George Michailidis

Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis

Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially regarding finite time bounds. For this setting, classical results on least-squares estimation of the dynamics parameters are not applicable and therefore new concepts and technical approaches need to be developed to address the issue. Unstable linear systems arise in key real applications in control theory, econometrics, and finance. This study establishes finite time bounds for the identification error of the least-squares estimates for a fairly large class of heavy-tailed noise distributions, and transition matrices of such systems. The results relate the time length (samples) required for estimation to a function of the problem dimension and key characteristics of the true underlying transition matrix and the noise distribution. To establish them, appropriate concentration inequalities for random matrices and for sequences of martingale differences are leveraged.

Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis

Performance of adaptive control policies is assessed through the regret with respect to the optimal regulator, which reflects the increase in the operating cost due to uncertainty about the dynamics parameters. However, available results in the literature do not provide a quantitative characterization of the effect of the unknown parameters on the regret. Further, there are problems regarding the efficient implementation of some of the existing adaptive policies. Finally, results regarding the accuracy with which the system's parameters are identified are scarce and rather incomplete. This study aims to comprehensively address these three issues. First, by introducing a novel decomposition of adaptive policies, we establish a sharp expression for the regret of an arbitrary policy in terms of the deviations from the optimal regulator. Second, we show that adaptive policies based on slight modifications of the Certainty Equivalence scheme are efficient. Specifically, we establish a regret of (nearly) square-root rate for two families of randomized adaptive policies. The presented regret bounds are obtained by using anti-concentration results on the random matrices employed for randomizing the estimates of the unknown parameters. Moreover, we study the minimal additional information on dynamics matrices that using them the regret will become of logarithmic order. Finally, the rates at which the unknown parameters of the system are being identified are presented.

Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis

Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There are many notions of controllability, one of them being structural controllability, which is intimately connected to finding maximum matchings on the underlying network topology. In this work, we study fast, scalable algorithms for finding maximum matchings for a large class of random networks. First, we illustrate that degree distribution random networks are realistic models for real networks in terms of structural controllability. Subsequently, we analyze a popular, fast and practical heuristic due to Karp and Sipser as well as a simplification of it. For both heuristics, we establish asymptotic optimality and provide results concerning the asymptotic size of maximum matchings for an extensive class of random networks.

Parvin Nazari, Ahmad Mousavi, Davoud Ataee Tarzanagh et al.

Bilevel programming has recently received attention in the literature due to its wide range of applications, including reinforcement learning and hyper-parameter optimization. However, it is widely assumed that the underlying bilevel optimization problem is solved either by a single machine or, in the case of multiple machines connected in a star-shaped network, i.e., in a federated learning setting. The latter approach suffers from a high communication cost on the central node (e.g., parameter server). Hence, there is an interest in developing methods that solve bilevel optimization problems in a communication-efficient, decentralized manner. To that end, this paper introduces a penalty function-based decentralized algorithm with theoretical guarantees for this class of optimization problems. Specifically, a distributed alternating gradient-type algorithm for solving consensus bilevel programming over a decentralized network is developed. A key feature of the proposed algorithm is the estimation of the hyper-gradient of the penalty function through decentralized computation of matrix-vector products and a few vector communications. The estimation is integrated into an alternating algorithm for solving the penalized reformulation of the bilevel optimization problem. Under appropriate step sizes and penalty parameters, our theoretical framework ensures non-asymptotic convergence to the optimal solution of the original problem under various convexity conditions. Our theoretical result highlights improvements in the iteration complexity of decentralized bilevel optimization, all while making efficient use of vector communication. Empirical results demonstrate that the proposed method performs well in real-world settings.

Kailash Budhathoki, George Michailidis, Dominik Janzing

Existing methods of explainable AI and interpretable ML cannot explain change in the values of an output variable for a statistical unit in terms of the change in the input values and the change in the "mechanism" (the function transforming input to output). We propose two methods based on counterfactuals for explaining unit-level changes at various input granularities using the concept of Shapley values from game theory. These methods satisfy two key axioms desirable for any unit-level change attribution method. Through simulations, we study the reliability and the scalability of the proposed methods. We get sensible results from a case study on identifying the drivers of the change in the earnings for individuals in the US.

