George Atia

Yue Wang, Alvaro Velasquez, George Atia et al.

In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on discounted MDPs, robust average-reward MDPs remain largely unexplored. In this paper, we focus on robust average-reward MDPs, where the goal is to find a policy that optimizes the worst-case average reward over an uncertainty set. We first take an approach that approximates average-reward MDPs using discounted MDPs. We prove that the robust discounted value function converges to the robust average-reward as the discount factor $γ$ goes to $1$, and moreover, when $γ$ is large, any optimal policy of the robust discounted MDP is also an optimal policy of the robust average-reward. We further design a robust dynamic programming approach, and theoretically characterize its convergence to the optimum. Then, we investigate robust average-reward MDPs directly without using discounted MDPs as an intermediate step. We derive the robust Bellman equation for robust average-reward MDPs, prove that the optimal policy can be derived from its solution, and further design a robust relative value iteration algorithm that provably finds its solution, or equivalently, the optimal robust policy.

Ismail Alkhouri, Sumit Jha, Andre Beckus et al.

Protein folding neural networks (PFNNs) such as AlphaFold predict remarkably accurate structures of proteins compared to other approaches. However, the robustness of such networks has heretofore not been explored. This is particularly relevant given the broad social implications of such technologies and the fact that biologically small perturbations in the protein sequence do not generally lead to drastic changes in the protein structure. In this paper, we demonstrate that AlphaFold does not exhibit such robustness despite its high accuracy. This raises the challenge of detecting and quantifying the extent to which these predicted protein structures can be trusted. To measure the robustness of the predicted structures, we utilize (i) the root-mean-square deviation (RMSD) and (ii) the Global Distance Test (GDT) similarity measure between the predicted structure of the original sequence and the structure of its adversarially perturbed version. We prove that the problem of minimally perturbing protein sequences to fool protein folding neural networks is NP-complete. Based on the well-established BLOSUM62 sequence alignment scoring matrix, we generate adversarial protein sequences and show that the RMSD between the predicted protein structure and the structure of the original sequence are very large when the adversarial changes are bounded by (i) 20 units in the BLOSUM62 distance, and (ii) five residues (out of hundreds or thousands of residues) in the given protein sequence. In our experimental evaluation, we consider 111 COVID-19 proteins in the Universal Protein resource (UniProt), a central resource for protein data managed by the European Bioinformatics Institute, Swiss Institute of Bioinformatics, and the US Protein Information Resource. These result in an overall GDT similarity test score average of around 34%, demonstrating a substantial drop in the performance of AlphaFold.

Akram S. Awad, George K. Atia

Domain Adaptation (DA) has recently received significant attention due to its potential to adapt a learning model across source and target domains with mismatched distributions. Since DA methods rely exclusively on the given source and target domain samples, they generally yield models that are vulnerable to noise and unable to adapt to unseen samples from the target domain, which calls for DA methods that guarantee the robustness and generalization of the learned models. In this paper, we propose DRDA, a distributionally robust domain adaptation method. DRDA leverages a distributionally robust optimization (DRO) framework to learn a robust decision function that minimizes the worst-case target domain risk and generalizes to any sample from the target domain by transferring knowledge from a given labeled source domain sample. We utilize the Maximum Mean Discrepancy (MMD) metric to construct an ambiguity set of distributions that provably contains the source and target domain distributions with high probability. Hence, the risk is shown to upper bound the out-of-sample target domain loss. Our experimental results demonstrate that our formulation outperforms existing robust learning approaches.

Suraj Singireddy, Precious Nwaorgu, Andre Beckus et al.

Reinforcement learning (RL) is a powerful tool for finding optimal policies in sequential decision processes. However, deep RL methods have two weaknesses: collecting the amount of agent experience required for practical RL problems is prohibitively expensive, and the learned policies exhibit poor generalization on tasks outside the training data distribution. To mitigate these issues, we introduce automaton distillation, a form of neuro-symbolic transfer learning in which Q-value estimates from a teacher are distilled into a low-dimensional representation in the form of an automaton. We then propose methods for generating Q-value estimates where symbolic information is extracted from a teacher's Deep Q-Network (DQN). The resulting Q-value estimates are used to bootstrap learning in the target discrete and continuous environment via a modified DQN and Twin-Delayed Deep Deterministic (TD3) loss function, respectively. We demonstrate that automaton distillation decreases the time required to find optimal policies for various decision tasks in new environments, even in a target environment different in structure from the source environment.

