We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter coefficients. This l1-norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in the mean square sense involving their transient and steady -state behaviors. This study relies on the vectorization argument and the paraunitary assumption imposed on the analysis filter banks, and thus does not restrict the input signal to being Gaussian or having another distribution. In addition, we propose to adjust adaptively the intensity parameter of the sparsity attraction term. Finally, simulation results in sparse system identification demonstrate the effectiveness of our theoretical results.

The digitalization of the legal domain has been ongoing for a couple of years. In that process, the application of different machine learning (ML) techniques is crucial. Tasks such as the classification of legal documents or contract clauses as well as the translation of those are highly relevant. On the other side, digitized documents are barely accessible in this field, particularly in Germany. Today, deep learning (DL) is one of the hot topics with many publications and various applications. Sometimes it provides results outperforming the human level. Hence this technique may be feasible for the legal domain as well. However, DL requires thousands of samples to provide decent results. A potential solution to this problem is multi-task DL to enable transfer learning. This approach may be able to overcome the data scarcity problem in the legal domain, specifically for the German language. We applied the state of the art multi-task model on three tasks: translation, summarization, and multi-label classification. The experiments were conducted on legal document corpora utilizing several task combinations as well as various model parameters. The goal was to find the optimal configuration for the tasks at hand within the legal domain. The multi-task DL approach outperformed the state of the art results in all three tasks. This opens a new direction to integrate DL technology more efficiently in the legal domain.

Modern machine learning focuses on highly expressive models that are able to fit or interpolate the data completely, resulting in zero training loss. For such models, we show that the stochastic gradients of common loss functions satisfy a strong growth condition. Under this condition, we prove that constant step-size stochastic gradient descent (SGD) with Nesterov acceleration matches the convergence rate of the deterministic setting for both convex and strongly-convex functions. In the non-convex setting, this condition implies that SGD can find a first-order stationary point as efficiently as full gradient descent. Under interpolation, we also show that all smooth loss functions with a finite-sum structure satisfy a weaker growth condition. Given this weaker condition, we prove that SGD with a constant step-size attains the deterministic convergence rate in both the strongly-convex and convex settings. Under additional assumptions, the above results enable us to prove an O(1/k^2) mistake bound for $k$ iterations of a stochastic perceptron algorithm using the squared-hinge loss. Finally, we validate our theoretical findings with experiments on synthetic and real datasets.

Valuable training data is often owned by independent organizations and located in multiple data centers. Most deep learning approaches require to centralize the multi-datacenter data for performance purpose. In practice, however, it is often infeasible to transfer all data to a centralized data center due to not only bandwidth limitation but also the constraints of privacy regulations. Model averaging is a conventional choice for data parallelized training, but its ineffectiveness is claimed by previous studies as deep neural networks are often non-convex. In this paper, we argue that model averaging can be effective in the decentralized environment by using two strategies, namely, the cyclical learning rate and the increased number of epochs for local model training. With the two strategies, we show that model averaging can provide competitive performance in the decentralized mode compared to the data-centralized one. In a practical environment with multiple data centers, we conduct extensive experiments using state-of-the-art deep network architectures on different types of data. Results demonstrate the effectiveness and robustness of the proposed method.

We demonstrate how self-concordance of the loss can be exploited to obtain asymptotically optimal rates for M-estimators in finite-sample regimes. We consider two classes of losses: (i) canonically self-concordant losses in the sense of Nesterov and Nemirovski (1994), i.e., with the third derivative bounded with the $3/2$ power of the second; (ii) pseudo self-concordant losses, for which the power is removed, as introduced by Bach (2010). These classes contain some losses arising in generalized linear models, including logistic regression; in addition, the second class includes some common pseudo-Huber losses. Our results consist in establishing the critical sample size sufficient to reach the asymptotically optimal excess risk for both classes of losses. Denoting $d$ the parameter dimension, and $d_{\text{eff}}$ the effective dimension which takes into account possible model misspecification, we find the critical sample size to be $O(d_{\text{eff}} \cdot d)$ for canonically self-concordant losses, and $O(\rho \cdot d_{\text{eff}} \cdot d)$ for pseudo self-concordant losses, where $\rho$ is the problem-dependent local curvature parameter. In contrast to the existing results, we only impose local assumptions on the data distribution, assuming that the calibrated design, i.e., the design scaled with the square root of the second derivative of the loss, is subgaussian at the best predictor $\theta_*$. Moreover, we obtain the improved bounds on the critical sample size, scaling near-linearly in $\max(d_{\text{eff}},d)$, under the extra assumption that the calibrated design is subgaussian in the Dikin ellipsoid of $\theta_*$. Motivated by these findings, we construct canonically self-concordant analogues of the Huber and logistic losses with improved statistical properties. Finally, we extend some of these results to $\ell_1$-regularized M-estimators in high dimensions.

