arXiv subjects

José M. F. Moura

Publications and source records attributed to José M. F. Moura.

At least 55 records · Page 3Linked to original sources

arXiv2020

Evaluating and Aggregating Feature-based Model Explanations

A feature-based model explanation denotes how much each input feature contributes to a model's output for a given data point. As the number of proposed explanation functions grows, we lack quantitative evaluation criteria to help practitioners know when to use which explanation function. This paper proposes quantitative evaluation criteria for feature-based explanations: low sensitivity, high faithfulness, and low complexity. We devise a framework for aggregating explanation functions. We develop a procedure for learning an aggregate explanation function with lower complexity and then derive a new aggregate Shapley value explanation function that minimizes sensitivity.

cs.LG↗

arXiv2020

Pooling in Graph Convolutional Neural Networks

Graph convolutional neural networks (GCNNs) are a powerful extension of deep learning techniques to graph-structured data problems. We empirically evaluate several pooling methods for GCNNs, and combinations of those graph pooling methods with three different architectures: GCN, TAGCN, and GraphSAGE. We confirm that graph pooling, especially DiffPool, improves classification accuracy on popular graph classification datasets and find that, on average, TAGCN achieves comparable or better accuracy than GCN and GraphSAGE, particularly for datasets with larger and sparser graph structures.

eess.SP↗

arXiv2020

Resilient Distributed Field Estimation

We study resilient distributed field estimation under measurement attacks. A network of agents or devices measures a large, spatially distributed physical field parameter. An adversary arbitrarily manipulates the measurements of some of the agents. Each agent's goal is to process its measurements and information received from its neighbors to estimate only a few specific components of the field. We present $\mathbf{SAFE}$, the Saturating Adaptive Field Estimator, a consensus+innovations distributed field estimator that is resilient to measurement attacks. Under sufficient conditions on the compromised measurement streams, the physical coupling between the field and the agents' measurements, and the connectivity of the cyber communication network, $\mathbf{SAFE}$ guarantees that each agent's estimate converges almost surely to the true value of the components of the parameter in which the agent is interested. Finally, we illustrate the performance of $\mathbf{SAFE}$ through numerical examples.

math.OC↗

arXiv2020

Forecaster: A Graph Transformer for Forecasting Spatial and Time-Dependent Data

Spatial and time-dependent data is of interest in many applications. This task is difficult due to its complex spatial dependency, long-range temporal dependency, data non-stationarity, and data heterogeneity. To address these challenges, we propose Forecaster, a graph Transformer architecture. Specifically, we start by learning the structure of the graph that parsimoniously represents the spatial dependency between the data at different locations. Based on the topology of the graph, we sparsify the Transformer to account for the strength of spatial dependency, long-range temporal dependency, data non-stationarity, and data heterogeneity. We evaluate Forecaster in the problem of forecasting taxi ride-hailing demand and show that our proposed architecture significantly outperforms the state-of-the-art baselines.

cs.LG↗

arXiv2019

Algebraic Signal Processing Theory

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and phi generalizes the concept of the z-transform to bijective linear mappings from a vector space of, e.g., signal samples, into the module M. A signal model provides the structure for a particular linear signal processing application, such as infinite and finite discrete time, or infinite or finite discrete space, or the various forms of multidimensional linear signal processing. As soon as a signal model is chosen, basic ingredients follow, including the associated notions of filtering, spectrum, and Fourier transform. The shift operator is a key concept in the algebraic theory: it is the generator of the algebra of filters A. Once the shift is chosen, a well-defined methodology leads to the associated signal model. Different shifts correspond to infinite and finite time models with associated infinite and finite z-transforms, and to infinite and finite space models with associated infinite and finite C-transforms (that we introduce). In particular, we show that the 16 discrete cosine and sine transforms are Fourier transforms for the finite space models. Other definitions of the shift naturally lead to new signal models and to new transforms as associated Fourier transforms in one and higher dimensions, separable and non-separable. We explain in algebraic terms shift-invariance (the algebra of filters A is commutative), the role of boundary conditions and signal extensions, the connections between linear transforms and linear finite Gauss-Markov fields, and several other concepts and connections.

cs.IT↗

arXiv2019

Resilient Distributed Recovery of Large Fields

This paper studies the resilient distributed recovery of large fields under measurement attacks, by a team of agents, where each measures a small subset of the components of a large spatially distributed field. An adversary corrupts some of the measurements. The agents collaborate to process their measurements, and each is interested in recovering only a fraction of the field. We present a field recovery consensus+innovations type distributed algorithm that is resilient to measurement attacks, where an agent maintains and updates a local state based on its neighbors states and its own measurement. Under sufficient conditions on the attacker and the connectivity of the communication network, each agent's state, even those with compromised measurements, converges to the true value of the field components that it is interested in recovering. Finally, we illustrate the performance of our algorithm through numerical examples.