Ismail R. Alkhouri, George K. Atia, Alvaro Velasquez

The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging datasets of the combinatorial structures of interest drawn from some distribution of problem instances. Reinforcement learning has also been employed to find such structures. In this paper, we propose a radically different approach in that no data is required for training the neural networks that produce the solution. In particular, we reduce the combinatorial optimization problem to a neural network and employ a dataless training scheme to refine the parameters of the network such that those parameters yield the structure of interest. We consider the combinatorial optimization problems of finding maximum independent sets and maximum cliques in a graph. In principle, since these problems belong to the NP-hard complexity class, our proposed approach can be used to solve any other NP-hard problem. Additionally, we propose a universal graph reduction procedure to handle large scale graphs. The reduction exploits community detection for graph partitioning and is applicable to any graph type and/or density. Experimental evaluation on both synthetic graphs and real-world benchmarks demonstrates that our method performs on par with or outperforms state-of-the-art heuristic, reinforcement learning, and machine learning based methods without requiring any data.

Mudit Gaur, Prashant Trivedi, Shuchin Aeron et al.

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing empirical success, the theoretical understanding of flow matching remains limited, particularly in terms of sample complexity results. In this work, we provide the first analysis of the sample complexity for flow-matching based generative models without assuming access to the empirical risk minimizer (ERM) of the loss function for estimating the velocity field. Under standard assumptions on the loss function for velocity field estimation and boundedness of the data distribution, we show that a sufficiently expressive neural network can learn a velocity field such that with $\mathcal{O}(ε^{-4})$ samples, such that the Wasserstein-2 distance between the learned and the true distribution is less than $\mathcal{O}(ε)$. The key technical idea is to decompose the velocity field estimation error into neural-network approximation error, statistical error due to the finite sample size, and optimization error due to the finite number of optimization steps for estimating the velocity field. Each of these terms are then handled via techniques that may be of independent interest.

Debamita Ghosh, George K. Atia, Yue Wang

The deployment of reinforcement learning (RL) agents in real-world applications is often hindered by performance degradation caused by mismatches between training and deployment environments. Distributionally robust RL (DR-RL) addresses this issue by optimizing worst-case performance over an uncertainty set of transition dynamics. However, existing work typically relies on substantial prior knowledge-such as access to a generative model or a large offline dataset-and largely focuses on tabular methods that do not scale to complex domains. We overcome these limitations by proposing an online DR-RL algorithm with general function approximation that learns an optimal robust policy purely through interaction with the environment, without requiring prior models or offline data, enabling deployment in high-dimensional tasks. We further provide a theoretical analysis establishing a near-optimal sublinear regret bound under a total variation uncertainty set, demonstrating the sample efficiency and effectiveness of our method.

Prashant Trivedi, Souradip Chakraborty, Avinash Reddy et al.

The alignment of large language models (LLMs) with human values is critical as these models become increasingly integrated into various societal and decision-making processes. Traditional methods, such as reinforcement learning from human feedback (RLHF), achieve alignment by fine-tuning model parameters, but these approaches are often computationally expensive and impractical when models are frozen or inaccessible for parameter modification. In contrast, prompt optimization is a viable alternative to RLHF for LLM alignment. While the existing literature has shown empirical promise of prompt optimization, its theoretical underpinning remains under-explored. We address this gap by formulating prompt optimization as an optimization problem and try to provide theoretical insights into the optimality of such a framework. To analyze the performance of the prompt optimization, we study theoretical suboptimality bounds and provide insights in terms of how prompt optimization depends upon the given prompter and target model. We also provide empirical validation through experiments on various datasets, demonstrating that prompt optimization can effectively align LLMs, even when parameter fine-tuning is not feasible.

