Moment Tensor Potentials: a class of systematically improvable interatomic potentials

Using a sparsity seeking solver to fit a tensor based functional expansion in Materials Science. Woohoo.

Moment Tensor Potentials: a class of systematically improvable interatomic potentials by  Alexander V. Shapeev

Density functional theory offers a very accurate way of computing materials properties from first principles. However, it is too expensive for modelling large-scale molecular systems whose properties are, in contrast, computed using interatomic potentials.
The present paper considers, from a mathematical point of view, the problem of constructing interatomic potentials that approximate a given quantum-mechanical interaction model. In particular, a new class of systematically improvable potentials is proposed, analyzed, and tested on an existing quantum-mechanical database.

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The Fall of Everything Else

People keep on talking about the fear of inflated expectations eventually yielding another winter for Artificial Intelligence. If anything, this year saw the Fall of Everything Else, Winter is coming to these fields and it takes the shape of the Great Convergence .

The Great Convergence is when several engineering fields and Machine Learning techniques are beginning to use very similar if not identical algorithms.

How ?

Well for one, we have witnessed several reconstruction solvers that can be built from data ( also here, here, here, here). It's not just that, the same goes for matrix factorization (cocktail party source separation or here ) or as Tomasz pointed out recently it is also the case in more traditional computer vision techniques (learning optical flow, or deblurring) or even investigation of new imaging modalities using ML algorithms (hence the reason for this recent entry Hamming's Time: Making Hyperspectral Imaging Mainstream)

We have also seen engineering physics getting closer to traditional signal processing ( see Physics-driven inverse problems made tractable with cosparse regularization, Sunday Morning Insight: Physics Driven Sensor Design ?, Sunday Morning Insight entry two years ago entitled "The Linear Boltzmann Equation and Co-Sparsity" ) or convex formulations being used in more traditional machine learning settings (3D Shape Reconstruction from 2D Landmarks: A Convex Formulation, Sparse Reinforcement Learning via Convex Optimization).

We should rejoice for the Great Convergence in the same way we should rejoice for the winter solstice. The Fall of Everything Else is a good thing.

h/t Tomasz Malisiewicz , Laurent Duval, Laurent Daudet for insightful discussions.

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The Great Convergence in Action: Learning optimal nonlinearities for iterative thresholding algorithms

Is Winter coming to applied mathematics ?

Learning optimal nonlinearities for iterative thresholding algorithms by Ulugbek S. Kamilov, Hassan Mansour

Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simple deep neural network (DNN) and developing a corresponding error backpropagation algorithm that allows to fine-tune the thresholding functions. Simulations on sparse statistical signals illustrate potential gains in estimation quality due to the proposed data adaptive ISTA.

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Sunday Morning Science Videos: Pluto and Charon Flyover Closeup Videos

Wow ! 

From the New Horizons Processed YouTube account, here are some processed shots of images taken by New Horizons over non-planets Pluto and Charon.

 Pluto

   

Charon

 

 

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Hamming's Time: Making Hyperspectral Imaging Mainstream

Friday afternoon is Hamming's time. Today I decided to compete in the Best Camera Application contest of XIMEA, a maker of small hyperspectral cameras. Here is my entry:

Challenging task: Make hyperspectral imaging mainstream

Idea: Create a large database of hyperspectral imagery for use in Machine/Deep Learning Competitions

Proposer: Igor Carron, http://nuit-blanche.blogspot.com , http://www.linkedin.com/in/IgorCarron

Background

Machine Learning is the field concerned with creating, training and using algorithms dedicated to making  sense of data. These algorithms are taking advantage of training data (images, videos) as a way of improving for tasks such as detection, classification, etc. In recent years, we have witnessed a spectacular growth in this field thanks to the joint availability of large datasets originating from the internet and the attendant curating/labeling efforts of said images and videos.

