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We consider optimization problems in which the objective requires an inner loop with many steps or is the limit of a sequence of increasingly costly approximations. Meta-learning, training recurrent neural networks, and optimization of the…
Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…
The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm that incorporates the gradient of the logarithm of the target density in its proposal distribution. In an earlier joint work \citet{pill:stu:12}, the author had…
We consider the frequency estimation of periodic signals using noisy time-of-arrival (TOA) information with missing (sparse) data contaminated with outliers. We tackle the problem from a mathematical optimization standpoint, formulating it…
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…
To provide backup and augmentation to global navigation satellite system (GNSS), Doppler shift from Low Earth Orbit (LEO) satellites can be employed as signals of opportunity (SOP) for position, navigation and timing (PNT). Since the…
Hybrid localization in GNSS-challenged environments using measured ranges and angles is becoming increasingly popular, in particular with the advent of multimodal communication systems. Here, we address the hybrid network localization…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…
We consider an optimization deployment problem of multistatic radar system (MSRS). Through the antenna placing and the transmitted power allocating, we optimally deploy the MSRS for two goals: 1) the first one is to improve the coverage…
This paper presents an analysis of target localization accuracy, attainable by the use of MIMO (Multiple-Input Multiple-Output) radar systems, configured with multiple transmit and receive sensors, widely distributed over a given area. The…
A popular method to estimate the positions or directions-of-arrival (DOAs) of multiple sound sources using an array of microphones is based on steered-response power (SRP) beamforming. For a three-dimensional scenario, SRP-based methods…
Wavefront phase retrieval from a set of intensity measurements can be formulated as an optimization problem. Two nonconvex objective models (MLP and its variants LS) based on maximum likelihood estimation are investigated. We develop…
Location-Based Services (LBSs) provide invaluable aid in the everyday activities of many individuals, however they also pose serious threats to the user' privacy. There is, therefore, a growing interest in the development of mechanisms to…
The accuracy of time difference of arrival (TDOA)-based source localization is influenced by sensor location deployment. Many studies focus on optimal sensor placement (OSP) for TDOA-based localization without sensor location noises…
This paper addresses maximum likelihood (ML) estimation based model fitting in the context of extrasolar planet detection. This problem is featured by the following properties: 1) the candidate models under consideration are highly…
Large language model (LLM) training is often bottlenecked by memory constraints and stochastic gradient noise in extremely high-dimensional parameter spaces. Motivated by empirical evidence that many LLM gradient matrices are effectively…
In this paper, we study estimators for geometric optimization problems in the sublinear geometric model. In this model, we have oracle access to a point set with size $n$ in a discrete space $[\Delta]^d$, where queries can be made to an…
We address the joint estimation of the number of targets and their direction-of-arrivals (DoAs) using antenna arrays. Target-number estimation can be formulated as a model-order selection problem and solved with the information theoretic…
A new method for estimating the relative positions of location-unaware nodes from the location-aware nodes and the received signal strength (RSS) between the nodes, in a wireless sensor network (WSN), is proposed. In the method, a…