Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract We sharply characterize the performance of different penalization schemes for the proble... more Abstract We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the Normal means model. This model, often used in the field of statistics, is a simplified model that provides a laboratory for studying complex procedures.
Abstract Extracting knowledge and providing insights into complex mechanisms underlying noisy hig... more Abstract Extracting knowledge and providing insights into complex mechanisms underlying noisy high-dimensional data sets is of utmost importance in many scientific domains. Statistical modeling has become ubiquitous in the analysis of high-dimensional functional data in search of better understanding of cognition mechanisms, in the exploration of large-scale gene regulatory networks in hope of developing drugs for lethal diseases, and in prediction of volatility in stock market in hope of beating the market.
Abstract: We consider the high-dimensional heteroscedastic regression model, where the mean and t... more Abstract: We consider the high-dimensional heteroscedastic regression model, where the mean and the log variance are modeled as a linear combination of input variables. Existing literature on high-dimensional linear regres-sion models has largely ignored non-constant error variances, even though they commonly occur in a variety of applications ranging from biostatis-tics to finance. In this paper we study a class of non-convex penalized pseudolikelihood estimators for both the mean and variance parameters.
Abstract: We consider the problem of detection and localization of a small block of weak activati... more Abstract: We consider the problem of detection and localization of a small block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive (linear) measurements. This is closely related to the problem of compressed sensing, where the task is to estimate a sparse vector using a small number of linear measurements.
Abstract: We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) ... more Abstract: We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in\ cite {fan08sis}, is an efficient and highly scalable way to remove many irrelevant variables from the set of all variables, while retaining all the relevant variables.
Abstract: We study the problem of estimating a temporally varying coefficient and varying structu... more Abstract: We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to iid data from an invariant model widely considered in current literature of structural estimation. In particular, we consider the scenario in which the model evolves in a piece-wise constant fashion.
Abstract We consider the problem of identifying a sparse set of relevant columns and rows in a la... more Abstract 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 co-clustering. Despite its great practical relevance, and although several ad-hoc methods are available for biclustering, theoretical analysis of the problem is largely non-existent.
Abstract: Many real world network problems often concern multivariate nodal attributes such as im... more Abstract: Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such data, neither can the theories developed around such methods be directly applied. In this paper, we propose a new principled framework for estimating multi-attribute networks.
Abstract Variable selection is an important and practical problem that arises in analysis of many... more Abstract Variable selection is an important and practical problem that arises in analysis of many high-dimensional datasets. Convex optimization procedures that arise from relaxing the NP-hard subset selection procedure, eg, the Lasso or Dantzig selector, have become the focus of intense theoretical investigations.
Abstract The time-varying multivariate Gaussian distribution and the undirected graph associated ... more Abstract 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 discovery.
Abstract We develop a penalized kernel smoothing method for the problem of selecting nonzero elem... more Abstract 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 assumptions on the underlying probability distribution and works well in the high-dimensional setting.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract To estimate the changing structure of a varying-coefficient varying-structure (VCVS) mod... more Abstract 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—piecewise constant VCVS models.
Abstract We sharply characterize the performance of different penalization schemes for the proble... more Abstract We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the Normal means model. This model, often used in the field of statistics, is a simplified model that provides a laboratory for studying complex procedures.
Abstract Extracting knowledge and providing insights into complex mechanisms underlying noisy hig... more Abstract Extracting knowledge and providing insights into complex mechanisms underlying noisy high-dimensional data sets is of utmost importance in many scientific domains. Statistical modeling has become ubiquitous in the analysis of high-dimensional functional data in search of better understanding of cognition mechanisms, in the exploration of large-scale gene regulatory networks in hope of developing drugs for lethal diseases, and in prediction of volatility in stock market in hope of beating the market.
Abstract: We consider the high-dimensional heteroscedastic regression model, where the mean and t... more Abstract: We consider the high-dimensional heteroscedastic regression model, where the mean and the log variance are modeled as a linear combination of input variables. Existing literature on high-dimensional linear regres-sion models has largely ignored non-constant error variances, even though they commonly occur in a variety of applications ranging from biostatis-tics to finance. In this paper we study a class of non-convex penalized pseudolikelihood estimators for both the mean and variance parameters.
Abstract: We consider the problem of detection and localization of a small block of weak activati... more Abstract: We consider the problem of detection and localization of a small block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive (linear) measurements. This is closely related to the problem of compressed sensing, where the task is to estimate a sparse vector using a small number of linear measurements.
Abstract: We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) ... more Abstract: We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in\ cite {fan08sis}, is an efficient and highly scalable way to remove many irrelevant variables from the set of all variables, while retaining all the relevant variables.
Abstract: We study the problem of estimating a temporally varying coefficient and varying structu... more Abstract: We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to iid data from an invariant model widely considered in current literature of structural estimation. In particular, we consider the scenario in which the model evolves in a piece-wise constant fashion.
Abstract We consider the problem of identifying a sparse set of relevant columns and rows in a la... more Abstract 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 co-clustering. Despite its great practical relevance, and although several ad-hoc methods are available for biclustering, theoretical analysis of the problem is largely non-existent.
Abstract: Many real world network problems often concern multivariate nodal attributes such as im... more Abstract: Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such data, neither can the theories developed around such methods be directly applied. In this paper, we propose a new principled framework for estimating multi-attribute networks.
Abstract Variable selection is an important and practical problem that arises in analysis of many... more Abstract Variable selection is an important and practical problem that arises in analysis of many high-dimensional datasets. Convex optimization procedures that arise from relaxing the NP-hard subset selection procedure, eg, the Lasso or Dantzig selector, have become the focus of intense theoretical investigations.
Abstract The time-varying multivariate Gaussian distribution and the undirected graph associated ... more Abstract 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 discovery.
Abstract We develop a penalized kernel smoothing method for the problem of selecting nonzero elem... more Abstract 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 assumptions on the underlying probability distribution and works well in the high-dimensional setting.
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Papers by Mladen Kolar