arXiv subjects

Alejandro Ribeiro

Publications and source records attributed to Alejandro Ribeiro.

At least 253 records · Page 14Linked to original sources

arXiv2018

Convolutional Neural Network Architectures for Signals Supported on Graphs

Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best performing GNN architecture.

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arXiv2018

Diffusion Scattering Transforms on Graphs

Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture "high-frequency" information, akin to the Euclidean Scattering.

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arXiv2018

Control Aware Radio Resource Allocation in Low Latency Wireless Control Systems

We consider the problem of allocating radio resources over wireless communication links to control a series of independent wireless control systems. Low-latency transmissions are necessary in enabling time-sensitive control systems to operate over wireless links with high reliability. Achieving fast data rates over wireless links thus comes at the cost of reliability in the form of high packet error rates compared to wired links due to channel noise and interference. However, the effect of the communication link errors on the control system performance depends dynamically on the control system state. We propose a novel control-communication co-design approach to the low-latency resource allocation problem. We incorporate control and channel state information to make scheduling decisions over time on frequency, bandwidth and data rates across the next-generation Wi-Fi based wireless communication links that close the control loops. Control systems that are closer to instability or further from a desired range in a given control cycle are given higher packet delivery rate targets to meet. Rather than a simple priority ranking, we derive precise packet error rate targets for each system needed to satisfy stability targets and make scheduling decisions to meet such targets while reducing total transmission time. The resulting Control-Aware Low Latency Scheduling (CALLS) method is tested in numerous simulation experiments that demonstrate its effectiveness in meeting control-based goals under tight latency constraints relative to control-agnostic scheduling.

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arXiv2018

Connecting the Dots: Identifying Network Structure via Graph Signal Processing

Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics impact the properties of the graph signals of interest. Such an assumption is often untenable beyond applications dealing with e.g., directly observable social and infrastructure networks; and typically adopted graph construction schemes are largely informal, distinctly lacking an element of validation. This tutorial offers an overview of graph learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology. Fairly mature statistical approaches are surveyed first, where correlation analysis takes center stage along with its connections to covariance selection and high-dimensional regression for learning Gaussian graphical models. Recent GSP-based network inference frameworks are also described, which postulate that the network exists as a latent underlying structure, and that observations are generated as a result of a network process defined in such a graph. A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks, nonlinear models of pairwise interaction, as well as extensions to directed graphs and their relation to causal inference. All in all, this paper introduces readers to challenges and opportunities for signal processing research in emerging topic areas at the crossroads of modeling, prediction, and control of complex behavior arising in networked systems that evolve over time.

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arXiv2018

Stochastic Policy Gradient Ascent in Reproducing Kernel Hilbert Spaces

Reinforcement learning consists of finding policies that maximize an expected cumulative long-term reward in a Markov decision process with unknown transition probabilities and instantaneous rewards. In this paper, we consider the problem of finding such optimal policies while assuming they are continuous functions belonging to a reproducing kernel Hilbert space (RKHS). To learn the optimal policy we introduce a stochastic policy gradient ascent algorithm with three unique novel features: (i) The stochastic estimates of policy gradients are unbiased. (ii) The variance of stochastic gradients is reduced by drawing on ideas from numerical differentiation. (iii) Policy complexity is controlled using sparse RKHS representations. Novel feature (i) is instrumental in proving convergence to a stationary point of the expected cumulative reward. Novel feature (ii) facilitates reasonable convergence times. Novel feature (iii) is a necessity in practical implementations which we show can be done in a way that does not eliminate convergence guarantees. Numerical examples in standard problems illustrate successful learning of policies with low complexity representations which are close to stationary points of the expected cumulative reward.

