We propose a novel estimation procedure for models with endogenous variables in the presence of spatial correlation based on Eigenvector Spatial Filtering. The procedure, called Moran's $I$ 2-Stage Lasso (Mi-2SL), uses a two-stage Lasso estimator where the Standardised Moran's I is used to set the Lasso tuning parameter. Unlike existing spatial econometric methods, this has the key benefit of not requiring the researcher to explicitly model the spatial correlation process, which is of interest in cases where they are only interested in removing the resulting bias when estimating the direct effect of covariates. We show the conditions necessary for consistent and asymptotically normal parameter estimation assuming the support (relevant) set of eigenvectors is known. Our Monte Carlo simulation results also show that Mi-2SL performs well against common alternatives in the presence of spatial correlation. Our empirical application replicates Cadena and Kovak (2016) instrumental variables estimates using Mi-2SL and shows that in that case, Mi-2SL can boost the performance of the first stage.
With the leaping advances in autonomous vehicles and transportation infrastructure, dual function radar-communication (DFRC) systems have become attractive due to the size, cost and resource efficiency. A frequency modulated continuous waveform (FMCW)-based radar-communication system (FRaC) utilizing both sparse multiple-input and multiple-output (MIMO) arrays and index modulation (IM) has been proposed to form a DFRC system specifically designed for vehicular applications. In this paper, the three-dimensional (3D) parameter estimation problem in the FRaC is considered. Since the 3D-parameters including range, direction of arrival (DOA) and velocity are coupled in the estimating matrix of the FRaC system, the existing estimation algorithms cannot estimate the 3D-parameters accurately. Hence, a novel decomposed decoupled atomic norm minimization (DANM) method is proposed by splitting the 3D-parameter estimating matrix into multiple 2D matrices with sparsity constraints. Then, the 3D-parameters are estimated and efficiently and separately with the optimized decoupled estimating matrix. Moreover, the Cram\'{e}r-Rao lower bound (CRLB) of the 3D-parameter estimation are derived, and the computational complexity of the proposed algorithm is analyzed. Simulation results show that the proposed decomposed DANM method exploits the advantage of the virtual aperture in the existence of coupling caused by IM and sparse MIMO array and outperforms the co-estimation algorithm with lower computation complexity.
Generating graphs that preserve characteristic structures while promoting sample diversity can be challenging, especially when the number of graph observations is small. Here, we tackle the problem of graph generation from only one observed graph. The classical approach of graph generation from parametric models relies on the estimation of parameters, which can be inconsistent or expensive to compute due to intractable normalisation constants. Generative modelling based on machine learning techniques to generate high-quality graph samples avoids parameter estimation but usually requires abundant training samples. Our proposed generating procedure, SteinGen, which is phrased in the setting of graphs as realisations of exponential random graph models, combines ideas from Stein's method and MCMC by employing Markovian dynamics which are based on a Stein operator for the target model. SteinGen uses the Glauber dynamics associated with an estimated Stein operator to generate a sample, and re-estimates the Stein operator from the sample after every sampling step. We show that on a class of exponential random graph models this novel "estimation and re-estimation" generation strategy yields high distributional similarity (high fidelity) to the original data, combined with high sample diversity.
This paper develops an adaptive state tracking control scheme for discrete-time systems, using the least-squares algorithm, as the new solution to the long-standing discrete-time adaptive state tracking control problem to which the Lyapunov method (well-developed for the continuous-time adaptive state tracking problem) is not applicable. The new adaptive state tracking scheme is based on a recently-developed new discrete-time error model which has been used for gradient algorithm based state tracking control schemes, and uses the least-squares algorithm for parameter adaptation. The new least-squares algorithm is derived to minimize an accumulative estimation error, to ensure certain optimality for parameter estimation. The system stability and output tracking properties are studied. Technical results are presented in terms of plant-model matching, error model, adaptive law, optimality formulation, and stability and tracking analysis. The developed adaptive control scheme is applied to a discrete-time multiple mobile robot system to meet an adaptive state tracking objective. In addition, a collision avoidance mechanism is proposed to prevent collisions in the whole tracking process. Simulation results are presented, which verify the desired system state tracking properties under the developed least-squares algorithm based adaptive control scheme.
