arXiv subjects

Petre Stoica

Publications and source records attributed to Petre Stoica.

At least 37 records · Page 2Linked to original sources

arXiv2022

Tuned Regularized Estimators for Linear Regression via Covariance Fitting

We consider the problem of finding tuned regularized parameter estimators for linear models. We start by showing that three known optimal linear estimators belong to a wider class of estimators that can be formulated as a solution to a weighted and constrained minimization problem. The optimal weights, however, are typically unknown in many applications. This begs the question, how should we choose the weights using only the data? We propose using the covariance fitting SPICE-methodology to obtain data-adaptive weights and show that the resulting class of estimators yields tuned versions of known regularized estimators - such as ridge regression, LASSO, and regularized least absolute deviation. These theoretical results unify several important estimators under a common umbrella. The resulting tuned estimators are also shown to be practically relevant by means of a number of numerical examples.

math.ST↗

arXiv2021

Learning Pareto-Efficient Decisions with Confidence

The paper considers the problem of multi-objective decision support when outcomes are uncertain. We extend the concept of Pareto-efficient decisions to take into account the uncertainty of decision outcomes across varying contexts. This enables quantifying trade-offs between decisions in terms of tail outcomes that are relevant in safety-critical applications. We propose a method for learning efficient decisions with statistical confidence, building on results from the conformal prediction literature. The method adapts to weak or nonexistent context covariate overlap and its statistical guarantees are evaluated using both synthetic and real data.

stat.ML↗

arXiv2021

Weighted SPICE Algorithms for Range-Doppler Imaging Using One-Bit Automotive Radar

We consider the problem of range-Doppler imaging using one-bit automotive LFMCW1 or PMCW radar that utilizes one-bit ADC sampling with time-varying thresholds at the receiver. The one-bit sampling technique can significantly reduce the cost as well as the power consumption of automotive radar systems. We formulate the one-bit LFMCW/PMCW radar rangeDoppler imaging problem as one-bit sparse parameter estimation. The recently proposed hyperparameter-free (and hence user friendly) weighted SPICE algorithms, including SPICE, LIKES, SLIM and IAA, achieve excellent parameter estimation performance for data sampled with high precision. However, these algorithms cannot be used directly for one-bit data. In this paper we first present a regularized minimization algorithm, referred to as 1bSLIM, for accurate range-Doppler imaging using onebit radar systems. Then, we describe how to extend the SPICE, LIKES and IAA algorithms to the one-bit data case, and refer to these extensions as 1bSPICE, 1bLIKES and 1bIAA. These onebit hyperparameter-free algorithms are unified within the one-bit weighted SPICE framework. Moreover, efficient implementations of the aforementioned algorithms are investigated that rely heavily on the use of FFTs. Finally, both simulated and experimental examples are provided to demonstrate the effectiveness of the proposed algorithms for range-Doppler imaging using one-bit automotive radar systems.

eess.SP↗

arXiv2021

RFI Mitigation for One-bit UWB Radar Systems

Radio frequency interference (RFI) mitigation is critical to the proper operation of ultra-wideband (UWB) radar systems since RFI can severely degrade the radar imaging capability and target detection performance. In this paper, we address the RFI mitigation problem for one-bit UWB radar systems. A one-bit UWB system obtains its signed measurements via a low-cost and high rate sampling scheme, referred to as the Continuous Time Binary Value (CTBV) technology. This sampling strategy compares the signal to a known threshold varying with slow-time and therefore can be used to achieve a rather high sampling rate and quantization resolution with rather simple and affordable hardware. This paper establishes a proper data model for the RFI sources and proposes a novel RFI mitigation method for the one-bit UWB radar system that uses the CTBV sampling technique. Specifically, we first model the RFI sources as a sum of sinusoids with frequencies fixed during the coherent processing interval (CPI) and we exploit the sparsity of the RFI spectrum. We extend a majorization-minimization based 1bRELAX algorithm, referred to as 1bMMRELAX, to estimate the RFI source parameters from the signed measurements obtained by using the CTBV sampling strategy. We also devise a new fast frequency initialization method based on the Alternating Direction Method of Multipliers (ADMM) methodology for the extended 1bMMRELAX algorithm to significantly improve its computational efficiency. Moreover, an ADMM-based sparse method is introduced to recover the desired radar echoes using the estimated RFI parameters. Both simulated and experimental results are presented to demonstrate that our proposed algorithm outperforms the existing digital integration method, especially for severe RFI cases.