Numerous labeled datasets available such as CIFAR [1], Imagenet [2], etc. routinely permit algorithms of increased complexity to be developed and compete in state of the art classification contests. For instance, the rise of deep learning algorithms comes from breaking all the state-of-the-art classification results in the “ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry” [3] More  recent examples of this heated competition results were recently shown at the NIPS conference  last week where teams at Microsoft Research produced breakthroughs in classification with an astounding 152 layer neural networks [4]. This intense competition between highly capable teams at universities and large internet companies is only possible because some large amount of training data is being made available.

Image or even video processing for hyperspectral imagery cannot follow the development of image processing that occurred for the past 40 years. The underlying reason stems from the fact that this development was performed at considerable expense by companies and governments alike and eventually yielded standards such as Jpegs, gif, Jpeg2000, mpeg, etc…Because such funding is no longer available we need to find ways of improving and working with new imaging modalities.

Technically, since hyperspectral imagery is still a niche market, most analysis performed in this field runs the risk of being seen as an outgrowth of normal imagery: i.e substandards tools such as JPEG or labor intensive computer vision tools are being used to classify and use this imagery without much thought into using the additional structure of the spectrum information. More sophisticated tools such as advanced matrix factorization (NMF, PCA, Sparse PCA, Dictionary learning, ….) in turn focus on the spectral information but seldomly use the spatial information. Both approaches suffer from not investigating more fully the inherent robust structure of this imagery.  

For hyperspectral imagery to become mainstream, algorithms for compression and for its day-to-day use has to take advantage of the current very active and highly competitive development in Machine Learning algorithms. In short, creating large and rich hyperspectral imagery datasets beyond what is currently available ([5-8] is central for this technology to grow out its niche markets and become central in our everyday lives.

The proposal

In order to make hyperspectral imagery mainstream, I propose to use a XIMEA camera and shoot imagery and video of different objects, locations and label these datasets.

The datasets will then be made available on the internet for use by parties interested in performing classification competition based on them (Kaggle, academic competitions,...).

As a co-organizer of the meetup, I also intend on enlisting some of the folks in the Paris Machine Learning meetup group ( with close to 3000 members it is one of the largest Machine Learning meetup in the world [9]) to help in enriching this dataset.

The dataset should be available from servers probably colocated at a university or some non-profit organization (to be identified). A report presenting the dataset should be eventually academically citable.

References

[1]Learning Multiple Layers of Features from Tiny Images, Alex Krizhevsky, 2009, https://www.cs.toronto.edu/~kriz/cifar.html

[2] Imagenet dataset, http://www.image-net.org/

[3] ImageNet Classification with Deep Convolutional Neural Networks, Alex Krizhevsky, Ilya Sutskever, Geoffrey E. Hinton, http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf

[4] Microsoft researchers win ImageNet computer vision challenge, http://blogs.microsoft.com/next/2015/12/10/microsoft-researchers-win-imagenet-computer-vision-challenge/

[5] https://engineering.purdue.edu/~biehl/MultiSpec/hyperspectral.html

[6] T.  Skauli and J. Farrell. “A collection of hyperspectral images for imaging systems research”. In Proceedings of the SPIE Electronic Imaging ‘2013, https://scien.stanford.edu/index.php/hyperspectral-image-data/

[7] Foster, D.H., Amano, K., Nascimento, S.M.C., & Foster, M.J. (2006). Frequency of metamerism in natural scenes. Journal of the Optical Society of America A, 23, 2359-2372., http://personalpages.manchester.ac.uk/staff/david.foster/Hyperspectral_images_of_natural_scenes_04.html

[8] Parraga CA, Brelstaff G, Troscianko T, Moorhead IR, Journal of the Optical Society of America 15 (3): 563-569, 1998 or G. Brelstaff, A. Párraga, T. Troscianko and D. Carr, SPIE. Vol. 2587. Geog. Inf. Sys. Photogram. and Geolog./Geophys. Remote Sensing, 150-159, 1995,

, http://www.cvc.uab.es/color_calibration/Bristol_Hyper/

[9] Paris Machine Learning meetup, http://www.meetup.com/Paris-Machine-learning-applications-group/

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Distributed Optimization with Arbitrary Local Solvers - implementation -

Distributed Optimization with Arbitrary Local Solvers by Chenxin Ma, Jakub Konečný, Martin Jaggi, Virginia Smith, Michael I. Jordan, Peter Richtárik, Martin Takáč

