arXiv subjects

Pramod K. Varshney

Publications and source records attributed to Pramod K. Varshney.

At least 55 records · Page 3Linked to original sources

arXiv2021

Decentralized Federated Learning via Mutual Knowledge Transfer

In this paper, we investigate the problem of decentralized federated learning (DFL) in Internet of things (IoT) systems, where a number of IoT clients train models collectively for a common task without sharing their private training data in the absence of a central server. Most of the existing DFL schemes are composed of two alternating steps, i.e., model updating and model averaging. However, averaging model parameters directly to fuse different models at the local clients suffers from client-drift especially when the training data are heterogeneous across different clients. This leads to slow convergence and degraded learning performance. As a possible solution, we propose the decentralized federated earning via mutual knowledge transfer (Def-KT) algorithm where local clients fuse models by transferring their learnt knowledge to each other. Our experiments on the MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100 datasets reveal that the proposed Def-KT algorithm significantly outperforms the baseline DFL methods with model averaging, i.e., Combo and FullAvg, especially when the training data are not independent and identically distributed (non-IID) across different clients.

cs.LG↗

arXiv2021

On Distributed Online Convex Optimization with Sublinear Dynamic Regret and Fit

In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex functions. The objective and constraint functions are revealed locally to the nodes, at each time, after taking an action. Naturally, the constraints cannot be instantaneously satisfied. Therefore, we reformulate the problem to satisfy these constraints in the long term. To this end, we propose a distributed primal-dual mirror descent based approach, in which the primal and dual updates are carried out locally at all the nodes. This is followed by sharing and mixing of the primal variables by the local nodes via communication with the immediate neighbors. To quantify the performance of the proposed algorithm, we utilize the challenging, but more realistic metrics of dynamic regret and fit. Dynamic regret measures the cumulative loss incurred by the algorithm, compared to the best dynamic strategy. On the other hand, fit measures the long term cumulative constraint violations. Without assuming the restrictive Slater's conditions, we show that the proposed algorithm achieves sublinear regret and fit under mild, commonly used assumptions.

math.OC↗

arXiv2021

Anomalous Example Detection in Deep Learning: A Survey

Deep Learning (DL) is vulnerable to out-of-distribution and adversarial examples resulting in incorrect outputs. To make DL more robust, several posthoc (or runtime) anomaly detection techniques to detect (and discard) these anomalous samples have been proposed in the recent past. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection for DL based applications. We provide a taxonomy for existing techniques based on their underlying assumptions and adopted approaches. We discuss various techniques in each of the categories and provide the relative strengths and weaknesses of the approaches. Our goal in this survey is to provide an easier yet better understanding of the techniques belonging to different categories in which research has been done on this topic. Finally, we highlight the unsolved research challenges while applying anomaly detection techniques in DL systems and present some high-impact future research directions.

cs.LG↗

arXiv2020

Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework

In this work, we focus on the study of stochastic zeroth-order (ZO) optimization which does not require first-order gradient information and uses only function evaluations. The problem of ZO optimization has emerged in many recent machine learning applications, where the gradient of the objective function is either unavailable or difficult to compute. In such cases, we can approximate the full gradients or stochastic gradients through function value based gradient estimates. Here, we propose a novel hybrid gradient estimator (HGE), which takes advantage of the query-efficiency of random gradient estimates as well as the variance-reduction of coordinate-wise gradient estimates. We show that with a graceful design in coordinate importance sampling, the proposed HGE-based ZO optimization method is efficient both in terms of iteration complexity as well as function query cost. We provide a thorough theoretical analysis of the convergence of our proposed method for non-convex, convex, and strongly-convex optimization. We show that the convergence rate that we derive generalizes the results for some prominent existing methods in the nonconvex case, and matches the optimal result in the convex case. We also corroborate the theory with a real-world black-box attack generation application to demonstrate the empirical advantage of our method over state-of-the-art ZO optimization approaches.

stat.ML↗

arXiv2020

On Performance Comparison of Multi-Antenna HD-NOMA, SCMA and PD-NOMA Schemes

In this paper, we study the uplink channel throughput performance of a proposed novel multiple-antenna hybrid-domain non-orthogonal multiple access (MA-HD-NOMA) scheme. This scheme combines the conventional sparse code multiple access (SCMA) and power-domain NOMA (PD-NOMA) schemes in order to increase the number of users served as compared to conventional NOMA schemes and uses multiple antennas at the base station. To this end, a joint resource allocation problem for the MA-HD-NOMA scheme is formulated that maximizes the sum rate of the entire system. For a comprehensive comparison, the joint resource allocation problems for the multi-antenna SCMA (MA-SCMA) and multi-antenna PD-NOMA (MA-PD-NOMA) schemes with the same overloading factor are formulated as well. Each of the formulated problems is a mixed-integer non-convex program, and hence, we apply successive convex approximation (SCA)- and reweighted $\ell_1$ minimization-based approaches to obtain rapidly converging solutions. Numerical results reveal that the proposed MA-HD-NOMA scheme has superior performance compared to MA-SCMA and MA-PD-NOMA.

