Daniel P. Palomar's research while affiliated with The Hong Kong University of Science and Technology and other places
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Publications (281)
We propose estimating the scale parameter (mean of the eigenvalues) of the scatter matrix of an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator of the scatter matrix. The proposed Tyler's weights-based estimate (TWE) of scale is then used to construct an affine equivariant Tyler's M-estimator as...
We propose estimating the scale parameter (mean of the eigenvalues) of the scatter matrix of an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator of the scatter matrix. The proposed Tyler's weights-based estimate (TWE) of scale is then used to construct an affine equivariant Tyler's M-estimator as...
The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express a preference among these efficient portfolios, investors have put forward many mean-variance portfolio (MVP) f...
Since Markowitz’s mean-variance framework, optimizing a portfolio that strikes a trade-off between maximizing profit and minimizing risk has been ubiquitous in the financial industry. Initially, profit and risk were measured by the first two moments of the portfolio’s return, a.k.a. the mean and variance, which are sufficient to characterize a Gaus...
The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express a preference among these efficient portfolios, investors have put forward many mean-variance portfolio (MVP) f...
We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. Such models have received increasing attention in recent years, and have shown interesting properties, e.g., the maximum likelihood estimator exists with as little as two observations regardless of the underlying dimension. In...
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 develop an efficient, provable convergent algorithm for...
Since Markowitz's mean-variance framework, optimizing a portfolio that maximizes the profit and minimizes the risk has been ubiquitous in the financial industry. Initially, profit and risk were measured by the first two moments of the portfolio's return, a.k.a. the mean and variance, which are sufficient to characterize a Gaussian distribution. How...
Inferring the covariance matrix of multivariate data is of great interest in statistics, finance, and data science. It is often carried out via the maximum likelihood estimation (MLE) principle, which seeks a covariance matrix estimator maximizing the observed data likelihood. However, such estimator is usually poor when number of samples is not su...
We study the problem of estimating precision matrices in multivariate Gaussian distributions where all partial correlations are nonnegative, also known as multivariate totally positive of order two ($\mathrm{MTP}_2$). Such models have received significant attention in recent years, primarily due to interesting properties, e.g., the maximum likeliho...
We consider the problem of graph learning under Gaussian Markov random fields, where all partial correlations are nonnegative. Such model is called attractive Gaussian Markov random fields, and has received considerable attention in recent years. The graph learning problem under this model can be formulated as the $\ell_1$-norm regularized Gaussian...
We propose the Terminating-Knockoff (T-Knock) filter, a fast variable selection method for high-dimensional data. The T-Knock filter controls a user-defined target false discovery rate (FDR) while maximizing the number of selected true positives. This is achieved by fusing the solutions of multiple early terminated random experiments. The experimen...
This paper proposes a framework for optimizing cost functions of orthonormal basis learning problems, such as principal component analysis (PCA), subspace recovery, orthogonal dictionary learning, etc. The optimization algorithm is derived using the majorization-minimization framework in conjunction with orthogonal projection reformulations to deal...
The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows th...
In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of practitioners' toolboxes. In this paper, we investigate the fundamental problem of learning undirected graphical...
A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues of the SCM. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator...
The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows th...
This paper proposes a framework for optimizing cost functions of orthonormal basis learning problems, such as principal component analysis (PCA), subspace recovery, orthogonal dictionary learning, etc. The optimization algorithm is derived using the majorization-minimization framework in conjunction with orthogonal Procrustes reformulations to deal...
The heuristic 1/N (i.e., equally weighted) portfolio and heuristic quintile portfolio are both popular simple strategies in financial investment. In the 1/N portfolio, a fraction of 1/N of the wealth is allocated to each of the N available assets. In the quintile portfolio, first the assets are sorted according to some characteristics, e.g., expect...
We consider the problem of learning a sparse graph under Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the precision matrix under Laplacian structural constraints. Like in the classical graphical lasso problem, recent works made use of the $\ell_1$-norm regularization...
A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues of the SCM. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator...
We investigate the problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market data. We show that Laplacian constraints have meaningful physical interpretations related to the market index factor and to the conditional correlations between stocks. Those interpretations lead to a...
This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor analysis (FA). By assuming the observed data to follow the multivariate Student’s t distribution, we can robu...
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-estimator of scatter matrix and a fully automatic dat...
The vector autoregressive (VAR) models provide a significant tool for multivariate time series analysis. Owing to the mathematical simplicity, existing works on VAR modeling are rigidly inclined towards the multivariate Gaussian distribution. However, heavy-tailed distributions are suggested more reasonable for capturing the real-world phenomena, l...
Since the 2008 financial crisis, risk management has become more important and portfolio approaches, such as the minimum-variance and equally weighted portfolios, have gained popularity. However, such portfolios still do not diversify the risk in the true sense. Recently, risk parity portfolios has been receiving significant interest from both the...
