Carolyn L. Beck

Xiaotian Xie, Dimitrios Katselis, Carolyn L. Beck et al.

We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph indicate that the state of the node at a particular time instant is influenced by the states of the corresponding parental nodes in the previous time instant. The associated edge weights determine the corresponding level of influence from each parental node. In the simplest setup, the Bernoulli parameter of a particular node's state variable is a convex combination of the parental node states in the previous time instant and an additional Bernoulli noise random variable. This paper focuses on the problem of edge weight identification using Maximum Likelihood (ML) estimation and proves that the ML estimator is strongly consistent for two variants of the BAR model. We additionally derive closed-form estimators for the aforementioned two variants and prove their strong consistency.

Reza Soleymanifar, Amber Srivastava, Carolyn Beck et al.

In this work we introduce two novel deterministic annealing based clustering algorithms to address the problem of Edge Controller Placement (ECP) in wireless edge networks. These networks lie at the core of the fifth generation (5G) wireless systems and beyond. These algorithms, ECP-LL and ECP-LB, address the dominant leader-less and leader-based controller placement topologies and have linear computational complexity in terms of network size, maximum number of clusters and dimensionality of data. Each algorithm tries to place controllers close to edge node clusters and not far away from other controllers to maintain a reasonable balance between synchronization and delay costs. While the ECP problem can be conveniently expressed as a multi-objective mixed integer non-linear program (MINLP), our algorithms outperform state of art MINLP solver, BARON both in terms of accuracy and speed. Our proposed algorithms have the competitive edge of avoiding poor local minima through a Shannon entropy term in the clustering objective function. Most ECP algorithms are highly susceptible to poor local minima and greatly depend on initialization.

Dimitrios Katselis, Carolyn L. Beck, R. Srikant

We introduce a novel multivariate random process producing Bernoulli outputs per dimension, that can possibly formalize binary interactions in various graphical structures and can be used to model opinion dynamics, epidemics, financial and biological time series data, etc. We call this a Bernoulli Autoregressive Process (BAR). A BAR process models a discrete-time vector random sequence of $p$ scalar Bernoulli processes with autoregressive dynamics and corresponds to a particular Markov Chain. The benefit from the autoregressive dynamics is the description of a $2^p\times 2^p$ transition matrix by at most $pd$ effective parameters for some $d\ll p$ or by two sparse matrices of dimensions $p\times p^2$ and $p\times p$, respectively, parameterizing the transitions. Additionally, we show that the BAR process mixes rapidly, by proving that the mixing time is $O(\log p)$. The hidden constant in the previous mixing time bound depends explicitly on the values of the chain parameters and implicitly on the maximum allowed in-degree of a node in the corresponding graph. For a network with $p$ nodes, where each node has in-degree at most $d$ and corresponds to a scalar Bernoulli process generated by a BAR, we provide a greedy algorithm that can efficiently learn the structure of the underlying directed graph with a sample complexity proportional to the mixing time of the BAR process. The sample complexity of the proposed algorithm is nearly order-optimal as it is only a $\log p$ factor away from an information-theoretic lower bound. We present simulation results illustrating the performance of our algorithm in various setups, including a model for a biological signaling network.

Shahzad Bhatti, Carolyn Beck, Angelia Nedic

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue decompositions. Several algorithms have been proposed in the recent past to accelerate spectral clustering, however they compromise on the accuracy of the spectral clustering to achieve faster speed. In this paper, we propose a novel spectral clustering algorithm based on a mixing process on a graph. Unlike the existing spectral clustering algorithms, our algorithm does not require computing eigenvectors. Specifically, it finds the equivalent of a linear combination of eigenvectors of the normalized similarity matrix weighted with corresponding eigenvalues. This linear combination is then used to partition the dataset into meaningful clusters. Simulations on real datasets show that partitioning datasets based on such linear combinations of eigenvectors achieves better accuracy than standard spectral clustering methods as the number of clusters increase. Our algorithm can easily be implemented in a distributed setting.

Dimitrios Katselis, Cristian R. Rojas, Carolyn L. Beck

Recently, a framework for application-oriented optimal experiment design has been introduced. In this context, the distance of the estimated system from the true one is measured in terms of a particular end-performance metric. This treatment leads to superior unknown system estimates to classical experiment designs based on usual pointwise functional distances of the estimated system from the true one. The separation of the system estimator from the experiment design is done within this new framework by choosing and fixing the estimation method to either a maximum likelihood (ML) approach or a Bayesian estimator such as the minimum mean square error (MMSE). Since the MMSE estimator delivers a system estimate with lower mean square error (MSE) than the ML estimator for finite-length experiments, it is usually considered the best choice in practice in signal processing and control applications. Within the application-oriented framework a related meaningful question is: Are there end-performance metrics for which the ML estimator outperforms the MMSE when the experiment is finite-length? In this paper, we affirmatively answer this question based on a simple linear Gaussian regression example.