arXiv subjects

Ramtin Pedarsani

Publications and source records attributed to Ramtin Pedarsani.

At least 91 records · Page 5Linked to original sources

arXiv2018

Maximizing Road Capacity Using Cars that Influence People

The emerging technology enabling autonomy in vehicles has led to a variety of new problems in transportation networks, such as planning and perception for autonomous vehicles. Other works consider social objectives such as decreasing fuel consumption and travel time by platooning. However, these strategies are limited by the actions of the surrounding human drivers. In this paper, we consider proactively achieving these social objectives by influencing human behavior through planned interactions. Our key insight is that we can use these social objectives to design local interactions that influence human behavior to achieve these goals. To this end, we characterize the increase in road capacity afforded by platooning, as well as the vehicle configuration that maximizes road capacity. We present a novel algorithm that uses a low-level control framework to leverage local interactions to optimally rearrange vehicles. We showcase our algorithm using a simulated road shared between autonomous and human-driven vehicles, in which we illustrate the reordering in action.

math.OC↗

arXiv2018

Routing for Traffic Networks with Mixed Autonomy

In this work we propose a macroscopic model for studying routing on networks shared between human-driven and autonomous vehicles that captures the effects of autonomous vehicles forming platoons. We use this to study inefficiency due to selfish routing and bound the Price of Anarchy (PoA), the maximum ratio between total delay experienced by selfish users and the minimum possible total delay. To do so, we establish two road capacity models, each corresponding to an assumption regarding the platooning capabilities of autonomous vehicles. Using these we develop a class of road delay functions, parameterized by the road capacity, that are polynomial with respect to vehicle flow. We then bound the PoA and the bicriteria, another measure of the inefficiency due to selfish routing. We find these bounds depend on: 1) the degree of the polynomial in the road cost function and 2) the degree of asymmetry, the difference in how human-driven and autonomous traffic affect congestion. We demonstrate that these bounds recover the classical bounds when no asymmetry exists. We show the bounds are tight in certain cases and that the PoA bound is order-optimal with respect to the degree of asymmetry.

math.OC↗

arXiv2018

Learning Mixtures of Sparse Linear Regressions Using Sparse Graph Codes

In this paper, we consider the mixture of sparse linear regressions model. Let $β^{(1)},\ldots,β^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear measurements are obtained in the form $y_i={x}_i^H β^{(\ell_i)} + w_i$, each of which is generated randomly from one of the sparse vectors with the label $ \ell_i $ unknown. The goal is to estimate the parameter vectors efficiently with low sample and computational costs. This problem presents significant challenges as one needs to simultaneously solve the demixing problem of recovering the labels $ \ell_i $ as well as the estimation problem of recovering the sparse vectors $ β^{(\ell)} $. Our solution to the problem leverages the connection between modern coding theory and statistical inference. We introduce a new algorithm, Mixed-Coloring, which samples the mixture strategically using query vectors $ {x}_i $ constructed based on ideas from sparse graph codes. Our novel code design allows for both efficient demixing and parameter estimation. In the noiseless setting, for a constant number of sparse parameter vectors, our algorithm achieves the order-optimal sample and time complexities of $Θ(K)$. In the presence of Gaussian noise, for the problem with two parameter vectors (i.e., $L=2$), we show that the Robust Mixed-Coloring algorithm achieves near-optimal $Θ(K polylog(n))$ sample and time complexities. When $K=O(n^α)$ for some constant $α\in(0,1)$ (i.e., $K$ is sublinear in $n$), we can achieve sample and time complexities both sublinear in the ambient dimension. In one of our experiments, to recover a mixture of two regressions with dimension $n=500$ and sparsity $K=50$, our algorithm is more than $300$ times faster than EM algorithm, with about one third of its sample cost.

cs.IT↗

arXiv2018

Combating Adversarial Attacks Using Sparse Representations

It is by now well-known that small adversarial perturbations can induce classification errors in deep neural networks (DNNs). In this paper, we make the case that sparse representations of the input data are a crucial tool for combating such attacks. For linear classifiers, we show that a sparsifying front end is provably effective against $\ell_{\infty}$-bounded attacks, reducing output distortion due to the attack by a factor of roughly $K / N$ where $N$ is the data dimension and $K$ is the sparsity level. We then extend this concept to DNNs, showing that a "locally linear" model can be used to develop a theoretical foundation for crafting attacks and defenses. Experimental results for the MNIST dataset show the efficacy of the proposed sparsifying front end.