Neuroinflammation immediately follows the onset of ischemic stroke in the middle cerebral artery. During this process, microglial cells are activated in and recruited to the penumbra. Microglial cells can be activated into two different phenotypes: M1, which can worsen brain injury; or M2, which can aid in long-term recovery. In this study, we contribute a summary of experimental data on microglial cell counts in the penumbra following ischemic stroke induced by middle cerebral artery occlusion (MCAO) in mice and compile available data sets into a single set suitable for time series analysis. Further, we formulate a mathematical model of microglial cells in the penumbra during ischemic stroke due to MCAO. Through use of global sensitivity analysis and Markov Chain Monte Carlo (MCMC)-based parameter estimation, we analyze the effects of the model parameters on the number of M1 and M2 cells in the penumbra and fit identifiable parameters to the compiled experimental data set. We utilize results from MCMC parameter estimation to ascertain uncertainty bounds and forward predictions for the number of M1 and M2 microglial cells over time. Results demonstrate the significance of parameters related to M1 and M2 activation on the number of M1 and M2 microglial cells. Simulations further suggest that potential outliers in the observed data may be omitted and forecast predictions suggest a lingering inflammatory response.
This work examines the optimal covariance steering problem for systems subject to unknown parameters that enter multiplicatively with the state and control, in addition to additive disturbances. In contrast to existing works, the unknown parameters are modeled as random variables and are estimated online. This work proposes the utilization of recursive least squares estimation for efficient parameter identification. A dual control problem is formulated in which the effect of the planned control policy on the parameter estimates is modeled and optimized for. The parameter estimates are then used to modify the pre-computed control policy online in an adaptive control fashion. Finally, the proposed approach is demonstrated in a vehicle control example with closed-loop parameter identification.
In adaptive control theory, the dynamic regressor extension and mixing (DREM) procedure has become widespread as it allows one to describe major of adaptive control problems in unified terms of the parameter estimation problem of a regression equation with a scalar regressor. However, when the system/parameterization is affected by perturbations, the estimation laws, which are designed on the basis of such equation, asymptotically provides only biased estimates. In this paper, based on the bias-eliminated least-squares (BELS) approach, a modification of DREM procedure is proposed to annihilate perturbations asymptotically and, consequently, asymptotically obtain unbiased estimates. The theoretical results are supported with mathematical modelling and can be used to design adaptive observers and control systems.
The ability to accurately infer cardiac electrophysiological (EP) properties is key to improving arrhythmia diagnosis and treatment. In this work, we developed a physics-informed neural networks (PINNs) framework to predict how different myocardial EP parameters are modulated by anti-arrhythmic drugs. Using $\textit{in vitro}$ optical mapping images and the 3-channel Fenton-Karma model, we estimated the changes in ionic channel conductance caused by these drugs. Our framework successfully characterised the action of drugs HMR1556, nifedipine and lidocaine - respectively, blockade of $I_{K}$, $I_{Ca}$, and $I_{Na}$ currents - by estimating that they decreased the respective channel conductance by $31.8\pm2.7\%$ $(p=8.2 \times 10^{-5})$, $80.9\pm21.6\%$ $(p=0.02)$, and $8.6\pm0.5\%$ $ (p=0.03)$, leaving the conductance of other channels unchanged. For carbenoxolone, whose main action is the blockade of intercellular gap junctions, PINNs also successfully predicted no significant changes $(p>0.09)$ in all ionic conductances. Our results are an important step towards the deployment of PINNs for model parameter estimation from experimental data, bringing this framework closer to clinical or laboratory images analysis and for the personalisation of mathematical models.
Nakagami imaging holds promise for visualizing and quantifying tissue scattering in ultrasound waves, with potential applications in tumor diagnosis and fat fraction estimation which are challenging to discern by conventional ultrasound B-mode images. Existing methods struggle with optimal window size selection and suffer from estimator instability, leading to degraded resolution images. To address this, here we propose a novel method called UNICORN (Ultrasound Nakagami Imaging via Score Matching and Adaptation), that offers an accurate, closed-form estimator for Nakagami parameter estimation in terms of the score function of ultrasonic envelope. Extensive experiments using simulation and real ultrasound RF data demonstrate UNICORN's superiority over conventional approaches in accuracy and resolution quality.
