arXiv subjects

George Atia

Publications and source records attributed to George Atia.

35 records · Page 2Linked to original sources

arXiv2018

A Game-Theoretic Framework for the Virtual Machines Migration Timing Problem

In a multi-tenant cloud, a number of Virtual Machines (VMs) are collocated on the same physical machine to optimize performance, power consumption and maximize profit. This, however, increases the risk of a malicious VM performing side-channel attacks and leaking sensitive information from neighboring VMs. To this end, this paper develops and analyzes a game-theoretic framework for the VM migration timing problem in which the cloud provider decides \emph{when} to migrate a VM to a different physical machine to reduce the risk of being compromised by a collocated malicious VM. The adversary decides the rate at which she launches new VMs to collocate with the victim VMs. Our formulation captures a data leakage model in which the cost incurred by the cloud provider depends on the duration of collocation with malicious VMs. It also captures costs incurred by the adversary in launching new VMs and by the defender in migrating VMs. We establish sufficient conditions for the existence of Nash equilibria for general cost functions, as well as for specific instantiations, and characterize the best response for both players. Furthermore, we extend our model to characterize its impact on the attacker's payoff when the cloud utilizes intrusion detection systems that detect side-channel attacks. Our theoretical findings are corroborated with extensive numerical results in various settings.

cs.CR↗

arXiv2017

Data Dropout in Arbitrary Basis for Deep Network Regularization

An important problem in training deep networks with high capacity is to ensure that the trained network works well when presented with new inputs outside the training dataset. Dropout is an effective regularization technique to boost the network generalization in which a random subset of the elements of the given data and the extracted features are set to zero during the training process. In this paper, a new randomized regularization technique in which we withhold a random part of the data without necessarily turning off the neurons/data-elements is proposed. In the proposed method, of which the conventional dropout is shown to be a special case, random data dropout is performed in an arbitrary basis, hence the designation Generalized Dropout. We also present a framework whereby the proposed technique can be applied efficiently to convolutional neural networks. The presented numerical experiments demonstrate that the proposed technique yields notable performance gain. Generalized Dropout provides new insight into the idea of dropout, shows that we can achieve different performance gains by using different bases matrices, and opens up a new research question as of how to choose optimal bases matrices that achieve maximal performance gain.

cs.CV↗

arXiv2017

Subspace Clustering via Optimal Direction Search

This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in the span of the data that has minimum projection on the other data points and non-vanishing projection on d. The obtained directions are subsequently leveraged to identify a neighborhood set for each data point. An alternating direction method of multipliers framework is provided to efficiently solve for the optimal directions. The proposed method is shown to notably outperform the existing subspace clustering methods, particularly for unwieldy scenarios involving high levels of noise and close subspaces, and yields the state-of-the-art results for the problem of face clustering using subspace segmentation.

cs.CV↗

arXiv2017

Innovation Pursuit: A New Approach to Subspace Clustering

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using a new geometrical idea whereby subspaces are identified based on their relative novelties. We present two frameworks in which the idea of innovation pursuit is used to distinguish the subspaces. Underlying the first framework is an iterative method that finds the subspaces consecutively by solving a series of simple linear optimization problems, each searching for a direction of innovation in the span of the data potentially orthogonal to all subspaces except for the one to be identified in one step of the algorithm. A detailed mathematical analysis is provided establishing sufficient conditions for iPursuit to correctly cluster the data. The proposed approach can provably yield exact clustering even when the subspaces have significant intersections. It is shown that the complexity of the iterative approach scales only linearly in the number of data points and subspaces, and quadratically in the dimension of the subspaces. The second framework integrates iPursuit with spectral clustering to yield a new variant of spectral-clustering-based algorithms. The numerical simulations with both real and synthetic data demonstrate that iPursuit can often outperform the state-of-the-art subspace clustering algorithms, more so for subspaces with significant intersections, and that it significantly improves the state-of-the-art result for subspace-segmentation-based face clustering.