Kevin Ross, Nicholas Bambos, George Michailidis

We consider a generalized processing system having several queues, where the available service rate combinations are fluctuating over time due to reliability and availability variations. The objective is to allocate the available resources, and corresponding service rates, in response to both workload and service capacity considerations, in order to maintain the long term stability of the system. The service configurations are completely arbitrary, including negative service rates which represent forwarding and service-induced cross traffic. We employ a trace-based trajectory asymptotic technique, which requires minimal assumptions about the arrival dynamics of the system. We prove that cone schedules, which leverage the geometry of the queueing dynamics, maximize the system throughput for a broad class of processing systems, even under adversarial arrival processes. We study the impact of fluctuating service availability, where resources are available only some of the time, and the schedule must dynamically respond to the changing available service rates, establishing both the capacity of such systems and the class of schedules which will stabilize the system at full capacity. The rich geometry of the system dynamics leads to important insights for stability, performance and scalability, and substantially generalizes previous findings. The processing system studied here models a broad variety of computer, communication and service networks, including varying channel conditions and cross-traffic in wireless networking, and call centers with fluctuating capacity. The findings have implications for bandwidth and processor allocation in communication networks and workforce scheduling in congested call centers.

Parvin Nazari, Bojian Hou, Davoud Ataee Tarzanagh et al.

Online bilevel optimization (OBO) is a powerful framework for machine learning problems where both outer and inner objectives evolve over time, requiring dynamic updates. Current OBO approaches rely on deterministic \textit{window-smoothed} regret minimization, which may not accurately reflect system performance when functions change rapidly. In this work, we introduce a novel search direction and show that both first- and zeroth-order (ZO) stochastic OBO algorithms leveraging this direction achieve sublinear {stochastic bilevel regret without window smoothing}. Beyond these guarantees, our framework enhances efficiency by: (i) reducing oracle dependence in hypergradient estimation, (ii) updating inner and outer variables alongside the linear system solution, and (iii) employing ZO-based estimation of Hessians, Jacobians, and gradients. Experiments on online parametric loss tuning and black-box adversarial attacks validate our approach.

Jiahe Lin, George Michailidis

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

Babak Barazandeh, Subhabrata Majumdar, Om Rajyaguru et al.

Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, offer compact and effective alternatives to full model fine-tuning by introducing low-rank updates to pre-trained weights. However, most existing approaches rely on global low rank structures, which can overlook spatial patterns spread across the parameter space. In this work, we propose Localized LoRA, a generalized framework that models weight updates as a composition of low-rank matrices applied to structured blocks of the weight matrix. This formulation enables dense, localized updates throughout the parameter space without increasing the total number of trainable parameters. We provide a formal comparison between global, diagonal-local, and fully localized low-rank approximations, and show that our method consistently achieves lower approximation error under matched parameter budgets. Experiments on both synthetic and practical settings demonstrate that Localized LoRA offers a more expressive and adaptable alternative to existing methods, enabling efficient fine-tuning with improved performance.

Jiahe Lin, Yikai Zhang, George Michailidis

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and investigate a deep neural network-based approach to estimate it. The method allows for flexible functional dependency on the covariate, and fits the data reasonably well in the absence of a Gaussianity assumption. Theoretical results with PAC guarantees are established for the method, under assumptions commonly used in an Empirical Risk Minimization framework. The performance of the proposed method is evaluated on several synthetic data settings and benchmarked against existing approaches. The method is further illustrated on real datasets involving data from neuroscience and finance, respectively, and produces interpretable results.

