Saturday, December 12, 2015

Saturday Morning Videos: New videos of ICML 2015 in Lille


As NIPS sessions have to turn away people, here are some videos of ICML this past summer. A month ago we mentioned some of these videos but here are some new ones:

Tutorials


Welcome Address


Welcome address
Joelle Pineau, David Blei, Francis R. Bach

Keynote Speakers

Awards

Deep Learning I





Learning Theory I




Deep Learning Computations



Matrix Factorization


Sparsity I



Optimization I

Structured Prediction I

Reinforcement Learning II

Gaussian Processes I

Transfer Learning I

Networks and Graphs I

Deep Learning II

Networks and Graphs II

Online Learning I

Probabilistic Models I

Learning Theory II

Transfer Learning II

Deep Learning and Vision







Monte Carlo Methods

Hashing

Feature Selection I

Kernel Methods

Computational Advertising and Social Science

Optimization II

Approximate Inference I

Bayesian Nonparametrics II

Time Series Analysis I

Feature Selection II

Unsupervised Learning I

Optimization III

Probabilistic Models II

Natural Language Processing I

Submodularity

Online Learning II

Unsupervised Learning II

Deep Learning III




 

Reinforcement Learning III


Supervised Learning II


Optimization IV

Bayesian Nonparametrics III

Sparsity II

Clustering I

Vision

Sparse optimization

Approximate Inference II

Natural Language Processing II

Time Series Analysis II

Clustering II

Learning Theory III



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Friday, December 11, 2015

Perfect Recovery Conditions For Non-Negative Sparse Modeling / Compressive hyperspectral imaging via adaptive sampling and dictionary learning

 


Perfect Recovery Conditions For Non-Negative Sparse Modeling by Yuki Itoh, Marco F. Duarte, Mario Parente

Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition and, accompanied with those applications, significant research has studied the theoretical limits and algorithm design for convex relaxations in sparse modeling. However, only little has been done for theoretical limits of non-negative versions of sparse modeling. The behavior is expected to be similar as the general sparse modeling, but a precise analysis has not been explored. This paper studies the performance of non-negative sparse modeling, especially for non-negativity constrained and ℓ1-penalized least squares, and gives an exact bound for which this problem can recover the correct signal elements. We pose two conditions to guarantee the correct signal recovery: minimum coefficient condition (MCC) and non-linearity vs. subset coherence condition (NSCC). The former defines the minimum weight for each of the correct atoms present in the signal and the latter defines the tolerable deviation from the linear model relative to the positive subset coherence (PSC), a novel type of "coherence" metric. We provide rigorous performance guarantees based on these conditions and experimentally verify their precise predictive power in a hyperspectral data unmixing application.
 
 

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using dictionary learning. We then perform an SVD on the dictionary and use the first few left singular vectors as the rows of the measurement matrix to obtain the compressive measurements for reconstruction. The proposed method provides significant improvement over the conventional compressive sensing approaches. The reconstruction performance is further improved by reconditioning the sensing matrix using matrix balancing. We also demonstrate that the combination of dictionary learning and SVD is robust by applying them to different datasets.
 
 
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Thursday, December 10, 2015

Compressive Sampling using Annihilating Filter-based Low-Rank Interpolation



Compressive Sampling using Annihilating Filter-based Low-Rank Interpolation by Jong Chul Ye, Jong Min Kim, Kyong Hwan Jin

While the recent theory of compressed sensing or compressive sampling (CS) provides an opportunity to overcome the Nyquist limit in recovering sparse signals, a recovery algorithm usually takes the form of penalized least squares or constraint optimization framework that is different from classical signal sampling theory. In this paper, we provide a drastically different compressive sampling framework that can exploit all the benefits of the CS, but can be still implemented in a classical sampling framework using a digital correction filter. The main idea is originated from the fundamental duality between the sparsity in the primary space and the low-rankness of a structured matrix in the reciprocal spaces, which demonstrates that the low-rank interpolator as a digital correction filter can enjoy all the optimality of the standard CS. We show that the idea can be generalised to recover signals in large class of signals such as piece-wise polynomial, and spline representations. Moreover, by restricting signal class as cardinal splines, the proposed low-rank interpolation approach can achieve inherent regularization to improve the noise robustness. Using the powerful dual certificates and golfing scheme by Gross, we show that the new framework still achieves the near-optimal sampling rate for signal recovery. Numerical results using various type of signals confirmed that the proposed scheme has significant better phase transition than the conventional CS approaches.
 
 
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Challenge: Computational Imaging for VLBI Image Reconstruction

Here is a reconstruction endeavor that could eventually help the Event Horizon Telescope: Computational Imaging for VLBI Image Reconstruction by Katherine L. Bouman, Michael D. Johnson, Daniel Zoran, Vincent L. Fish, Sheperd S. Doeleman, William T. Freeman

Very long baseline interferometry (VLBI) is a technique for imaging celestial radio emissions by simultaneously observing a source from telescopes distributed across Earth. The challenges in reconstructing images from fine angular resolution VLBI data are immense. The data is extremely sparse and noisy, thus requiring statistical image models such as those designed in the computer vision community. In this paper we present a novel Bayesian approach for VLBI image reconstruction. While other methods require careful tuning and parameter selection for different types of images, our method is robust and produces good results under different settings such as low SNR or extended emissions. The success of our method is demonstrated on realistic synthetic experiments as well as publicly available real data. We present this problem in a way that is accessible to members of the computer vision community, and provide a dataset website (vlbiimaging.csail.mit.edu) to allow for controlled comparisons across algorithms. This dataset can foster development of new methods by making VLBI easily approachable to computer vision researchers.
At vlbiimaging.csail.mit.edu, they have a Dataset Designed to Train and Test Very Long Baseline Interferometry Image Reconstruction Algorithms. From the first page:

Welcome to the VLBI Reconstruction Dataset!

The goal of this website is to provide a testbed for developing new VLBI reconstruction algorithms. By supplying a large set of easy to understand training and testing data, we hope to make the problem more accessible to those less familiar with the VLBI field. Specifically, this website contains a:

What is VLBI Imaging?

Imaging distant celestial sources with high resolving power requires telescopes with prohibitively large diameters due to the inverse relationship between angular resolution and telescope diameter. However, by simultaneously collecting data from an array of telescopes located around the Earth, it is possible to emulate samples from a single telescope with a diameter equal to the maximum distance between telescopes in the array. Using multiple telescopes in this manner is referred to as very long baseline interferometry (VLBI).
Reconstructing an image using VLBI measurements is an ill-posed problem, and as such each there are an infinite number of possible images that explain the data. The challenge is to find an explanation that respects these prior assumptions while still satisfying the observed data. The goal of this website to aid in the process of developing these algorithms as well as evaluate their performance.

The ongoing international effort to create an Event Horizon Telescope capable of imaging the enviroment around a black hole’s event horizon calls for the use of VLBI reconstruction algorithms. The angular resolution necessary for these measurements requires overcoming many challenges, all of which make image reconstruction more difficult. For instance, at the mm/sub-mm wavelengths being observed, rapidly varying inhomogeneities in the atmosphere introduce additional measurement errors. Robust algorithms that are able to reconstruct images in this fine angular resolution regime are essential for scientific progress.
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