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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)
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)
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)
We develop a penalized kernel smoothing method for the problem of selecting non-zero 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 study a simple two step procedure for estimating sparse precision matrices from data with missing values, which is tractable in high-dimensions and does not require impu-tation of the missing values. We provide rates of convergence for this estimator in the spectral norm, Frobenius norm and element-wise ∞ norm. Simulation studies show that this estimator(More)
Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study sketching from an optimization point of view: we first show that the iterative Hessian sketch is an optimization process(More)