cs.CV↗

arXiv2017

Coherence Pursuit: Fast, Simple, and Robust Principal Component Analysis

This paper presents a remarkably simple, yet powerful, algorithm termed Coherence Pursuit (CoP) to robust Principal Component Analysis (PCA). As inliers lie in a low dimensional subspace and are mostly correlated, an inlier is likely to have strong mutual coherence with a large number of data points. By contrast, outliers either do not admit low dimensional structures or form small clusters. In either case, an outlier is unlikely to bear strong resemblance to a large number of data points. Given that, CoP sets an outlier apart from an inlier by comparing their coherence with the rest of the data points. The mutual coherences are computed by forming the Gram matrix of the normalized data points. Subsequently, the sought subspace is recovered from the span of the subset of the data points that exhibit strong coherence with the rest of the data. As CoP only involves one simple matrix multiplication, it is significantly faster than the state-of-the-art robust PCA algorithms. We derive analytical performance guarantees for CoP under different models for the distributions of inliers and outliers in both noise-free and noisy settings. CoP is the first robust PCA algorithm that is simultaneously non-iterative, provably robust to both unstructured and structured outliers, and can tolerate a large number of unstructured outliers.

cs.LG↗

arXiv2017

Spatial Random Sampling: A Structure-Preserving Data Sketching Tool

Random column sampling is not guaranteed to yield data sketches that preserve the underlying structures of the data and may not sample sufficiently from less-populated data clusters. Also, adaptive sampling can often provide accurate low rank approximations, yet may fall short of producing descriptive data sketches, especially when the cluster centers are linearly dependent. Motivated by that, this paper introduces a novel randomized column sampling tool dubbed Spatial Random Sampling (SRS), in which data points are sampled based on their proximity to randomly sampled points on the unit sphere. The most compelling feature of SRS is that the corresponding probability of sampling from a given data cluster is proportional to the surface area the cluster occupies on the unit sphere, independently from the size of the cluster population. Although it is fully randomized, SRS is shown to provide descriptive and balanced data representations. The proposed idea addresses a pressing need in data science and holds potential to inspire many novel approaches for analysis of big data.

cs.LG↗

arXiv2017

High Dimensional Low Rank plus Sparse Matrix Decomposition

This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems with complexity that scales with the dimension of the data, which limits their scalability. Furthermore, existing randomized approaches mostly rely on uniform random sampling, which is quite inefficient for many real world data matrices that exhibit additional structures (e.g. clustering). In this paper, a scalable subspace-pursuit approach that transforms the decomposition problem to a subspace learning problem is proposed. The decomposition is carried out using a small data sketch formed from sampled columns/rows. Even when the data is sampled uniformly at random, it is shown that the sufficient number of sampled columns/rows is roughly O(rμ), where μis the coherency parameter and r the rank of the low rank component. In addition, adaptive sampling algorithms are proposed to address the problem of column/row sampling from structured data. We provide an analysis of the proposed method with adaptive sampling and show that adaptive sampling makes the required number of sampled columns/rows invariant to the distribution of the data. The proposed approach is amenable to online implementation and an online scheme is proposed.

math.NA↗

arXiv2017

Low Rank Matrix Recovery with Simultaneous Presence of Outliers and Sparse Corruption

We study a data model in which the data matrix D can be expressed as D = L + S + C, where L is a low rank matrix, S an element-wise sparse matrix and C a matrix whose non-zero columns are outlying data points. To date, robust PCA algorithms have solely considered models with either S or C, but not both. As such, existing algorithms cannot account for simultaneous element-wise and column-wise corruptions. In this paper, a new robust PCA algorithm that is robust to simultaneous types of corruption is proposed. Our approach hinges on the sparse approximation of a sparsely corrupted column so that the sparse expansion of a column with respect to the other data points is used to distinguish a sparsely corrupted inlier column from an outlying data point. We also develop a randomized design which provides a scalable implementation of the proposed approach. The core idea of sparse approximation is analyzed analytically where we show that the underlying ell_1-norm minimization can obtain the representation of an inlier in presence of sparse corruptions.