Debamita Ghosh, George K. Atia, Yue Wang

We investigate reinforcement learning (RL) in the presence of distributional mismatch between training and deployment, where policies trained in simulators often underperform in practice due to mismatches between training and deployment conditions, and thereby reliable guarantees on real-world performance are essential. Distributionally robust RL addresses this issue by optimizing worst-case performance over an uncertainty set of environments and providing an optimized lower bound on deployment performance. However, existing studies typically assume access to either a generative model or offline datasets with broad coverage of the deployment environment-assumptions that limit their practicality in unknown environments without prior knowledge. In this work, we study a more practical and challenging setting: online distributionally robust RL, where the agent interacts only with a single unknown training environment while seeking policies that are robust with respect to an uncertainty set around this nominal model. We consider general $f$-divergence-based ambiguity sets, including $χ^2$ and KL divergence balls, and design a computationally efficient algorithm that achieves sublinear regret for the robust control objective under minimal assumptions, without requiring generative or offline data access. Moreover, we establish a corresponding minimax lower bound on the regret of any online algorithm, demonstrating the near-optimality of our method. Experiments across diverse environments with model misspecification show that our approach consistently improves worst-case performance and aligns with the theoretical guarantees.

Zachary Roch, Chi Zhang, George Atia et al.

Robust reinforcement learning (RL) under the average-reward criterion is essential for long-term decision-making, particularly when the environment may differ from its specification. However, a significant gap exists in understanding the finite-sample complexity of these methods, as most existing work provides only asymptotic guarantees. This limitation hinders their principled understanding and practical deployment, especially in data-limited scenarios. We close this gap by proposing \textbf{Robust Halpern Iteration (RHI)}, a new algorithm designed for robust Markov Decision Processes (MDPs) with transition uncertainty characterized by $\ell_p$-norm and contamination models. Our approach offers three key advantages over previous methods: (1). Weaker Structural Assumptions: RHI only requires the underlying robust MDP to be communicating, a less restrictive condition than the commonly assumed ergodicity or irreducibility; (2). No Prior Knowledge: Our algorithm operates without requiring any prior knowledge of the robust MDP; (3). State-of-the-Art Sample Complexity: To learn an $ε$-optimal robust policy, RHI achieves a sample complexity of $\tilde{\mathcal O}\left(\frac{SA\mathcal H^{2}}{ε^{2}}\right)$, where $S$ and $A$ denote the numbers of states and actions, and $\mathcal H$ is the robust optimal bias span. This result represents the tightest known bound. Our work hence provides essential theoretical understanding of sample efficiency of robust average reward RL.

Chi Zhang, Ziying Jia, George K. Atia et al.

Transfer reinforcement learning aims to derive a near-optimal policy for a target environment with limited data by leveraging abundant data from related source domains. However, it faces two key challenges: the lack of performance guarantees for the transferred policy, which can lead to undesired actions, and the risk of negative transfer when multiple source domains are involved. We propose a novel framework based on the pessimism principle, which constructs and optimizes a conservative estimation of the target domain's performance. Our framework effectively addresses the two challenges by providing an optimized lower bound on target performance, ensuring safe and reliable decisions, and by exhibiting monotonic improvement with respect to the quality of the source domains, thereby avoiding negative transfer. We construct two types of conservative estimations, rigorously characterize their effectiveness, and develop efficient distributed algorithms with convergence guarantees. Our framework provides a theoretically sound and practically robust solution for transfer learning in reinforcement learning.

Akram S. Awad, Shihab Ahmed, Yue Wang et al.

Robust Markov Decision Processes (MDPs) address environmental shift through distributionally robust optimization (DRO) by finding an optimal worst-case policy within an uncertainty set of transition kernels. However, standard DRO approaches require enlarging the uncertainty set under large shifts, which leads to overly conservative and pessimistic policies. In this paper, we propose a framework for transfer under environment shift that derives a robust target-domain policy via estimate-centered uncertainty sets, constructed through constrained estimation that integrates limited target samples with side information about the source-target dynamics. The side information includes bounds on feature moments, distributional distances, and density ratios, yielding improved kernel estimates and tighter uncertainty sets. The side information includes bounds on feature moments, distributional distances, and density ratios, yielding improved kernel estimates and tighter uncertainty sets. Error bounds and convergence results are established for both robust and non-robust value functions. Moreover, we provide a finite-sample guarantee on the learned robust policy and analyze the robust sub-optimality gap. Under mild low-dimensional structure on the transition model, the side information reduces this gap and improves sample efficiency. We assess the performance of our approach across OpenAI Gym environments and classic control problems, consistently demonstrating superior target-domain performance over state-of-the-art robust and non-robust baselines.