stat.ML↗

arXiv2018

Sparsity-based Defense against Adversarial Attacks on Linear Classifiers

Deep neural networks represent the state of the art in machine learning in a growing number of fields, including vision, speech and natural language processing. However, recent work raises important questions about the robustness of such architectures, by showing that it is possible to induce classification errors through tiny, almost imperceptible, perturbations. Vulnerability to such "adversarial attacks", or "adversarial examples", has been conjectured to be due to the excessive linearity of deep networks. In this paper, we study this phenomenon in the setting of a linear classifier, and show that it is possible to exploit sparsity in natural data to combat $\ell_{\infty}$-bounded adversarial perturbations. Specifically, we demonstrate the efficacy of a sparsifying front end via an ensemble averaged analysis, and experimental results for the MNIST handwritten digit database. To the best of our knowledge, this is the first work to show that sparsity provides a theoretically rigorous framework for defense against adversarial attacks.

stat.ML↗

arXiv2018

Sub-linear Time Support Recovery for Compressed Sensing using Sparse-Graph Codes

We study the support recovery problem for compressed sensing, where the goal is to reconstruct the a high-dimensional $K$-sparse signal $\mathbf{x}\in\mathbb{R}^N$, from low-dimensional linear measurements with and without noise. Our key contribution is a new compressed sensing framework through a new family of carefully designed sparse measurement matrices associated with minimal measurement costs and a low-complexity recovery algorithm. The measurement matrix in our framework is designed based on the well-crafted sparsification through capacity-approaching sparse-graph codes, where the sparse coefficients can be recovered efficiently in a few iterations by performing simple error decoding over the observations. We formally connect this general recovery problem with sparse-graph decoding in packet communication systems, and analyze our framework in terms of the measurement cost, time complexity and recovery performance. In the noiseless setting, our framework can recover any arbitrary $K$-sparse signal in $O(K)$ time using $2K$ measurements asymptotically with high probability. In the noisy setting, when the sparse coefficients take values in a finite and quantized alphabet, our framework can achieve the same goal in time $O(K\log(N/K))$ using $O(K\log(N/K))$ measurements obtained from measurement matrix with elements $\{-1,0,1\}$. When the sparsity $K$ is sub-linear in the signal dimension $K=O(N^δ)$ for some $0<δ<1$, our results are order-optimal in terms of measurement costs and run-time, both of which are sub-linear in the signal dimension $N$. The sub-linear measurement cost and run-time can also be achieved with continuous-valued sparse coefficients, with a slight increment in the logarithmic factors. This offers the desired scalability of our framework that can potentially enable real-time or near-real-time processing for massive datasets featuring sparsity.

cs.IT↗

arXiv2018

Speeding Up Distributed Machine Learning Using Codes

Codes are widely used in many engineering applications to offer robustness against noise. In large-scale systems there are several types of noise that can affect the performance of distributed machine learning algorithms -- straggler nodes, system failures, or communication bottlenecks -- but there has been little interaction cutting across codes, machine learning, and distributed systems. In this work, we provide theoretical insights on how coded solutions can achieve significant gains compared to uncoded ones. We focus on two of the most basic building blocks of distributed learning algorithms: matrix multiplication and data shuffling. For matrix multiplication, we use codes to alleviate the effect of stragglers, and show that if the number of homogeneous workers is $n$, and the runtime of each subtask has an exponential tail, coded computation can speed up distributed matrix multiplication by a factor of $\log n$. For data shuffling, we use codes to reduce communication bottlenecks, exploiting the excess in storage. We show that when a constant fraction $α$ of the data matrix can be cached at each worker, and $n$ is the number of workers, \emph{coded shuffling} reduces the communication cost by a factor of $(α+ \frac{1}{n})γ(n)$ compared to uncoded shuffling, where $γ(n)$ is the ratio of the cost of unicasting $n$ messages to $n$ users to multicasting a common message (of the same size) to $n$ users. For instance, $γ(n) \simeq n$ if multicasting a message to $n$ users is as cheap as unicasting a message to one user. We also provide experiment results, corroborating our theoretical gains of the coded algorithms.

