Javad Heydari

Quickest detection of Gauss-Markov random fields

The problem of quickest data-adaptive and sequential search for clusters in a Gauss-Markov random field is considered. In the existing literature, such search for clusters is often performed using fixed sample size and non-adaptive strategies. In order to accommodate large networks, in which data adaptivity leads to significant gains in detection quality and agility, in this paper sequential and data-adaptive detection strategies are proposed and are shown to enjoy asymptotic optimality. The quickest detection problem is abstracted by adopting an acyclic dependency graph to model the mutual effects of different random variables in the field and decision making rules are derived for general random fields and specialized for Gauss-Markov random fields. Performance evaluations demonstrate the gains of the data-adaptive schemes over existing techniques in terms of sampling complexity and error exponents.

Quickest linear search over correlated sequences

Linear search arises in many application domains. The problem of linear search over multiple sequences in order to identify one sequence with a desired statistical feature is considered. The quickest linear search optimizes a balance between two opposing performance measures, one being the delay in detecting a desirable sequence, and the other one being the quality of the decision. The existing approaches in the quickest search literature rely on the assumption that the sequences are statistically independent. In many applications, however, due to the underlying physical couplings, generations of available sequences are not necessarily independent. Driven by such underlying couplings, this paper considers searching over correlated sequences, in which the distribution of each sequence depends on the distribution of its preceding one. The closed-form characterization of the sampling process for the optimal search is delineated. The analysis reveals that depending on the correlation structure, the optimal search strategy can be similar to (in spirit) or dramatically different from the optimal search strategy over independent sequences.

Quickest Localization of Anomalies in Power Grids: A Stochastic Graphical Framework

Agile localization of anomalous events plays a pivotal role in enhancing the overall reliability of the grid and avoiding cascading failures. This is especially of paramount significance in the large-scale grids due to their geographical expansions and the large volume of data generated. This paper proposes a stochastic graphical framework, by leveraging which it aims to localize the anomalies with the minimum amount of data. This framework capitalizes on the strong correlation structures observed among the measurements collected from different buses. The proposed approach, at its core, collects the measurements sequentially and progressively updates its decision about the location of the anomaly. The process resumes until the location of the anomaly can be identified with desired reliability. We provide a general theory for the quickest anomaly localization and also investigate its application for quickest line outage localization. Simulations in the IEEE 118-bus model are provided to establish the gains of the proposed approach.

Quickest change detection in structured data with incomplete information

This paper considers a network of agents generating correlated data according to a known kernel. The correlation structure might undergo a change at an unknown time instant, where the post-change kernel is not fully known. Moreover, due to the data processing and communication costs, only a subset of agents can be observed at any time instant. The objective is to detect the change-point with minimum average delay, while the rate of false alarms is controlled. This paper proposes a coupled data acquisition and decision-making process for change detection and establishes its optimality properties.

Quickest search and learning over multiple sequences

Consider a set of random sequences, each consisting of independent and identically distributed random variables. Each sequence is generated according to one of the two possible distributions F0 or F1 with unknown prior probabilities (1 − ∊) and ∊, respectively. The objective is to design a sequential decision-making procedure that identifies a sequence generated according to F1 with the fewest number of measurements. Earlier analyses of this search problem have demonstrated that the optimal design of the sequential rules strongly hinge on the exact value of ∊. Such information, however, might not be available in certain applications, especially in anomaly detection where the anomalous sequences occur with unpredicted patterns. Motivated by this premise, this paper designs a sequential inference mechanism that forms two coupled decisions for identifying a sequence of interest, and also learning the value of ∊. The paper devises three strategies that place different levels of emphasis on each of these inference goals.