Mahyar Alinejad, Alvaro Velasquez, Yue Wang et al.

Reinforcement Learning (RL) in environments with complex, history-dependent reward structures poses significant challenges for traditional methods. In this work, we introduce a novel approach that leverages automaton-based feedback to guide the learning process, replacing explicit reward functions with preferences derived from a deterministic finite automaton (DFA). Unlike conventional approaches that use automata for direct reward specification, our method employs the structure of the DFA to generate preferences over trajectories that are used to learn a reward function, eliminating the need for manual reward engineering. Our framework introduces a static approach that uses the learned reward function directly for policy optimization and a dynamic approach that involves continuous refining of the reward function and policy through iterative updates until convergence. Our experiments in both discrete and continuous environments demonstrate that our approach enables the RL agent to learn effective policies for tasks with temporal dependencies, outperforming traditional reward engineering and automaton-based baselines such as reward machines and LTL-guided methods. Our results highlight the advantages of automaton-based preferences in handling non-Markovian rewards, offering a scalable, efficient, and human-independent alternative to traditional reward modeling. We also provide a convergence guarantee showing that under standard assumptions our automaton-guided preference-based framework learns a policy that is near-optimal with respect to the true non-Markovian objective.

Akram Heidarizadeh, Connor Hatfield, Lorenzo Lazzarotto et al.

Traditional adversarial attacks typically aim to alter the predicted labels of input images by generating perturbations that are imperceptible to the human eye. However, these approaches often lack explainability. Moreover, most existing work on adversarial attacks focuses on single-stage classifiers, but multi-stage classifiers are largely unexplored. In this paper, we introduce instance-based adversarial attacks for multi-stage classifiers, leveraging Layer-wise Relevance Propagation (LRP), which assigns relevance scores to pixels based on their influence on classification outcomes. Our approach generates explainable adversarial perturbations by utilizing LRP to identify and target key features critical for both coarse and fine-grained classifications. Unlike conventional attacks, our method not only induces misclassification but also enhances the interpretability of the model's behavior across classification stages, as demonstrated by experimental results.

Noah Topper, Alvaro Velasquez, George Atia

Inverse reinforcement learning (IRL) is the problem of inferring a reward function from expert behavior. There are several approaches to IRL, but most are designed to learn a Markovian reward. However, a reward function might be non-Markovian, depending on more than just the current state, such as a reward machine (RM). Although there has been recent work on inferring RMs, it assumes access to the reward signal, absent in IRL. We propose a Bayesian IRL (BIRL) framework for inferring RMs directly from expert behavior, requiring significant changes to the standard framework. We define a new reward space, adapt the expert demonstration to include history, show how to compute the reward posterior, and propose a novel modification to simulated annealing to maximize this posterior. We demonstrate that our method performs well when optimizing according to its inferred reward and compares favorably to an existing method that learns exclusively binary non-Markovian rewards.

Yue Wang, Alvaro Velasquez, George Atia et al.

Robust Markov decision processes (MDPs) address the challenge of model uncertainty by optimizing the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on the robust average-reward MDPs under the model-free setting. We first theoretically characterize the structure of solutions to the robust average-reward Bellman equation, which is essential for our later convergence analysis. We then design two model-free algorithms, robust relative value iteration (RVI) TD and robust RVI Q-learning, and theoretically prove their convergence to the optimal solution. We provide several widely used uncertainty sets as examples, including those defined by the contamination model, total variation, Chi-squared divergence, Kullback-Leibler (KL) divergence and Wasserstein distance.