With the growth of data and necessity for distributed optimization methods, solvers that work well on a single machine must be re-designed to leverage distributed computation. Recent work in this area has been limited by focusing heavily on developing highly specific methods for the distributed environment. These special-purpose methods are often unable to fully leverage the competitive performance of their well-tuned and customized single machine counterparts. Further, they are unable to easily integrate improvements that continue to be made to single machine methods. To this end, we present a framework for distributed optimization that both allows the flexibility of arbitrary solvers to be used on each (single) machine locally, and yet maintains competitive performance against other state-of-the-art special-purpose distributed methods. We give strong primal-dual convergence rate guarantees for our framework that hold for arbitrary local solvers. We demonstrate the impact of local solver selection both theoretically and in an extensive experimental comparison. Finally, we provide thorough implementation details for our framework, highlighting areas for practical performance gains.

 The CoCoA solver is here on Github. Thanks Martin !
 

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Four and a half million page views: The Numbers Game in Long Distance Blogging

 

I know it's just a number but there is some Long Distance Blogging behind this figure. It roughly amounts to about a million page views per year. Here are the historical figures:

• December 17, 2015, 4.5 million page views
• May 21, 2015, 4 million page views
• December 2, 2014, 3.5 million page views
• June 7, 2014 3 million page views
• November 07, 2013, 2.5 million page views
• May 27, 2013 2 million page views
• October 25, 2012, 1.5 million page views

a page view is not the same as a "unique visit", here is that figure:  

or about 261,000 unique visits this year which amounts to 745 unique visits per day on average, a number that is consistent with Google's sessions numbers. There are also 800 people who receive the blog posts by Email directly.

Here are some interesting tags developed over the years:

• CS (2279) for Compressive Sensing
• MF (593) for Matrix Factorization
• implementation (408) that features work that has code implementation associated with them.
• ML (322)  for Machine Learning
• every month, there is a review of the month's blog entries. They are summarized in the  NuitBlancheReview tag (40 so far, so I have been doing this summaries for the past 3 years already)

 the social network "extension" of the blog include:

• The Google+ Community (1652),
• the CompressiveSensing subreddit (1077),
• the Facebook page (115 likes)
• the LinkedIn Compressive Sensing group (3428) or the Advanced Matrix Factorization Group (1100)
• blog announcements are also featured on my twitter handle among other things;

Reference pages include The Big Picture in Compressive Sensing and the Learning Compressive Sensing page as well as the Advanced Matrix Factorization Jungle Page, the Highly Technical Reference Pages - Aggregators.

  There are also 

• These Technologies Do Not Exist, 
• CAI: Cable And Igor's Adventures in Matrix Factorization, and 
• the Reproducible Research page

Finally, the Paris Machine Learning Meetup

• Meetup Archives (featuring more than 100 slides presentations and videos -season2 and 3-)
• Meetup.com to register (there are 2945 members, it is the largest ML meetup outside the US, top 3 worldwide in terms of region), 
• LinkedIn to post jobs (947),
• Google+(271) 
• Facebook (93 likes)
• Twitter (388 followers)
  

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L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework

Martin let me know of this preprint and attendant implementation this morning:

L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework by Virginia Smith, Simone Forte, Michael I. Jordan, Martin Jaggi

Despite the importance of sparsity in many big data applications, there are few existing methods for efficient distributed optimization of sparsely-regularized objectives. In this paper, we present a communication-efficient framework for L1-regularized optimization in distributed environments. By taking a non-traditional view of classical objectives as part of a more general primal-dual setting, we obtain a new class of methods that can be efficiently distributed and is applicable to common L1-regularized regression and classification objectives, such as Lasso, sparse logistic regression, and elastic net regression. We provide convergence guarantees for this framework and demonstrate strong empirical performance as compared to other state-of-the-art methods on several real-world distributed datasets.

 The implementation is here.

Thanks Martin !

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Householder QR Factorization: Adding Randomization for Column Pivoting

Getting to the core of linear algebra with randomized techniques, woohoo !  