In this paper, we study the problem of monotone (weakly) DR-submodular continuous maximization. While previous methods require the gradient information of the objective function, we propose a derivative-free algorithm LDGM for the first time. We define $\beta$ and $\alpha$ to characterize how close a function is to continuous DR-submodulr and submodular, respectively. Under a convex polytope constraint, we prove that LDGM can achieve a $(1-e^{-\beta}-\epsilon)$-approximation guarantee after $O(1/\epsilon)$ iterations, which is the same as the best previous gradient-based algorithm. Moreover, in some special cases, a variant of LDGM can achieve a $((\alpha/2)(1-e^{-\alpha})-\epsilon)$-approximation guarantee for (weakly) submodular functions. We also compare LDGM with the gradient-based algorithm Frank-Wolfe under noise, and show that LDGM can be more robust. Empirical results on budget allocation verify the effectiveness of LDGM.

In order to implement large scale quantum computations it is necessary to be able to store and manipulate quantum information in a manner that is robust to the unavoidable errors introduced through interaction of the physical qubits with a noisy environment. The known strategy for achieving such robustness is to encode a single logical qubit into the state of many physical qubits, via a quantum error correcting code, from which it is possible to actively diagnose and correct errors that may occur [1, 2]. While many quantum error correcting codes exist, topological quantum codes [1-8], in which only local operations are required to diagnose and correct errors, are of particular interest as a result of their experimental feasibility [9-15]. In particular, the surface code has emerged as an especially promising candidate for large-scale fault-tolerant quantum computation, due to the combination of its comparatively low overhead and locality requirements, coupled with the availability of convenient strategies for the implementation of all required logical gates [16, 17]. In fact, current road maps towards the realization of robust quantum computing have identified surface code based approaches as the most feasible methodology for achieving this goal [18].

In this paper we propose to view the acceptance rate of the Metropolis-Hastings algorithm as a universal objective for learning to sample from target distribution - given either as a set of samples or in the form of unnormalized density. To reveal the connection we derive the lower bound on the acceptance rate and treat it as the objective for learning explicit and implicit samplers. The form of the lower bound allows for doubly stochastic gradient optimization in case the target distribution factorizes (i.e. over data points). Bayesian framework and deep learning have become more and more interrelated during recent years. Recently Bayesian deep neural networks were used for estimating uncertainty (Gal & Ghahramani, 2016), ensembling (Gal & Ghahramani, 2016) and model compression (Molchanov et al., 2017). On the other hand, deep neural networks may be used to improve approximate inference in Bayesian models (Kingma & Welling, 2014). Learning modern Bayesian neural networks requires inference in the spaces with dimension up to several million by conditioning the weights of DNN on hundreds of thousands of objects.

Most of the works on planning and learning, e.g., planning by (model based) reinforcement learning, are based on two main assumptions: (i) the set of states of the planning domain is fixed; (ii) the mapping between the observations from the real word and the states is implicitly assumed, and is not part of the planning domain. Consequently, the focus is on learning the transitions between states. Current approaches address neither the problem of learning new states of the planning domain, nor the problem of representing and updating the mapping between the real world perceptions and the states. In this paper, we drop such assumptions. We provide a formal framework in which (i) the agent can learn dynamically new states of the planning domain; (ii) the mapping between abstract states and the perception from the real world, represented by continuous variables, is part of the planning domain; (iii) such mapping is learned and updated along the "life" of the agent. We define and develop an algorithm that interleaves planning, acting, and learning. We provide a first experimental evaluation that shows how this novel framework can effectively learn coherent abstract planning models.

Flying cars, augmented reality glasses and contact lenses that can detect diabetes: They're all innovations born out of Google X, the skunkworks division of Alphabet. Three years ago Spanish telco giant Telefónica established Alpha, a lab in Barcelona staffed by around 100 people, working in stealth on innovative technology that holds the promise of a potential new revenue streams. The person running all things AI at the lab is Pascal Weinberger, 21. Weinberger is originally from Germany and like many other computer programmers is self-taught. He dropped out of a bachelor's degree, having "enrolled to keep my parents happy," but by 15 had already taken several remote courses in programming at MIT.