cs.IT↗

arXiv2020

Parallel Restarted SPIDER -- Communication Efficient Distributed Nonconvex Optimization with Optimal Computation Complexity

In this paper, we propose a distributed algorithm for stochastic smooth, non-convex optimization. We assume a worker-server architecture where $N$ nodes, each having $n$ (potentially infinite) number of samples, collaborate with the help of a central server to perform the optimization task. The global objective is to minimize the average of local cost functions available at individual nodes. The proposed approach is a non-trivial extension of the popular parallel-restarted SGD algorithm, incorporating the optimal variance-reduction based SPIDER gradient estimator into it. We prove convergence of our algorithm to a first-order stationary solution. The proposed approach achieves the best known communication complexity $O(ε^{-1})$ along with the optimal computation complexity. For finite-sum problems (finite $n$), we achieve the optimal computation (IFO) complexity $O(\sqrt{Nn}ε^{-1})$. For online problems ($n$ unknown or infinite), we achieve the optimal IFO complexity $O(ε^{-3/2})$. In both the cases, we maintain the linear speedup achieved by existing methods. This is a massive improvement over the $O(ε^{-2})$ IFO complexity of the existing approaches. Additionally, our algorithm is general enough to allow non-identical distributions of data across workers, as in the recently proposed federated learning paradigm.

math.OC↗

arXiv2020

Joint Collaboration and Compression Design for Distributed Sequential Estimation in a Wireless Sensor Network

In this work, we propose a joint collaboration-compression framework for sequential estimation of a random vector parameter in a resource constrained wireless sensor network (WSN). Specifically, we propose a framework where the local sensors first collaborate (via a collaboration matrix) with each other. Then a subset of sensors selected to communicate with the FC linearly compress their observations before transmission. We design near-optimal collaboration and linear compression strategies under power constraints via alternating minimization of the sequential minimum mean square error. We show that the objective function for collaboration design can be non-convex depending on the network topology. We reformulate and solve the collaboration design problem using quadratically constrained quadratic program (QCQP). Moreover, the compression design problem is also formulated as a QCQP. We propose two versions of compression design, one centralized where the compression strategies are derived at the FC and the other decentralized, where the local sensors compute their individual compression matrices independently. It is noted that the design of decentralized compression strategy is a non-convex problem. We obtain a near-optimal solution by using the bisection method. In contrast to the one-shot estimator, our proposed algorithm is capable of handling dynamic system parameters such as channel gains and energy constraints. Importantly, we show that the proposed methods can also be used for estimating time-varying random vector parameters. Finally, numerical results are provided to demonstrate the effectiveness of the proposed framework.

eess.SP↗

arXiv2020

A Novel Spectrally-Efficient Uplink Hybrid-Domain NOMA System

This paper proposes a novel hybrid-domain (HD) non-orthogonal multiple access (NOMA) approach to support a larger number of uplink users than the recently proposed code-domain NOMA approach, i.e., sparse code multiple access (SCMA). HD-NOMA combines the code-domain and power-domain NOMA schemes by clustering the users in small path loss (strong) and large path loss (weak) groups. The two groups are decoded using successive interference cancellation while within the group users are decoded using the message passing algorithm. To further improve the performance of the system, a spectral-efficiency maximization problem is formulated under a user quality-of-service constraint, which dynamically assigns power and subcarrier to the users. The problem is non-convex and has sparsity constraints. The alternating optimization procedure is used to solve it iteratively. We apply successive convex approximation and reweighted $\ell_1$ minimization approaches to deal with the non-convexity and sparsity constraints, respectively. The performance of the proposed HD-NOMA is evaluated and compared with the conventional SCMA scheme through numerical simulation. The results show the potential of HD-NOMA in increasing the number of uplink users.

eess.SP↗

arXiv2020

A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning applications. It is used for solving optimization problems similarly to gradient-based methods. However, it does not require the gradient, using only function evaluations. Specifically, ZO optimization iteratively performs three major steps: gradient estimation, descent direction computation, and solution update. In this paper, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles and recent advances in convergence analysis. Moreover, we demonstrate promising applications of ZO optimization, such as evaluating robustness and generating explanations from black-box deep learning models, and efficient online sensor management.