Householder QR Factorization: Adding Randomization for Column Pivoting. FLAME Working Note #78  by Per-Gunnar Martinsson, Gregorio Quintana-Orti, Nathan Heavner, Robert van de Geijn

A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrix-matrix multiplication, which greatly limits the benefits of so-called blocked algorithms. This paper describes a technique for selecting groups of pivot vectors by means of randomized projections. It is demonstrated that the asymptotic flop count for the proposed method is 2mn2−(2/3)n3 for an m×n matrix with m≥n, identical to that of the best classical Householder QR factorization (with or without pivoting). Experiments demonstrate improvements in speed of substantial integer factors (between a factor of 3 and 5) relative to LAPACK's geqp3 implementation on a modern CPU.

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NIPS2015 Papers and posters

  After the blogs, here are the papers and posters listed on the NIPS site, some have already been mentioned here and some caught my attention, here they are:

• Space-Time Local Embeddings Ke Sun, Jun Wang, Alexandros Kalousis, Stephane Marchand-Maillet
• A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements Qinqing Zheng, John Lafferty
• Galileo: Perceiving Physical Object Properties by Integrating a Physics Engine with Deep Learning Jiajun Wu, Ilker Yildirim, Joseph J. Lim, Bill Freeman, Josh Tenenbaum
• On the Limitation of Spectral Methods: From the Gaussian Hidden Clique Problem to Rank-One Perturbations of Gaussian Tensors Andrea Montanari, Daniel Reichman, Ofer Zeitouni
• A fast, universal algorithm to learn parametric nonlinear embeddings Miguel A. Carreira-Perpinan, Max Vladymyrov
• Orthogonal NMF through Subspace Exploration Megasthenis Asteris, Dimitris Papailiopoulos, Alexandros G. Dimakis
• Deeply Learning the Messages in Message Passing Inference Guosheng Lin, Chunhua Shen, Ian Reid, Anton van den Hengel
• Accelerated Proximal Gradient Methods for Nonconvex Programming Huan Li, Zhouchen Lin
• Approximating Sparse PCA from Incomplete Data ABHISEK KUNDU, Petros Drineas, Malik Magdon-Ismail
• Column Selection via Adaptive Sampling Saurabh Paul, Malik Magdon-Ismail, Petros Drineas
• HONOR: Hybrid Optimization for NOn-convex Regularized problems Pinghua Gong, Jieping Ye
• Tensorizing Neural Networks Alexander Novikov, Dmitrii Podoprikhin, Anton Osokin, Dmitry P. Vetrov
• Parallelizing MCMC with Random Partition Trees Xiangyu Wang, Fangjian Guo, Katherine A. Heller, David B. Dunson
• On the Global Linear Convergence of Frank-Wolfe Optimization Variants Simon Lacoste-Julien, Martin Jaggi
• Efficient Compressive Phase Retrieval with Constrained Sensing Vectors Sohail Bahmani, Justin Romberg
• Compressive spectral embedding: sidestepping the SVD Dinesh Ramasamy, Upamanyu Madhow
• A Nonconvex Optimization Framework for Low Rank Matrix Estimation Tuo Zhao, Zhaoran Wang, Han Liu
• Automatic Variational Inference in Stan Alp Kucukelbir, Rajesh Ranganath, Andrew Gelman, David Blei
• Training Restricted Boltzmann Machine via the Thouless-Anderson-Palmer free energy Marylou Gabrie, Eric W. Tramel, Florent Krzakala
• Robust Regression via Hard Thresholding Kush Bhatia, Prateek Jain, Purushottam Kar
• Sparse Local Embeddings for Extreme Multi-label Classification Kush Bhatia, Himanshu Jain, Purushottam Kar, Manik Varma, Prateek Jain
• Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems Yuxin Chen, Emmanuel Candes