math.OC↗

arXiv2019

CLEVR-Dialog: A Diagnostic Dataset for Multi-Round Reasoning in Visual Dialog

Visual Dialog is a multimodal task of answering a sequence of questions grounded in an image, using the conversation history as context. It entails challenges in vision, language, reasoning, and grounding. However, studying these subtasks in isolation on large, real datasets is infeasible as it requires prohibitively-expensive complete annotation of the 'state' of all images and dialogs. We develop CLEVR-Dialog, a large diagnostic dataset for studying multi-round reasoning in visual dialog. Specifically, we construct a dialog grammar that is grounded in the scene graphs of the images from the CLEVR dataset. This combination results in a dataset where all aspects of the visual dialog are fully annotated. In total, CLEVR-Dialog contains 5 instances of 10-round dialogs for about 85k CLEVR images, totaling to 4.25M question-answer pairs. We use CLEVR-Dialog to benchmark performance of standard visual dialog models; in particular, on visual coreference resolution (as a function of the coreference distance). This is the first analysis of its kind for visual dialog models that was not possible without this dataset. We hope the findings from CLEVR-Dialog will help inform the development of future models for visual dialog. Our dataset and code are publicly available.

cs.CV↗

arXiv2019

Distributed Global Optimization by Annealing

The paper considers a distributed algorithm for global minimization of a nonconvex function. The algorithm is a first-order consensus + innovations type algorithm that incorporates decaying additive Gaussian noise for annealing, converging to the set of global minima under certain technical assumptions. The paper presents simple methods for verifying that the required technical assumptions hold and illustrates it with a distributed target-localization application.

math.OC↗

arXiv2019

Resilient Distributed Parameter Estimation with Heterogeneous Data

This paper studies resilient distributed estimation under measurement attacks. A set of agents each makes successive local, linear, noisy measurements of an unknown vector field collected in a vector parameter. The local measurement models are heterogeneous across agents and may be locally unobservable for the unknown parameter. An adversary compromises some of the measurement streams and changes their values arbitrarily. The agents' goal is to cooperate over a peer-to-peer communication network to process their (possibly compromised) local measurements and estimate the value of the unknown vector parameter. We present SAGE, the Saturating Adaptive Gain Estimator, a distributed, recursive, consensus+innovations estimator that is resilient to measurement attacks. We demonstrate that, as long as the number of compromised measurement streams is below a particular bound, then, SAGE guarantees that all of the agents' local estimates converge almost surely to the value of the parameter. The resilience of the estimator -- i.e., the number of compromised measurement streams it can tolerate -- does not depend on the topology of the inter-agent communication network. Finally, we illustrate the performance of SAGE through numerical examples.

math.OC↗

arXiv2019

EigenNetworks

Many applications donot have the benefit of the laws of physics to derive succinct descriptive models for observed data. In alternative, interdependencies among $N$ time series $\{ x_{nk}, k>0 \}_{n=1}^{N}$ are nowadays often captured by a graph or network $G$ that in practice may be very large. The network itself may change over time as well (i.e., as $G_k$). Tracking brute force the changes of time varying networks presents major challenges, including the associated computational problems. Further, a large set of networks may not lend itself to useful analysis. This paper approximates the time varying networks $\left\{G_k\right\}$ as weighted linear combinations of eigennetworks. The eigennetworks are fixed building blocks that are estimated by first learning the time series of graphs $G_k$ from the data $\{ x_{nk}, k>0 \}_{n=1}^{N}$, followed by a Principal Network Analysis procedure. The weights of the eigennetwork representation are eigenfeatures and the time varying networks $\left\{G_k\right\}$ describe a trajectory in eigennetwork space. These eigentrajectories should be smooth since the networks $G_k$ vary at a much slower rate than the data $x_{nk}$, except when structural network shifts occur reflecting potentially an abrupt change in the underlying application and sources of the data. Algorithms for learning the time series of graphs $\left\{G_k\right\}$, deriving the eigennetworks, eigenfeatures and eigentrajectories, and detecting changepoints are presented. Experiments on simulated data and with two real time series data (a voting record of the US senate and genetic expression data for the \textit{Drosophila Melanogaster} as it goes through its life cycle) demonstrate the performance of the learning and provide interesting interpretations of the eigennetworks.

stat.ML↗

arXiv2018

Detecting random walks on graphs with heterogeneous sensors

We consider the problem of detecting a random walk on a graph, based on observations of the graph nodes. When visited by the walk, each node of the graph observes a signal of elevated mean, which we assume can be different across different nodes. Outside of the path of the walk, and also in its absence, nodes measure only noise. Assuming the Neyman-Pearson setting, our goal then is to characterize detection performance by computing the error exponent for the probability of a miss, under a constraint on the probability of false alarm. Since exact computation of the error exponent is known to be difficult, equivalent to computation of the Lyapunov exponent, we approximate its value by finding a tractable lower bound. The bound reveals an interesting detectability condition: the walk is detectable whenever the entropy of the walk is smaller than one half of the expected signal-to-noise ratio. We derive the bound by extending the notion of Markov types to Gauss-Markov types. These are sequences of state-observation pairs with a given number of node-to-node transition counts and the same average signal values across nodes, computed from the measurements made during the times the random walk was visiting each node's respective location. The lower bound has an intuitive interpretation: among all Gauss-Markov types that are asymptotically feasible in the absence of the walk, the bound finds the most typical one under the presence of the walk. Finally, we show by a sequence of judicious problem reformulations that computing the bound reduces to solving a convex optimization problem, which is a result in its own right.

