142 accepted papers
We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical risk minimization (ERM) with a primal-dual training scheme. Th…
We address real-time sampling and estimation of autoregressive Markovian sources in dynamic yet structurally similar multi-hop wireless networks. Each node caches samples from others and communicates over wireless collision channels, aiming to minimize time-average estimation error via decentralized…
The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as graphs. A key property of GNNs is transferability: models tr…
Coverage control is the problem of navigating a robot swarm to collaboratively monitor features or a phenomenon of interest not known a priori . The problem is challenging in decentralized settings with robots that have limited communication and sensing capabilities. We propose a learnable Perceptio…
We propose MADP, a novel diffusion-model-based approach for collaboration in decentralized robot swarms. MADP leverages diffusion models to generate samples from complex and high-dimensional action distributions that capture the interdependencies between agents' actions. Each robot conditions policy…
Unlearning in diffusion models aims to remove undesirable data or concepts while preserving the utility of pretrained models---two fundamentally conflicting objectives. We propose a principled constrained optimization framework that formulates unlearning as minimizing the deviation from a pretrained…
Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still lacking. Previous GNN generalization bounds ignore the underlying g…
We study the problem of computing an optimal large language model (LLM) policy for the constrained alignment problem, where the goal is to maximize a primary reward objective while satisfying constraints on secondary utilities. Despite the popularity of Lagrangian-based LLM policy search in constrai…
Diffusion models have become prevalent in generative modeling due to their ability to sample from complex distributions. To improve the quality of generated samples and their compliance with user requirements, two commonly used methods are: (i) Alignment, which involves finetuning a diffusion model…
The multi-objective coverage control problem requires a robot swarm to collaboratively provide sensor coverage to multiple heterogeneous importance density fields (IDFs) simultaneously. We pose this as an optimization problem with constraints and study two different formulations: (1) Fair coverage,
We study the problem of computing deterministic optimal policies for constrained Markov decision processes (MDPs) with continuous state and action spaces, which are widely encountered in constrained dynamical systems. Designing deterministic policy gradient methods in continuous state and action spa…
The proliferation of digital microscopy images, driven by advances in automated whole slide scanning, presents significant opportunities for biomedical research and clinical diagnostics. However, accurately annotating densely packed information in these images remains a major challenge. To address t…
Large language models (LLMs) provide robots with powerful contextual reasoning abilities and a natural human interface. Yet, current LLM-enabled robots typically depend on cloud-hosted models, limiting their usability in environments with unreliable communication infrastructure, such as outdoor or i…
We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL dema…
Existing approaches based on context prompting or reinforcement learning (RL) to improve the reasoning capacities of large language models (LLMs) depend on the LLMs' internal knowledge to produce reliable Chain-Of-Thought (CoT). However, no matter the size of LLMs, certain problems cannot be resolve…
Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. However, the current analysis of GNN generalization relies on the assumption that training and testing data are independent and identically distributed (i.i.d). This im…
Positional encodings (PEs) are essential for effective graph representation learning because they provide position awareness in inherently position-agnostic transformer architectures and increase the expressive capacity of Graph Neural Networks (GNNs). However, designing powerful and efficient PEs f…
The goal of continual learning (CL) is to train a model that can solve multiple tasks presented sequentially. Recent CL approaches have achieved strong performance by leveraging large pre-trained models that generalize well to downstream tasks. However, such methods lack theoretical guarantees, maki…
In this study, we address the challenge of packet based information routing in large-scale wireless communication networks. We approach this scenario by framing the problem as a statistical learning problem, where each node in the network relies only on the local data. Our exploration focuses on the…
Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes are prone to generating samples that reflect biases in a trai…
Graph Neural Networks (GNNs) are powerful representation learning tools that have achieved remarkable performance in various downstream tasks. However, there are still open questions regarding their ability to count and list substructures, which play a crucial role in biological and social networks.…
