The schooling behavior of fish can be studied through simulations involving a large number of interacting particles. In such systems, each individual particle is guided by behavior rules, which include aggregation towards a centroid, collision avoidance, and direction alignment. The movement vector of each particle may be expressed as a linear combination of behaviors, with unknown parameters that define a trade-off among several behavioral constraints. A fitness function for collective schooling behavior encompasses all individual particle parameters. For a large number of interacting particles in a complex environment, heuristic methods, such as evolutionary algorithms, are used to optimize the fitness function, ensuring that the resulting decision rule preserves collective behavior. However, these algorithms exhibit slow convergence, making them inefficient in terms of CPU time cost. This paper proposes a CPU-efficient iterative (Cluster, Partition, Refine -- CPR) algorithm for estimating decision rule parameters for a large number of interacting particles. In the first step, we employ the K-Means (unsupervised learning) algorithm to cluster candidate solutions. Then, we partition the search space using Voronoi tessellation over the defined clusters. We assess the quality of each cluster based on the fitness function, with the centroid of their Voronoi cells representing the clusters. Subsequently, we refine the search space by introducing new cells into a number of identified well-fitting Voronoi cells. This process is repeated until convergence. A comparison of the performance of the CPR algorithm with a standard Genetic Algorithm reveals that the former converges faster than the latter. We also demonstrate that the application of the CPR algorithm results in a schooling behavior consistent with empirical observations.
Neuromorphic sampling is a bioinspired and opportunistic analog-to-digital conversion technique, where the measurements are recorded only when there is a significant change in the signal amplitude. Neuromorphic sampling has paved the way for a new class of vision sensors called event cameras or dynamic vision sensors (DVS), which consume low power, accommodate a high-dynamic range, and provide sparse measurements with high temporal resolution making it convenient for downstream inference tasks. In this paper, we consider neuromorphic sensing of signals with a finite rate of innovation (FRI), including a stream of Dirac impulses, sum of weighted and time-shifted pulses, and piecewise-polynomial functions. We consider a sampling-theoretic approach and leverage the close connection between neuromorphic sensing and time-based sampling, where the measurements are encoded temporally. Using Fourier-domain analysis, we show that perfect signal reconstruction is possible via parameter estimation using high-resolution spectral estimation methods. We develop a kernel-based sampling approach, which allows for perfect reconstruction with a sample complexity equal to the rate of innovation of the signal. We provide sufficient conditions on the parameters of the neuromorphic encoder for perfect reconstruction. Furthermore, we extend the analysis to multichannel neuromorphic sampling of FRI signals, in the single-input multi-output (SIMO) and multi-input multi-output (MIMO) configurations. We show that the signal parameters can be jointly estimated using multichannel measurements. Experimental results are provided to substantiate the theoretical claims.
In this paper, we investigate sub-6 GHz V2X sidelink positioning scenarios in 5G vehicular networks through a comprehensive end-to-end methodology encompassing ray-tracing-based channel modeling, novel theoretical performance bounds, high-resolution channel parameter estimation, and geometric positioning using a round-trip-time (RTT) protocol. We first derive a novel, approximate Cram\'er-Rao bound (CRB) on the connected road user (CRU) position, explicitly taking into account multipath interference, path merging, and the RTT protocol. Capitalizing on tensor decomposition and ESPRIT methods, we propose high-resolution channel parameter estimation algorithms specifically tailored to dense multipath V2X sidelink environments, designed to detect multipath components (MPCs) and extract line-of-sight (LoS) parameters. Finally, using realistic ray-tracing data and antenna patterns, comprehensive simulations are conducted to evaluate channel estimation and positioning performance, indicating that sub-meter accuracy can be achieved in sub-6 GHz V2X with the proposed algorithms.
