Deep Learning methods are currently the state-of-the-art in many problems which can be tackled via machine learning, in particular classification problems. However there is still lack of understanding on how those methods work, why they work and what are the limitations involved in using them. In this chapter we will describe in detail the transition from shallow to deep networks, include examples of code on how to implement them, as well as the main issues one faces when training a deep network. Afterwards, we introduce some theoretical background behind the use of deep models, and discuss their limitations. Training restricted boltzmann machines: An introduction.

For autonomous agents to successfully operate in the real world, anticipation of future events and states of their environment is a key competence. This problem has been formalized as a sequence extrapolation problem, where a number of observations are used to predict the sequence into the future. Real-world scenarios demand a model of uncertainty of such predictions, as predictions become increasingly uncertain -- in particular on long time horizons. While impressive results have been shown on point estimates, scenarios that induce multi-modal distributions over future sequences remain challenging. Our work addresses these challenges in a Gaussian Latent Variable model for sequence prediction. Our core contribution is a "Best of Many" sample objective that leads to more accurate and more diverse predictions that better capture the true variations in real-world sequence data. Beyond our analysis of improved model fit, our models also empirically outperform prior work on three diverse tasks ranging from traffic scenes to weather data.

Computable Stein discrepancies have been deployed for a variety of applications, including sampler selection in posterior inference, approximate Bayesian inference, and goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational cost that grows quadratically in the sample size. While linear-time Stein discrepancies have been proposed for goodness-of-fit testing, they exhibit avoidable degradations in testing power---even when power is explicitly optimized. To address these shortcomings, we introduce feature Stein discrepancies ($\Phi$SDs), a new family of quality measures that can be cheaply approximated using importance sampling. We show how to construct $\Phi$SDs that provably determine the convergence of a sample to its target and develop high-accuracy approximations---random $\Phi$SDs (R$\Phi$SDs)---which are computable in near-linear time. In our experiments with sampler selection for approximate posterior inference and goodness-of-fit testing, R$\Phi$SDs typically perform as well or better than quadratic-time KSDs while being orders of magnitude faster to compute.

We study the stochastic block model with two communities where vertices contain side information in the form of a vertex label. These vertex labels may have arbitrary label distributions, depending on the community memberships. We analyze a linearized version of the popular belief propagation algorithm. We show that this algorithm achieves the highest accuracy possible whenever a certain function of the network parameters has a unique fixed point. Whenever this function has multiple fixed points, the belief propagation algorithm may not perform optimally. We show that increasing the information in the vertex labels may reduce the number of fixed points and hence lead to optimality of belief propagation.

The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn't. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the sign of stochastic gradients, whereas the update magnitude is determined by an estimate of their relative variance. We disentangle these two aspects and analyze them in isolation, gaining insight into the mechanisms underlying ADAM. This analysis also extends recent results on adverse effects of ADAM on generalization, isolating the sign aspect as the problematic one. Transferring the variance adaptation to SGD gives rise to a novel method, completing the practitioner's toolbox for problems where ADAM fails.

High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in offline detection and estimation of regime changes in the topology of sparse graphical models. However, the online setting remains largely unexplored, despite its high relevance to applications in sensor networks and other engineering monitoring systems, as well as financial markets. To that end, this work introduces a novel scalable online algorithm for detecting an unknown number of abrupt changes in the inverse covariance matrix of sparse Gaussian graphical models with small delay. The proposed algorithm is based upon monitoring the conditional log-likelihood of all nodes in the network and can be extended to a large class of continuous and discrete graphical models. We also investigate asymptotic properties of our procedure under certain mild regularity conditions on the graph size, sparsity level, number of samples, and pre- and post-changes in the topology of the network. Numerical works on both synthetic and real data illustrate the good performance of the proposed methodology both in terms of computational and statistical efficiency across numerous experimental settings.

Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive as they potentially require fewer communication rounds to converge. However, there are significant drawbacks that impede their wide adoption, such as the computation and the communication of a large Hessian matrix. In this paper we present a new algorithm for distributed training of generalized linear models that only requires the computation of diagonal blocks of the Hessian matrix on the individual workers. To deal with this approximate information we propose an adaptive approach that - akin to trust-region methods - dynamically adapts the auxiliary model to compensate for modeling errors. We provide theoretical rates of convergence for a wide class of problems including L1-regularized objectives. We also demonstrate that our approach achieves state-of-the-art results on multiple large benchmark datasets.

As the backbone technology of machine learning, deep neural networks (DNNs) have have quickly ascended to the spotlight. Running DNNs on resource-constrained mobile devices is, however, by no means trivial, since it incurs high performance and energy overhead. While offloading DNNs to the cloud for execution suffers unpredictable performance, due to the uncontrolled long wide-area network latency. To address these challenges, in this paper, we propose Edgent, a collaborative and on-demand DNN co-inference framework with device-edge synergy. Edgent pursues two design knobs: (1) DNN partitioning that adaptively partitions DNN computation between device and edge, in order to leverage hybrid computation resources in proximity for real-time DNN inference. (2) DNN right-sizing that accelerates DNN inference through early-exit at a proper intermediate DNN layer to further reduce the computation latency. The prototype implementation and extensive evaluations based on Raspberry Pi demonstrate Edgent's effectiveness in enabling on-demand low-latency edge intelligence.

We propose a novel reinforcement learning approach for finite Markov decision processes (MDPs) with delayed rewards. In this work, biases of temporal difference (TD) estimates are proved to be corrected only exponentially slowly in the number of delay steps. Furthermore, variances of Monte Carlo (MC) estimates are proved to increase the variance of other estimates, the number of which can exponentially grow in the number of delay steps. We introduce RUDDER, a return decomposition method, which creates a new MDP with same optimal policies as the original MDP but with redistributed rewards that have largely reduced delays. If the return decomposition is optimal, then the new MDP does not have delayed rewards and TD estimates are unbiased. In this case, the rewards track Q-values so that the future expected reward is always zero. We experimentally confirm our theoretical results on bias and variance of TD and MC estimates. On artificial tasks with different lengths of reward delays, we show that RUDDER is exponentially faster than TD, MC, and MC Tree Search (MCTS). RUDDER outperforms rainbow, A3C, DDQN, Distributional DQN, Dueling DDQN, Noisy DQN, and Prioritized DDQN on the delayed reward Atari game Venture in only a fraction of the learning time. RUDDER considerably improves the state-of-the-art on the delayed reward Atari game Bowling in much less learning time. Source code is available at https://github.com/ml-jku/baselines-rudder, with demonstration videos at https://goo.gl/EQerZV.

Multiple kernel learning (MKL) method is generally believed to perform better than single kernel method. However, some empirical studies show that this is not always true: the combination of multiple kernels may even yield an even worse performance than using a single kernel. There are two possible reasons for the failure: (i) most existing MKL methods assume that the optimal kernel is a linear combination of base kernels, which may not hold true; and (ii) some kernel weights are inappropriately assigned due to noises and carelessly designed algorithms. In this paper, we propose a novel MKL framework by following two intuitive assumptions: (i) each kernel is a perturbation of the consensus kernel; and (ii) the kernel that is close to the consensus kernel should be assigned a large weight. Impressively, the proposed method can automatically assign an appropriate weight to each kernel without introducing additional parameters, as existing methods do. The proposed framework is integrated into a unified framework for graph-based clustering and semi-supervised classification. We have conducted experiments on multiple benchmark datasets and our empirical results verify the superiority of the proposed framework.