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Directed graphical models such as Bayesian networks are a favored formalism for modeling the dependency structures in complex multivariate systems such as those encountered in biology and neural science. When a system is undergoing dynamic transformation, temporally rewiring networks are needed for capturing the dynamic causal influences between covariates.(More)
MOTIVATION Gene regulatory networks underlying temporal processes, such as the cell cycle or the life cycle of an organism, can exhibit significant topological changes to facilitate the underlying dynamic regulatory functions. Thus, it is essential to develop methods that capture the temporal evolution of the regulatory networks. These methods will be an(More)
We consider the problem of identifying a sparse set of relevant columns and rows in a large data matrix with highly corrupted entries. This problem of identifying groups from a collection of bipartite variables such as proteins and drugs, biological species and gene sequences, malware and signatures, etc is commonly referred to as biclustering or(More)
We consider the problem of identifying a small sub-matrix of activation in a large noisy matrix. We establish the minimax rate for the problem by showing tight (up to constants) upper and lower bounds on the signal strength needed to identify the sub-matrix. We consider several natural computationally tractable procedures and show that under most parameter(More)
Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant network from observation data, little has been done toward estimating time-varying networks from time series of entity(More)
To estimate the changing structure of a varying-coefficient varying-structure (VCVS) model remains an important and open problem in dynamic system modelling, which includes learning trajectories of stock prices, or uncovering the topology of an evolving gene network. In this paper, we investigate sparsistent learning of a sub-family of this model —(More)
The time-varying multivariate Gaussian distribution and the undirected graph associated with it, as introduced in Zhou et al. (2008), provide a useful statistical framework for modeling complex dynamic networks. In many application domains, it is of high importance to estimate the graph structure of the model consistently for the purpose of scientific(More)
We develop a penalized kernel smoothing method for the problem of selecting nonzero elements of the conditional precision matrix, known as conditional covariance selection. This problem has a key role in many modern applications such as finance and computational biology. However, it has not been properly addressed. Our estimator is derived under minimal(More)
We consider the problems of detection and support recovery of a contiguous block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive (linear) measurements. We characterize the tradeoffs between the various problem dimensions, the signal strength and the number of measurements required to reliably detect and(More)
We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (SOMP) procedure to perform variable selection in ultra-high dimensional multiple output regression problems, which is the first attempt to utilize multiple outputs to perform fast removal of the irrelevant variables. As our main theoretical contribution, we show that the S-OMP(More)