Graph Neural Networks (GNNs) are powerful architectures that have demonstrated remarkable performance in various node-level and graph-level tasks. Despite this success, prominent analysis shows that their representation power is limited and that they are at most as expressive as the Weisfeiler-Lehma…
Several applications in time series forecasting require predicting multiple steps ahead. Despite the vast amount of literature in the topic, both classical and recent deep learning based approaches have mostly focused on minimising performance averaged over the predicted window. We observe that this…
With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with genera…
Neural tangent kernels (NTKs) provide a theoretical regime to analyze the learning and generalization behavior of over-parametrized neural networks. For a supervised learning task, the association between the eigenvectors of the NTK and given data (a concept referred to as alignment in this paper) c…
In this paper we discuss the results recently published in [1] about algebraic signal models (ASMs) based on non commutative algebras and their use in convolutional neural networks. Relying on the general tools from algebraic signal processing (ASP), we study the filtering and stability properties o…
In this paper we present a new approach to Mobile Infrastructure on Demand (MID) where a dedicated team of robots creates and sustains a wireless network that satisfies the communication requirements of a different team of task-oriented robots seeking to coordinate their actions in the absence of ex…
We study a class of constrained reinforcement learning (RL) problems in which multiple constraint specifications are not identified before training. It is challenging to identify appropriate constraint specifications due to the undefined trade-off between the reward maximization objective and the co…
We consider the problem of routing network packets in a large-scale communication system where the nodes have access to only local information. We formulate this problem as a constrained learning problem, which can be solved using a distributed optimization algorithm. We approach this distributed op…
Optimal power flow is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. This is a non-convex problem shown to be NP-hard. We use a graph neural network to learn a nonlinear function between the power demanded and the correspondin…
Accurate and robust state estimation is critical for autonomous navigation of robot teams. This task is especially challenging for large groups of size, weight, and power (SWAP) constrained aerial robots operating in perceptually-degraded GPS-denied environments. We can, however, actively increase t…
Group convolutional neural networks are a useful tool for utilizing symmetries known to be in a signal; however, they require that the signal is defined on the group itself. Existing approaches either work directly with group signals, or they impose a lifting step with heuristics to compute the conv…
Underlying data structures, such as symmetries or invariance to transformations, are often exploited to improve the solution of learning tasks. However, embedding these properties in models or learning algorithms can be challenging and computationally intensive. Data augmentation, on the other hand,…
The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds. The building block for information processing architectures with desirable theoretical properties such as invariance and stability is convolutional filteri…
In computational neuroscience, there has been an increased interest in developing machine learning algorithms that leverage brain imaging data to provide estimates of "brain age" for an individual. Importantly, the discordance between brain age and chronological age (referred to as "brain age gap")…
We study the problem of computing an optimal policy of an infinite-horizon discounted constrained Markov decision process (constrained MDP). Despite the popularity of Lagrangian-based policy search methods used in practice, the oscillation of policy iterates in these methods has not been fully under…
Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do…
In this paper, we introduce a convolutional architecture to perform learning when information is supported on multigraphs. Exploiting algebraic signal processing (ASP), we propose a convolutional signal processing model on multigraphs (MSP). Then, we introduce multigraph convolutional neural network…
Multi-task learning aims to acquire a set of functions, either regressors or classifiers, that perform well for diverse tasks. At its core, the idea behind multi-task learning is to exploit the intrinsic similarity across data sources to aid in the learning process for each individual domain. In thi…
Enabling low precision implementations of deep learning models, without considerable performance degradation, is necessary in resource and latency constrained settings. Moreover, exploiting the differences in sensitivity to quantization across layers can allow mixed precision implementations to achi…
The deviation between chronological age and biological age is a well-recognized biomarker associated with cognitive decline and neurodegeneration. Age-related and pathology-driven changes to brain structure are captured by various neuroimaging modalities. These datasets are characterized by high dim…
When deploying machine learning solutions, they must satisfy multiple requirements beyond accuracy, such as fairness, robustness, or safety. These requirements are imposed during training either implicitly, using penalties, or explicitly, using constrained optimization methods based on Lagrangian du…