cs.LG↗

arXiv2020

Anomaly Detection Under Controlled Sensing Using Actor-Critic Reinforcement Learning

We consider the problem of detecting anomalies among a given set of processes using their noisy binary sensor measurements. The noiseless sensor measurement corresponding to a normal process is 0, and the measurement is 1 if the process is anomalous. The decision-making algorithm is assumed to have no knowledge of the number of anomalous processes. The algorithm is allowed to choose a subset of the sensors at each time instant until the confidence level on the decision exceeds the desired value. Our objective is to design a sequential sensor selection policy that dynamically determines which processes to observe at each time and when to terminate the detection algorithm. The selection policy is designed such that the anomalous processes are detected with the desired confidence level while incurring minimum cost which comprises the delay in detection and the cost of sensing. We cast this problem as a sequential hypothesis testing problem within the framework of Markov decision processes, and solve it using the actor-critic deep reinforcement learning algorithm. This deep neural network-based algorithm offers a low complexity solution with good detection accuracy. We also study the effect of statistical dependence between the processes on the algorithm performance. Through numerical experiments, we show that our algorithm is able to adapt to any unknown statistical dependence pattern of the processes.

eess.SP↗

arXiv2020

Distributed Stochastic Non-Convex Optimization: Momentum-Based Variance Reduction

In this work, we propose a distributed algorithm for stochastic non-convex optimization. We consider a worker-server architecture where a set of $K$ worker nodes (WNs) in collaboration with a server node (SN) jointly aim to minimize a global, potentially non-convex objective function. The objective function is assumed to be the sum of local objective functions available at each WN, with each node having access to only the stochastic samples of its local objective function. In contrast to the existing approaches, we employ a momentum based "single loop" distributed algorithm which eliminates the need of computing large batch size gradients to achieve variance reduction. We propose two algorithms one with "adaptive" and the other with "non-adaptive" learning rates. We show that the proposed algorithms achieve the optimal computational complexity while attaining linear speedup with the number of WNs. Specifically, the algorithms reach an $ε$-stationary point $x_a$ with $\mathbb{E}\| \nabla f(x_a) \| \leq \tilde{O}(K^{-1/3}T^{-1/2} + K^{-1/3}T^{-1/3})$ in $T$ iterations, thereby requiring $\tilde{O}(K^{-1} ε^{-3})$ gradient computations at each WN. Moreover, our approach does not assume identical data distributions across WNs making the approach general enough for federated learning applications.

math.OC↗

arXiv2020

Prospect Theory Based Crowdsourcing for Classification in the Presence of Spammers

We consider the $M$-ary classification problem via crowdsourcing, where crowd workers respond to simple binary questions and the answers are aggregated via decision fusion. The workers have a reject option to skip answering a question when they do not have the expertise, or when the confidence of answering that question correctly is low. We further consider that there are spammers in the crowd who respond to the questions with random guesses. Under the payment mechanism that encourages the reject option, we study the behavior of honest workers and spammers, whose objectives are to maximize their monetary rewards. To accurately characterize human behavioral aspects, we employ prospect theory to model the rationality of the crowd workers, whose perception of costs and probabilities are distorted based on some value and weight functions, respectively. Moreover, we estimate the number of spammers and employ a weighted majority voting decision rule, where we assign an optimal weight for every worker to maximize the system performance. The probability of correct classification and asymptotic system performance are derived. We also provide simulation results to demonstrate the effectiveness of our approach.

cs.HC↗

arXiv2020

Decentralized Gaussian Filters for Cooperative Self-localization and Multi-target Tracking

Scalable and decentralized algorithms for Cooperative Self-localization (CS) of agents, and Multi-Target Tracking (MTT) are important in many applications. In this work, we address the problem of Simultaneous Cooperative Self-localization and Multi-Target Tracking (SCS-MTT) under target data association uncertainty, i.e., the associations between measurements and target tracks are unknown. Existing CS and tracking algorithms either make the assumption of no data association uncertainty or employ a hard-decision rule for measurement-to-target associations. We propose a novel decentralized SCS-MTT method for an unknown and time-varying number of targets under association uncertainty. Marginal posterior densities for agents and targets are obtained by an efficient belief propagation (BP) based scheme while data association is handled by marginalizing over all target-to-measurement association probabilities. Decentralized single Gaussian and Gaussian mixture implementations are provided based on average consensus schemes, which require communication only with one-hop neighbors. An additional novelty is a decentralized Gibbs mechanism for efficient evaluation of the product of Gaussian mixtures. Numerical experiments show the improved CS and MTT performance compared to the conventional approach of separate localization and target tracking.