Jialiang Geng, George Michailidis

The paper studies the problem of detecting and locating change points in multivariate time-evolving data. The problem has a long history in statistics and signal processing and various algorithms have been developed primarily for simple parametric models. In this work, we focus on modeling the data through feed-forward neural networks and develop a detection strategy based on the following two-step procedure. In the first step, the neural network is trained over a prespecified window of the data, and its test error function is calibrated over another prespecified window. Then, the test error function is used over a moving window to identify the change point. Once a change point is detected, the procedure involving these two steps is repeated until all change points are identified. The proposed strategy yields consistent estimates for both the number and the locations of the change points under temporal dependence of the data-generating process. The effectiveness of the proposed strategy is illustrated on synthetic data sets that provide insights on how to select in practice tuning parameters of the algorithm and in real data sets. Finally, we note that although the detection strategy is general and can work with different neural network architectures, the theoretical guarantees provided are specific to feed-forward neural architectures.

Jiahe Lin, Huitian Lei, George Michailidis

Granger causality has been widely used in various application domains to capture lead-lag relationships amongst the components of complex dynamical systems, and the focus in extant literature has been on a single dynamical system. In certain applications in macroeconomics and neuroscience, one has access to data from a collection of related such systems, wherein the modeling task of interest is to extract the shared common structure that is embedded across them, as well as to identify the idiosyncrasies within individual ones. This paper introduces a Variational Autoencoder (VAE) based framework that jointly learns Granger-causal relationships amongst components in a collection of related-yet-heterogeneous dynamical systems, and handles the aforementioned task in a principled way. The performance of the proposed framework is evaluated on several synthetic data settings and benchmarked against existing approaches designed for individual system learning. The method is further illustrated on a real dataset involving time series data from a neurophysiological experiment and produces interpretable results.

Michael Weylandt, George Michailidis

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected over time, such as interactions between users of a social media platform on different days, or across multiple subjects, such as in multi-subject studies of brain connectivity. When analyzing multiple large networks, dimensionality reduction techniques are often used to embed networks in a more tractable low-dimensional space. To this end, we develop a framework for principal components analysis (PCA) on collections of networks via a specialized tensor decomposition we term Semi-Symmetric Tensor PCA or SS-TPCA. We derive computationally efficient algorithms for computing our proposed SS-TPCA decomposition and establish statistical efficiency of our approach under a standard low-rank signal plus noise model. Remarkably, we show that SS-TPCA achieves the same estimation accuracy as classical matrix PCA, with error proportional to the square root of the number of vertices in the network and not the number of edges as might be expected. Our framework inherits many of the strengths of classical PCA and is suitable for a wide range of unsupervised learning tasks, including identifying principal networks, isolating meaningful changepoints or outlying observations, and for characterizing the "variability network" of the most varying edges. Finally, we demonstrate the effectiveness of our proposal on simulated data and on an example from empirical legal studies. The techniques used to establish our main consistency results are surprisingly straightforward and may find use in a variety of other network analysis problems.

Aditya Modi, Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari et al.

Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear systems to estimate their transition matrices more accurately. To address this problem, the current paper investigates methods for jointly estimating the transition matrices of multiple systems. It is assumed that the transition matrices are unknown linear functions of some unknown shared basis matrices. We establish finite-time estimation error rates that fully reflect the roles of trajectory lengths, dimension, and number of systems under consideration. The presented results are fairly general and show the significant gains that can be achieved by pooling data across systems in comparison to learning each system individually. Further, they are shown to be robust against model misspecifications. To obtain the results, we develop novel techniques that are of interest for addressing similar joint-learning problems. They include tightly bounding estimation errors in terms of the eigen-structures of transition matrices, establishing sharp high probability bounds for singular values of dependent random matrices, and capturing effects of misspecified transition matrices as the systems evolve over time.