This paper addresses the problem of active collaborative localization in heterogeneous robot teams with unknown data association. It involves positioning a small number of identical unmanned ground vehicles (UGVs) at desired positions so that an unmanned aerial vehicle (UAV) can, through unlabelled…
Space-time graph neural networks (ST-GNNs) are recently developed architectures that learn efficient graph representations of time-varying data. ST-GNNs are particularly useful in multi-agent systems, due to their stability properties and their ability to respect communication delays between the age…
In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use this convolution operation to define tangent bundle filters and tangent bundle neural networks (TNNs), novel continuous architectures operating on ta…
Graph Neural Networks (GNNs) rely on graph convolutions to exploit meaningful patterns in networked data. Based on matrix multiplications, convolutions incur in high computational costs leading to scalability limitations in practice. To overcome these limitations, proposed methods rely on training G…
We consider the pool-based active learning problem, where only a subset of the training data is labeled, and the goal is to query a batch of unlabeled samples to be labeled so as to maximally improve model performance. We formulate the problem using constrained learning, where a set of constraints b…
We consider the problem of power control in wireless networks, consisting of multiple transmitter-receiver pairs communicating with each other over a single shared wireless medium. To achieve both a high total rate and a level of fairness across users, we formulate a policy optimization problem with…
Federated Learning (FL) has emerged as the tool of choice for training deep models over heterogeneous and decentralized datasets. As a reflection of the experiences from different clients, severe class imbalance issues are observed in real-world FL problems. Moreover, there exists a drastic mismatc…
This paper develops a decentralized approach to mobile sensor coverage by a multi-robot system. We consider a scenario where a team of robots with limited sensing range must position itself to effectively detect events of interest in a region characterized by areas of varying importance. Towards thi…
In this letter we propose a data-driven approach to optimizing the algebraic connectivity of a team of robots. While a considerable amount of research has been devoted to this problem, we lack a method that scales in a manner suitable for online applications for more than a handful of agents. To tha
We introduce space-time graph neural network (ST-GNN), a novel GNN architecture, tailored to jointly process the underlying space-time topology of time-varying network data. The cornerstone of our proposed architecture is the composition of time and graph convolutional filters followed by pointwise…
Graph Neural Networks (GNNs) show impressive performance in many practical scenarios, which can be largely attributed to their stability properties. Empirically, GNNs can scale well on large size graphs, but this is contradicted by the fact that existing stability bounds grow with the number of node…
We consider the problem of resource allocation in large scale wireless networks. When contextualizing wireless network structures as graphs, we can model the limits of very large wireless systems as manifolds. To solve the problem in the machine learning framework, we propose the use of Manifold Neu…
Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we leverage the stability property of GNNs as a typing point in orde…
Graph neural networks (GNN) are an effective framework that exploit inter-relationships within graph-structured data for learning. Principal component analysis (PCA) involves the projection of data on the eigenspace of the covariance matrix and draws similarities with the graph convolutional filters…
Despite strong performance in numerous applications, the fragility of deep learning to input perturbations has raised serious questions about its use in safety-critical domains. While adversarial training can mitigate this issue in practice, state-of-the-art methods are increasingly application-dep…
Network data can be conveniently modeled as a graph signal, where data values are assigned to the nodes of a graph describing the underlying network topology. Successful learning from network data requires methods that effectively exploit this graph structure. Graph neural networks (GNNs) provide on…
Dynamical systems comprised of autonomous agents arise in many relevant problems such as multi-agent robotics, smart grids, or smart cities. Controlling these systems is of paramount importance to guarantee a successful deployment. Optimal centralized controllers are readily available but face limit…
Graph neural networks (GNNs) are learning architectures that rely on knowledge of the graph structure to generate meaningful representations of large-scale network data. GNN stability is thus important as in real-world scenarios there are typically uncertainties associated with the graph. We analyze…
In this letter, we present a learning method to solve the unlabelled motion problem with motion constraints and space constraints in 2D space for a large number of robots. To solve the problem of arbitrary dynamics and constraints we propose formulating the problem as a multi-agent problem. We are a