Interference management is a fundamental issue in device-to-device (D2D) communications whenever the transmitter-and-receiver pairs are located in close proximity and frequencies are fully reused, so active links may severely interfere with each other. This paper devises an optimization strategy named FPLinQ to coordinate the link scheduling decisi...
This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor analysis (FA). By assuming the observed data to follow the multivariate Student's t distribution, we can robu...
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In this paper, we first show that for a set of important graph families it is possible to convert the structural c...
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In this paper, we first show, for a set of important graph families it is possible to convert the combinatorial co...
The topic of sequence design has received considerable attention due to its wide applications in active sensing. One important desired property for the design sequence is the spectral shape. In this paper, the sequence design problem is formulated by minimizing the regularized spectral level ratio (SLR) subject to a peak-to-average power (PAR) cons...
In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex) regularization function. The proposed algorithm incorporates ideas from several existing approaches such as a...
In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex) regularization function. The proposed algorithm incorporates ideas from several existing approaches such as a...
This paper considers the robust estimation of the mean and covariance matrix for incomplete multivariate observations with the monotone missing-data pattern. First, we develop two efficient numerical algorithms for the existing robust estimator for the monotone incomplete data, i.e., the maximum likelihood (ML) estimator assuming the samples are fr...
The autoregressive (AR) model is a widely used model to represent the time series data from numerous applications, for example, financial time series, DNA microarray data, etc. In all such applications, issues with missing values frequently occur in the data observation or recording process. Traditionally, the parameter estimation for AR models of...
This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor analysis (FA). By assuming the observed data to follow the multivariate Student's t distribution, we can robu...
In this paper, we study the graph Laplacian estimation
problem under a given connectivity topology. We aim
at enriching the unified graph learning framework proposed by
Egilmez et al. and improve the optimality performance of the
Combinatorial Graph Laplacian (CGL) case. We apply the wellknown
Alternating Direction Method of Multipliers (ADMM) and...
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying graphical models from data. Learning a graph with a specific structure is essential for interpretability and identific...
Learning a graph with a specific structure is essential
for interpretability and identification of the
relationships among data. Existing graph learning
methods are tailored to specific structures that
cannot be generalized to other graph structures,
and also computationally prohibitive owing to
multi-stage implementation. In this project, we intro...
In this paper, the pipeline leak localization problem using transient data is investigated.
The signal processing techniques that proved successful in wireless communications and acoustics are adapted and tested for leak identification. More specifically, Bartlett's beamforming (BF) (also known as conventional BF, matched field, or phased array),...
The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are non-Gaussian, therefore, the AR model with more general heavytailed innovations is preferred. Another issue th...
In this paper, the optimal mean-reverting portfolio (MRP) design problem is considered, which plays an important role for the statistical arbitrage (a.k.a. pairs trading) strategy in financial markets. The target of the optimal MRP design is to construct a portfolio from the underlying assets that can exhibit a satisfactory mean reversion property...
The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data are non-Gaussian, therefore, the AR model with more general heavy-tailed innovations are preferred. Another issue t...
Interference management is a fundamental issue in device-to-device (D2D) communications whenever the transmitter-and-receiver pairs are located geographically in close proximity and frequencies are fully reused, so active links may severely interfere with each other. This paper devises an optimization strategy named FPLinQ to coordinate the link sc...
In this paper, we will solve the phase retrieval (PR) problem over a distributed network, where each agent only has a subset of the measurements. The problem is formulated as minimizing the squared loss between the measurements and linear sensing intensity. To solve the problem in a distributed setting, an algorithm named distributed Wirtinger flow...
In this paper, we study the problem of option portfolio design under the Markowitz mean-variance framework. We extend the common practice of a pure-stock portfolio and include options in the design. The options returns are modeled statistically with first- and second-order moments, enriching the conventional delta-gamma approximation. The naive mea...
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The problem is formulated to minimize the least squares loss with a sparsity-inducing penalty considering an orth...
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 to the array by considering different practical wa...
This paper considers the mean-reverting portfolio (MRP) design problem arising from statistical arbitrage (a.k.a. pairs trading) in the financial markets. It aims at designing a portfolio of underlying assets by optimizing the mean reversion strength of the portfolio, while taking into consideration the portfolio variance and an investment budget c...
Downlink channel estimation is an important task in any wireless communication system, and 5G massive multiple-input multiple-output (MIMO) in particular---because the receiver must estimate and feed back to the transmitter a high-dimensional multiple-input single-output (MISO) vector channel for each receiving element. This is a serious burden in...
In econometrics and finance, the vector error correction model (VECM) is an important time series model for cointegration analysis, which is used to estimate the long-run equilibrium variable relationships. The traditional analysis and estimation methodologies assume the underlying Gaussian distribution but, in practice, heavy-tailed data and outli...
