We consider the joint problem of online experiment design and parameter estimation for identifying nonlinear system models, while adhering to system constraints. We utilize a receding horizon approach and propose a new adaptive input design criterion, which is tailored to continuously updated parameter estimates, along with a new sequential estimator. We demonstrate the ability of the method to design informative experiments online, while steering the system within operational constraints.

Inventory control is subject to service-level requirements, in which sufficient stock levels must be maintained despite unknown demand. We propose a data-driven order policy that certifies any prescribed service level under minimal assumptions on the demand process. The policy achieves this by adding an adjustment to any base policy. We further propose a method for forecasting the policy's operational costs that is valid in finite samples. Properties and guarantees of the method are illustrated using both synthetic and real-world data.

We consider the problem of tracking moving targets using mobile wireless sensors (of possibly different types). This is a joint estimation and control problem in which a tracking system must take into account both target and sensor dynamics. We make minimal assumptions about the target dynamics, namely only that their accelerations are bounded. We develop a control law that determines the sensor motion control signals so as to maximize target resolvability as the target dynamics evolve. The method is given a tractable formulation that is amenable to an efficient search method and is evaluated in a series of experiments involving both round-trip time based ranging and Doppler frequency shift measurements

Graph learning is an important problem in the field of graph signal processing. However, the data available in real-world applications are often contaminated with outliers, which makes the application of traditional methods challenging. In this paper, we address this problem by developing an algorithm that effectively learns the graph Laplacian matrix from node signals corrupted by outliers. Specifically, we maximize the penalized log-likelihood of the uncorrupted data, where the penalty is chosen via the false discovery rate (FDR) principle, with respect to both the number of outliers and their locations, as well as the precision matrix of the data under the graph Laplacian constraints. To illustrate the robustness to outliers, we compare our method with two state-of-the-art graph learning methods, one that considers outliers in the data and one that does not, using different performance metrics. Our findings demonstrate that the proposed method efficiently detects the number and positions of outliers and accurately learns the graph in their presence.

In this article, we propose a robust technique for direction-of-arrival (DOA) estimation in the presence of outliers, which may be caused by either impulsive noise or malfunctioning sensors in the array. Conventional DOA estimation algorithms like multiple signal classification (MUSIC) cannot accurately estimate the DOAs from outlier-corrupted data because the array covariance matrix is poorly estimated. We propose a penalized likelihood approach to robustly estimate the signal (low-rank) part of the array covariance matrix and apply MUSIC to this estimated covariance matrix to find the DOAs. The penalty in the proposed algorithm is derived from the principle of false discovery rate. Simulation results verify the effectiveness of the proposed approach when compared with state-of-the-art robust DOA estimation algorithms.

In this letter we present a framework for estimating sparse covariance matrices, wherein we solve the l(0)-norm penalized maximum likelihood estimation problem using the extended Bayesian information criterion (EBIC), a high dimensional model selection rule. The framework combines choosing the sparsity pattern and estimating the covariance matrix in a single step, eliminating the need for any hyper-parameter tuning. Using the framework we propose a cyclic majorization-minimization based technique and apply it to synthetic data to evaluate its performance in terms of normalized root mean square error (NRMSE) and Kullback Leibler (KL) divergence.

In this correspondence we develop an algorithm for maximum likelihood (ML) source localization using received signal strength (RSS) measurements. Unlike the conventional methods that resort to first-order Taylor series approximations to linearize the RSS data model, we use the actual non-linear data model and propose an algorithm for solving the associated ML estimation problem. More specifically, we reformulate the original ML minimization as a min-max problem which we solve using a majorization-minimization technique. Each iteration of the resultant algorithm involves solving a simple convex problem and monotonically decreases the (negative) ML criterion. Several numerical simulation results illustrate the accuracy of the proposed method when compared against state-of-the-art methods.

In many applications, system identification experiments must be performed in closed loop to ensure safety or to maintain system operation. In this paper, we consider the recursive design of informative experiments for ARMAX models by adding a bounded probing signal to the input generated by a fixed output feedback controller. The resulting output perturbations should be kept within user-specified limits. We analyze the identifiability and feasibility conditions of this setting and then proceed to derive a probing signal that can be efficiently computed in closed form. We demonstrate the effectiveness and properties of the design in numerical experiments.

In this letter, we revisit the recently proposed cell outlier-resistant method cellMCD (minimum covariance determinant) and derive a version of it called cellMCD+ that has better performance. We illustrate the performance gain of cellMCD+ via numerical simulations in the case of estimating low-rank structured covariance matrices.