Many algorithms for control of multi-robot teams operate under the assumption that low-latency, global state information necessary to coordinate agent actions can readily be disseminated among the team. However, in harsh environments with no existing communication infrastructure, robots must form ad…
The multi-robot coverage problem is an essential building block for systems that perform tasks like inspection, exploration, or search and rescue. We discretize the coverage problem to induce a spatial graph of locations and represent robots as nodes in the graph. Then, we train a Graph Neural Netwo…
Graph convolutional neural networks (GCNNs) learn compositional representations from network data by nesting linear graph convolutions into nonlinearities. In this work, we approach GCNNs from a state-space perspective revealing that the graph convolutional module is a minimalistic linear state-spac…
Multi-agent systems play an important role in modern robotics. Due to the nature of these systems, coordination among agents via communication is frequently necessary. Indeed, Perception-Action-Communication (PAC) loops, or Perception-Action loops closed over a communication channel, are a critical
Algebraic neural networks (AlgNNs) are composed of a cascade of layers each one associated to and algebraic signal model, and information is mapped between layers by means of a nonlinearity function. AlgNNs provide a generalization of neural network architectures where formal convolution operators a…
We consider optimal resource allocation problems under asynchronous wireless network setting. Without explicit model knowledge, we design an unsupervised learning method based on Aggregation Graph Neural Networks (Agg-GNNs). Depending on the localized aggregated information structure on each network…
Decentralized coordination of a robot swarm requires addressing the tension between local perceptions and actions, and the accomplishment of a global objective. In this work, we propose to learn decentralized controllers based solely on raw visual inputs. For the first time, this integrates the lear…
Stochastic graph neural networks (SGNNs) are information processing architectures that can learn representations from data over random graphs. SGNNs are trained with respect to the expected performance, but this training comes with no guarantee about the deviation of particular output realizations a…
Graph neural networks (GNNs) learn representations from network data with naturally distributed architectures, rendering them well-suited candidates for decentralized learning. Oftentimes, this decentralized graph support changes with time due to link failures or topology variations. These changes c…
Optimal resource allocation in real-world wireless systems is rather challenging, not only due to the unavailability of accurate statistical channel models, but also because expressions of maximal or achievable information rates are most often unknown, or not adequately precise. Under a modular stoc…
Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-sizes is required for exact asymptotic convergence with the fact that larg…
Despite the simplicity and intuitive interpretation of minimum mean squared error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of stability, as the volatility of the estimation error is left uncons…
In this paper, we propose a Distributed Accumulated Newton Conjugate gradiEnt (DANCE) method in which sample size is gradually increasing to quickly obtain a solution whose empirical loss is under satisfactory statistical accuracy. Our proposed method is multistage in which the solution of a stage s…
In federated learning, a centralized model is realized based on information received from a group of agents each collecting data. This setting has two major challenges: the agents observe data over different distributions and they have only limited capabilities of sending data over the network to th…
Effective communication is key to successful, decentralized, multi-robot path planning. Yet, it is far from obvious what information is crucial to the task at hand, and how and when it must be shared among robots. To side-step these issues and move beyond hand-crafted heuristics, we propose a combin…
Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these coefficients are shared and do not depend on the graph, one can envis…
In this paper, we consider the problem of projecting networks onto metric spaces. Networks are structures that encode relationships between pairs of elements or nodes. However, these relationships can be independent of each other, and need not be defined for every pair of nodes. This is in contrast…
In this work, we introduce Mobile Wireless Infrastructure on Demand: a framework for providing wireless connectivity to multi-robot teams via autonomously reconfiguring ad-hoc networks. In many cases, previous multi-agent systems either assumed the availability of existing communication infrastructu…
Optimal power flow (OPF) is one of the most important optimization problems in the energy industry. In its simplest form, OPF attempts to find the optimal power that the generators within the grid have to produce to satisfy a given demand. Optimality is measured with respect to the cost that each ge…