Yicong He, George K. Atia

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is hindered by prevalent large data sizes, missing entries, and corruption with outliers. In this work, we propose a scalable and robust TR decomposition algorithm capable of handling large-scale tensor data with missing entries and gross corruptions. We first develop a novel auto-weighted steepest descent method that can adaptively fill the missing entries and identify the outliers during the decomposition process. Further, taking advantage of the tensor ring model, we develop a novel fast Gram matrix computation (FGMC) approach and a randomized subtensor sketching (RStS) strategy which yield significant reduction in storage and computational complexity. Experimental results demonstrate that the proposed method outperforms existing TR decomposition methods in the presence of outliers, and runs significantly faster than existing robust tensor completion algorithms.

Ismail R. Alkhouri, Alvaro Velasquez, George K. Atia

The design of additive imperceptible perturbations to the inputs of deep classifiers to maximize their misclassification rates is a central focus of adversarial machine learning. An alternative approach is to synthesize adversarial examples from scratch using GAN-like structures, albeit with the use of large amounts of training data. By contrast, this paper considers one-shot synthesis of adversarial examples; the inputs are synthesized from scratch to induce arbitrary soft predictions at the output of pre-trained models, while simultaneously maintaining high similarity to specified inputs. To this end, we present a problem that encodes objectives on the distance between the desired and output distributions of the trained model and the similarity between such inputs and the synthesized examples. We prove that the formulated problem is NP-complete. Then, we advance a generative approach to the solution in which the adversarial examples are obtained as the output of a generative network whose parameters are iteratively updated by optimizing surrogate loss functions for the dual-objective. We demonstrate the generality and versatility of the framework and approach proposed through applications to the design of targeted adversarial attacks, generation of decision boundary samples, and synthesis of low confidence classification inputs. The approach is further extended to an ensemble of models with different soft output specifications. The experimental results verify that the targeted and confidence reduction attack methods developed perform on par with state-of-the-art algorithms.

Taylor Dohmen, Noah Topper, George Atia et al.

The success of reinforcement learning in typical settings is predicated on Markovian assumptions on the reward signal by which an agent learns optimal policies. In recent years, the use of reward machines has relaxed this assumption by enabling a structured representation of non-Markovian rewards. In particular, such representations can be used to augment the state space of the underlying decision process, thereby facilitating non-Markovian reinforcement learning. However, these reward machines cannot capture the semantics of stochastic reward signals. In this paper, we make progress on this front by introducing probabilistic reward machines (PRMs) as a representation of non-Markovian stochastic rewards. We present an algorithm to learn PRMs from the underlying decision process and prove results around its correctness and convergence.

Yicong He, George K. Atia

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Data corruption due to prevailing outliers poses major challenges to traditional tensor completion algorithms, which catalyzed the development of robust algorithms that alleviate the effect of outliers. However, existing robust methods largely presume that the corruption is sparse, which may not hold in practice. In this paper, we develop a two-stage robust tensor completion approach to deal with tensor completion of visual data with a large amount of gross corruption. A novel coarse-to-fine framework is proposed which uses a global coarse completion result to guide a local patch refinement process. To efficiently mitigate the effect of a large number of outliers on tensor recovery, we develop a new M-estimator-based robust tensor ring recovery method which can adaptively identify the outliers and alleviate their negative effect in the optimization. The experimental results demonstrate the superior performance of the proposed approach over state-of-the-art robust algorithms for tensor completion.

Alvaro Velasquez, Ismail Alkhouri, Andre Beckus et al.

Given a Markov decision process (MDP) and a linear-time ($ω$-regular or LTL) specification, the controller synthesis problem aims to compute the optimal policy that satisfies the specification. More recently, problems that reason over the asymptotic behavior of systems have been proposed through the lens of steady-state planning. This entails finding a control policy for an MDP such that the Markov chain induced by the solution policy satisfies a given set of constraints on its steady-state distribution. This paper studies a generalization of the controller synthesis problem for a linear-time specification under steady-state constraints on the asymptotic behavior. We present an algorithm to find a deterministic policy satisfying $ω$-regular and steady-state constraints by characterizing the solutions as an integer linear program, and experimentally evaluate our approach.