eess.SP↗

arXiv2020

Measurement Bounds for Compressed Sensing in Sensor Networks with Missing Data

In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in compressed sensing is known to provide excellent reconstruction accuracy. However, when there is missing data, the theoretical guarantees associated with sparse recovery have not been well studied. Therefore, in this paper, we derive an upper bound on the minimum number of measurements required to ensure faithful recovery of a sparse signal when the generation of missing data is modeled using a Bernoulli erasure channel. We analyze three different network topologies, namely, star, (relay aided-)tree, and serial-star topologies. Our analysis establishes how the minimum required number of measurements for recovery scales with the network parameters, the properties of the measurement matrix, and the recovery algorithm. Finally, through numerical simulations, we show the variation of the minimum required number of measurements with different system parameters and validate our theoretical results.

eess.SP↗

arXiv2019

Byzantine Resilient Non-Convex SVRG with Distributed Batch Gradient Computations

In this work, we consider the distributed stochastic optimization problem of minimizing a non-convex function $f(x) = \mathbb{E}_{ξ\sim \mathcal{D}} f(x; ξ)$ in an adversarial setting, where the individual functions $f(x; ξ)$ can also be potentially non-convex. We assume that at most $α$-fraction of a total of $K$ nodes can be Byzantines. We propose a robust stochastic variance-reduced gradient (SVRG) like algorithm for the problem, where the batch gradients are computed at the worker nodes (WNs) and the stochastic gradients are computed at the server node (SN). For the non-convex optimization problem, we show that we need $\tilde{O}\left( \frac{1}{ε^{5/3} K^{2/3}} + \frac{α^{4/3}}{ε^{5/3}} \right)$ gradient computations on average at each node (SN and WNs) to reach an $ε$-stationary point. The proposed algorithm guarantees convergence via the design of a novel Byzantine filtering rule which is independent of the problem dimension. Importantly, we capture the effect of the fraction of Byzantine nodes $α$ present in the network on the convergence performance of the algorithm.

math.OC↗

arXiv2019

Fusion of Deep Neural Networks for Activity Recognition: A Regular Vine Copula Based Approach

In this paper, we propose regular vine copula based fusion of multiple deep neural network classifiers for the problem of multi-sensor based human activity recognition. We take the cross-modal dependence into account by employing regular vine copulas that are extremely flexible and powerful graphical models to characterize complex dependence among multiple modalities. Multiple deep neural networks are used to extract high-level features from multi-sensing modalities, with each deep neural network processing the data collected from a single sensor. The extracted high-level features are then combined using a regular vine copula model. Numerical experiments are conducted to demonstrate the effectiveness of our approach.

eess.SP↗

arXiv2019

Distributed Sequential Hypothesis Testing with Dependent Sensor Observations

In this paper, we consider the problem of distributed sequential detection using wireless sensor networks (WSNs) in the presence of imperfect communication channels between the sensors and the fusion center (FC). We assume that sensor observations are spatially dependent. We propose a copula-based distributed sequential detection scheme that characterizes the spatial dependence. Specifically, each local sensor collects observations regarding the phenomenon of interest and forwards the information obtained to the FC over noisy channels. The FC fuses the received messages using a copula-based sequential test. Moreover, we show the asymptotic optimality of the proposed copula-based sequential test. Numerical experiments are conducted to demonstrate the effectiveness of our approach.

eess.SP↗

arXiv2019

Multiple-Source Ellipsoidal Localization Using Acoustic Energy Measurements

In this paper, the multiple-source ellipsoidal localization problem based on acoustic energy measurements is investigated via set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurements are complicated nonlinear functions of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. First, when the energy parameter and the position of the source are bounded in an interval and a ball respectively, the nonlinear remainder bound of the Taylor series expansion is obtained analytically on-line. Next, based on the separability of the nonlinear measurement function, an efficient estimation procedure is developed. It solves the multiple-source localization problem by using an alternating optimization iterative algorithm, in which the remainder bound needs to be known on-line. For this reason, we first derive the remainder bound analytically. When the energy decay factor is unknown but bounded, an efficient estimation procedure is developed based on interval mathematics. Finally, numerical examples demonstrate the effectiveness of the ellipsoidal localization algorithms for multiple-source localization. In particular, our results show that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the EM localization algorithm.

cs.IT↗