Abhishek Kaul, George Michailidis

We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. To that end, we develop a locally refitted least squares estimator and obtain component-wise and simultaneous rates of estimation of the underlying change points. The simultaneous rate is the sharpest available in the literature by at least a factor of $\log p,$ while the component-wise one is optimal. These results enable existence of limiting distributions. Component-wise distributions are characterized under both vanishing and non-vanishing jump size regimes, while joint distributions for any finite subset of change point estimates are characterized under the latter regime, which also yields asymptotic independence of these estimates. The combined results are used to construct asymptotically valid component-wise and simultaneous confidence intervals for the change point parameters. The results are established under a high dimensional scaling, allowing for diminishing jump sizes, in the presence of diverging number of change points and under subexponential errors. They are illustrated on synthetic data and on sensor measurements from smartphones for activity recognition.

Babak Barazandeh, Tianjian Huang, George Michailidis

Min-max saddle point games have recently been intensely studied, due to their wide range of applications, including training Generative Adversarial Networks (GANs). However, most of the recent efforts for solving them are limited to special regimes such as convex-concave games. Further, it is customarily assumed that the underlying optimization problem is solved either by a single machine or in the case of multiple machines connected in centralized fashion, wherein each one communicates with a central node. The latter approach becomes challenging, when the underlying communications network has low bandwidth. In addition, privacy considerations may dictate that certain nodes can communicate with a subset of other nodes. Hence, it is of interest to develop methods that solve min-max games in a decentralized manner. To that end, we develop a decentralized adaptive momentum (ADAM)-type algorithm for solving min-max optimization problem under the condition that the objective function satisfies a Minty Variational Inequality condition, which is a generalization to convex-concave case. The proposed method overcomes shortcomings of recent non-adaptive gradient-based decentralized algorithms for min-max optimization problems that do not perform well in practice and require careful tuning. In this paper, we obtain non-asymptotic rates of convergence of the proposed algorithm (coined DADAM$^3$) for finding a (stochastic) first-order Nash equilibrium point and subsequently evaluate its performance on training GANs. The extensive empirical evaluation shows that DADAM$^3$ outperforms recently developed methods, including decentralized optimistic stochastic gradient for solving such min-max problems.

Babak Barazandeh, Davoud Ataee Tarzanagh, George Michailidis

Adaptive momentum methods have recently attracted a lot of attention for training of deep neural networks. They use an exponential moving average of past gradients of the objective function to update both search directions and learning rates. However, these methods are not suited for solving min-max optimization problems that arise in training generative adversarial networks. In this paper, we propose an adaptive momentum min-max algorithm that generalizes adaptive momentum methods to the non-convex min-max regime. Further, we establish non-asymptotic rates of convergence for the proposed algorithm when used in a reasonably broad class of non-convex min-max optimization problems. Experimental results illustrate its superior performance vis-a-vis benchmark methods for solving such problems.

Michael Weylandt, George Michailidis, T. Mitchell Roddenberry

Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same underlying phenomenon. To integrate these different data sources, graph alignment techniques attempt to find the best correspondence between vertices of two graphs. We consider a generalization of this problem, where there is no natural one-to-one mapping between vertices, but where there is correspondence between the community structures of each graph. Because we seek to learn structure at this higher community level, we refer to this problem as "coarse" graph alignment. To this end, we propose a novel regularized partial least squares method which both incorporates the observed graph structures and imposes sparsity in order to reflect the underlying block community structure. We provide efficient algorithms for our method and demonstrate its effectiveness in simulations.

Michael Weylandt, George Michailidis

Clustering of time series data exhibits a number of challenges not present in other settings, notably the problem of registration (alignment) of observed signals. Typical approaches include pre-registration to a user-specified template or time warping approaches which attempt to optimally align series with a minimum of distortion. For many signals obtained from recording or sensing devices, these methods may be unsuitable as a template signal is not available for pre-registration, while the distortion of warping approaches may obscure meaningful temporal information. We propose a new method for automatic time series alignment within a clustering problem. Our approach, Temporal Registration using Optimal Unitary Transformations (TROUT), is based on a novel dissimilarity measure between time series that is easy to compute and automatically identifies optimal alignment between pairs of time series. By embedding our new measure in a optimization formulation, we retain well-known advantages of computational and statistical performance. We provide an efficient algorithm for TROUT-based clustering and demonstrate its superior performance over a range of competitors.