eess.SP↗

arXiv2021

Sinusoidal Parameter Estimation from Signed Measurements via Majorization-Minimization Based RELAX

We consider the problem of sinusoidal parameter estimation using signed observations obtained via one-bit sampling with fixed as well as time-varying thresholds. In a previous paper, a relaxation-based algorithm, referred to as 1bRELAX, has been proposed to iteratively maximize the likelihood function. However, the exhaustive search procedure used in each iteration of 1bRELAX is time-consuming. In this paper, we present a majorization-minimization (MM) based 1bRELAX algorithm, referred to as 1bMMRELAX, to enhance the computational efficiency of 1bRELAX. Using the MM technique, 1bMMRELAX maximizes the likelihood function iteratively using simple FFT operations instead of the more computationally intensive search used by 1bRELAX. Both simulated and experimental results are presented to show that 1bMMRELAX can significantly reduce the computational cost of 1bRELAX while maintaining its excellent estimation accuracy.

eess.SP↗

arXiv2021

Joint RFI Mitigation and Radar Echo Recovery for One-Bit UWB Radar

Radio frequency interference (RFI) mitigation and radar echo recovery are critically important for the proper functioning of ultra-wideband (UWB) radar systems using one-bit sampling techniques. We recently introduced a technique for one-bit UWB radar, which first uses a majorization-minimization method for RFI parameter estimation followed by a sparse method for radar echo recovery. However, this technique suffers from high computational complexity due to the need to estimate the parameters of each RFI source separately and iteratively. In this paper, we present a computationally efficient joint RFI mitigation and radar echo recovery framework to greatly reduce the computational cost. Specifically, we exploit the sparsity of RFI in the fast-frequency domain and the sparsity of radar echoes in the fast-time domain to design a one-bit weighted SPICE (SParse Iterative Covariance-based Estimation) based framework for the joint RFI mitigation and radar echo recovery of one-bit UWB radar. Both simulated and experimental results are presented to show that the proposed one-bit weighted SPICE framework can not only reduce the computational cost but also outperform the existing approach for decoupled RFI mitigation and radar echo recovery of one-bit UWB radar.

eess.SP↗

arXiv2021

Robust Localization in Wireless Networks From Corrupted Signals

We address the problem of timing-based localization in wireless networks, when an unknown fraction of data is corrupted by nonideal signal conditions. While timing-based techniques enable accurate localization, they are also sensitive to such corrupted data. We develop a robust method that is applicable to a range of localization techniques, including time-of-arrival, time-difference-of-arrival and time-difference in schedule-based transmissions. The method is nonparametric and requires only an upper bound on the fraction of corrupted data, thus obviating distributional assumptions of the corrupting noise distribution. The robustness of the method is demonstrated in numerical experiments.

cs.IT↗

arXiv2020

Prediction of Spatial Point Processes: Regularized Method with Out-of-Sample Guarantees

A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using a regularized criterion. We prove that the proposed method exhibits out-of-sample prediction performance guarantees which, unlike standard estimators, are valid even when the spatial model is misspecified. The method is demonstrated using synthetic as well as real spatial data.

stat.ML↗

arXiv2020

Robust Prediction when Features are Missing

Predictors are learned using past training data which may contain features that are unavailable at the time of prediction. We develop an approach that is robust against outlying missing features, based on the optimality properties of an oracle predictor which observes them. The robustness properties of the approach are demonstrated on both real and synthetic data.

eess.SP↗

arXiv2019

Effect Inference from Two-Group Data with Sampling Bias

In many applications, different populations are compared using data that are sampled in a biased manner. Under sampling biases, standard methods that estimate the difference between the population means yield unreliable inferences. Here we develop an inference method that is resilient to sampling biases and is able to control the false positive errors under moderate bias levels in contrast to the standard approach. We demonstrate the method using synthetic and real biomarker data.

math.ST↗

arXiv2019

Max-Min Fairness Design for MIMO Interference Channels: a Minorization-Maximization Approach