stat.ML↗

arXiv2016

Robust and Scalable Column/Row Sampling from Corrupted Big Data

Conventional sampling techniques fall short of drawing descriptive sketches of the data when the data is grossly corrupted as such corruptions break the low rank structure required for them to perform satisfactorily. In this paper, we present new sampling algorithms which can locate the informative columns in presence of severe data corruptions. In addition, we develop new scalable randomized designs of the proposed algorithms. The proposed approach is simultaneously robust to sparse corruption and outliers and substantially outperforms the state-of-the-art robust sampling algorithms as demonstrated by experiments conducted using both real and synthetic data.

cs.LG↗

arXiv2016

Sparsity-Based Error Detection in DC Power Flow State Estimation

This paper presents a new approach for identifying the measurement error in the DC power flow state estimation problem. The proposed algorithm exploits the singularity of the impedance matrix and the sparsity of the error vector by posing the DC power flow problem as a sparse vector recovery problem that leverages the structure of the power system and uses $l_1$-norm minimization for state estimation. This approach can provably compute the measurement errors exactly, and its performance is robust to the arbitrary magnitudes of the measurement errors. Hence, the proposed approach can detect the noisy elements if the measurements are contaminated with additive white Gaussian noise plus sparse noise with large magnitude. The effectiveness of the proposed sparsity-based decomposition-DC power flow approach is demonstrated on the IEEE 118-bus and 300-bus test systems.

cs.IT↗

arXiv2016

Sparse Signal Processing with Linear and Nonlinear Observations: A Unified Shannon-Theoretic Approach

We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features. In general, sparse signal processing problems can be characterized in terms of the following Markovian property. We are given a set of $N$ variables $X_1,X_2,\ldots,X_N$, and there is an unknown subset of variables $S \subset \{1,\ldots,N\}$ that are relevant for predicting outcomes $Y$. More specifically, when $Y$ is conditioned on $\{X_n\}_{n\in S}$ it is conditionally independent of the other variables, $\{X_n\}_{n \not \in S}$. Our goal is to identify the set $S$ from samples of the variables $X$ and the associated outcomes $Y$. We characterize this problem as a version of the noisy channel coding problem. Using asymptotic information theoretic analyses, we establish mutual information formulas that provide sufficient and necessary conditions on the number of samples required to successfully recover the salient variables. These mutual information expressions unify conditions for both linear and nonlinear observations. We then compute sample complexity bounds for the aforementioned models, based on the mutual information expressions in order to demonstrate the applicability and flexibility of our results in general sparse signal processing models.

cs.IT↗

arXiv2016

A New Statistical Model of Electroencephalogram Noise Spectra for Real-time Brain-Computer Interfaces

$Objective$: A characteristic of neurological signal processing is high levels of noise from sub-cellular ion channels up to whole-brain processes. In this paper, we propose a new model of electroencephalogram (EEG) background periodograms, based on a family of functions which we call generalized van der Ziel--McWhorter (GVZM) power spectral densities (PSDs). To the best of our knowledge, the GVZM PSD function is the only EEG noise model which has relatively few parameters, matches recorded EEG PSD's with high accuracy from 0 Hz to over 30 Hz, and has approximately $1/f^θ$ behavior in the mid-frequencies without infinities. $Methods$: We validate this model using three approaches. First, we show how GVZM PSDs can arise in population of ion channels in maximum entropy equilibrium. Second, we present a class of mixed autoregressive models, which simulate brain background noise and whose periodograms are asymptotic to the GVZM PSD. Third, we present two real-time estimation algorithms for steady-state visual evoked potential (SSVEP) frequencies, and analyze their performance statistically. $Results$: In pairwise comparisons, the GVZM-based algorithms showed statistically significant accuracy improvement over two well-known and widely-used SSVEP estimators. $Conclusion$: The GVZM noise model can be a useful and reliable technique for EEG signal processing. $Significance$: Understanding EEG noise is essential for EEG-based neurology and applications such as real-time brain-computer interfaces (BCIs), which must make accurate control decisions from very short data epochs. The GVZM approach represents a successful new paradigm for understanding and managing this neurological noise.