In a previous work we introduced, in the context of gravitational wave science, an initial study on an automated domain-decomposition approach for reduced basis through hp-greedy refinement. The approach constructs local reduced bases of lower dimensionality than global ones, with the same or higher accuracy. These ``light'' local bases should imply both faster evaluations when predicting new waveforms and faster data analysis, in particular faster statistical inference (the forward and inverse problems, respectively). In this approach, however, we have previously found important dependence on several hyperparameters, which do not appear in global reduced basis. This naturally leads to the problem of hyperparameter optimization (HPO), which is the subject of this paper. We tackle the problem through a Bayesian optimization, and show its superiority when compared to grid or random searches. We find that for gravitational waves from the collision of two spinning but non-precessing black holes, for the same accuracy, local hp-greedy reduced bases with HPO have a lower dimensionality of up to $4 \times$ for the cases here studied, depending on the desired accuracy. This factor should directly translate in a parameter estimation speedup, for instance. Such acceleration might help in the near real-time requirements for electromagnetic counterparts of gravitational waves from compact binary coalescences. In addition, we find that the Bayesian approach used in this paper for HPO is two orders of magnitude faster than, for example, a grid search, with about a $100 \times$ acceleration. The code developed for this project is available as open source from public repositories.
Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.
Motivated by the need to localise faults along electrical power lines, this paper adopts a frequency-domain approach to parameter estimation for an infinite-dimensional linear dynamical system with one spatial variable. Since the time of the fault is unknown, and voltages and currents are measured at only one end of the line, distance information must be extracted from the post-fault transients. To properly account for high-frequency transient behaviour, the line dynamics is modelled directly by the Telegrapher's equation, rather than the more commonly used lumped-parameter approximations. First, the governing equations are non-dimensionalised to avoid ill-conditioning. A closed-form expression for the transfer function is then derived. Finally, nonlinear least-squares optimisation is employed to search for the fault location. Requirements on fault bandwidth, sensor bandwidth and simulation time-step are also presented. The result is a novel end-to-end algorithm for data generation and fault localisation, the effectiveness of which is demonstrated via simulation.
Recently, channel extrapolation has been widely investigated in frequency division duplex (FDD) massive MIMO systems. However, in time division duplex (TDD) fifth generation (5G) new radio (NR) systems, the channel extrapolation problem also arises due to the hopping uplink pilot pattern, which has not been fully researched yet. This paper addresses this gap by formulating a channel extrapolation problem in TDD massive MIMO-OFDM systems for 5G NR, incorporating imperfection factors. A novel two-stage two-dimensional (2D) channel extrapolation scheme in both frequency and time domain is proposed, designed to mitigate the negative effects of imperfection factors and ensure high-accuracy channel estimation. Specifically, in the channel estimation stage, we propose a novel multi-band and multi-timeslot based high-resolution parameter estimation algorithm to achieve 2D channel extrapolation in the presence of imperfection factors. Then, to avoid repeated multi-timeslot based channel estimation, a channel tracking stage is designed during the subsequent time instants, in which a sparse Markov channel model is formulated to capture the dynamic sparsity of massive MIMO-OFDM channels under the influence of imperfection factors. Next, an expectation-maximization (EM) based compressive channel tracking algorithm is designed to jointly estimate unknown imperfection and channel parameters by exploiting the high-resolution prior information of the delay/angle parameters from the previous timeslots. Simulation results underscore the superior performance of our proposed channel extrapolation scheme over baselines.
The thermal inertia of buildings brings considerable flexibility to the heating and cooling load, which is known to be a promising demand response resource. The aggregate model that can describe the thermal dynamics of the building cluster is an important interference for energy systems to exploit its intrinsic thermal inertia. However, the private information of users, such as the indoor temperature and heating/cooling power, needs to be collected in the parameter estimation procedure to obtain the aggregate model, causing severe privacy concerns. In light of this, we propose a novel privacy-preserved parameter estimation approach to infer the aggregate model for the thermal dynamics of the building cluster for the first time. Using it, the parameters of the aggregate thermal dynamic model (ATDM) can be obtained by the load aggregator without accessing the individual's privacy information. More specifically, this method not only exploits the block coordinate descent (BCD) method to resolve its non-convexity in the estimation but investigates the transformation-based encryption (TE) associated with its secure aggregation protocol (SAP) techniques to realize privacy-preserved computation. Its capability of preserving privacy is also theoretically proven. Finally, simulation results using real-world data demonstrate the accuracy and privacy-preserved performance of our proposed method.