Despite the frequent use of agent-based models (ABMs) for studying social phenomena, parameter estimation remains a challenge, often relying on costly simulation-based heuristics. This work uses variational inference to estimate the parameters of an opinion dynamics ABM, by transforming the estimation problem into an optimization task that can be solved directly. Our proposal relies on probabilistic generative ABMs (PGABMs): we start by synthesizing a probabilistic generative model from the ABM rules. Then, we transform the inference process into an optimization problem suitable for automatic differentiation. In particular, we use the Gumbel-Softmax reparameterization for categorical agent attributes and stochastic variational inference for parameter estimation. Furthermore, we explore the trade-offs of using variational distributions with different complexity: normal distributions and normalizing flows. We validate our method on a bounded confidence model with agent roles (leaders and followers). Our approach estimates both macroscopic (bounded confidence intervals and backfire thresholds) and microscopic ($200$ categorical, agent-level roles) more accurately than simulation-based and MCMC methods. Consequently, our technique enables experts to tune and validate their ABMs against real-world observations, thus providing insights into human behavior in social systems via data-driven analysis.
Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models presents a substantial challenge, either due to the high computational requirements of model-based approaches or the limited robustness of deep learning (DL) methods. We propose a novel framework that leverages the unique strengths of both approaches in a synergistic manner. Our method incorporates a DL ensemble for initial parameter estimation, facilitating efficient downstream evolutionary sampling initialized with this DL-based prior. We showcase the effectiveness of integrating a rapid deep-learning algorithm with a high-precision evolution strategy in estimating brain tumor cell concentrations from magnetic resonance images. The DL-Prior plays a pivotal role, significantly constraining the effective sampling-parameter space. This reduction results in a fivefold convergence acceleration and a Dice-score of 95%.
This study addresses the challenges in parameter estimation of stochastic differential equations driven by non-Gaussian noises, which are critical in understanding dynamic phenomena such as price fluctuations and the spread of infectious diseases. Previous research highlighted the potential of LSTM networks in estimating parameters of alpha stable Levy driven SDEs but faced limitations including high time complexity and constraints of the LSTM chaining property. To mitigate these issues, we introduce the PEnet, a novel CNN-LSTM-based three-stage model that offers an end to end approach with superior accuracy and adaptability to varying data structures, enhanced inference speed for long sequence observations through initial data feature condensation by CNN, and high generalization capability, allowing its application to various complex SDE scenarios. Experiments on synthetic datasets confirm PEnet significant advantage in estimating SDE parameters associated with noise characteristics, establishing it as a competitive method for SDE parameter estimation in the presence of Levy noise.
We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) constructed from an overfitted latent mixing measure. Our proposed method bridges agglomerative hierarchical clustering and mixture modeling. The dendrogram's construction is derived from the theory of convergence of the mixing measures, and as a result, we can both consistently select the true number of mixing components and obtain the pointwise optimal convergence rate for parameter estimation from the tree, even when the model parameters are only weakly identifiable. In theory, it explicates the choice of the optimal number of clusters in hierarchical clustering. In practice, the dendrogram reveals more information on the hierarchy of subpopulations compared to traditional ways of summarizing mixture models. Several simulation studies are carried out to support our theory. We also illustrate the methodology with an application to single-cell RNA sequence analysis.
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions (e.g., maximum likelihood estimation for Gaussian distribution), or by iterative numerical methods such as Newton-Raphson method when closed-form solution does not exist (e.g., for Beta distribution). In this paper we propose a transformer-based approach to parameter estimation. Compared with existing solutions, our approach does not require a closed-form solution or any mathematical derivations. It does not even require knowing the probability density function, which is needed by numerical methods. After the transformer model is trained, only a single inference is needed to estimate the parameters of the underlying distribution based on a sample of observations. In the empirical study we compared our approach with maximum likelihood estimation on commonly used distributions such as normal distribution, exponential distribution and beta distribution. It is shown that our approach achieves similar or better accuracy as measured by mean-square-errors.