Abhishek Kaul, Hongjin Zhang, Konstantinos Tsampourakis et al.

We develop an estimator for the change point parameter for a dynamically evolving graphical model, and also obtain its asymptotic distribution under high dimensional scaling. To procure the latter result, we establish that the proposed estimator exhibits an $O_p(ψ^{-2})$ rate of convergence, wherein $ψ$ represents the jump size between the graphical model parameters before and after the change point. Further, it retains sufficient adaptivity against plug-in estimates of the graphical model parameters. We characterize the forms of the asymptotic distribution under the both a vanishing and a non-vanishing regime of the magnitude of the jump size. Specifically, in the former case it corresponds to the argmax of a negative drift asymmetric two sided Brownian motion, while in the latter case to the argmax of a negative drift asymmetric two sided random walk, whose increments depend on the distribution of the graphical model. Easy to implement algorithms are provided for estimating the change point and their performance assessed on synthetic data. The proposed methodology is further illustrated on RNA-sequenced microbiome data and their changes between young and older individuals.

Parvin Nazari, Davoud Ataee Tarzanagh, George Michailidis

In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages of past gradients to update search directions and learning rates have recently attracted a lot of attention for solving optimization problems that arise in machine learning. Nevertheless, their convergence analysis almost exclusively requires smoothness and/or convexity of the objective function. In contrast, we establish non-asymptotic rates of convergence of first and zeroth-order adaptive methods and their proximal variants for a reasonably broad class of nonsmooth \& nonconvex optimization problems. Experimental results indicate how the proposed algorithms empirically outperform stochastic gradient descent and its zeroth-order variant for solving such optimization problems.

Hossein Keshavarz, George Michailidis

The problem of identifying change points in high-dimensional Gaussian graphical models (GGMs) in an online fashion is of interest, due to new applications in biology, economics and social sciences. The offline version of the problem, where all the data are a priori available, has led to a number of methods and associated algorithms involving regularized loss functions. However, for the online version, there is currently only a single work in the literature that develops a sequential testing procedure and also studies its asymptotic false alarm probability and power. The latter test is best suited for the detection of change points driven by global changes in the structure of the precision matrix of the GGM, in the sense that many edges are involved. Nevertheless, in many practical settings the change point is driven by local changes, in the sense that only a small number of edges exhibit changes. To that end, we develop a novel test to address this problem that is based on the $\ell_\infty$ norm of the normalized covariance matrix of an appropriately selected portion of incoming data. The study of the asymptotic distribution of the proposed test statistic under the null (no presence of a change point) and the alternative (presence of a change point) hypotheses requires new technical tools that examine maxima of graph-dependent Gaussian random variables, and that of independent interest. It is further shown that these tools lead to the imposition of mild regularity conditions for key model parameters, instead of more stringent ones required by leveraging previously used tools in related problems in the literature. Numerical work on synthetic data illustrates the good performance of the proposed detection procedure both in terms of computational and statistical efficiency across numerous experimental settings.

Davoud Ataee Tarzanagh, George Michailidis

We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To capture such complex structures, a double core tensor (DCOT) factorization model is introduced together with a family of smoothing loss functions. By leveraging the proposed smoothing function, the model accurately estimates the model factors, even in the presence of missing entries. A linearized ADMM method is employed to solve regularized versions of DCOT factorizations, that avoid large tensor operations and large memory storage requirements. Further, we establish theoretically its global convergence, together with consistency of the estimates of the model parameters. The effectiveness of the DCOT model is illustrated on several real-world examples including image completion, recommender systems, subspace clustering and detecting modules in heterogeneous Omics multi-modal data, since it provides more insightful decompositions than conventional tensor methods.