As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior has become paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased, unsafe, and prejudiced solutions. To tackle these problems,…
In this paper, we consider the problem of computing the barycenter of a set of probability distributions under the Sinkhorn divergence. This problem has recently found applications across various domains, including graphics, learning, and vision, as it provides a meaningful mechanism to aggregate…
Graph Recurrent Neural Networks (GRNNs) are a neural network architecture devised to learn from graph processes, which are time sequences of graph signals. Similarly to traditional recurrent neural networks, GRNNs experience the problem of vanishing/exploding gradients when learning long term causal…
Graph neural networks (GNNs), consisting of a cascade of layers applying a graph convolution followed by a pointwise nonlinearity, have become a powerful architecture to process signals supported on graphs. Graph convolutions (and thus, GNNs), rely heavily on knowledge of the graph for operation. Ho…
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. However, current GNN implementations assume ideal distributed scenarios and ignore link fluctuations that occur due to environment or hu…
Modeling how a robot interacts with the environment around it is an important prerequisite for designing control and planning algorithms. In fact, the performance of controllers and planners is highly dependent on the quality of the model. One popular approach is to learn data driven models in order…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to incorporate prior knowledge and impose desired structural an…
In many network problems, graphs may change by the addition of nodes, or the same problem may need to be solved in multiple similar graphs. This generates inefficiency, as analyses and systems that are not transferable have to be redesigned. To address this, we consider graphons, which are both limi…
We consider the problem of finding optimal power allocations subject to system constraints in ad-hoc wireless networks. The resulting optimization problem has the form of a constrained learning problem, motivating the use of a function parameterization such as a neural network. While such a policy c…
Graph neural networks (GNNs) regularize classical neural networks by exploiting the underlying irregular structure supporting graph data, extending its application to broader data domains. The aggregation GNN presented here is a novel GNN that exploits the fact that the data collected at a single no…
Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning~(RL), these problems are addressed by (i)~designing a reward function…
We consider the problem of allocating radio resources over wireless communication links to control a series of independent low-latency wireless control systems common in industrial settings. Supporting wireless control in time sensitive settings requires fast data rates over wireless links, which co…
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 deform…
We consider the problem of finding optimal resource allocations subject to system constraints in a generic class of problems in wireless communications. These problems are inherently challenging due to functional optimization and potential non-convexities. However, these problems can be observed to…
In this paper, the problem of learning policies to control a large number of homogeneous robots is considered. To this end, we propose a new algorithm we call Graph Policy Gradients (GPG) that exploits the underlying graph symmetry among the robots. The curse of dimensionality one encounters when wo
Reducing the variance of estimators for policy gradient has long been the focus of reinforcement learning research. While classic algorithms like REINFORCE find an $\epsilon$-approximate first-order stationary point in $\OM({1}/{\epsilon^4})$ random trajectory simulations, no provable improvement o…
We envision a system that concisely describes the rules of air traffic control, assists human operators and supports dense autonomous air traffic around commercial airports. We develop a method to learn the rules of air traffic control from real data as a cost function via maximum entropy inverse re…
We consider the problem of finding distributed controllers for large networks of mobile robots with interacting dynamics and sparsely available communications. Our approach is to learn local controllers that require only local information and communications at test time by imitating the policy of ce
In this paper, we present a learning approach to goal assignment and trajectory planning for unlabeled robots operating in 2D, obstacle-filled workspaces. More specifically, we tackle the unlabeled multi-robot motion planning problem with motion constraints as a multi-agent reinforcement learning pr…
Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs. By replacing regular convolutions with linear shift-invariant graph filters (LSI-GFs), GNNs take into account the (irregular) structure of the graph…
Reproducing kernel ilbert spaces (RKHSs) have been at the core of successful non-parametric tools in signal processing, statistics, and machine learning. Despite their success, the computational complexity of these models often hinders their use in practice. Indeed, fitting RKHS models typically rel…