We propose an approach utilizing gamma-distributed random variables, coupled with log-Gaussian modeling, to generate synthetic datasets suitable for training neural networks. This addresses the challenge of limited real observations in various applications. We apply this methodology to both Raman and coherent anti-Stokes Raman scattering (CARS) spectra, using experimental spectra to estimate gamma process parameters. Parameter estimation is performed using Markov chain Monte Carlo methods, yielding a full Bayesian posterior distribution for the model which can be sampled for synthetic data generation. Additionally, we model the additive and multiplicative background functions for Raman and CARS with Gaussian processes. We train two Bayesian neural networks to estimate parameters of the gamma process which can then be used to estimate the underlying Raman spectrum and simultaneously provide uncertainty through the estimation of parameters of a probability distribution. We apply the trained Bayesian neural networks to experimental Raman spectra of phthalocyanine blue, aniline black, naphthol red, and red 264 pigments and also to experimental CARS spectra of adenosine phosphate, fructose, glucose, and sucrose. The results agree with deterministic point estimates for the underlying Raman and CARS spectral signatures.
Future wireless networks are envisioned to provide ubiquitous sensing services, which also gives rise to a substantial demand for high-dimensional non-convex parameter estimation, i.e., the associated likelihood function is non-convex and contains numerous local optima. Variational Bayesian inference (VBI) provides a powerful tool for modeling complex estimation problems and reasoning with prior information, but poses a long-standing challenge on computing intractable posteriori distributions. Most existing variational methods generally rely on assumptions about specific distribution families to derive closed-form solutions, and are difficult to apply in high-dimensional, non-convex scenarios. Given these challenges, firstly, we propose a parallel stochastic particle variational Bayesian inference (PSPVBI) algorithm. Thanks to innovations such as particle approximation, additional updates of particle positions, and parallel stochastic successive convex approximation (PSSCA), PSPVBI can flexibly drive particles to fit the posteriori distribution with acceptable complexity, yielding high-precision estimates of the target parameters. Furthermore, additional speedup can be obtained by deep-unfolding (DU) the PSPVBI algorithm. Specifically, superior hyperparameters are learned to dramatically reduce the number of algorithmic iterations. In this PSPVBI-induced Deep-Unfolding Networks, some techniques related to gradient computation, data sub-sampling, differentiable sampling, and generalization ability are also employed to facilitate the practical deployment. Finally, we apply the LPSPVBI to solve several important parameter estimation problems in wireless sensing scenarios. Simulations indicate that the LPSPVBI algorithm outperforms existing solutions.
We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the covariance of a Gaussian up to spectral error $\alpha$ requires $\tilde{\Omega}\left(\frac{d^{3/2}}{\alpha \varepsilon} + \frac{d}{\alpha^2}\right)$ samples, which is tight up to logarithmic factors. This result improves over previous work which established this for $\alpha \le O\left(\frac{1}{\sqrt{d}}\right)$, and is also simpler than previous work. Next, we prove that estimating the mean of a heavy-tailed distribution with bounded $k$th moments requires $\tilde{\Omega}\left(\frac{d}{\alpha^{k/(k-1)} \varepsilon} + \frac{d}{\alpha^2}\right)$ samples. Previous work for this problem was only able to establish this lower bound against pure differential privacy, or in the special case of $k = 2$. Our techniques follow the method of fingerprinting and are generally quite simple. Our lower bound for heavy-tailed estimation is based on a black-box reduction from privately estimating identity-covariance Gaussians. Our lower bound for covariance estimation utilizes a Bayesian approach to show that, under an Inverse Wishart prior distribution for the covariance matrix, no private estimator can be accurate even in expectation, without sufficiently many samples.
