Machine learning is one of the fastest-growing and most exciting fields out there, and deep learning represents its true bleeding edge. In this course, you'll develop a clear understanding of the motivation for deep learning, and design intelligent systems that learn from complex and/or large-scale datasets. We'll show you how to train and optimize basic neural networks, convolutional neural networks, and long short term memory networks. Complete learning systems in TensorFlow will be introduced via projects and assignments. You will learn to solve new classes of problems that were once thought prohibitively challenging, and come to better appreciate the complex nature of human intelligence as you solve these same problems effortlessly using deep learning methods.

Machine Learning is one of the hottest new technologies impacting everything. Laurence Moroney meets with Joshua Gordon over coffee to talk about Machine Learning and his new show to help developers get started! P.S., in the video we used the word'class' - really, it's a tutorial series, very informal. Check out the first episode here: https://goo.gl/RpvlJl Subscribe to the Google Developers channel at http://goo.gl/mQyv5L

SAN JOSE, Calif.?Nvidia Corp. is stepping up plans to expand beyond computer graphics into the field of artificial intelligence, unveiling an unusual processor for the purpose and a computer that uses it to solve scientific problems at extremely high speed. The company on Tuesday said the new Tesla P100 chip, designed for use in corporate data centers, achieves very high performance by packing 15 billion transistors on a piece of silicon. That is roughly twice as many as Nvidia's prior high-end graphics processor and some new server chips Intel Corp. announced last week. "It's the largest chip that has ever been made," said Jen-Hsun Huang, Nvidia's chief executive, during a speech kicking off the company's annual technology conference here. He predicted the chip would initially be purchased by unidentified cloud computing services and next year would begin arrive in servers sold by other companies.

SAN JOSE, CA--(Marketwired - Apr 5, 2016) - GPU Technology Conference -- NVIDIA (NASDAQ: NVDA) today announced that it is a founding technology partner of the MGH Clinical Data Science Center, which aims to advance healthcare by applying the latest artificial intelligence techniques to improve the detection, diagnosis, treatment and management of diseases. Massachusetts General Hospital -- which conducts the largest hospital-based research program in the United States, and is the top-ranked hospital on this year's US News and World Report "Best Hospitals" list -- recently established the MGH Clinical Data Science Center in Boston. The center will train a deep neural network using Mass General's vast stores of phenotypic, genetics and imaging data. The hospital has a database containing some 10 billion medical images. To process this massive amount of data, the center will deploy the NVIDIA DGX-1 -- a server designed for AI applications, launched earlier today at the GPU Technology Conference -- and deep learning algorithms created by NVIDIA engineers and Mass General data scientists.

Structure discovery in graphical models is the determination of the topology of a graph that encodes conditional independence properties of the joint distribution of all variables in the model. For some class of probability distributions, an edge between two variables is present if and only if the corresponding entry in the precision matrix is non-zero. For a finite sample estimate of the precision matrix, entries close to zero may be due to low sample effects, or due to an actual association between variables; these two cases are not readily distinguishable. %Fisher provided a hypothesis test based on a parametric approximation to the distribution of an entry in the precision matrix of a Gaussian distribution, but this may not provide valid upper bounds on $p$-values for non-Gaussian distributions. Many related works on this topic consider potentially restrictive distributional or sparsity assumptions that may not apply to a data sample of interest, and direct estimation of the uncertainty of an estimate of the precision matrix for general distributions remains challenging. Consequently, we make use of results for $U$-statistics and apply them to the covariance matrix. By probabilistically bounding the distortion of the covariance matrix, we can apply Weyl's theorem to bound the distortion of the precision matrix, yielding a conservative, but sound test threshold for a much wider class of distributions than considered in previous works. The resulting test enables one to answer with statistical significance whether an edge is present in the graph, and convergence results are known for a wide range of distributions. The computational complexities is linear in the sample size enabling the application of the test to large data samples for which computation time becomes a limiting factor. We experimentally validate the correctness and scalability of the test on multivariate distributions for which the distributional assumptions of competing tests result in underestimates of the false positive ratio. By contrast, the proposed test remains sound, promising to be a useful tool for hypothesis testing for diverse real-world problems.

This paper is a comment on the survey paper by Biau and Scornet (2016) about random forests. We focus on the problem of quantifying the impact of each ingredient of random forests on their performance. We show that such a quantification is possible for a simple pure forest, leading to conclusions that could apply more generally. Then, we consider "holdout" random forests, which are a good middle point between "toy" pure forests and Breiman's original random forests. We would like to thank G. Biau and E. Scornet for their clear and thought-provoking survey (Biau and Scornet, 2016).

Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This opens the way to the application of efficient inference algorithms in the machine learning literature to solve the smoothing problem for reciprocal processes. Such algorithms are known to converge if the underlying graph is a tree. This is not the case for a reciprocal process, whose associated graphical model is a single loop network. The contribution of this paper is twofold. First, we introduce belief propagation for Gaussian reciprocal processes. Second, we establish a link between convergence analysis of belief propagation for Gaussian reciprocal processes and stability theory for differentially positive systems.

The back-propagation algorithm is widely used for learning in artificial neural networks. A challenge in machine learning is to create models that generalize to new data samples not seen in the training data. Recently, a common flaw in several machine learning algorithms was discovered: small perturbations added to the input data lead to consistent misclassification of data samples. Samples that easily mislead the model are called adversarial examples. Training a "maxout" network on adversarial examples has shown to decrease this vulnerability, but also increase classification performance. This paper shows that adversarial training has a regularizing effect also in networks with logistic, hyperbolic tangent and rectified linear units. A simple extension to the back-propagation method is proposed, that adds an adversarial gradient to the training. The extension requires an additional forward and backward pass to calculate a modified input sample, or mini batch, used as input for standard back-propagation learning. The first experimental results on MNIST show that the "adversarial back-propagation" method increases the resistance to adversarial examples and boosts the classification performance. The extension reduces the classification error on the permutation invariant MNIST from 1.60% to 0.95% in a logistic network, and from 1.40% to 0.78% in a network with rectified linear units. Results on CIFAR-10 indicate that the method has a regularizing effect similar to dropout in fully connected networks. Based on these promising results, adversarial back-propagation is proposed as a stand-alone regularizing method that should be further investigated.

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that $2K$ projection vectors are sufficient for the independence preservation of any $K$ class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reduction algorithm that theoretically preserves this structure for a given dataset. We support our theoretical analysis with empirical results on both synthetic and real world data achieving \textit{state-of-the-art} results compared to popular dimensionality reduction techniques.

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing sparsity in the solutions while the constraint set models the noise tolerance and incorporates other prior information for data fitting. To solve this class of constrained optimization problems, a common approach is the penalty method. However, there is little theory on exact penalization for problems with nonconvex and non-Lipschitz objective functions. In this paper, we study the existence of exact penalty parameters regarding local minimizers, stationary points and $\epsilon$-minimizers under suitable assumptions. Moreover, we discuss a penalty method whose subproblems are solved via a nonmonotone proximal gradient method with a suitable update scheme for the penalty parameters, and prove the convergence of the algorithm to a KKT point of the constrained problem. Preliminary numerical results demonstrate the efficiency of the penalty method for finding sparse solutions of underdetermined linear systems.