cs.DC↗

arXiv2017

The Price of Anarchy for Transportation Networks with Mixed Autonomy

We study routing behavior in transportation networks with mixed autonomy, that is, networks in which a fraction of the vehicles on each road are equipped with autonomous capabilities such as adaptive cruise control that enable reduced headways and increased road capacity. Motivated by capacity models developed for such roads with mixed autonomy, we consider transportation networks in which the delay on each road or link is an affine function of two quantities: the number of vehicles with autonomous capabilities on the link and the number of regular vehicles on the link. We particularly study the price of anarchy for such networks, that is, the ratio of the total delay experienced by selfish routing to the socially optimal routing policy. Unlike the case when all vehicles are of the same type, for which the price of anarchy is known to be bounded, we first show that the price of anarchy can be arbitrarily large for such mixed autonomous networks. Next, we define a notion of asymmetry equal to the maximum possible travel time improvement due to the presence of autonomous vehicles. We show that when the degree of asymmetry of all links in the network is bounded by a factor less than 4, the price of anarchy is bounded. We also bound the bicriteria, which is a bound on the cost of selfishly routing traffic compared to the cost of optimally routing additional traffic. These bounds depend on the degree of asymmetry and recover classical bounds on the price of anarchy and bicriteria in the case when no asymmetry exists. Further, we show with examples that these bound are tight in particular cases.

math.OC↗

arXiv2017

Latency Analysis of Coded Computation Schemes over Wireless Networks

Large-scale distributed computing systems face two major bottlenecks that limit their scalability: straggler delay caused by the variability of computation times at different worker nodes and communication bottlenecks caused by shuffling data across many nodes in the network. Recently, it has been shown that codes can provide significant gains in overcoming these bottlenecks. In particular, optimal coding schemes for minimizing latency in distributed computation of linear functions and mitigating the effect of stragglers was proposed for a wired network, where the workers can simultaneously transmit messages to a master node without interference. In this paper, we focus on the problem of coded computation over a wireless master-worker setup with straggling workers, where only one worker can transmit the result of its local computation back to the master at a time. We consider 3 asymptotic regimes (determined by how the communication and computation times are scaled with the number of workers) and precisely characterize the total run-time of the distributed algorithm and optimum coding strategy in each regime. In particular, for the regime of practical interest where the computation and communication times of the distributed computing algorithm are comparable, we show that the total run-time approaches a simple lower bound that decouples computation and communication, and demonstrate that coded schemes are $Θ(\log(n))$ times faster than uncoded schemes.

cs.IT↗

arXiv2017

PhaseCode: Fast and Efficient Compressive Phase Retrieval based on Sparse-Graph-Codes

We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of the $K$ non-zero signal components using only slightly more than $4K$ measurements when the support of the signal is uniformly random, with order-optimal time and memory complexity of $Θ(K)$. It is known that the fundamental limit for the number of measurements in compressive phase retrieval problem is $4K - o(K)$ to recover the signal exactly and with no assumptions on its support distribution. This shows that under mild relaxation of the conditions, our algorithm is the first constructive \emph{capacity-approaching} compressive phase retrieval algorithm: in fact, our algorithm is also order-optimal in complexity and memory. Next, motivated by some important practical classes of optical systems, we consider a Fourier-friendly constrained measurement setting, and show that its performance matches that of the unconstrained setting. In the Fourier-friendly setting that we consider, the measurement matrix is constrained to be a cascade of Fourier matrices and diagonal matrices. We further demonstrate how PhaseCode can be robustified to noise. Throughout, we provide extensive simulation results that validate the practical power of our proposed algorithms for the sparse unconstrained and Fourier-friendly measurement settings, for noiseless and noisy scenarios. A key contribution of our work is the novel use of coding-theoretic tools like density evolution methods for the design and analysis of fast and efficient algorithms for compressive phase-retrieval problems.

cs.IT↗

arXiv2017

Platoons of connected vehicles can double throughput in urban roads

Intersections are the bottlenecks of the urban road system because an intersection's capacity is only a fraction of the flows that the roads connecting to the intersection can carry. This capacity can be increased if vehicles can cross the intersections in platoons rather than one by one as they do today. Platoon formation is enabled by connected vehicle technology. This paper assesses the potential mobility benefits of platooning. It argues that saturation flow rates, and hence intersection capacity, can be doubled or tripled by platooning. The argument is supported by the analysis of three queuing models and by the simulation of a road network with 16 intersections and 73 links. The queuing analysis and the simulations reveal that a signalized network with fixed time control will support an increase in demand by a factor of (say) two or three if all saturation flows are increased by the same factor, with no change in the control. Furthermore, despite the increased demand vehicles will experience the same delay and travel time. The same scaling improvement is achieved when the fixed time control is replaced by the max pressure adaptive control. Part of the capacity increase can alternatively be used to reduce queue lengths and the associated queuing delay by decreasing the cycle time. Impediments to the control of connected vehicles to achieve platooning at intersections appear to be small.