Multistatic localization techniques employ noisy range measurements collected via multiple transmitters and receivers to localize a target. However, in many realistic scenarios the data are corrupted by outliers which may be due to the failure of or malicious attack on one or more sensors. The presence of outliers leads to performance degradation in terms of target localization accuracy. In this letter, we address the problem of multistatic target localization when the measurements contain outliers. We employ a multi-hypothesis testing method based on the false discovery rate (FDR) to detect the outliers. More specifically, we consider a penalized maximum likelihood problem for joint estimation of the number and positions of the outliers as well as the target position, and the noise variance. To solve this problem, an iterative algorithm employing the majorization-minimization technique that minimizes the objective in a monotonic manner is developed. Through numerical simulations, we compare the proposed algorithm with other robust state-of-the-art algorithms and show that the proposed algorithm has superior performance.

This paper investigates the transmit beamforming design for multiple-input multiple-output systems to support both multi-target localization and multi-user communications. To enhance the target localization performance, we derive the asymptotic Cramér-Rao bound (CRB) for target angle estimation by assuming that the receive array is linear and uniform. Then we formulate a beamforming design problem based on minimizing an upper bound on the asymptotic CRB (which is shown to be equivalent to maximizing the harmonic mean of the weighted beampattern responses at the target directions). Moreover, we impose a constraint on the SINR of each received communication signal to guarantee reliable communication performance. Two iterative algorithms are derived to tackle the non-convex design problem: one is based on the alternating direction method of multipliers, and the other uses the majorization-minimization technique to solve an equivalent minimax problem. Numerical results show that, through elaborate dual-function beamforming matrix design, the proposed algorithms can simultaneously achieve superior angle estimation performance as well as high-quality multi-user communications.

We consider the problem of evaluating the performance of a decision policy using past observational data. The outcome of a policy is measured in terms of a loss (aka. disutility or negative reward) and the main problem is making valid inferences about its out-of-sample loss when the past data was observed under a different and possibly unknown policy. Using a sample-splitting method, we show that it is possible to draw such inferences with finite-sample coverage guarantees about the entire loss distribution, rather than just its mean. Importantly, the method takes into account model misspecifications of the past policy - including unmeasured confounding. The evaluation method can be used to certify the performance of a policy using observational data under a specified range of credible model assumptions.

In this paper, we propose a numerical method for the optimal placement of the receivers in a multistatic target localization system (with a single transmitter and multiple receivers) in order to improve the achievable target estimation accuracy of time-sum-of-arrival (TSOA) localization techniques, for 2D and 3D scenarios. The proposed algorithm is based on the principle of block majorization minimization (block MM) which is a combination of block coordinate descent and majorization-minimization (MM) methods. More precisely, we formulate the design objective for the placement of sensors performing TSOA measurements using A - and D - optimality criteria, and propose an iterative algorithm to find the optimal solution by first splitting the design variable into M blocks (where M is the number of receivers) and then applying the principle of MM on each block. The proposed method can additionally handle the cases where the transmitter also acts as a receiver. The framework can also be applied to the case of non-uniform noise variances at the receivers. Several numerical simulation results are included to show the benefits offered by the developed design algorithm.

In a recent paper we have proposed an approach for estimating the covariance matrix from a multivariate data set {y( t )} that may contain outliers. If y( t ) is flagged as outlying by this approach, then the entire vector y( t ) is considered to contain no useful information and it is discarded. However, in some applications the data contains cell outliers, that is to say, not all elements of y( t ) are outlying but only some of them. One then wants to eliminate only the cell outliers from the data, rather than the entire vector y( t ). In this paper, we propose a penalized maximum likelihood approach to outlier detection and covariance matrix estimation from data with cell outliers. Specifically we estimate the positions of the outliers in the data set, for a given estimate of the covariance matrix, by maximizing the penalized likelihood of the data with the penalty being derived from a property of the likelihood ratio and the false discovery rate (FDR) principle. We alternate this step with a majorization-minimization (MM) technique that estimates the covariance matrix for given outlier positions. The MM is more flexible than the expectation maximization (EM) algorithm commonly used for estimating the covariance matrix from data with missing cells, as the former can be utilized in cases in which the latter is not usable. The closest competitor of our approach is the cellMCD (minimum covariance determinant) method, compared with which the proposed approach has a number of advantages described in the introduction and the numerical study section.