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arXiv2018

A Newton-Based Method for Nonconvex Optimization with Fast Evasion of Saddle Points

Machine learning problems such as neural network training, tensor decomposition, and matrix factorization, require local minimization of a nonconvex function. This local minimization is challenged by the presence of saddle points, of which there can be many and from which descent methods may take inordinately large number of iterations to escape. This paper presents a second-order method that modifies the update of Newton's method by replacing the negative eigenvalues of the Hessian by their absolute values and uses a truncated version of the resulting matrix to account for the objective's curvature. The method is shown to escape saddles in at most $1 + \log_{3/2} (δ/2\varepsilon)$ iterations where $\varepsilon$ is the target optimality and $δ$ characterizes a point sufficiently far away from the saddle. This base of this exponential escape is $3/2$ independently of problem constants. Adding classical properties of Newton's method, the paper proves convergence to a local minimum with probability $1-p$ in $O\left(\log(1/p)) + O(\log(1/\varepsilon)\right)$ iterations.

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arXiv2018

Scalable Centralized Deep Multi-Agent Reinforcement Learning via Policy Gradients

In this paper, we explore using deep reinforcement learning for problems with multiple agents. Most existing methods for deep multi-agent reinforcement learning consider only a small number of agents. When the number of agents increases, the dimensionality of the input and control spaces increase as well, and these methods do not scale well. To address this, we propose casting the multi-agent reinforcement learning problem as a distributed optimization problem. Our algorithm assumes that for multi-agent settings, policies of individual agents in a given population live close to each other in parameter space and can be approximated by a single policy. With this simple assumption, we show our algorithm to be extremely effective for reinforcement learning in multi-agent settings. We demonstrate its effectiveness against existing comparable approaches on co-operative and competitive tasks.

cs.LG↗

arXiv2018

Nonparametric Stochastic Compositional Gradient Descent for Q-Learning in Continuous Markov Decision Problems

We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address this problem by considering Bellman's optimality equation defined over action-value functions, which we reformulate into a nested non-convex stochastic optimization problem defined over a Reproducing Kernel Hilbert Space (RKHS). We develop a functional generalization of stochastic quasi-gradient method to solve it, which, owing to the structure of the RKHS, admits a parameterization in terms of scalar weights and past state-action pairs which grows proportionately with the algorithm iteration index. To ameliorate this complexity explosion, we apply Kernel Orthogonal Matching Pursuit to the sequence of kernel weights and dictionaries, which yields a controllable error in the descent direction of the underlying optimization method. We prove that the resulting algorithm, called KQ-Learning, converges with probability 1 to a stationary point of this problem, yielding a fixed point of the Bellman optimality operator under the hypothesis that it belongs to the RKHS. Under constant learning rates, we further obtain convergence to a small Bellman error that depends on the chosen learning rates. Numerical evaluation on the Continuous Mountain Car and Inverted Pendulum tasks yields convergent parsimonious learned action-value functions, policies that are competitive with the state of the art, and exhibit reliable, reproducible learning behavior.

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arXiv2018

Distributed Inertial Best-Response Dynamics

The note considers the problem of computing pure Nash equilibrium (NE) strategies in distributed (i.e., network-based) settings. The paper studies a class of inertial best response dynamics based on the fictitious play (FP) algorithm. It is shown that inertial best response dynamics are robust to informational limitations common in distributed settings. Fully distributed variants of FP with inertia and joint strategy FP with inertia are developed and convergence is proven to the set of pure NE. The distributed algorithms rely on consensus methods. Results are validated using numerical simulations.

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arXiv2018

MIMO Graph Filters for Convolutional Neural Networks

Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise nonlinearity. Since the two first operations are well-defined only on regular-structured data such as audio or images, application of CNNs to contemporary datasets where the information is defined in irregular domains is challenging. This paper investigates CNNs architectures to operate on signals whose support can be modeled using a graph. Architectures that replace the regular convolution with a so-called linear shift-invariant graph filter have been recently proposed. This paper goes one step further and, under the framework of multiple-input multiple-output (MIMO) graph filters, imposes additional structure on the adopted graph filters, to obtain three new (more parsimonious) architectures. The proposed architectures result in a lower number of model parameters, reducing the computational complexity, facilitating the training, and mitigating the risk of overfitting. Simulations show that the proposed simpler architectures achieve similar performance as more complex models.