q-bio.NC↗

arXiv2016

Randomized Robust Subspace Recovery for High Dimensional Data Matrices

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low dimensional embedding, while in the other, sketching is based on random column and row sampling. Both designs are shown to bring about substantial savings in complexity and memory requirements for robust subspace learning over conventional approaches that use the full scale data. A characterization of the sample and computational complexity of both designs is derived in the context of two distinct outlier models, namely, sparse and independent outlier models. The proposed randomized approach can provably recover the correct subspace with computational and sample complexity that are almost independent of the size of the data. The results of the mathematical analysis are confirmed through numerical simulations using both synthetic and real data.

stat.ML↗

arXiv2014

A Subspace Method for Array Covariance Matrix Estimation

This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is typically much smaller than the dimension of the full space. Based on this idea, a subspace based covariance matrix estimator is proposed. The estimator is obtained as a solution to a semi-definite convex optimization problem. While the optimization problem has no closed-form solution, a nearly optimal closed-form solution is proposed making it easy to implement. In comparison to the conventional approaches, the proposed method yields higher estimation accuracy because it eliminates the estimation error which does not lie in the subspace of the true covariance matrices. The numerical examples indicate that the proposed covariance matrix estimator can significantly improve the estimation quality of the covariance matrix.

math.NA↗

arXiv2014

Change Detection with Compressive Measurements

Quickest change point detection is concerned with the detection of statistical change(s) in sequences while minimizing the detection delay subject to false alarm constraints. In this paper, the problem of change point detection is studied when the decision maker only has access to compressive measurements. First, an expression for the average detection delay of Shiryaev's procedure with compressive measurements is derived in the asymptotic regime where the probability of false alarm goes to zero. Second, the dependence of the delay on the compression ratio and the signal to noise ratio is explicitly quantified. The ratio of delays with and without compression is studied under various sensing matrix constructions, including Gaussian ensembles and random projections. For a target ratio of the delays after and before compression, a sufficient condition on the number of measurements required to meet this objective with prespecified probability is derived.

cs.IT↗

arXiv2013

Controlled Sensing for Multihypothesis Testing

The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error probability corresponds to the maximum Chernoff information over the choice of controls, and a pure stationary open-loop control policy is asymptotically optimal within the larger class of all causal control policies. For multihypothesis testing in the fixed sample size setting, lower and upper bounds on the optimal error exponent are derived. It is also shown through an example with three hypotheses that the optimal causal control policy can be strictly better than the optimal open-loop control policy. In the sequential setting, a test based on earlier work by Chernoff for binary hypothesis testing, is shown to be first-order asymptotically optimal for multihypothesis testing in a strong sense, using the notion of decision making risk in place of the overall probability of error. Another test is also designed to meet hard risk constrains while retaining asymptotic optimality. The role of past information and randomization in designing optimal control policies is discussed.

cs.IT↗

arXiv2012

Stuck in Traffic (SiT) Attacks: A Framework for Identifying Stealthy Attacks that Cause Traffic Congestion

Recent advances in wireless technologies have enabled many new applications in Intelligent Transportation Systems (ITS) such as collision avoidance, cooperative driving, congestion avoidance, and traffic optimization. Due to the vulnerable nature of wireless communication against interference and intentional jamming, ITS face new challenges to ensure the reliability and the safety of the overall system. In this paper, we expose a class of stealthy attacks -- Stuck in Traffic (SiT) attacks -- that aim to cause congestion by exploiting how drivers make decisions based on smart traffic signs. An attacker mounting a SiT attack solves a Markov Decision Process problem to find optimal/suboptimal attack policies in which he/she interferes with a well-chosen subset of signals that are based on the state of the system. We apply Approximate Policy Iteration (API) algorithms to derive potent attack policies. We evaluate their performance on a number of systems and compare them to other attack policies including random, myopic and DoS attack policies. The generated policies, albeit suboptimal, are shown to significantly outperform other attack policies as they maximize the expected cumulative reward from the standpoint of the attacker.

cs.NI↗