Quickest Search for Local Structures in Random Graphs

A network of agents that form a random graph is considered. Each agent represents an information source that generates a sequence of random variables (RVs). The RVs generated by an unknown subset of nodes are correlated according to a known kernel, while the remaining nodes generate independent and identically distributed random variables. To identify and localize the desired unknown subset of correlated nodes, this paper formalizes and delineates a quickest search process, which is the strategy that minimizes the average number of measurements. Despite its widespread applications, the problem of identifying subgraphs with such desired correlation structures is often investigated under the fixed sample-size settings, in which the data acquisition process and the inferential mechanisms are decoupled. Motivated by the significant advantages of sequential methods for agile inference, this paper analyzes this problem under a fully sequential setting. Specifically, it offers a framework that unifies the intertwined processes of information gathering and decision making, and through a constructive proof, it provides an optimal sequential data-gathering process as well as the attendant decision rules for the quickest search of interest.

Quickest detection of Markov networks

Detecting correlation structures in large networks arises in many domains. Such detection problems are often studied independently of the underlying data acquisition process, rendering settings in which data acquisition policies and the associated sample size are pre-specified. Motivated by the advantages of data-adaptive sampling in data dimensionality reduction, especially in large networks, as well as enhancing the agility of the sampling process, this paper treats the inherently problems of data acquisition and correlation detection. Specifically, this paper considers a network of nodes generating random variables and designs the quickest sequential sampling strategy for collecting data and reliably deciding whether the network is a Markov network with a known correlation structure. By abstracting the Markov network as an undirected graph, in which the vertices represent the random variables and their connectivities model the correlation structure of interest, designing the quickest sampling strategy becomes equivalent to sequentially and data-adaptively identifying and sampling a sequence of vertices in the graph. Optimal sampling strategies are proposed and their associated optimality guarantees are established. Performance evaluations are provided to demonstrate the gains of the proposed sequential approaches.

Quickest search over correlated sequences with model uncertainty

An ordered set of data sequences is given where, broadly, the data sequences are categorized into normal and abnormal ones. The normal sequences consist of random variables generated according to a known distribution, while there exist uncertainties about the distributions of the abnormal sequences. Moreover, the generations of different sequences are correlated, induced by an underlying physical coupling, where a sequence being normal or abnormal depends on the status of the rest of the sequences according to a known dependency kernel. The objective is to design the quickest sequential and data-adaptive sampling procedure for identifying one abnormal sequence. This quickest search strategy strikes a balance between the quality and agility of the search process, as two opposing figures of merit. This paper characterizes the sampling and search strategy. Motivated by the fact that full characterization of such strategies can become computationally prohibitive, this paper also proposes asymptotically optimal sampling and search strategies that are computationally efficient.

A graphical approach to quickest outage localization in power grids

Line outage detection and localization play pivotal roles in contingency analysis, power flow optimization, and situational awareness delivery in power grids. Hence, agile detection and localization of line outages enhance the efficiency of operations and their resilience against cascading failures. This paper proposes a stochastic graphical framework for localizing line outage events. This framework capitalizes on the correlation among the measurements generated across the grid, where the correlation is induced by the connectivity topology of the grid. By formalizing a proper correlation model, this paper designs data-adaptive coupled data-acquisition and decision-making processes for the quickest localization of the line outages. This leads to efficient outage localization by partially observing the grid and is shown to outperform the existing dimensionality reduction methods.

Quickest search for local structures in line networks

A large network of agents in which each agent generates one random variable is considered. The random variables generated by an unknown subset of nodes form a correlation structure, while the remaining nodes generate independent and identically distributed random variables. This paper formalizes and analyzes the quickest search strategy, the goal of which is to identify the unknown subset of correlated nodes with the fewest number of measurements. Despite its widespread applications, the problem of identifying subnetworks with such desired correlation structures is often investigated under the fixed sample-size setting, in which the data acquisition process and the inferential mechanisms are decoupled. Motivated by the significant advantages of sequential detection for agile inference, this paper analyzes this problem under a fully sequential setting. Specifically, it formalizes a framework that incorporates the intertwined processes of data-adaptive information gathering and decision making. Additionally, through a constructive proof, it also offers an optimal sequential data-gathering process as well as the attendant decision rules for identifying a structured subnetwork of interest in a given line network.