cs.IT↗

arXiv2018

Visual Coreference Resolution in Visual Dialog using Neural Module Networks

Visual dialog entails answering a series of questions grounded in an image, using dialog history as context. In addition to the challenges found in visual question answering (VQA), which can be seen as one-round dialog, visual dialog encompasses several more. We focus on one such problem called visual coreference resolution that involves determining which words, typically noun phrases and pronouns, co-refer to the same entity/object instance in an image. This is crucial, especially for pronouns (e.g., `it'), as the dialog agent must first link it to a previous coreference (e.g., `boat'), and only then can rely on the visual grounding of the coreference `boat' to reason about the pronoun `it'. Prior work (in visual dialog) models visual coreference resolution either (a) implicitly via a memory network over history, or (b) at a coarse level for the entire question; and not explicitly at a phrase level of granularity. In this work, we propose a neural module network architecture for visual dialog by introducing two novel modules - Refer and Exclude - that perform explicit, grounded, coreference resolution at a finer word level. We demonstrate the effectiveness of our model on MNIST Dialog, a visually simple yet coreference-wise complex dataset, by achieving near perfect accuracy, and on VisDial, a large and challenging visual dialog dataset on real images, where our model outperforms other approaches, and is more interpretable, grounded, and consistent qualitatively.

cs.CV↗

arXiv2018

Single Index Latent Variable Models for Network Topology Inference

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of interacting entities. This formulation jointly estimates non-linearities in the underlying data generation, the direct interactions between measured entities, and the indirect effects of unmeasured processes on the observed data. The learning is posed as regularized empirical risk minimization. Details of the algorithm for learning the model are outlined. Experiments demonstrate the performance of the learned model on real data.

stat.ML↗

arXiv2018

Resilient Distributed Estimation: Sensor Attacks

This paper studies multi-agent distributed estimation under sensor attacks. Individual agents make sensor measurements of an unknown parameter belonging to a compact set, and, at every time step, a fraction of the agents' sensor measurements may fall under attack and take arbitrary values. We present the Saturated Innovation Update ($\mathcal{SIU}$) algorithm for distributed estimation resilient to sensor attacks. Under the iterative $\mathcal{SIU}$ algorithm, if less than one half of the agent sensors fall under attack, then, all of the agents' estimates converge at a polynomial rate (with respect to the number of iterations) to the true parameter. The resilience of $\mathcal{SIU}$ to sensor attacks does not depend on the topology of the inter-agent communication network, as long as it remains connected. We demonstrate the performance of $\mathcal{SIU}$ with numerical examples.

math.OC↗

arXiv2018

The Internet of Things: Secure Distributed Inference

The growth in the number of devices connected to the Internet of Things (IoT) poses major challenges in security. The integrity and trustworthiness of data and data analytics are increasingly important concerns in IoT applications. These are compounded by the highly distributed nature of IoT devices, making it infeasible to prevent attacks and intrusions on all data sources. Adversaries may hijack devices and compromise their data. As a result, reactive countermeasures, such as intrusion detection and resilient analytics, become vital components of security. This paper overviews algorithms for secure distributed inference in IoT.

cs.DC↗

arXiv2018

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.

eess.SP↗

arXiv2018

SILVar: Single Index Latent Variable Models

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows joint estimation of certain non-linearities in the system, the direct interactions between measured variables, and the effects of unmodeled elements on the observed system. The particular form of the model adopted is justified, and learning is posed as a regularized empirical risk minimization. This leads to classes of structured convex optimization problems with a "sparse plus low-rank" flavor. Relations between the proposed model and several common model paradigms, such as those of Robust Principal Component Analysis (PCA) and Vector Autoregression (VAR), are established. Particularly in the VAR setting, the low-rank contributions can come from broad trends exhibited in the time series. Details of the algorithm for learning the model are presented. Experiments demonstrate the performance of the model and the estimation algorithm on simulated and real data.

stat.ML↗

arXiv2018

Graph Signal Processing: Filter Design and Spectral Statistics

Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to the graph shift operator, polynomial functions of the shift matrix perform filtering. An application considered in this paper, convergence acceleration filters for distributed average consensus may be viewed as lowpass graph filters periodically applied to the states. Design of graph filters depends on the shift matrix eigendecomposition. Consequently, random graphs present a challenge as this information is often difficult to obtain. Nevertheless, the asymptotic behavior of the shift matrix empirical spectral distribution provides a substitute for suitable random matrix models. This paper employs deterministic approximations for empirical spectral statistics from other works to propose optimization criteria for consensus acceleration filters, evaluating the results through simulation.

eess.SP↗