Yicong He, George K. Atia

Tensor completion aims to recover the missing entries of a partially observed tensor by exploiting its low-rank structure, and has been applied to visual data recovery. In applications where the data arrives sequentially such as streaming video completion, the missing entries of the tensor need to be dynamically recovered in a streaming fashion. Traditional streaming tensor completion algorithms treat the entire visual data as a tensor, which may not work satisfactorily when there is a big change in the tensor subspace along the temporal dimension, such as due to strong motion across the video frames. In this paper, we develop a novel patch tracking-based streaming tensor ring completion framework for visual data recovery. Given a newly incoming frame, small patches are tracked from the previous frame. Meanwhile, for each tracked patch, a patch tensor is constructed by stacking similar patches from the new frame. Patch tensors are then completed using a streaming tensor ring completion algorithm, and the incoming frame is recovered using the completed patch tensors. We propose a new patch tracking strategy that can accurately and efficiently track the patches with missing data. Further, a new streaming tensor ring completion algorithm is proposed which can efficiently and accurately update the latent core tensors and complete the missing entries of the patch tensors. Extensive experimental results demonstrate the superior performance of the proposed algorithms compared with both batch and streaming state-of-the-art tensor completion methods.

George K. Atia, Andre Beckus, Ismail Alkhouri et al.

The planning domain has experienced increased interest in the formal synthesis of decision-making policies. This formal synthesis typically entails finding a policy which satisfies formal specifications in the form of some well-defined logic. While many such logics have been proposed with varying degrees of expressiveness and complexity in their capacity to capture desirable agent behavior, their value is limited when deriving decision-making policies which satisfy certain types of asymptotic behavior in general system models. In particular, we are interested in specifying constraints on the steady-state behavior of an agent, which captures the proportion of time an agent spends in each state as it interacts for an indefinite period of time with its environment. This is sometimes called the average or expected behavior of the agent and the associated planning problem is faced with significant challenges unless strong restrictions are imposed on the underlying model in terms of the connectivity of its graph structure. In this paper, we explore this steady-state planning problem that consists of deriving a decision-making policy for an agent such that constraints on its steady-state behavior are satisfied. A linear programming solution for the general case of multichain Markov Decision Processes (MDPs) is proposed and we prove that optimal solutions to the proposed programs yield stationary policies with rigorous guarantees of behavior.

Yicong He, George K. Atia

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization of the inherent low-rank structure of a tensor. While some low-tubal-rank tensor completion algorithms with favorable performance have been recently proposed, these algorithms utilize second-order statistics to measure the error residual, which may not work well when the observed entries contain large outliers. In this paper, we propose a new objective function for low-tubal-rank tensor completion, which uses correntropy as the error measure to mitigate the effect of the outliers. To efficiently optimize the proposed objective, we leverage a half-quadratic minimization technique whereby the optimization is transformed to a weighted low-tubal-rank tensor factorization problem. Subsequently, we propose two simple and efficient algorithms to obtain the solution and provide their convergence and complexity analysis. Numerical results using both synthetic and real data demonstrate the robust and superior performance of the proposed algorithms.

Andre Beckus, George K. Atia

We consider an approach for community detection in time-varying networks. At its core, this approach maintains a small sketch graph to capture the essential community structure found in each snapshot of the full network. We demonstrate how the sketch can be used to explicitly identify six key community events which typically occur during network evolution: growth, shrinkage, merging, splitting, birth and death. Based on these detection techniques, we formulate a community detection algorithm which can process a network concurrently exhibiting all processes. One advantage afforded by the sketch-based algorithm is the efficient handling of large networks. Whereas detecting events in the full graph may be computationally expensive, the small size of the sketch allows changes to be quickly assessed. A second advantage occurs in networks containing clusters of disproportionate size. The sketch is constructed such that there is equal representation of each cluster, thus reducing the possibility that the small clusters are lost in the estimate. We present a new standardized benchmark based on the stochastic block model which models the addition and deletion of nodes, as well as the birth and death of communities. When coupled with existing benchmarks, this new benchmark provides a comprehensive suite of tests encompassing all six community events. We provide analysis and a set of numerical results demonstrating the advantages of our approach both in run time and in the handling of small clusters.