In this paper, we show how convolutional neural networks (CNN) can be used in regression and classification learning problems of noisy and non-noisy functional data. The main idea is to transform the functional data into a 28 by 28 image. We use a specific but typical architecture of a convolutional neural network to perform all the regression exercises of parameter estimation and functional form classification. First, we use some functional case studies of functional data with and without random noise to showcase the strength of the new method. In particular, we use it to estimate exponential growth and decay rates, the bandwidths of sine and cosine functions, and the magnitudes and widths of curve peaks. We also use it to classify the monotonicity and curvatures of functional data, algebraic versus exponential growth, and the number of peaks of functional data. Second, we apply the same convolutional neural networks to Lyapunov exponent estimation in noisy and non-noisy chaotic data, in estimating rates of disease transmission from epidemic curves, and in detecting the similarity of drug dissolution profiles. Finally, we apply the method to real-life data to detect Parkinson's disease patients in a classification problem. The method, although simple, shows high accuracy and is promising for future use in engineering and medical applications.
Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework -- named AI-Aristotle -- combines eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification. We test the accuracy, speed, flexibility and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model, and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. While the current work focuses on the performance of AI-Aristotle based on synthetic data, it can equally handle noisy experimental data and can even be used for black-box identification in just a few minutes on a laptop. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond.
The integration of power electronic converters (PECs) and distributed energy resources (DERs) in modern power systems has introduced dynamism and complexity. Accurate simulation becomes essential to comprehend the influence of converter domination on the power grid. This study addresses the fast-switching and stochastic behaviors exhibited by inverter-based resources in converter-dominated power systems, highlighting the necessity for precise analytical models. In the realm of modeling real-world systems, multiple methodologies exist. Notably, black-box and data-driven system identification techniques are employed to construct PEC models using experimental data, without relying on a priori knowledge of the internal system physics. This approach entails a systematic process of model class selection, parameter estimation, and model validation. While a range of linear and nonlinear model structures and estimation algorithms are at our disposal, it remains imperative to harness creativity and a profound understanding of the physical system to craft data-driven models that align seamlessly with their intended applications. These applications may encompass simulation, prediction, control, or fault detection. This report offers valuable insights into the collection of datasets from commercial off-the-shelf inverters, along with the presentation of intricate simulation models.
We present the HOH (Human-Object-Human) Handover Dataset, a large object count dataset with 136 objects, to accelerate data-driven research on handover studies, human-robot handover implementation, and artificial intelligence (AI) on handover parameter estimation from 2D and 3D data of person interactions. HOH contains multi-view RGB and depth data, skeletons, fused point clouds, grasp type and handedness labels, object, giver hand, and receiver hand 2D and 3D segmentations, giver and receiver comfort ratings, and paired object metadata and aligned 3D models for 2,720 handover interactions spanning 136 objects and 20 giver-receiver pairs-40 with role-reversal-organized from 40 participants. We also show experimental results of neural networks trained using HOH to perform grasp, orientation, and trajectory prediction. As the only fully markerless handover capture dataset, HOH represents natural human-human handover interactions, overcoming challenges with markered datasets that require specific suiting for body tracking, and lack high-resolution hand tracking. To date, HOH is the largest handover dataset in number of objects, participants, pairs with role reversal accounted for, and total interactions captured.
In order to further advance the accuracy and robustness of the incremental parameter estimation-based rotation averaging methods, in this paper, a new member of the Incremental Rotation Averaging (IRA) family is introduced, which is termed as IRAv4. As its most significant feature, a task-specific connected dominating set is extracted in IRAv4 to serve as a more reliable and accurate reference for rotation local-to-global alignment. This alignment reference is incrementally constructed, together with the absolute rotations of the vertices belong to it simultaneously estimated. Comprehensive evaluations are performed on the 1DSfM dataset, by which the effectiveness of both the reference construction method and the entire rotation averaging pipeline proposed in this paper is demonstrated.