In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state-of-the-art methods, which either use regularization techniques or penalize the likelihood to impose sparsity, we solve the MLE problem based on an estimated covariance graph. More specifically, we propose a two-stage procedure: in the first stage, we determine the sparsity pattern of the target covariance matrix (in other words the marginal independence in the covariance graph under a Gaussian graphical model) using the multiple hypothesis testing method of false discovery rate (FDR), and in the second stage we use either a block coordinate descent approach to estimate the non-zero values or a proximal distance approach that penalizes the distance between the estimated covariance graph and the target covariance matrix. Doing so gives rise to two different methods, each with its own advantage: the coordinate descent approach does not require tuning of any hyper-parameters, whereas the proximal distance approach is computationally fast but requires a careful tuning of the penalty parameter. Both methods are effective even in cases where the number of observed samples is less than the dimension of the data. For performance evaluation, we test the proposed methods on both simulated and real-world data and show that they provide more accurate estimates of the sparse covariance matrix than the state-of-the-art methods.

The robust estimation of the covariance matrix is a frequent task in practical applications in which, more often than not, some data samples are outliers. There are several methods that can be used to robustly estimate a covariance matrix from corrupted data, a representative example of which is the m inimum c ovariance d eterminant (MCD) method. In this paper we present a maximum conditional likelihood interpretation of MCD that provides a new motivation of as well as further insights into this method. To perform at its best MCD requires information on the number of outliers in the data, which usually is not available. We propose two new methods for covariance matrix estimation from data with outliers that do not suffer from this problem: TEST (multiple-hypothesis test ing method) which uses the FDR (false discovery rate) to test a set of model hypotheses and hence estimate the number of outliers and their locations, and LIKE (penalized like lihood method) that solves the outlier estimation problem using a GIC (generalized information criterion) to penalize the complexity of a high-dimensional data model. We show by means of numerical simulations that the performances of TEST and LIKE are relatively similar to one another as well as to the performance of the oracle MCD (which uses the true number of outliers) and significantly better than the performance of MCD that uses an upper bound on the outlier number.

The Pearson-Matthews correlation coefficient (usually abbreviated MCC) is considered to be one of the most useful metrics for the performance of a binary classification. For multinary classification tasks (with more than two classes) the existing extension of MCC, commonly called the R K metric, has also been successfully used in many applications. The present paper begins with an introductory discussion on certain aspects of MCC. Then we go on to discuss the topic of multinary classification that is the main focus of this paper and which, despite its practical and theoretical importance, appears to be less developed than the topic of binary classification. Our discussion of the R K is followed by the introduction of two other metrics for multinary classification derived from the multivariate Pearson correlation (MPC) coefficients. We show that both R K and the MPC metrics suffer from the problem of not decisively indicating poor classification results when they should, and introduce three new enhanced metrics that do not suffer from this problem. We also present an additional new metric for multinary classification which can be viewed as a direct extension of MCC.

Assessment of model fitness is a key part of machine learning. The standard paradigm is to learn models by minimizing a chosen loss function averaged over training data, with the aim of achieving small losses on future data. In this paper, we consider the use of a finite calibration data set to characterize the future, out-of-sample losses of a model. We propose a simple model diagnostic tool that provides finite-sample guarantees under weak assumptions. The tool is simple to compute and to interpret. Several numerical experiments are presented to show how the proposed method quantifies the impact of distribution shifts, aids the analysis of regression, and enables model selection as well as hyper-parameter tuning.

We consider the problem of online prediction using linear smoothers that are functions of a nominal covariance model with unknown parameters. The model parameters are often learned using cross-validation or maximum-likelihood techniques. But when training data arrives in a streaming fashion, the implementation of such techniques can only be done in an approximate manner. Even if this limitation could be overcome, there appears to be no clear-cut results on the statistical properties of the resulting predictor. Here we consider a covariance-fitting method to learn the model parameters, which was initially developed for spectral estimation. We first show that the use of this approach results in a computationally efficient online learning method in which the resulting predictor can be updated sequentially. We then prove that, with high probability, its out-of-sample error approaches the optimal level at a root-$n$ rate, where $n$ is the number of data samples. This is so even if the nominal covariance model is misspecified. Moreover, we show that the resulting predictor enjoys two robustness properties. First, it corresponds to a predictor that minimizes the out-of-sample error with respect to the least favourable distribution within a given Wasserstein distance from the empirical distribution. Second, it is robust against errors in the covariate training data. We illustrate the performance of the proposed method in a numerical experiment.