Index tracking is a popular passive portfolio management strategy that aims at constructing a portfolio that replicates or tracks the performance of a financial index. The tracking error can be minimized by purchasing all the assets of the index in appropriate amounts. However, to avoid small and illiquid positions and large transaction costs, it i...
We propose a novel heuristic method for optimizing planar pixel antennas which we refer to as Successive Exhaustive Boolean Optimization (SEBO). The key step in SEBO is to cyclically optimize a multivariable binary optimization problem by exhaustively searching a subset of binary variables. An adaptive version of SEBO is also introduced. We provide...
This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence results. The extensions, acceleration schemes, and conne...
This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. We first propose a general problem formulation aimed at finding a portfolio of underlying component assets by optimizing a mean-reversion criterion characterizing the mean-reversion strength, taking into consideration the va...
This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. The problem is formulated by optimizing a criterion characterizing the mean-reversion strength of the portfolio and taking into consideration the variance of the portfolio and an investment budget constraint at the same time...
In this paper, we conduct the joint design of transmitting sequence(s) and receiving filters subject to the Peak-to- Average Ratio (PAR) constraint in radar and communications applications. We consider optimizing the worst-case performance and the resulting optimization problem takes a maximin format. We propose two algorithms based on the MM (Majo...
The ambiguity function plays an important role in radar systems. In fact, many radar design problems can be interpreted from the perspective of persuing desired ambiguity functions to adapt to various application scenes. In this paper, we consider designing a radar sequence, subject to a peak-toaverage power ratio (PAR) constraint, to maximize the...
In this paper, we consider the low autocorrelation sequence design problem. We optimize a unified metric over a general constraint set. The unified metric includes the integrated sidelobe level (ISL) and the peak sidelobe level (PSL) as special cases, and the general constraint set contains the unimodular constraint, Peak-to-Average Ratio (PAR) con...
Phase noise correction is crucial to exploit full advantage of orthogonal frequency division multiplexing (OFDM) in modern high-data-rate communications. OFDM channel estimation with simultaneous phase noise compensation has therefore drawn much attention and stimulated continuing efforts. Existing methods, however, either have not taken into accou...
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with superior performance based on the majorization-minimization (MM) framework. The proposed algorithms are referred t...
This paper considers robust low-rank matrix completion in the presence of outliers. The objective is to recover a low-rank data matrix from a small number of noisy observations. We exploit the bilinear factorization formulation and develop a novel algorithm fully utilizing parallel computing resources. Our main contributions are i) providing two sm...
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce the number of required measurements since a recent theory established that $M\approx4N$ intensity measurements...
The twelve papers in this special issue presents relevant research contributions from the disciplines of finance, mathematics, data science and engineering to facilitate scientific cross-fertilization. It will also serve the signal processing community to be exposed to the state of the art in mathematical finance, financial engineering, financial s...
This paper addresses the problem of the clutter subspace projector estimation in the context of a disturbance composed of a low rank heterogeneous (Compound Gaussian) clutter and white Gaussian noise. We derive two algorithms based on the block majorization-minimization framework to reach the maximum likelihood estimator of the considered model. Th...
This paper considers a network of energy harvesting wireless nodes transmitting simultaneously in a Gaussian interference channel and investigates a distributed power allocation algorithm that maximizes the sum-rate. The power consumption model is based on a series of step functions that allow to model, among others, radio frequency circuits being...
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with a known mean. In applications where the covariance matrix naturally possesses a certain structure, taking the prior structure information into account in the estimation procedure is beneficial to improving the estim...
We study nonconvex distributed optimization in multiagent networks wherein the communications between nodes is modeled as a time-varying sequence of arbitrary digraphs. We introduce a novel broadcast-based algorithmic framework for the (constrained) minimization of the sum of a smooth (possibly nonconvex and nonseparable) function, i.e., the agents...
An original estimator of the orthogonal projector onto the signal subspace is proposed. This estimator is derived as the maximum likelihood estimator for a model of sources plus orthogonal outliers, both with varying power (modeled by Compound Gaussians process), embedded in a white Gaussian noise. Validity and interest — in terms of performance an...
We present an approach to solve the nonconvex optimization problem that arises when designing the transmit covariance matrices in multiuser multiple-input multiple-output (MIMO) broadcast networks implementing simultaneous wireless information and power transfer (SWIPT). The MIMO SWIPT problem is formulated as a general multi-objective optimization...
Citations
... 15ˆ of portfolio using TWE [44] of portfolio using OPP [ ...
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... Despite the extensive literature on solving similar, yet simpler, problems [20], [21], [22], [23], [24], [25], [26], [27], [28], [11], [29], [30], the only approach for handling (P ) suggests to apply the following semidefinite (SDP) relaxation [13]: ...