We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition. By assuming the input matrices to be perturbations of noise-free, simultaneously diagonalizable ground-truth matrices, the approximate joint triangularizers are expected to be perturbations of the exact joint triangularizers of the ground-truth matrices. We provide a priori and a posteriori perturbation bounds on the `distance' between an approximate joint triangularizer and its exact counterpart. The a priori bounds are theoretical inequalities that involve functions of the ground-truth matrices and noise matrices, whereas the a posteriori bounds are given in terms of observable quantities that can be computed from the input matrices. From a practical perspective, the problem of finding the best approximate joint triangularizer of a set of noisy matrices amounts to solving a nonconvex optimization problem. We show that, under a condition on the noise level of the input matrices, it is possible to find a good initial triangularizer such that the solution obtained by any local descent-type algorithm has certain global guarantees. Finally, we discuss the application of approximate joint matrix triangularization to canonical tensor decomposition and we derive novel estimation error bounds.

Early diagnosis, playing an important role in preventing progress and treating the Alzheimer's disease (AD), is based on classification of features extracted from brain images. The features have to accurately capture main AD-related variations of anatomical brain structures, such as, e.g., ventricles size, hippocampus shape, cortical thickness, and brain volume. This paper proposes to predict the AD with a deep 3D convolutional neural network (3D-CNN), which can learn generic features capturing AD biomarkers and adapt to different domain datasets. The 3D-CNN is built upon a 3D convolutional autoencoder, which is pre-trained to capture anatomical shape variations in structural brain MRI scans. Fully connected upper layers of the 3D-CNN are then fine-tuned for each task-specific AD classification. Experiments on the \emph{ADNI} MRI dataset with no skull-stripping preprocessing have shown our 3D-CNN outperforms several conventional classifiers by accuracy and robustness. Abilities of the 3D-CNN to generalize the features learnt and adapt to other domains have been validated on the \emph{CADDementia} dataset.

In high dimensions we propose and analyze an aggregation estimator of the precision matrix for Gaussian graphical models. This estimator, called graphical Exponential Screening (gES), linearly combines a suitable set of individual estimators with different underlying graphs, and balances the estimation error and sparsity. We study the risk of this aggregation estimator and show that it is comparable to that of the best estimator based on a single graph, chosen by an oracle. Numerical performance of our method is investigated using both simulated and real datasets, in comparison with some state-of-art estimation procedures.

This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a double-detector scheme is introduced in which a sensor level threshold detector is integrated into network level GLRT to improve the performance. The detection criteria of oracle and clairvoyant detectors are also derived. Simulation results show that with careful design of the threshold detector, the overall detection performance of double-detector scheme would be better than the sign-GLRT proposed in [1] and close to oracle and clairvoyant detectors. Also, the proposed detector is applied to spectrum sensing and the results are near the well known energy detector which uses the real valued data while the proposed detector only uses the sign of the data.

In this paper, we consider the joint task of simultaneously optimizing (i) the weights of a deep neural network, (ii) the number of neurons for each hidden layer, and (iii) the subset of active input features (i.e., feature selection). While these problems are generally dealt with separately, we present a simple regularized formulation allowing to solve all three of them in parallel, using standard optimization routines. Specifically, we extend the group Lasso penalty (originated in the linear regression literature) in order to impose group-level sparsity on the network's connections, where each group is defined as the set of outgoing weights from a unit. Depending on the specific case, the weights can be related to an input variable, to a hidden neuron, or to a bias unit, thus performing simultaneously all the aforementioned tasks in order to obtain a compact network. We perform an extensive experimental evaluation, by comparing with classical weight decay and Lasso penalties. We show that a sparse version of the group Lasso penalty is able to achieve competitive performances, while at the same time resulting in extremely compact networks with a smaller number of input features. We evaluate both on a toy dataset for handwritten digit recognition, and on multiple realistic large-scale classification problems.