• Subspace Clustering with Irrelevant Features via Robust Dantzig Selector Chao Qu, Huan Xu
• Sparse PCA via Bipartite Matchings Megasthenis Asteris, Dimitris Papailiopoulos, Anastasios Kyrillidis, Alexandros G. Dimakis
• Fast Randomized Kernel Ridge Regression with Statistical Guarantees Ahmed Alaoui, Michael W. Mahoney
• Quartz: Randomized Dual Coordinate Ascent with Arbitrary Sampling Zheng Qu, Peter Richtarik, Tong Zhang
• Matrix Manifold Optimization for Gaussian Mixtures Reshad Hosseini, Suvrit Sra
• Fast and Guaranteed Tensor Decomposition via Sketching Yining Wang, Hsiao-Yu Tung, Alex J. Smola, Anima Anandkumar
• Differentially private subspace clustering Yining Wang, Yu-Xiang Wang, Aarti Singh
• Non-convex Statistical Optimization for Sparse Tensor Graphical Model Wei Sun, Zhaoran Wang, Han Liu, Guang Cheng
• Optimal Rates for Random Fourier Features Bharath Sriperumbudur, Zoltan Szabo
• Practical and Optimal LSH for Angular Distance Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig Schmidt
• Learning to Linearize Under Uncertainty Ross Goroshin, Michael F. Mathieu, Yann LeCun
• Matrix Completion from Fewer Entries: Spectral Detectability and Rank Estimation Alaa Saade, Florent Krzakala, Lenka Zdeborová
• Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition Cameron Musco, Christopher Musco
• Optimal Linear Estimation under Unknown Nonlinear Transform Xinyang Yi, Zhaoran Wang, Constantine Caramanis, Han Liu
• Sum-of-Squares Lower Bounds for Sparse PCA Tengyu Ma, Avi Wigderson
• Learning with Incremental Iterative Regularization Lorenzo Rosasco, Silvia Villa
• Halting in Random Walk Kernels Mahito Sugiyama, Karsten Borgwardt
• MCMC for Variationally Sparse Gaussian Processes James Hensman, Alexander G. Matthews, Maurizio Filippone, Zoubin Ghahramani
• Less is More: Nyström Computational Regularization Alessandro Rudi, Raffaello Camoriano, Lorenzo Rosasco
• Analysis of Robust PCA via Local Incoherence Huishuai Zhang, Yi Zhou, Yingbin Liang
• Spherical Random Features for Polynomial Kernels Jeffrey Pennington, Felix Yu, Sanjiv Kumar
• Matrix Completion Under Monotonic Single Index Models Ravi Sastry Ganti, Laura Balzano, Rebecca Willett
• Robust PCA with compressed data Wooseok Ha, Rina Foygel Barber
• b-bit Marginal Regression Martin Slawski, Ping Li
• Beyond Sub-Gaussian Measurements: High-Dimensional Structured Estimation with Sub-Exponential Designs Vidyashankar Sivakumar, Arindam Banerjee, Pradeep K. Ravikumar
• Scale Up Nonlinear Component Analysis with Doubly Stochastic Gradients Bo Xie, Yingyu Liang, Le Song
• Generalization in Adaptive Data Analysis and Holdout Reuse Cynthia Dwork, Vitaly Feldman, Moritz Hardt, Toni Pitassi, Omer Reingold, Aaron Roth
• Sparse Linear Programming via Primal and Dual Augmented Coordinate Descent Ian En-Hsu Yen, Kai Zhong, Cho-Jui Hsieh, Pradeep K. Ravikumar, Inderjit S. Dhillon
• Training Very Deep Networks Rupesh K. Srivastava, Klaus Greff, Juergen Schmidhuber
• End-To-End Memory Networks Sainbayar Sukhbaatar, arthur szlam, Jason Weston, Rob Fergus
• Spectral Representations for Convolutional Neural Networks Oren Rippel, Jasper Snoek, Ryan P. Adams
• Recognizing retinal ganglion cells in the dark Emile Richard, Georges A. Goetz, E. J. Chichilnisky
• Hidden Technical Debt in Machine Learning Systems D. Sculley, Gary Holt, Daniel Golovin, Eugene Davydov, Todd Phillips, Dietmar Ebner, Vinay Chaudhary, Michael Young, Jean-François Crespo, Dan Dennison
