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Fast Orthonormal Sparsifying Transforms Based on Householder Reflectors

arXiv.org Machine Learning

Abstract--Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative algorithms. Furthermore, the resulting transforms obtained generally lack structure that permits their fast application to data. T o address this issue, this paper develops a framework for learning orthonormal dictionaries which are built from products of a few Householder reflectors. Two algorithms are proposed to learn the reflector coefficients: one that considers a sequential update of the reflectors and one with a simultaneous update of all reflectors that imposes an additional internal orthogonal constraint. The proposed methods have low computational complexity and are shown to converge to local minimum points which can be described in terms of the spectral properties of the matrices involved. Simulations of the proposed algorithms are shown in the image processing setting where well-known fast transforms are available for comparisons. The proposed algorithms have favorable reconstruction error and the advantage of a fast implementation relative to the classical, unstructured, dictionaries. Index Terms--sparsifying transforms, fast transforms, dictionary learning, compressed sensing. Sparsifying transforms [1] allow efficient representation of data when a data-dependent overcomplete dictionary is available. Overcomplete dictionaries are useful in image processing [2], [3], [4], speech processing [5] and wireless communications [6], [7]. Unfortunately, the selection of a sparsifying transform involves solving a non-convex optimization problem for a dictionary matrixD such that a real data set can be represented with a sparse representation matrixX whose sparsity level is constrained. Because direct solution of the optimization method is difficult [8], [9], proposed algorithms seek a suboptimal solution via alternating minimization. Most prior work considers alternating minimization for dictionaries that are overcomplete.


Take the Complete Machine Learning Bundle Online Now

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Machines are becoming smarter than ever before, and all that artificial intelligence is going to play a crucial role in the future of society - affecting everything from self-driving cars to medicine. There's now a huge demand for people who know how to work with these algorithms to make AI smarter and faster - while keeping it under control. The Complete Machine Learning Bundle is a deep dive into everything you'll need to get your machine learning career started - or to just take your obsession with robotics and AI to the next level. This package gives you access to 10 different machine learning courses, including "An Introduction To Deep Learning & Computer Vision" and "An Introduction to Machine Learning & NLP in Python," which is taught by Silicon Valley experts. Best of all, the bundle is totally online, so you can study in your own time, and it's available on ScienceAlert Academy for the sale price of US$29.


How Root Wants to Bring Coding to Every Classroom

IEEE Spectrum Robotics

This is a guest post. The views expressed here are solely those of the authors and do not represent positions of IEEE Spectrum or the IEEE. The push to teach coding in U.S. schools has been growing: Thanks to initiatives like the White House's CS for All program, computer science is now recognized as a core skill for today's students. A new study by Gallup and Google revealed that 90 percent of parents want their child to learn CS, yet only 40 percent of K-12 school districts offer some kind of CS course. Teacher recruitment and training efforts are beginning to solve the problem at the high-school level, but in K-8 schools (where very few schools offer CS and many teachers are generalists) the challenges are different.


BigML and CICE Join Forces to Revolutionalize Machine Learning Education

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Democratizing Machine Learning has always been BigML's founding mission, so we are continually searching for new opportunities. As such, when a company is interested in our technology and is willing to help us further our cause of "Machine Learning for everyone", we feel the urge to collaborate. This is exactly what happened with our new education partner. Today we are happy to announce our educational collaboration with CICE, the Leading School in New Technologies Training in Madrid, Spain. CICE, the only Official Training Center in Spain for more than 20 multinational companies, is already a community of 70,000 students from 30 different countries.


Would you know if one of your Teaching Assistants was a bot? โ€“ CognitiveBusiness

#artificialintelligence

Online learning is becoming the norm in universities across the globe, bringing sweeping changes to the way we learn. But earlier this year on online graduate class at Georgia Tech took things a stage further. "Our Teaching Assistants are getting bogged down answering routine questions," said Ashok Goel, who teaches a graduate science course. Students in the class typically post 10,000 messages a semester on the Piazza forum for the course, many of which are either variations on a theme or simple logistical questions. To address this problem, Ashok turned to IBM Watson to create a virtual TA called Jill Watson who was trained on 40,000 posts and released to the wild on the live forum in March as an addition to the other eight TAs.


Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization

arXiv.org Machine Learning

Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While current methods offer efficiencies by adaptively choosing new configurations to train, an alternative strategy is to adaptively allocate resources across the selected configurations. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinitely many armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce Hyperband for this framework and analyze its theoretical properties, providing several desirable guarantees. Furthermore, we compare Hyperband with state-of-the-art methods on a suite of hyperparameter optimization problems. We observe that Hyperband provides five times to thirty times speedup over state-of-the-art Bayesian optimization algorithms on a variety of deep-learning and kernel-based learning problems.


Education Artificial Intelligence?

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These days, it seems that nearly everything is a smart product. We have smart boards in K-12 classrooms, smart watches, and even smart refrigerators. You can immediately tell that manufacturers love to use this misguided descriptor whenever they integrate modern technology, like touch screens or internet connectivity, to a previously existing product. Do products like these deserve this term? What exactly makes them smart?


How to steal the mind of an AI: Machine-learning models vulnerable to reverse engineering

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Amazon, Baidu, Facebook, Google and Microsoft, among other technology companies, have been investing heavily in artificial intelligence and related disciplines like machine learning because they see the technology enabling services that become a source of revenue. Consultancy Accenture earlier this week quantified this enthusiasm, predicting that AI "could double annual economic growth rates by 2035 by changing the nature of work and spawning a new relationship between man and machine" and by boosting labor productivity by 40 per cent. Certainly things could work out well for Accenture, which a day later announced a partnership with Google to help companies deploy Google technology like machine learning. It's as if the global services firm has a stake in the future it foresees. But the machine learning algorithms underpinning this harmonious union of people and circuits aren't secure. In a paper [PDF] presented in August at the 25th Annual Usenix Security Symposium, researchers at ร‰cole Polytechnique Fรฉdรฉrale de Lausanne, Cornell University, and The University of North Carolina at Chapel Hill showed that machine learning models can be stolen and that basic security measures don't really mitigate attacks.


Art and AI - Pyragraph

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According to the Financial Times, Pablo Picasso once said, "Computers are useless. They can only give you answers." Unfortunately for us, computers may now be asking more questions than they answer. As a result, the possibilities are rather overwhelming, with answers more ambiguous and uncertain than straightforward. Similarly, we might ask ourselves where we draw the line when it comes to what we find ethically acceptable in terms of artificial intelligence (AI) as it relates to composition/creation in the worlds of art, writing, performing arts and music--as well as liberal arts education. Most of us are aware of music streaming services that select songs for us based on data about users' listening preferences.


Lecture 1 Building a Linear Classifier (MLP) With Deeplearning4j

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Tom provides an overview of how to build a simple neural net in this introductory tutorial. This screencast shows how to build a Linear Classifier using Deeplearning4j.