math.DS↗

arXiv2016

Robust Scheduling for Flexible Processing Networks

Modern processing networks often consist of heterogeneous servers with widely varying capabilities, and process job flows with complex structure and requirements. A major challenge in designing efficient scheduling policies in these networks is the lack of reliable estimates of system parameters, and an attractive approach for addressing this challenge is to design robust policies, i.e., policies that do not use system parameters such as arrival and/or service rates for making scheduling decisions. In this paper, we propose a general framework for the design of robust policies. The main technical novelty is the use of a stochastic gradient projection method that reacts to queue-length changes in order to find a balanced allocation of service resources to incoming tasks. We illustrate our approach on two broad classes of processing systems, namely the flexible fork-join networks and the flexible queueing networks, and prove the rate stability of our proposed policies for these networks under non-restrictive assumptions.

math.PR↗

arXiv2016

Fast and Robust Compressive Phase Retrieval with Sparse-Graph Codes

In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a $K$-sparse complex signal $s \in \mathbb{C}^n$, from a set of $m$ noisy quadratic measurements: $ y_i=| a_i^H s |^2+w_i$, where $a_i^H\in\mathbb{C}^n$ is the $i$th row of the measurement matrix $A\in\mathbb{C}^{m\times n}$, and $w_i$ is the additive noise to the $i$th measurement. We consider the regime where $K=βn^δ$, with constants $β>0$ and $δ\in(0,1)$. We use the architecture of PhaseCode algorithm, and robustify it using two schemes: the almost-linear scheme and the sublinear scheme. We prove that with high probability, the almost-linear scheme recovers $s$ with sample complexity $Θ(K \log(n))$ and computational complexity $Θ(n \log(n))$, and the sublinear scheme recovers $s$ with sample complexity $Θ(K\log^3(n))$ and computational complexity $Θ(K\log^3(n))$. To the best of our knowledge, this is the first scheme that achieves sublinear computational complexity for compressive phase retrieval problem. Finally, we provide simulation results that support our theoretical contributions.

cs.IT↗

arXiv2015

SAFFRON: A Fast, Efficient, and Robust Framework for Group Testing based on Sparse-Graph Codes

Group testing tackles the problem of identifying a population of $K$ defective items from a set of $n$ items by pooling groups of items efficiently in order to cut down the number of tests needed. The result of a test for a group of items is positive if any of the items in the group is defective and negative otherwise. The goal is to judiciously group subsets of items such that defective items can be reliably recovered using the minimum number of tests, while also having a low-complexity decoding procedure. We describe SAFFRON (Sparse-grAph codes Framework For gROup testiNg), a non-adaptive group testing paradigm that recovers at least a $(1-ε)$-fraction (for any arbitrarily small $ε> 0$) of $K$ defective items with high probability with $m=6C(ε)K\log_2{n}$ tests, where $C(ε)$ is a precisely characterized constant that depends only on $ε$. For instance, it can provably recover at least $(1-10^{-6})K$ defective items with $m \simeq 68 K \log_2{n}$ tests. The computational complexity of the decoding algorithm of SAFFRON is $\mathcal{O}(K\log n)$, which is order-optimal. Further, we robustify SAFFRON such that it can reliably recover the set of $K$ defective items even in the presence of erroneous or noisy test results. We also propose Singleton-Only-SAFFRON, a variant of SAFFRON, that recovers all the $K$ defective items with $m=2e(1+α)K\log K \log_2 n$ tests with probability $1-\mathcal{O}{\left(\frac{1}{K^α}\right)}$, where $α>0$ is a constant. By leveraging powerful design and analysis tools from modern sparse-graph coding theory, SAFFRON is the first approach to reliable, large-scale probabilistic group testing that offers both precisely characterizable number of tests needed (down to the constants) together with order-optimal decoding complexity.