cs.LG↗

arXiv2018

Learning Sample-Efficient Target Reaching for Mobile Robots

In this paper, we propose a novel architecture and a self-supervised policy gradient algorithm, which employs unsupervised auxiliary tasks to enable a mobile robot to learn how to navigate to a given goal. The dependency on the global information is eliminated by providing only sparse range-finder measurements to the robot. The partially observable planning problem is addressed by splitting it into a hierarchical process. We use convolutional networks to plan locally, and a differentiable memory to provide information about past time steps in the trajectory. These modules, combined in our network architecture, produce globally consistent plans. The sparse reward problem is mitigated by our modified policy gradient algorithm. We model the robots uncertainty with unsupervised tasks to force exploration. The novel architecture we propose with the modified version of the policy gradient algorithm allows our robot to reach the goal in a sample efficient manner, which is orders of magnitude faster than the current state of the art policy gradient algorithm. Simulation and experimental results are provided to validate the proposed approach.

cs.RO↗

arXiv2018

Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problems

In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent nonquadratic Lyapunov functions that can generate convergence rates in addition to proving asymptotic convergence. Using Integral Quadratic Constraints (IQCs) from robust control theory, we propose a Linear Matrix Inequality (LMI) to guide the search for the parameters of the Lyapunov function in order to establish a rate bound. Based on this result, we formulate a Semidefinite Programming (SDP) whose solution yields the best convergence rate that can be certified by the class of Lyapunov functions under consideration. We illustrate the utility of our results by analyzing the gradient method, proximal algorithms and their accelerated variants for (strongly) convex problems. We also develop the continuous-time counterpart, whereby we analyze the gradient flow and the continuous-time limit of Nesterov's accelerated method.

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arXiv2018

Convolutional Neural Networks Via Node-Varying Graph Filters

Convolutional neural networks (CNNs) are being applied to an increasing number of problems and fields due to their superior performance in classification and regression tasks. Since two of the key operations that CNNs implement are convolution and pooling, this type of networks is implicitly designed to act on data described by regular structures such as images. Motivated by the recent interest in processing signals defined in irregular domains, we advocate a CNN architecture that operates on signals supported on graphs. The proposed design replaces the classical convolution not with a node-invariant graph filter (GF), which is the natural generalization of convolution to graph domains, but with a node-varying GF. This filter extracts different local features without increasing the output dimension of each layer and, as a result, bypasses the need for a pooling stage while involving only local operations. A second contribution is to replace the node-varying GF with a hybrid node-varying GF, which is a new type of GF introduced in this paper. While the alternative architecture can still be run locally without requiring a pooling stage, the number of trainable parameters is smaller and can be rendered independent of the data dimension. Tests are run on a synthetic source localization problem and on the 20NEWS dataset.

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arXiv2018

Surpassing Gradient Descent Provably: A Cyclic Incremental Method with Linear Convergence Rate

Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly convex functions where the number of functions $n$ is large. Gradient descent method (GD) is successful in minimizing convex problems at a fast linear rate; however, it is not applicable to the considered large-scale optimization setting because of the high computational complexity. Incremental methods resolve this drawback of gradient methods by replacing the required gradient for the descent direction with an incremental gradient approximation. They operate by evaluating one gradient per iteration and executing the average of the $n$ available gradients as a gradient approximate. Although, incremental methods reduce the computational cost of GD, their convergence rates do not justify their advantage relative to GD in terms of the total number of gradient evaluations until convergence. In this paper, we introduce a Double Incremental Aggregated Gradient method (DIAG) that computes the gradient of only one function at each iteration, which is chosen based on a cyclic scheme, and uses the aggregated average gradient of all the functions to approximate the full gradient. The iterates of the proposed DIAG method uses averages of both iterates and gradients in oppose to classic incremental methods that utilize gradient averages but do not utilize iterate averages. We prove that not only the proposed DIAG method converges linearly to the optimal solution, but also its linear convergence factor justifies the advantage of incremental methods on GD. In particular, we prove that the worst case performance of DIAG is better than the worst case performance of GD.