Mahlagha Sedghi, George Atia, Michael Georgiopoulos

The problem of representative selection amounts to sampling few informative exemplars from large datasets. This paper presents MOSAIC, a novel representative selection approach from high-dimensional data that may exhibit non-linear structures. Resting upon a novel quadratic formulation, Our method advances a multi-criteria selection approach that maximizes the global representation power of the sampled subset, ensures diversity, and rejects disruptive information by effectively detecting outliers. Through theoretical analyses we characterize the obtained sketch and reveal that the sampled representatives maximize a well-defined notion of data coverage in a transformed space. In addition, we present a highly scalable randomized implementation of the proposed algorithm shown to bring about substantial speedups. MOSAIC's superiority in achieving the desired characteristics of a representative subset all at once while exhibiting remarkable robustness to various outlier types is demonstrated via extensive experiments conducted on both real and synthetic data with comparisons to state-of-the-art algorithms.

Amir Emad Marvasti, Ehsan Emad Marvasti, George Atia et al.

We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models constructed in our framework assign probabilities to uncertain realizations, leading to Kullback-Leibler Divergence (KLD) as the linear layer. In our model construction, we also arrive at a structure similar to ReLU activation supported with Bayes' theorem. The non-linearities in our framework are normalization layers with ReLU and Sigmoid as element-wise approximations. Additionally, the pooling function is derived as a marginalization of spatial random variables according to the mechanics of the framework. As such, Max Pooling is an approximation to the aforementioned marginalization process. Since our models are comprised of finite state distributions (FSD) as variables and parameters, exact computation of information-theoretic quantities such as entropy and KLD is possible, thereby providing more objective measures to analyze networks. Unlike existing designs that rely on heuristics, the proposed framework restricts subjective interpretations of CNNs and sheds light on the functionality of neural networks from a completely new perspective.

Andre Beckus, Alexandru Tamasan, George K. Atia

We consider the non-line-of-sight (NLOS) imaging of an object using the light reflected off a diffusive wall. The wall scatters incident light such that a lens is no longer useful to form an image. Instead, we exploit the 4D spatial coherence function to reconstruct a 2D projection of the obscured object. The approach is completely passive in the sense that no control over the light illuminating the object is assumed and is compatible with the partially coherent fields ubiquitous in both the indoor and outdoor environments. We formulate a multi-criteria convex optimization problem for reconstruction, which fuses the reflected field's intensity and spatial coherence information at different scales. Our formulation leverages established optics models of light propagation and scattering and exploits the sparsity common to many images in different bases. We also develop an algorithm based on the alternating direction method of multipliers to efficiently solve the convex program proposed. A means for analyzing the null space of the measurement matrices is provided as well as a means for weighting the contribution of individual measurements to the reconstruction. This paper holds promise to advance passive imaging in the challenging NLOS regimes in which the intensity does not necessarily retain distinguishable features and provides a framework for multi-modal information fusion for efficient scene reconstruction.

Mostafa Rahmani, Andre Beckus, Adel Karimian et al.

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is first applied to a sub-matrix of the graph's adjacency matrix associated with a reduced graph sketch constructed using random sampling. Then, the clusters of the full graph are inferred based on the clusters extracted from the sketch using a correlation-based retrieval step. Uniform random node sampling is shown to improve the computational complexity over clustering of the full graph when the cluster sizes are balanced. A new random degree-based node sampling algorithm is presented which significantly improves upon the performance of the clustering algorithm even when clusters are unbalanced. This framework improves the phase transitions for matrix-decomposition-based clustering with regard to computational complexity and minimum cluster size, which are shown to be nearly dimension-free in the low inter-cluster connectivity regime. A third sampling technique is shown to improve balance by randomly sampling nodes based on spatial distribution. We provide analysis and numerical results using a convex clustering algorithm based on matrix completion.

Ahmed H. Anwar, George Atia, Mina Guirguis

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.

Mostafa Rahmani, George Atia

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.

Mostafa Rahmani, George Atia

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.

Mostafa Rahmani, George Atia

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.

Mostafa Rahmani, George Atia

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.

Mostafa Rahmani, George Atia

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.

M. Hadi Amini, Mostafa Rahmani, Kianoosh G. Boroojeni et al.

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.

Mostafa Rahmani, George Atia

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.

Mostafa Rahmani, George Atia

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.

Mostafa Rahmani, George Atia

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.

Cem Aksoylar, George Atia, Venkatesh Saligrama

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.