Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine.

We introduce the first system towards the novel task of answering complex multi-sentence recommendation questions in the tourism domain. Our solution uses a pipeline of two modules: question understanding and answering. For question understanding, we define an SQL-like query language that captures the semantic intent of a question; it supports operators like subset, negation, preference and similarity, which are often found in recommendation questions. We train and compare traditional CRFs as well as bidirectional LSTM-based models for converting a question to its semantic representation. We extend these models to a semi-supervised setting with partially labeled sequences gathered through crowdsourc-ing. We find that our best model performs semi-supervised training of BiDiL-STM CRF with hand-designed features and CCM(Chang et al., 2007) constraints. Finally, in an end to end QA system, our answering component converts our question representation into queries fired on underlying knowledge sources. Our experiments on two different answer corpora demonstrate that our system can significantly outperform baselines with up to 20 pt higher accuracy and 17 pt higher recall.

We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the estimation of the topic/dictionary matrix by maximum marginal likelihood estimation. In particular, this explains the robustness of this estimator to over-specified values of the factorization rank and in particular its ability to automatically prune spurious dictionary columns, as empirically observed in previous work. The marginalization of the activation matrix leads in turn to a new Monte-Carlo Expectation-Maximization algorithm with favorable properties.

We propose a modification of the cost function of the Hopfield model whose salient features shine in its Taylor expansion and result in more than pairwise interactions with alternate signs, suggesting a unified framework for handling both with deep learning and network pruning. In our analysis, we heavily rely on the Hamilton-Jacobi correspondence relating the statistical model with a mechanical system. In this picture, our model is nothing but the relativistic extension of the original Hopfield model (whose cost function is a quadratic form in the Mattis magnetization which mimics the non-relativistic Hamiltonian for a free particle). We focus on the low-storage regime and solve the model analytically by taking advantage of the mechanical analogy, thus obtaining a complete characterization of the free energy and the associated self-consistency equations in the thermodynamic limit. On the numerical side, we test the performances of our proposal with MC simulations, showing that the stability of spurious states (limiting the capabilities of the standard Hebbian construction) is sensibly reduced due to presence of unlearning contributions in this extended framework.

Poisson matrix factorization (PF) is a nonnegative matrix factorization (NMF) model (Lee and Seung, 1999) often used for recommender systems (Ma et al., 2011; Gopalan et al., 2015), text information retrieval (Canny, 2004; Buntine and Jakulin, 2006) or dictionary learning for image processing (Cemgil, 2009). The data is assumed to be drawn from the Poisson distribution making it specially well suited for count/integer-valued data. Since the Netflix Prize (Bennett et al., 2007), collaborative filtering (CF) has been giving the state-of-the-art results for recommender systems. CF exploits data relating users to items, like historical data. These data can either be explicit (ratings given by users to items) or implicit (count data from users listening to songs, clicking on web pages, watching videos, etc).

We study the necessary and sufficient complexity of ReLU neural networks-in terms of depth and number of weights-required for approximating classifier functions in an $L^2$-sense. As a model, we consider the set $\mathcal{E}^\beta (\mathbb{R}^d)$ of possibly discontinuous piecewise $C^\beta$ functions $f : [-1/2, 1/2]^d \to \mathbb{R}$, where the different 'smooth regions' of $f$ are separated by $C^\beta$ hypersurfaces. For given dimension $d \geq 2$, regularity $\beta > 0$, and accuracy $\varepsilon > 0$, we construct ReLU neural networks that approximate functions from $\mathcal{E}^\beta(\mathbb{R}^d)$ up to an $L^2$ error of $\varepsilon$. The constructed networks have a fixed number of layers, depending only on $d$ and $\beta$ and they have $O(\varepsilon^{-2(d-1)/\beta})$ many nonzero weights, which we prove to be optimal. In addition to the optimality in terms of the number of weights, we show that in order to achieve this optimal approximation rate, one needs ReLU networks of a certain minimal depth. Precisely, for piecewise $C^\beta(\mathbb{R}^d)$ functions, this minimal depth is given-up to a multiplicative constant-by $\beta/d$. Up to a log factor, our constructed networks match this bound. This partly explains the benefits of depth for ReLU networks by showing that deep networks are necessary to achieve efficient approximation of (piecewise) smooth functions. Finally, we analyze approximation in high-dimensional spaces where the function $f$ to be approximated can be factorized into a smooth dimension reducing feature map $\tau$ and classifier function $g$-defined on a low-dimensional feature space-as $f = g \circ \tau$. We show that in this case the approximation rate depends only on the dimension of the feature space and not the input dimension.

Recent work on follow the perturbed leader (FTPL) algorithms for the adversarial multi-armed bandit problem has highlighted the role of the hazard rate of the distribution generating the perturbations. Assuming that the hazard rate is bounded, it is possible to provide regret analyses for a variety of FTPL algorithms for the multi-armed bandit problem. This paper pushes the inquiry into regret bounds for FTPL algorithms beyond the bounded hazard rate condition. There are good reasons to do so: natural distributions such as the uniform and Gaussian violate the condition. We give regret bounds for both bounded support and unbounded support distributions without assuming the hazard rate condition. We also disprove a conjecture that the Gaussian distribution cannot lead to a low-regret algorithm. In fact, it turns out that it leads to near optimal regret, up to logarithmic factors. A key ingredient in our approach is the introduction of a new notion called the generalized hazard rate.

The Institute for Public Policy Research seems to think it is expounding some new ideas on the dangers of future technology (Poorest to fare worst in age of automation, 28 December), but in fact these ideas are half a century old. Norbert Wiener pointed them out in his book on Cybernetics, written in 1947 and published in 1948. His argument, in paraphrase, was that the first industrial revolution – the coming of steam power in the late 18th century – represented the devaluation of muscle, so that humans only found purpose as controllers of machines, in factories. The second industrial revolution, in the last century through automation and the digital economy, represents the devaluation of the human brain. If you devalue a man's (or woman's) muscles and also his brain, what has he got to sell in terms of his labour?

He is recognized as a Visionary and Thought Leader in guiding organizations in their digital journey by assisting them in setting transformation roadmaps to ensure competitive advantage and differentiation. He is very well versed in adopting technologies like Social, Mobile, Big Data, Analytics, Cloud and IoT into business solutions to accelerate Superior Customer Experiences or bring in new Revenue Generation opportunities to companies. He has built leading digital practices in multinational organizations Cognizant and Atos. Dileep along with his partners runs an Advisory company Powerfluence which helps organization to rapidly scale for success in their Digital journeys. He advises SME companies in meeting their transformation goals and positions them for success.

The question about chatbots seems to have always been, "Can this automation technology actually fool a human into thinking it's also human?" CRM experts, vendors and other industry soothsayers say the question is changing to something more like this for CRM chatbots: "If a chatbot can solve a basic problem and save customers the angst of being stuck on hold and the CRM team the cost in human bandwidth, does it matter how'human' it comes across?" The gold standard in determining chatbot "humanity" and the effectiveness of conversational artificial intelligence is the Turing test, developed in 1950 by Alan Turing, the noted computing and AI futurist. Turing first made tech history by helping Britain crack the daily changed German Enigma code and other encrypted messages that governed military movements, ultimately contributing to the Allies' victory in World War II. For Facebook chatbots and those on other social and web platforms that comprise ground zero for AI in marketing, sales, service and even e-commerce, the bar is much lower than the Turing test. Customers know they could be dealing with bots most of the time and are willing to work with them for basic tasks like checking a bank balance, changing a password or ordering a pizza.