcelona 2014 are here.


Here are a few:

Sequential Learning

Compressed Counting Meets Compressed Sensing
Ping Li

Invited Speakers
48 views, 56:26  Invited Talk On the Computational and Statistical Interface and "BIG DATA" Michael I. Jordan

Invited Speakers
48 views, 56:26  Invited Talk On the Computational and Statistical Interface and "BIG DATA" Michael I. Jordan	[syn]  5 views, 50:22  Invited Talk Implementing the "Wisdom of the Crowd" Yishay Mansour
Unsupervised Learning; Dictionary Learning; Latent Variable Models
[syn]  7 views, 16:20   New Algorithms for Learning Incoherent and Overcomplete Dictionaries Ankur Moitra

Unsupervised Learning; Mixture Models
[syn]  1 view, 13:44   The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixtures Joseph Anderson	[syn]  15 views, 19:38   Faster and Sample Near-Optimal Algorithms for Proper Learning Mixtures of Gaussians Gautam Kamath

Online Learning

[syn]  3 views, 08:55   Online Learning with Composite Loss Functions Ofer Dekel

[syn]  6 views, 06:15   Most Correlated Arms Identification Sébastien Bubeck

Computational Learning Theory/Algorithmic Results

[syn]  4 views, 15:40   Fast Matrix Completion Without the Condition Number Mary Wootters

Computational Learning Theory/Lower Bounds
[syn]  3 views, 18:23   Computational Limits for Matrix Completion Benjamin Weitz	[syn]  3 views, 15:16   Lower bounds on the performance of polynomial-time algorithms for sparse linear regression Yuchen Zhang

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It's Friday afternoon, it's Hamming's time: Higher Order Antipode Maps ?

When reading the presentation of Rod Kennedy on Kernel-Based Formulations of Spatio-Spectral and Three Related Transforms on the Sphere featured in the Science on the Sphere workshop, I was reminded of this earlier blog entry ( It's Friday afternoon, it's Hamming's time: Antipode Seismic Maps ? )

Could the second map be roughly approximated through the use of correlation between zero-th, first and higher order harmonic on the sphere ?

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Last Call for Contributions - TCMM 2014 International Workshop on Technical Computing for Machine Learning and Mathematical Engineering, 8 - 12 September, 2014 - Leuven, Belgium

Marco just sent me the following:

Dear Igor, could you be so kind to post the attached CFP  (last call for contributions - TCMM 2014) on Nuit Blanche? kind regards Marco -- dr. Marco Signoretto FWO research fellow, ESAT - STADIUS, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 LEUVEN - HEVERLEE (BELGIUM) Homepage: http://homes.esat.kuleuven.be/~msignore/

Sure Marco, here is the call:
                                                                                                                                                                                                                                                               

Last Call for Contributions - TCMM 2014 International Workshop on Technical Computing for Machine Learning and Mathematical Engineering 8 - 12 September, 2014 - Leuven, Belgium Workshop homepage: http://www.esat.kuleuven.be/stadius/tcmm2014/ The workshop will provide a venue for researchers and practitioners to interact on the latest developments in technical computing in relation to machine learning and mathematical engineering problems and methods (including also optimization, system identification, computational statistics, signal processing, data visualization, deep learning, compressed sensing and big-data). The emphasis is especially on open-source implementations in high-level programming languages, including but not limited to Julia, Python, Scala and R. For further information see the workshop homepage. The 3 days main event (8-10 September) will consist of invited and contributed talks as well as poster presentations. It will be followed by a 2 days additional event (11-12 September) including software demos and hands-on tutorials on selected topics.  Attendees can register to the main event only or to the full workshop. Submission of extended abstracts are solicited for the main event. Submission of demo presentations are solicited for the two days additional event. For further information (including Registration, Location and Venue) see details at the workshop website. Important dates:  Deadline extended abstract/demo submission: 31 July 2014 Deadline for registration: 1 September 2014 Confirmed invited speakers (talks and tutorials):  James Bergstra, Center for Theoretical Neuroscience, University of Waterloo: Theano and Hyperopt: Modelling, Training, and Hyperparameter Optimization in Python Jeff Bezanson, MIT: TBA Luis Pedro Coelho, European Molecular Biology Laboratory (EMBL): Large Scale Analysis of Bioimages Using Python Steven Diamond, Stanford University Convex Optimization in Python with CVXPY Stefan Karpinski, MIT TBA Graham Taylor, School of Engineering, University of Guelph: An Overview of Deep Learning and Its Challenges for Technical Computing Ewout van den Berg, IBM T.J. Watson Research Center: Tools and Techniques for Sparse Optimization and Beyond Organizing committee:  Marco Signoretto, Department of Electrical Engineering, KU Leuven Johan Suykens, Department of Electrical Engineering, KU Leuven Vilen Jumutc , Department of Electrical Engineering, KU Leuven For further information (including Registration, Location and Venue) see http://www.esat.kuleuven.be/stadius/tcmm2014/

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Fast matrix completion without the condition number - implementation -

Fast matrix completion without the condition number by Moritz Hardt, Mary Wootters

We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix. To the best of our knowledge, all previous algorithms either incurred a quadratic dependence on the condition number of the unknown matrix or a quadratic dependence on the dimension of the matrix in the running time. Our algorithm is based on a novel extension of Alternating Minimization which we show has theoretical guarantees under standard assumptions even in the presence of noise.

The attendant implementation is on Mary Wootters research page.

You can also watch a video of Mary at COLT:  Fast Matrix Completion Without the Condition Number, Mary Wootters

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The 200 Million Dollar Assumption

There used to be the Six Million Dollar Man, but now with inflation and all, we have the 200 Million Dollar Assumption. In some of the Slides from the workshop on Science on the Sphere, you may have noticed this slide from Tom Kitching on Weak lensing on the sphere

I went ahead and asked Tom what he meant by mentioning a 200M$ assumption, here is what he responded:

Dear Igor,

Thank you for your email.

The the plot on the slide is from this paper http://arxiv.org/pdf/1007.2953.pdf where we investigated the impact of the "Limber approximation" on weak lensing statistics and forecasted cosmological parameter error. The approximation replaces Bessel functions with delta functions to make calculations easier, and should be ok for small scales (where the functional approximation is asymptotically ok). What we found was that the predicted marginalised 1-sigma error bars using the Limber approximation are about 20% larger than when the approximation is not used.

Future experiments such as Euclid, LSST and SKA are to cost about 1 billion euros/dollars so a 20% increase in error bars on the key parameters is the equivalent cost of nearly 200M.

This was a slightly provocative statement aimed to stimulate discussion on how we can avoid this and other approximations to fully exploit these new experiments. In fact it reminds me of a sporting analogy where it is often said that the "aggregated effect of marginal gains" (e.g. http://www.bbc.co.uk/sport/0/olympics/19174302) can result in wins; where small differences can all add up to a significant difference.

I hope that helps, let me know if you have any further questions.

Best Regards
Tom

Thanks Tom !

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