Sparse modeling seeks to represent signals as a linear combination of a small number of atoms from an overparametrized dictionary. Despite the success of these linear models, they can be too restrictive for applications involving nonlinear measurements. Using nonlinear atoms, however, poses an addit…
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to transl…
We present a reinforcement learning algorithm for learning sparse non-parametric controllers in a Reproducing Kernel Hilbert Space. We improve the sample complexity of this approach by imposing a structure of the state-action function through a normalized advantage function (NAF). This representatio…
In this work, we jointly exploit tools from graph signal processing and control theory to drive a bandlimited graph signal that is being diffused on a random time-varying graph from a subset of nodes. As our main contribution, we rely only on the statistics of the graph to introduce the concept of c…
Modern neuroimaging techniques offer disctinct views on brain structure and function. Data acquired using these techniques can be analyzed in terms of its network structure to identify organizing principles at the systems level. Graph representations are flexible frameworks where nodes are related t…
Most second order methods are inapplicable to large scale empirical risk minimization (ERM) problems because both, the number of samples N and number of parameters p are large. Large N makes it costly to evaluate Hessians and large p makes it costly to invert Hessians. This paper propose a novel ada…
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 m…
This paper considers the resource allocation problem in wireless systems over an unknown time-varying non-stationary channel. The goal is to maximize a utility function, such as a capacity function, over a set of wireless nodes while satisfying a set of resource constraints. To bypass the need for a…
This paper develops new designs for recommender systems inspired by recent advances in graph signal processing. Recommender systems aim to predict unknown ratings by exploiting the information revealed in a subset of user-item observed ratings. Leveraging the notions of graph frequency and graph fil…
We consider the problem of dictionary learning over training sets whose sample size and parameter dimension are large-scale, which is formulated as a non-convex stochastic program where the objective decomposes into a smooth non-convex part and a convex sparsity-promoting penalty. We propose a Doubl…
Signal processing is rich in inherently continuous applications, such as radar, MRI, and source localization, in which sparsity priors play a key role in obtaining state-of-the-art results. To cope with the infinite dimensionality and non-convexity of these estimation problems, they are typically di…
This paper considers the problem of minimizing the average of a finite set of strongly convex functions. 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 aggre…
We present an incremental Broyden-Fletcher-Goldfarb-Shanno (BFGS) method as a quasi-Newton algorithm with a cyclically iterative update scheme for solving large-scale optimization problems. The proposed incremental quasi-Newton (IQN) algorithm reduces computational cost relative to traditional quasi…
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…
This paper examines metric spaces in which the distance between any pair of nodes is given by an interval. The goal is to investigate methods for hierarchical clustering, i.e., a family of nested partitions indexed by a connectivity parameter, deduced from the underlying distance intervals of the me…
This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters recently generalized to irregular graph domains defines brain graph frequencies associated with different levels of spatial smoothness across the brain r…
This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic methods. In contrast to traditional methods that attempt to solve…
We consider supervised learning problems over training sets in which both the number of training examples and the dimension of the feature vectors are large. We focus on the case where the loss function defining the quality of the parameter we wish to estimate may be non-convex, but also has a conve…
We consider stochastic nonparametric regression problems in a reproducing kernel Hilbert space (RKHS), an extension of expected risk minimization to nonlinear function estimation. Popular perception is that kernel methods are inapplicable to online settings, since the generalization of stochastic me…
We address the problem of identifying a graph structure from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable indirect relationships generated by a diffusion process on the…
Advancing a holistic theory of networks and network processes requires the extension of existing results in the processing of time-varying signals to signals supported on graphs. This paper focuses on the definition of stationarity and power spectral density for random graph signals, generalizes the…
In this paper, we study the problem of jointly routing and scheduling traffic in an energy harvesting network. To this end, we leverage stochastic dual descent methods to propose a generalization of the well-known backpressure algorithm to energy harvesting networks. We name this policy energy harve…
Sampling is a fundamental topic in graph signal processing with applications in estimation, clustering, and video compression. In contrast to traditional signal processing, however, the irregularity of the signal domain makes the selection of the sampling points non-trivial and hard to analyze. Inde…
