On paper alone you would never guess that I grew up poor and hungry. My most recent annual salary was over $700,000. I am a Truman National Security Fellow and a term member at the Council on Foreign Relations. My publisher has just released my latest book series on quantitative finance in worldwide distribution. None of it feels like enough though. I feel as though I am wired for a permanent state of flight or fight, waiting for the other shoe to drop, or the metaphorical week when I don't eat. I've chosen not to have children, partly because--despite any success--I still don't feel I have a safety net. I have a huge minimum checking account balance in mind before I would ever consider having children. If you knew me personally, you might get glimpses of stress, self-doubt, anxiety, and depression.

Here at Udacity, we are tremendously excited to announce the kick-off of the second term of our Artificial Intelligence Nanodegree program. Because we are able to provide a depth of education that is commensurate with university education; because we are bridging the gap between universities and industry by providing you with hands-on projects and partnering with the top industries in the field; and last but certainly not least, because we are able to bring this education to many more people across the globe, at a cost that makes a top-notch AI education realistic for all aspiring learners. During the first term, you've enjoyed learning about Game Playing Agents, Simulated Annealing, Constraint Satisfaction, Logic and Planning, and Probabilistic AI from some of the biggest names in the field: Sebastian Thrun, Peter Norvig, and Thad Starner. Term 2 will be focused on one of the cutting-edge advancements of AI -- Deep Learning. In this Term, you will learn about the foundations of neural networks, understand how to train these neural networks with techniques such as gradient descent and backpropagation, and learn different types of architectures that make neural networks work for a variety of different applications.

The densification of small-cell base stations in a 5G architecture is a promising approach to enhance the coverage area and facilitate the ever increasing capacity demand of end users. However, the bottleneck is an intelligent management of a backhaul/fronthaul network for these small-cell base stations. This involves efficient association and placement of the backhaul hubs that connects these small-cells with the core network. Terrestrial hubs suffer from an inefficient non line of sight link limitations and unavailability of a proper infrastructure in an urban area. Seeing the popularity of flying platforms, we employ here an idea of using networked flying platform (NFP) such as unmanned aerial vehicles (UAVs), drones, unmanned balloons flying at different altitudes, as aerial backhaul hubs. The association problem of these NFP-hubs and small-cell base stations is formulated considering backhaul link and NFP related limitations such as maximum number of supported links and bandwidth. Then, this paper presents an efficient and distributed solution of the designed problem, which performs a greedy search in order to maximize the sum rate of the overall network. A favorable performance is observed via a numerical comparison of our proposed method with optimal exhaustive search algorithm in terms of sum rate and run-time speed.

In this work and the supporting Part II, we examine the performance of stochastic sub-gradient learning strategies under weaker conditions than usually considered in the literature. The new conditions are shown to be automatically satisfied by several important cases of interest including SVM, LASSO, and Total-Variation denoising formulations. In comparison, these problems do not satisfy the traditional assumptions used in prior analyses and, therefore, conclusions derived from these earlier treatments are not directly applicable to these problems. The results in this article establish that stochastic sub-gradient strategies can attain linear convergence rates, as opposed to sub-linear rates, to the steady-state regime. A realizable exponential-weighting procedure is employed to smooth the intermediate iterates and guarantee useful performance bounds in terms of convergence rate and excessive risk performance. Part I of this work focuses on single-agent scenarios, which are common in stand-alone learning applications, while Part II extends the analysis to networked learners. The theoretical conclusions are illustrated by several examples and simulations, including comparisons with the FISTA procedure.

Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on assumptions of linearity and Gaussianity that are rarely met in practice. In this paper, we introduced a new dynamical smoothing method that exploits the remarkable capabilities of convolutional neural networks to approximate complex non-linear functions. The main idea is to generate a training set composed of both latent states and observations from an ensemble of simulators and to train the deep network to recover the former from the latter. Importantly, this method only requires the availability of the simulators and can therefore be applied in situations in which either the latent dynamical model or the observation model cannot be easily expressed in closed form. In our simulation studies, we show that the resulting ConvNet smoother has almost optimal performance in the Gaussian case even when the parameters are unknown. Furthermore, the method can be successfully applied to extremely non-linear and non-Gaussian systems. Finally, we empirically validate our approach via the analysis of measured brain signals.

Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We present a novel method to train a class of probabilistic models with discrete latent variables using the variational autoencoder framework, including backpropagation through the discrete latent variables. The associated class of probabilistic models comprises an undirected discrete component and a directed hierarchical continuous component. The discrete component captures the distribution over the disconnected smooth manifolds induced by the continuous component. As a result, this class of models efficiently learns both the class of objects in an image, and their specific realization in pixels, from unsupervised data, and outperforms state-of-the-art methods on the permutation-invariant MNIST, Omniglot, and Caltech-101 Silhouettes datasets.

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenvalues. We leverage upon this observation to construct a local-entropy-based objective function that favors well-generalizable solutions lying in large flat regions of the energy landscape, while avoiding poorly-generalizable solutions located in the sharp valleys. Conceptually, our algorithm resembles two nested loops of SGD where we use Langevin dynamics in the inner loop to compute the gradient of the local entropy before each update of the weights. We show that the new objective has a smoother energy landscape and show improved generalization over SGD using uniform stability, under certain assumptions. Our experiments on convolutional and recurrent networks demonstrate that Entropy-SGD compares favorably to state-of-the-art techniques in terms of generalization error and training time.

In this paper we introduce a new feature selection algorithm to remove the irrelevant or redundant features in the data sets. In this algorithm the importance of a feature is based on its fitting to the Catastrophe model. Akaike information crite- rion value is used for ranking the features in the data set. The proposed algorithm is compared with well-known RELIEF feature selection algorithm. Breast Cancer, Parkinson Telemonitoring data and Slice locality data sets are used to evaluate the model.

Bandit structured prediction describes a stochastic optimization framework where learning is performed from partial feedback. This feedback is received in the form of a task loss evaluation to a predicted output structure, without having access to gold standard structures. We advance this framework by lifting linear bandit learning to neural sequence-to-sequence learning problems using attention-based recurrent neural networks. Furthermore, we show how to incorporate control variates into our learning algorithms for variance reduction and improved generalization. We present an evaluation on a neural machine translation task that shows improvements of up to 5.89 BLEU points for domain adaptation from simulated bandit feedback.

Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs. We show that stationarity is expressed through the graph localization operator reminiscent of translation. We prove that stationary graph signals are characterized by a well-defined Power Spectral Density that can be efficiently estimated even for large graphs. We leverage this new concept to derive Wiener-type estimation procedures of noisy and partially observed signals and illustrate the performance of this new model for denoising and regression.