math.OC↗

arXiv2018

Approximate Supermodularity Bounds for Experimental Design

This work provides performance guarantees for the greedy solution of experimental design problems. In particular, it focuses on A- and E-optimal designs, for which typical guarantees do not apply since the mean-square error and the maximum eigenvalue of the estimation error covariance matrix are not supermodular. To do so, it leverages the concept of approximate supermodularity to derive non-asymptotic worst-case suboptimality bounds for these greedy solutions. These bounds reveal that as the SNR of the experiments decreases, these cost functions behave increasingly as supermodular functions. As such, greedy A- and E-optimal designs approach (1-1/e)-optimality. These results reconcile the empirical success of greedy experimental design with the non-supermodularity of the A- and E-optimality criteria.

cs.LG↗

arXiv2018

Random Access Communication for Wireless Control Systems with Energy Harvesting Sensors

In this paper, we study wireless networked control systems in which the sensing devices are powered by energy harvesting. We consider a scenario with multiple plants, where the sensors communicate their measurements to their respective controllers over a shared wireless channel. Due to the shared nature of the medium, sensors transmitting simultaneously can lead to packet collisions. In order to deal with this, we propose the use of random access communication policies and, to this end, we translate the control performance requirements to successful packet reception probabilities. The optimal scheduling decision is to transmit with a certain probability, which is adaptive to plant, channel and battery conditions. Moreover, we provide a stochastic dual method to compute the optimal scheduling solution, which is decoupled across sensors, with only some of the dual variables needed to be shared between nodes. Furthermore, we also consider asynchronicity in the values of the variables across sensor nodes and provide theoretical guarantees on the stability of the control systems under the proposed random access mechanism. Finally, we provide extensive numerical results that corroborate our claims.

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arXiv2018

A Graph Signal Processing View on Functional Brain Imaging

Modern neuroimaging techniques provide us with unique views on brain structure and function; i.e., how the brain is wired, and where and when activity takes place. Data acquired using these techniques can be analyzed in terms of its network structure to reveal organizing principles at the systems level. Graph representations are versatile models where nodes are associated to brain regions and edges to structural or functional connections. Structural graphs model neural pathways in white matter that are the anatomical backbone between regions. Functional graphs are built based on functional connectivity, which is a pairwise measure of statistical interdependency between activity traces of regions. Therefore, most research to date has focused on analyzing these graphs reflecting structure or function. Graph signal processing (GSP) is an emerging area of research where signals recorded at the nodes of the graph are studied atop the underlying graph structure. An increasing number of fundamental operations have been generalized to the graph setting, allowing to analyze the signals from a new viewpoint. Here, we review GSP for brain imaging data and discuss their potential to integrate brain structure, contained in the graph itself, with brain function, residing in the graph signals. We review how brain activity can be meaningfully filtered based on concepts of spectral modes derived from brain structure. We also derive other operations such as surrogate data generation or decompositions informed by cognitive systems. In sum, GSP offers a novel framework for the analysis of brain imaging data.

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arXiv2017

Hierarchical Overlapping Clustering of Network Data Using Cut Metrics

A novel method to obtain hierarchical and overlapping clusters from network data -i.e., a set of nodes endowed with pairwise dissimilarities- is presented. The introduced method is hierarchical in the sense that it outputs a nested collection of groupings of the node set depending on the resolution or degree of similarity desired, and it is overlapping since it allows nodes to belong to more than one group. Our construction is rooted on the facts that a hierarchical (non-overlapping) clustering of a network can be equivalently represented by a finite ultrametric space and that a convex combination of ultrametrics results in a cut metric. By applying a hierarchical (non-overlapping) clustering method to multiple dithered versions of a given network and then convexly combining the resulting ultrametrics, we obtain a cut metric associated to the network of interest. We then show how to extract a hierarchical overlapping clustering structure from the aforementioned cut metric. Furthermore, the so-called overlapping function is presented as a tool for gaining insights about the data by identifying meaningful resolutions of the obtained hierarchical structure. Additionally, we explore hierarchical overlapping quasi-clustering methods that preserve the asymmetry of the data contained in directed networks. Finally, the presented method is illustrated via synthetic and real-world classification problems including handwritten digit classification and authorship attribution of famous plays.

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