The ability to obtain accurate estimators from a set of measurements is a key factor in science and engineering. Typically, there is an inherent assumption that the measurements were taken in a sequential order, be it in space or time. However, data is increasingly irregular so this assumption of se…
We consider empirical risk minimization for large-scale datasets. We introduce Ada Newton as an adaptive algorithm that uses Newton's method with adaptive sample sizes. The main idea of Ada Newton is to increase the size of the training set by a factor larger than one in a way that the minimization…
Network processes are often represented as signals defined on the vertices of a graph. To untangle the latent structure of such signals, one can view them as outputs of linear graph filters modeling underlying network dynamics. This paper deals with the problem of joint identification of a graph fil…
This paper presents diffusion filtering as a method to smooth signals defined on the nodes of a graph or network. Diffusion filtering considers the given signals as initial temperature distributions in the nodes and diffuses heat through the edges of the graph. The filtered signal is determined by t…
In this paper we propose a hybrid architecture that allows a team of mobile robots to self-organize into a multi-hop ad-hoc network and solve the joint mobility and communication problem in complex environments to complete a given task. The system consists of an outer global planning loop and an inn
We introduce node-variant graph filters, which allow the simultaneous implementation of multiple (regular) graph filters at different nodes, and study their design to implement arbitrary linear transformations between graph signals. Node-variant graph filters can be implemented distributedly, making…
In pursuit of increasing the operational tempo of a ground robotics platform in unknown domains, we consider the problem of predicting the distribution of structural state-estimation error due to poorly-modeled platform dynamics as well as environmental effects. Such predictions are a critical compo…
We present a novel method to hierarchically cluster networked data allowing nodes to simultaneously belong to multiple clusters. Given a network, our method outputs a cut metric on the underlying node set, which can be related to data coverings at different resolutions. The cut metric is obtained by…
High order networks are weighted complete hypergraphs collecting relationships between elements of tuples. Valid metric distances between high order networks have been defined but they are difficult to compute when the number of nodes is large. We relate high order networks to the filtrations of sim…
We consider stochastic optimization problems in multi-agent settings, where a network of agents aims to learn decision variables which are optimal in terms of a global objective, while giving preference to locally and sequentially observed information. To do so, we formulate a problem where each age…
A novel scheme for sampling graph signals is proposed. Space-shift sampling can be understood as a hybrid scheme that combines selection sampling -- observing the signal values on a subset of nodes - and aggregation sampling - observing the signal values at a single node after successive aggregation…
In this paper, we present a hybrid system architecture that enables a team of robots to self-organize into a multi-hop ad-hoc network allowing for the completion of a given task while providing the desired end-to-end data rates between designated robots. This architecture consists of a two stage fee…
Agents of a network have access to strongly convex local functions f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> and attempt to minimize the aggregate function f(x) = Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://…
We consider discriminative dictionary learning in a distributed online setting, where a team of networked robots aims to jointly learn both a common basis of the feature space and a classifier over this basis from sequentially observed signals. We formulate this problem as a distributed stochastic p…
This paper presents two families of distances in the space of high order proximity networks. The distances measure differences between networks and are shown to be valid metrics in the space of high order proximity networks modulo permutation isomorphisms. Practical implications are explored by comp…
A game-theoretic framework based on smart pricing in power grids that incorporates heterogeneous user preferences and renewable power uncertainty is considered. The system operator adopts an adaptive pricing policy that depends on total consumption and renewable generation. The pricing policy sets u…
An algorithm to learn optimal actions in distributed convex repeated games is developed. Learning is repeated because cost functions are revealed sequentially and distributed because they are revealed to agents of a network that can exchange information with neighboring nodes only. Learning is measu…
This paper introduces a formal definition of continuity and generalizes an existing notion of stability for node centrality measures in weighted graphs. It is shown that the frequently used measures of degree, closeness and eigenvector centrality are stable and continuous whereas betweenness central…