This work proposes a maximum likelihood (ML)-based parameter estimation framework for a millimeter wave (mmWave) integrated sensing and communication (ISAC) system in a multi-static configuration using energy-efficient hybrid digital-analog arrays. Due to the typically large arrays deployed in the higher frequency bands to mitigate isotropic path loss, such arrays may operate in the near-field regime. The proposed parameter estimation in this work consists of a two-stage estimation process, where the first stage is based on far-field assumptions, and is used to obtain a first estimate of the target parameters. In cases where the target is determined to be in the near-field of the arrays, a second estimation based on near-field assumptions is carried out to obtain more accurate estimates. In particular, we select beamfocusing array weights designed to achieve a constant gain over an extended spatial region and re-estimate the target parameters at the receivers. We evaluate the effectiveness of the proposed framework in numerous scenarios through numerical simulations and demonstrate the impact of the custom-designed flat-gain beamfocusing codewords in increasing the communication performance of the system.
We consider secure transmission of a deterministic complex-valued parameter vector from a transmitter to an intended receiver in the presence of an eavesdropper in a reconfigurable intelligent surface (RIS)-integrated environment. We aim to jointly optimize the RIS phase profile and the power allocation matrix at the transmitter to enhance the estimation accuracy at the intended receiver while limiting that at the eavesdropper. We utilize the trace of the Fisher information matrix (FIM), equivalently, the average Fisher information, as the estimation accuracy metric, and obtain its closed form expression for the intended receiver and the eavesdropper. Accordingly, the joint RIS phase profile and power allocation problem is formulated, and it is solved via alternating optimization. When the power allocation matrix is fixed during alternating optimization, the optimal RIS phase profile design problem is formulated as a non-convex problem and it is solved via semidefinite relaxation and rank reduction. When the RIS phase profile is fixed, a linear programming formulation is obtained for optimal power allocation. Via simulations, the effects of RIS phase design and power allocation are illustrated individually and jointly. Moreover, extensions are provided by considering the presence of line of sight paths in the environment and the availability of RIS elements with adjustable magnitudes.
Mathematical models (MMs) are a powerful tool to help us understand and predict the dynamics of tumour growth under various conditions. In this work, we use 5 MMs with an increasing number of parameters to explore how certain (often overlooked) decisions in estimating parameters from data of experimental tumour growth affect the outcome of the analysis. In particular, we propose a framework for including tumour volume measurements that fall outside the upper and lower limits of detection, which are normally discarded. We demonstrate how excluding censored data results in an overestimation of the initial tumour volume and the MM-predicted tumour volumes prior to the first measurements, and an underestimation of the carrying capacity and the MM-predicted tumour volumes beyond the latest measurable time points. We show in which way the choice of prior for the MM parameters can impact the posterior distributions, and illustrate that reporting the highest-likelihood parameters and their 95% credible interval can lead to confusing or misleading interpretations. We hope this work will encourage others to carefully consider choices made in parameter estimation and to adopt the approaches we put forward herein.
In recent years, dynamic parameterization of acoustic environments has raised increasing attention in the field of audio processing. One of the key parameters that characterize the local room acoustics in isolation from orientation and directivity of sources and receivers is the geometric room volume. Convolutional neural networks (CNNs) have been widely selected as the main models for conducting blind room acoustic parameter estimation, which aims to learn a direct mapping from audio spectrograms to corresponding labels. With the recent trend of self-attention mechanisms, this paper introduces a purely attention-based model to blindly estimate room volumes based on single-channel noisy speech signals. We demonstrate the feasibility of eliminating the reliance on CNN for this task and the proposed Transformer architecture takes Gammatone magnitude spectral coefficients and phase spectrograms as inputs. To enhance the model performance given the task-specific dataset, cross-modality transfer learning is also applied. Experimental results demonstrate that the proposed model outperforms traditional CNN models across a wide range of real-world acoustics spaces, especially with the help of the dedicated pretraining and data augmentation schemes.