20 accepted papers
Controlling the false discovery rate (FDR) in high-dimensional variable selection requires balancing rigorous error control with statistical power. Existing methods with provable guarantees are often overly conservative, creating a persistent gap between the realized false discovery proportion (FDP)…
In high-dimensional data analysis, such as financial index tracking or biomedical applications, it is crucial to select the few relevant variables while maintaining control over the false discovery rate (FDR). In these applications, strong dependencies often exist among the variables (e.g., stock re…
The Passive-Aggressive (PA) method is widely used in online regression problems for handling large-scale streaming data, typically updating model parameters in a passive-aggressive manner based on whether the error exceeds a predefined threshold. However, this approach struggles with determining opt…
Learning a graph from data is the key to taking advantage of graph signal processing tools. Most of the conventional algorithms for graph learning require complete data statistics, which might not be available in some scenarios. In this work, we aim to learn a graph from incomplete time-series obser…
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection. Sparse PCA algorithms are usually expressed as a trade-off be…
We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. Such models have shown interesting properties, e.g., the maximum likelihood estimator exists with as little as two observations in the case of M-matrices, and exists even with o…
Gaussian Markov random fields, a class of graphical models, play an increasingly important role in real-world problems, where they are often applied to uncover conditional correlations between pairs of entities in a network. Motivated by recent applications of graphs in financial markets, we investi…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be formulated as a sign-constrained log-determinant program. Current al…
This paper studies the problem of learning the large-scale Gaussian graphical models that are multivariate totally positive of order two ($\text{MTP}_2$). By introducing the concept of bridge, which commonly exists in large-scale sparse graphs, we show that the entire problem can be equivalently opt…
Monotonicity is often a fundamental assumption involved in the modeling of a number of real-world applications. From an optimization perspective, monotonicity is formulated as partial order constraints among the optimization variables, commonly known as isotone optimization. In this paper, we develo…
We investigate the problem of learning an undirected, weighted bipartite graph under the Gaussian Markov random field model, for which we present an optimization formulation along with an efficient algorithm based on the projected gradient descent. Motivated by practical applications, where outliers…
Heavy-tailed statistical distributions have long been considered a more realistic statistical model for the data generating process in financial markets in comparison to their Gaussian counterpart. Nonetheless, mathematical nuisances, including nonconvexities, involved in estimating graphs in heavy-…
The vector autoregressive (VAR) models provide a significant tool for multivariate time series analysis. Most existing works on VAR modeling are based on the multivariate Gaussian distribution. However, heavy-tailed distributions are suggested more reasonable for capturing the real-world phenomena,…
The heuristic 1/N (equally weighted) portfolio and long-only quintile portfolio are both popular simple strategies in financial investment. In the 1/N portfolio, a fraction of 1/N of wealth is allocated to each of the N available assets. In the long-only quintile portfolio, first the assets are sort…
A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general approach is considered in which the SCM is replaced by an M-est…
Minimax multiple-input multiple-output (MIMO) transmit beampattern matching is a fundamental and important problem in many MIMO systems. The problem is formulated to minimize the maximum beampattern matching error as well as suppress the cross-correlation beampatterns while taking different practica…
In this paper, the multiple-input multiple-output (MIMO) transmit beampattern matching problem is considered. The problem is formulated to approximate a desired transmit beampattern (i.e., an energy distribution in space and frequency) and to minimize the cross-correlation of signals reflected back…
This paper proposes a novel and structured framework for parameter estimation from incomplete time series data under heavy-tailed random walk model. Traditionally, maximum likelihood estimation (MLE) for Gaussian random walk model from incomplete data has been considered. However, it is not applicab…
Unimodular sequences have been widely used in communications and radars, for which some numerical algorithms have been proposed recently to obtain good autocorrelation properties [1,2]. Design of such "good" sequences, however, does not take into account any prior information of the channel to be es…
Unimodular sequences with low autocorrelations are desired in many applications, especially in the area of radar and code-division multiple access (CDMA). In this paper, we propose a new algorithm to design unimodular sequences with low integrated sidelobe level (ISL), which is a widely used measure…