cs.IT↗

arXiv2015

Stability of Multiclass Queueing Networks under Longest-Queue and Longest-Dominating-Queue Scheduling

We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The arrival and potential service processes and routing decisions at the queues are independent, stationary and ergodic. A scheduling policy is called robust if it does not depend on the arrival and service rates nor on the routing probabilities. A policy is called throughput-optimal if it makes the system stable whenever the parameters are such that the system can be stable. We propose two robust polices: longest-queue scheduling and a new policy called longest-dominating-queue scheduling. We show that longest-queue scheduling is throughput-optimal for two groups of two queues. We also prove the throughput-optimality of longest-dominating-queue scheduling when the network topology is acyclic, for an arbitrary number of groups and queues.

math.PR↗

arXiv2015

Capacity-Approaching PhaseCode for Low-Complexity Compressive Phase Retrieval

In this paper, we tackle the general compressive phase retrieval problem. The problem is to recover a K-sparse complex vector of length n, $x\in \mathbb{C}^n$, from the magnitudes of m linear measurements, $y=|Ax|$, where $A \in \mathbb{C}^{m \times n}$ can be designed, and the magnitudes are taken component-wise for vector $Ax\in \mathbb{C}^m$. We propose a variant of the PhaseCode algorithm, and show that, using an irregular left-degree sparse-graph code construction, the algorithm can recover almost all the K non-zero signal components using only slightly more than 4K measurements under some mild assumptions, with optimal time and memory complexity of ${\cal O}(K)$. It is known that the fundamental limit for the number of measurements in compressive phase retrieval problem is $4K - o(K)$. To the best of our knowledge, this is the first constructive capacity-approaching compressive phase retrieval algorithm. As a second contribution, we propose another variant of the PhaseCode algorithm that is based on a Compressive Sensing framework involving sparse-graph codes. Our proposed algorithm is an instance of a more powerful "separation" architecture that can be used to address the compressive phase-retrieval problem in general. This modular design features a compressive sensing outer layer, and a trigonometric-based phase-retrieval inner layer. The compressive-sensing layer operates as a linear phase-aware compressive measurement subsystem, while the trig-based phase-retrieval layer provides the desired abstraction between the actually targeted nonlinear phase-retrieval problem and the induced linear compressive-sensing problem. Invoking this architecture based on the use of sparse-graph codes for the compressive sensing layer, we show that we can exactly recover a signal from only the magnitudes of its linear measurements using only slightly more than 6K measurements.

cs.IT↗

arXiv2014

Analysis of Fixed-Time Control

A network of signalized intersections is modeled as a queuing network. The intersections are regulated by fixed-time (FT) controls, all with the same cycle length or period, $T$. Vehicles arrive from outside the network at entry links in a deterministic periodic stream, also with period $T$, make turns at intersections in fixed proportions, and eventually leave the network. Vehicles take a fixed time to travel along each link, and at the end of the link they join a queue. There is a separate queue at each intersection for each movement. The storage capacity of the queues is infinite, so there is no spill back. The state of the network at time $t$ is the vector $x(t)$ of all queue lengths, together with the position of vehicles traveling along the links. The state evolves according to a delay-differential equation. Suppose the network is stable, that is, $x(t)$ is bounded. Then (1) there exists a unique periodic trajectory $x^*(t)$, with period $T$; (2) every trajectory converges to this periodic trajectory; (3) if vehicles do not follow loops, the convergence occurs in finite time. The periodic trajectory determines the performance of the entire network.

math.DS↗

arXiv2013

Online Coded Caching

We consider a basic content distribution scenario consisting of a single origin server connected through a shared bottleneck link to a number of users each equipped with a cache of finite memory. The users issue a sequence of content requests from a set of popular files, and the goal is to operate the caches as well as the server such that these requests are satisfied with the minimum number of bits sent over the shared link. Assuming a basic Markov model for renewing the set of popular files, we characterize approximately the optimal long-term average rate of the shared link. We further prove that the optimal online scheme has approximately the same performance as the optimal offline scheme, in which the cache contents can be updated based on the entire set of popular files before each new request. To support these theoretical results, we propose an online coded caching scheme termed coded least-recently sent (LRS) and simulate it for a demand time series derived from the dataset made available by Netflix for the Netflix Prize. For this time series, we show that the proposed coded LRS algorithm significantly outperforms the popular least-recently used (LRU) caching algorithm.

cs.IT↗