• Deep Convolutional Inverse Graphics Network Tejas D. Kulkarni, William F. Whitney, Pushmeet Kohli, Josh Tenenbaum
• Sparse and Low-Rank Tensor Decomposition Parikshit Shah, Nikhil Rao, Gongguo Tang
• Super-Resolution Off the Grid Qingqing Huang, Sham M. Kakade
• Taming the Wild: A Unified Analysis of Hogwild-Style Algorithms Christopher M. De Sa, Ce Zhang, Kunle Olukotun, Christopher Ré, Christopher Ré
• Associative Memory via a Sparse Recovery Model Arya Mazumdar, Ankit Singh Rawat
• Robust Spectral Inference for Joint Stochastic Matrix Factorization Moontae Lee, David Bindel, David Mimno
• Fast, Provable Algorithms for Isotonic Regression in all L_p-norms Rasmus Kyng, Anup Rao, Sushant Sachdeva
• Grammar as a Foreign Language Oriol Vinyals, Łukasz Kaiser, Terry Koo, Slav Petrov, Ilya Sutskever, Geoffrey Hinton
• Regularization-Free Estimation in Trace Regression with Symmetric Positive Semidefinite Matrices Martin Slawski, Ping Li, Matthias Hein
• Winner-Take-All Autoencoders Alireza Makhzani, Brendan J. Frey
• Subsampled Power Iteration: a Unified Algorithm for Block Models and Planted CSP's Vitaly Feldman, Will Perkins, Santosh Vempala
• Accelerated Mirror Descent in Continuous and Discrete Time Walid Krichene, Alexandre Bayen, Peter L. Bartlett
• The Human Kernel Andrew G. Wilson, Christoph Dann, Chris Lucas, Eric P. Xing
• Structured Estimation with Atomic Norms: General Bounds and Applications Sheng Chen, Arindam Banerjee
• Preconditioned Spectral Descent for Deep Learning David E. Carlson, Edo Collins, Ya-Ping Hsieh, Lawrence Carin, Volkan Cevher
• Nearly Optimal Private LASSO Kunal Talwar, Abhradeep Thakurta, Li Zhang
• Convergence Analysis of Prediction Markets via Randomized Subspace Descent Rafael Frongillo, Mark D. Reid
• Structured Transforms for Small-Footprint Deep Learning Vikas Sindhwani, Tara Sainath, Sanjiv Kumar
• BinaryConnect: Training Deep Neural Networks with binary weights during propagations Matthieu Courbariaux, Yoshua Bengio, Jean-Pierre David
• Interpolating Convex and Non-Convex Tensor Decompositions via the Subspace Norm Qinqing Zheng, Ryota Tomioka
• Fast and Memory Optimal Low-Rank Matrix Approximation Se-Young Yun, marc lelarge, Alexandre Proutiere
• The Self-Normalized Estimator for Counterfactual Learning Adith Swaminathan, Thorsten Joachims
• Semi-Supervised Factored Logistic Regression for High-Dimensional Neuroimaging Data Danilo Bzdok, Michael Eickenberg, Olivier Grisel, Bertrand Thirion, Gael Varoquaux
• Gaussian Process Random Fields David Moore, Stuart J. Russell
• M-Statistic for Kernel Change-Point Detection Shuang Li, Yao Xie, Hanjun Dai, Le Song
• Semi-Proximal Mirror-Prox for Nonsmooth Composite Minimization Niao He, Zaid Harchaoui
• LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements CHRISTOS THRAMPOULIDIS, Ehsan Abbasi, Babak Hassibi
• Matrix Completion with Noisy Side Information Kai-Yang Chiang, Cho-Jui Hsieh, Inderjit S. Dhillon

Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

Date: 11 December 2015
Satellite: Rosetta
Depicts: Comet 67P/Churyumov-Gerasimenko
Copyright: See below

Single-frame OSIRIS narrow-angle camera (NAC) image taken on 10 December 2015, when Rosetta was 103.2 km from the nucleus of Comet 67P/Churyumov-Gerasimenko. The scale is 1.87 m/pixel.

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