We address the problem of linear precoder (beamformer) design in a multiple-input multiple-output interference channel (MIMO-IC). The aim is to design the transmit covariance matrices in order to achieve max-min utility fairness for all users. The corresponding optimization problem is non-convex and NP-hard in general. We devise an efficient algorithm based on the minorization-maximization (MM) technique to obtain quality solutions to this problem. The proposed method solves a second-order cone convex program (SOCP) at each iteration. We prove that the devised method converges to stationary points of the problem. We also extend our algorithm to the case where there are uncertainties in the noise covariance matrices or channel state information (CSI). Simulation results show the effectiveness of the proposed method compared with its main competitor.

eess.SP↗

arXiv2019

Data Consistency Approach to Model Validation

In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The contribution in this paper is a general criterion to evaluate the consistency of a set of statistical models with respect to observed data. This is achieved by automatically gauging the models' ability to generate data that is similar to the observed data. Importantly, the criterion follows from the model class itself and is therefore directly applicable to a broad range of inference problems with varying data types, ranging from independent univariate data to high-dimensional time-series. The proposed data consistency criterion is illustrated, evaluated and compared to several well-established methods using three synthetic and two real data sets.

stat.ME↗

arXiv2018

Model-Robust Counterfactual Prediction Method

We develop a novel method for counterfactual analysis based on observational data using prediction intervals for units under different exposures. Unlike methods that target heterogeneous or conditional average treatment effects of an exposure, the proposed approach aims to take into account the irreducible dispersions of counterfactual outcomes so as to quantify the relative impact of different exposures. The prediction intervals are constructed in a distribution-free and model-robust manner based on the conformal prediction approach. The computational obstacles to this approach are circumvented by leveraging properties of a tuning-free method that learns sparse additive predictor models for counterfactual outcomes. The method is illustrated using both real and synthetic data.

math.ST↗

arXiv2018

Recursive nonlinear-system identification using latent variables

In this paper we develop a method for learning nonlinear systems with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood principle we derive a criterion for learning the model. The resulting optimization problem is tackled using a majorization-minimization approach. Finally, we develop a convex majorization technique and show that it enables a recursive identification method. The method learns parsimonious predictive models and is tested on both synthetic and real nonlinear systems.

stat.ML↗

arXiv2017

Prediction performance after learning in Gaussian process regression

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean square-error (MSE). This approach, however, does not take into account that the statistical model is learned from the data. We show that this omission leads to a systematic underestimation of the prediction errors. Starting from a generalization of the Cramér-Rao bound, we derive a more accurate MSE bound which provides a measure of uncertainty for prediction of Gaussian processes. The improved bound is easily computed and we illustrate it using synthetic and real data examples. of uncertainty for prediction of Gaussian processes and illustrate it using synthetic and real data examples.

stat.ML↗

arXiv2017

Online Learning for Distribution-Free Prediction

We develop an online learning method for prediction, which is important in problems with large and/or streaming data sets. We formulate the learning approach using a covariance-fitting methodology, and show that the resulting predictor has desirable computational and distribution-free properties: It is implemented online with a runtime that scales linearly in the number of samples; has a constant memory requirement; avoids local minima problems; and prunes away redundant feature dimensions without relying on restrictive assumptions on the data distribution. In conjunction with the split conformal approach, it also produces distribution-free prediction confidence intervals in a computationally efficient manner. The method is demonstrated on both real and synthetic datasets.

cs.LG↗

arXiv2017

PUMA criterion = MODE criterion

We show that the recently proposed (enhanced) PUMA estimator for array processing minimizes the same criterion function as the well-established MODE estimator. (PUMA = principal-singular-vector utilization for modal analysis, MODE = method of direction estimation.)

stat.OT↗

arXiv2017

Sparse Methods for Direction-of-Arrival Estimation

Direction-of-arrival (DOA) estimation refers to the process of retrieving the direction information of several electromagnetic waves/sources from the outputs of a number of receiving antennas that form a sensor array. DOA estimation is a major problem in array signal processing and has wide applications in radar, sonar, wireless communications, etc. With the development of sparse representation and compressed sensing, the last decade has witnessed a tremendous advance in this research topic. The purpose of this article is to provide an overview of these sparse methods for DOA estimation, with a particular highlight on the recently developed gridless sparse methods, e.g., those based on covariance fitting and the atomic norm. Several future research directions are also discussed.

cs.IT↗