Clint P. George, Wei Xia, George Michailidis

As electronically stored data grow in daily life, obtaining novel and relevant information becomes challenging in text mining. Thus people have sought statistical methods based on term frequency, matrix algebra, or topic modeling for text mining. Popular topic models have centered on one single text collection, which is deficient for comparative text analyses. We consider a setting where one can partition the corpus into subcollections. Each subcollection shares a common set of topics, but there exists relative variation in topic proportions among collections. Including any prior knowledge about the corpus (e.g. organization structure), we propose the compound latent Dirichlet allocation (cLDA) model, improving on previous work, encouraging generalizability, and depending less on user-input parameters. To identify the parameters of interest in cLDA, we study Markov chain Monte Carlo (MCMC) and variational inference approaches extensively, and suggest an efficient MCMC method. We evaluate cLDA qualitatively and quantitatively using both synthetic and real-world corpora. The usability study on some real-world corpora illustrates the superiority of cLDA to explore the underlying topics automatically but also model their connections and variations across multiple collections.

Davoud Ataee Tarzanagh, Mohamad Kazem Shirani Faradonbeh, George Michailidis

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further establish its rate of convergence and show how it relates to the number of nodes employed in the distributed computation, the effective rank of the data matrix under consideration, and the gap in the spectrum of the underlying population covariance matrix. The proposed algorithm is illustrated on low-rank approximation and $\boldsymbol{k}$-means clustering tasks. The numerical results show a substantial computational speed-up vis-a-vis standard distributed PCA algorithms, without compromising learning accuracy.

Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis

Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the decision-maker about the dynamical parameter. Two randomized algorithms are proposed for this problem, but the performance is not sufficiently investigated. Further, the effect of key parameters of the algorithms such as the magnitude and the frequency of applying the randomizations is not currently available. This work studies the stabilization speed and the failure probability of data-driven procedures. We provide numerical analyses for the performance of two methods: stochastic feedback, and stochastic parameter. The presented results imply that as long as the number of statistically independent randomizations is not too small, fast stabilization is guaranteed.

Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis

In decision making problems for continuous state and action spaces, linear dynamical models are widely employed. Specifically, policies for stochastic linear systems subject to quadratic cost functions capture a large number of applications in reinforcement learning. Selected randomized policies have been studied in the literature recently that address the trade-off between identification and control. However, little is known about policies based on bootstrapping observed states and actions. In this work, we show that bootstrap-based policies achieve a square root scaling of regret with respect to time. We also obtain results on the accuracy of learning the model's dynamics. Corroborative numerical analysis that illustrates the technical results is also provided.

Parvin Nazari, Davoud Ataee Tarzanagh, George Michailidis

Adaptive gradient-based optimization methods such as \textsc{Adagrad}, \textsc{Rmsprop}, and \textsc{Adam} are widely used in solving large-scale machine learning problems including deep learning. A number of schemes have been proposed in the literature aiming at parallelizing them, based on communications of peripheral nodes with a central node, but incur high communications cost. To address this issue, we develop a novel consensus-based distributed adaptive moment estimation method (\textsc{Dadam}) for online optimization over a decentralized network that enables data parallelization, as well as decentralized computation. The method is particularly useful, since it can accommodate settings where access to local data is allowed. Further, as established theoretically in this work, it can outperform centralized adaptive algorithms, for certain classes of loss functions used in applications. We analyze the convergence properties of the proposed algorithm and provide a dynamic regret bound on the convergence rate of adaptive moment estimation methods in both stochastic and deterministic settings. Empirical results demonstrate that \textsc{Dadam} works also well in practice and compares favorably to competing online optimization methods.