The White House has said that up to 116 civilians have been killed by drone and other US strikes in Pakistan, Yemen, Somalia and Libya since Barack Obama took office in 2009, a figure that has been slammed by watchdog groups as an undercount, which suggests that the real figure could be as high as 1,100. Published by the Director of National Intelligence on Friday, the report said that between January 20, 2009, and December 31, 2015, the US carried out 473 strikes, which killed up to 2,581 "combatants" and anywhere from 64 to 116 civilians. The civilian casualties disclosed in the report were from nations not recognised as "battlefields," and did not reflect US air attacks in "areas of active hostilities" such as Afghanistan, Iraq or Syria. Watchdog and rights groups have long claimed that the US administration does not know how many civilians it has killed and does not do enough to prevent civilian casualties when carrying out counterterrorism operations. Reprieve, an international human rights organisation, said the US government's previous statements about the drone programme have proven to be false by its own internal documents. It said the Obama administration has "shifted the goalposts on what counts as a'civilian' to such an extent that any estimate may be far removed from reality".

The man killed in a crash while using the autopilot function of a Tesla Model S electric vehicle posted a YouTube video a month before the fatal crash showing the technology saving him from another collision and wrote that he was "very impressed." I have done a lot of testing with the sensors in the car and the software capabilities," Joshua Brown, 40, of Canton, Ohio, wrote on April 5 in comments posted with the 41-second video. "I have always been impressed with the car, but I had not tested the car's side collision avoidance," he said. Then on May 7, Brown, a former Navy Seal, was killed when his Tesla crashed into a tractor trailer in Williston, Fla. Federal regulators said Thursday they had opened an investigation into the fatality, thought to be the first in the auto industry involving an autonomous driving feature. The National Highway Traffic Safety Administration said its Office of Defects Investigation was conducting a preliminary evaluation of the autopilot function. The agency is expected to issue guidelines for autonomous vehicles this month. Automakers do not need to have autonomous driving functions approved by NHTSA but must certify their vehicles meet safety standards. Calling Brown's death "a tragic loss," Tesla said it was the first-known fatality involving its autopilot feature. The technology, which is in public beta testing and must be activated by the driver, has been used in 130 million miles of driving without a fatality, the company said. The crash took place at 3:40 p.m. May 7 on U.S. Route 27A during clear and dry conditions, according to the accident report from the Florida Highway Patrol. Brown's vehicle was headed east when a tractor trailer driven by Frank Baressi of Palm Harbor, Fla., traveling in the opposite direction, made a left turn onto a side street. The Tesla's roof hit the underside of the tractor trailer. The car skidded under the truck and off the road, plowing through two wire fences before crashing into a utility pole, the accident report said. Baressi told the Associated Press that Brown was "playing'Harry Potter' on the TV screen" in the car when the crash took place. Kim Montes, a spokeswoman for the Florida Highway Patrol, told The Times that a portable DVD player was found in the Tesla but said she did not know whether it had been in use. "At the time of the impact, we don't know what the status of that DVD player was.

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Softmax Regression (synonyms: Multinomial Logistic, Maximum Entropy Classifier, or just Multi-class Logistic Regression) is a generalization of logistic regression that we can use for multi-class classification (under the assumption that the classes are mutually exclusive). In contrast, we use the (standard) Logistic Regression model in binary classification tasks. Now, let me briefly explain how that works and how softmax regression differs from logistic regression. As the name suggests, in softmax regression (SMR), we replace the sigmoid logistic function by the so-called softmax function?: Now, this softmax function computes the probability that this training sample x(i) belongs to class j given the weight and net input z(i). So, we compute the probability p(y j x(i); wj) for each class label in j 1, ..., k.

The U.S. announced Thursday the first fatality in a wreck involving a car in self-driving mode. The government said it is investigating the design and performance of the system aboard the Tesla Model S sedan. Model S with Autopilot engaged. The Ohio man who died while using the "Autopilot" feature on his Tesla electric car was watching Harry Potter when he was fatally injured in a wreck while the car was in self-drive mood, according to a witness. Joshua Brown, 40, of Canton, Ohio, died from injuries he sustained when a tractor-trailer made a left turn in front of his 2015 Tesla on a highway near Williston, Fla., in May.