Monika Bhattacharjee, Moulinath Banerjee, George Michailidis

We consider the problem of estimating the location of a single change point in a dynamic stochastic block model. We propose two methods of estimating the change point, together with the model parameters. The first employs a least squares criterion function and takes into consideration the full structure of the stochastic block model and is evaluated at each point in time. Hence, as an intermediate step, it requires estimating the community structure based on a clustering algorithm at every time point. The second method comprises of the following two steps: in the first one, a least squares function is used and evaluated at each time point, but ignores the community structures and just considers a random graph generating mechanism exhibiting a change point. Once the change point is identified, in the second step, all network data before and after it are used together with a clustering algorithm to obtain the corresponding community structures and subsequently estimate the generating stochastic block model parameters. A comparison between these two methods is illustrated. Further, for both methods under their respective identifiability and certain additional regularity conditions, we establish rates of convergence and derive the asymptotic distributions of the change point estimators. The results are illustrated on synthetic data.

Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis

This paper studies adaptive algorithms for simultaneous regulation (i.e., control) and estimation (i.e., learning) of Multiple Input Multiple Output (MIMO) linear dynamical systems. It proposes practical, easy to implement control policies based on perturbations of input signals. Such policies are shown to achieve a worst-case regret that scales as the square-root of the time horizon, and holds uniformly over time. Further, it discusses specific settings where such greedy policies attain the information theoretic lower bound of logarithmic regret. To establish the results, recent advances on self-normalized martingales together with a novel method of policy decomposition are leveraged.

Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis

Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to regulation. Therefore, the adaptive stabilization needs to be completed in finite time. In order to achieve this goal, asymptotic approaches are not very helpful. There are only a few existing non-asymptotic results and a full treatment of the problem is not currently available. In this work, leveraging the novel method of random linear feedbacks, we establish high probability guarantees for finite time stabilization. Our results hold for remarkably general settings because we carefully choose a minimal set of assumptions. These include stabilizability of the underlying system and restricting the degree of heaviness of the noise distribution. To derive our results, we also introduce a number of new concepts and technical tools to address regularity and instability of the closed-loop matrix.

Hossein Keshavarz, George Michailidis, Yves Atchade

High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in offline detection and estimation of regime changes in the topology of sparse graphical models. However, the online setting remains largely unexplored, despite its high relevance to applications in sensor networks and other engineering monitoring systems, as well as financial markets. To that end, this work introduces a novel scalable online algorithm for detecting an unknown number of abrupt changes in the inverse covariance matrix of sparse Gaussian graphical models with small delay. The proposed algorithm is based upon monitoring the conditional log-likelihood of all nodes in the network and can be extended to a large class of continuous and discrete graphical models. We also investigate asymptotic properties of our procedure under certain mild regularity conditions on the graph size, sparsity level, number of samples, and pre- and post-changes in the topology of the network. Numerical works on both synthetic and real data illustrate the good performance of the proposed methodology both in terms of computational and statistical efficiency across numerous experimental settings.

Subhabrata Majumdar, George Michailidis

The rapid development of high-throughput technologies has enabled the generation of data from biological or disease processes that span multiple layers, like genomic, proteomic or metabolomic data, and further pertain to multiple sources, like disease subtypes or experimental conditions. In this work, we propose a general statistical framework based on Gaussian graphical models for horizontal (i.e. across conditions or subtypes) and vertical (i.e. across different layers containing data on molecular compartments) integration of information in such datasets. We start with decomposing the multi-layer problem into a series of two-layer problems. For each two-layer problem, we model the outcomes at a node in the lower layer as dependent on those of other nodes in that layer, as well as all nodes in the upper layer. We use a combination of neighborhood selection and group-penalized regression to obtain sparse estimates of all model parameters. Following this, we develop a debiasing technique and asymptotic distributions of inter-layer directed edge weights that utilize already computed neighborhood selection coefficients for nodes in the upper layer. Subsequently, we establish global and simultaneous testing procedures for these edge weights. Performance of the proposed methodology is evaluated on synthetic and real data.

Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis

The main challenge for adaptive regulation of linear-quadratic systems is the trade-off between identification and control. An adaptive policy needs to address both the estimation of unknown dynamics parameters (exploration), as well as the regulation of the underlying system (exploitation). To this end, optimism-based methods which bias the identification in favor of optimistic approximations of the true parameter are employed in the literature. A number of asymptotic results have been established, but their finite time counterparts are few, with important restrictions. This study establishes results for the worst-case regret of optimism-based adaptive policies. The presented high probability upper bounds are optimal up to logarithmic factors. The non-asymptotic analysis of this work requires very mild assumptions; (i) stabilizability of the system's dynamics, and (ii) limiting the degree of heaviness of the noise distribution. To establish such bounds, certain novel techniques are developed to comprehensively address the probabilistic behavior of dependent random matrices with heavy-tailed distributions.

Michael Kallitsis, Stilian Stoev, George Michailidis

Distributed Denial of Service (DDoS) attacks have become more prominent recently, both in frequency of occurrence, as well as magnitude. Such attacks render key Internet resources unavailable and disrupt its normal operation. It is therefore of paramount importance to quickly identify malicious Internet activity. The DDoS threat model includes characteristics such as: (i) heavy-hitters that transmit large volumes of traffic towards "victims", (ii) persistent-hitters that send traffic, not necessarily large, to specific destinations to be used as attack facilitators, (iii) host and port scanning for compiling lists of un-secure servers to be used as attack amplifiers, etc. This conglomeration of problems motivates the development of space/time efficient summaries of data traffic streams that can be used to identify heavy-hitters associated with the above attack vectors. This paper presents a hashing-based framework and fast algorithms that take into account the large-dimensionality of the incoming network stream and can be employed to quickly identify the culprits. The algorithms and data structures proposed provide a synopsis of the network stream that is not taxing to fast-memory, and can be efficiently implemented in hardware due to simple bit-wise operations. The methods are evaluated using real-world Internet data from a large academic network.

Ali Shojaie, Alexandra Jauhiainen, Michael Kallitsis et al.

Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or are expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimating a regulatory network. The proposed approach is based on a three-step algorithm to estimate the underlying directed but cyclic network, that uses as input both perturbation screens and steady state gene expression data. In the first step, the algorithm determines causal orderings of the genes that are consistent with the perturbation data, by combining an exhaustive search method with a fast heuristic that in turn couples a Monte Carlo technique with a fast search algorithm. In the second step, for each obtained causal ordering, a regulatory network is estimated using a penalized likelihood based method, while in the third step a consensus network is constructed from the highest scored ones. Extensive computational experiments show that the algorithm performs well in reconstructing the underlying network and clearly outperforms competing approaches that rely only on a single data source. Further, it is established that the algorithm produces a consistent estimate of the regulatory network.

Michael Kallitsis, Stilian Stoev, George Michailidis

The robustness and integrity of IP networks require efficient tools for traffic monitoring and analysis, which scale well with traffic volume and network size. We address the problem of optimal large-scale flow monitoring of computer networks under resource constraints. We propose a stochastic optimization framework where traffic measurements are done by exploiting the spatial (across network links) and temporal relationship of traffic flows. Specifically, given the network topology, the state-space characterization of network flows and sampling constraints at each monitoring station, we seek an optimal packet sampling strategy that yields the best traffic volume estimation for all flows of the network. The optimal sampling design is the result of a concave minimization problem; then, Kalman filtering is employed to yield a sequence of traffic estimates for each network flow. We evaluate our algorithm using real-world Internet2 data.

Shawn Mankad, George Michailidis

Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and time-varying community detection in time-evolving graph sequences. The matrix factorization model allows the user to home in on and display interesting, underlying structure and its evolution over time. The methods are scalable to weighted networks with a large number of time points or nodes, and can accommodate sudden changes to graph topology. Our techniques are demonstrated with several dynamic graph series from both synthetic and real world data, including citation and trade networks. These examples illustrate how users can steer the techniques and combine them with existing methods to discover and display meaningful patterns in sizable graphs over many time points.