Purpose: Echo modulation curve (EMC) modeling can provide accurate and reproducible quantification of T2 relaxation times. The standard EMC-T2 mapping framework, however, requires sufficient echoes and cumbersome pixel-wise dictionary-matching steps. This work proposes a deep learning version of EMC-T2 mapping, called DeepEMC-T2 mapping, to efficiently estimate accurate T2 maps from fewer echoes without a dictionary. Methods: DeepEMC-T2 mapping was developed using a modified U-Net to estimate both T2 and Proton Density (PD) maps directly from multi-echo spin-echo (MESE) images. The modified U-Net employs several new features to improve the accuracy of T2/PD estimation. MESE datasets from 68 subjects were used for training and evaluation of the DeepEMC-T2 mapping technique. Multiple experiments were conducted to evaluate the impact of the proposed new features on DeepEMC-T2 mapping. Results: DeepEMC-T2 mapping achieved T2 estimation errors ranging from 3%-12% in different T2 ranges and 0.8%-1.7% for PD estimation with 10/7/5/3 echoes, which yielded more accurate parameter estimation than standard EMC-T2 mapping. The new features proposed in DeepEMC-T2 mapping enabled improved parameter estimation. The use of a larger echo spacing with fewer echoes can maintain the accuracy of T2 and PD estimations while reducing the number of 180-degree refocusing pulses. Conclusions: DeepEMC-T2 mapping enables simplified, efficient, and accurate T2 quantification directly from MESE images without a time-consuming dictionary-matching step and requires fewer echoes. This allows for increased volumetric coverage and/or decreased SAR by reducing the number of 180-degree refocusing pulses.
This paper addresses a critical preliminary step in radar signal processing: detecting the presence of a radar signal and robustly estimating its bandwidth. Existing methods which are largely statistical feature-based approaches face challenges in electronic warfare (EW) settings where prior information about signals is lacking. While alternate deep learning based methods focus on more challenging environments, they primarily formulate this as a binary classification problem. In this research, we propose a novel methodology that not only detects the presence of a signal, but also localises it in the time domain and estimates its operating frequency band at that point in time. To achieve robust estimation, we introduce a compound loss function that leverages complementary information from both time-domain and frequency-domain representations. By integrating these approaches, we aim to improve the efficiency and accuracy of radar signal detection and parameter estimation, reducing both unnecessary resource consumption and human effort in downstream tasks.
This work presents an algorithm for determining the parameters of a nonlinear dynamic model of the respiratory system in patients undergoing assisted ventilation. Using the pressure and flow signals measured at the mouth, the model's quadratic pressure-volume characteristic is fit to this data in each respiratory cycle by appropriate estimates of the model parameters. Parameter changes during ventilation can thus also be detected. The algorithm is first refined and assessed using data derived from simulated patients represented through a sigmoidal pressure-volume characteristic with hysteresis. As satisfactory results are achieved with the simulated data, the algorithm is evaluated with real data obtained from actual patients undergoing assisted ventilation. The proposed nonlinear dynamic model and associated parameter estimation algorithm yield closer fits than the static linear models computed by respiratory machines, with only a minor increase in computation. They also provide more information to the physician, such as the pressure-volume (P-V) curvature and the condition of the lung (whether normal, under-inflated, or over-inflated). This information can be used to provide safer ventilation for patients, for instance by ventilating them in the linear region of the respiratory system.
Dynamic parameterization of acoustic environments has drawn widespread attention in the field of audio processing. Precise representation of local room acoustic characteristics is crucial when designing audio filters for various audio rendering applications. Key parameters in this context include reverberation time (RT60) and geometric room volume. In recent years, neural networks have been extensively applied in the task of blind room parameter estimation. However, there remains a question of whether pure attention mechanisms can achieve superior performance in this task. To address this issue, this study employs blind room parameter estimation based on monaural noisy speech signals. Various model architectures are investigated, including a proposed attention-based model. This model is a convolution-free Audio Spectrogram Transformer, utilizing patch splitting, attention mechanisms, and cross-modality transfer learning from a pretrained Vision Transformer. Experimental results suggest that the proposed attention mechanism-based model, relying purely on attention mechanisms without using convolution, exhibits significantly improved performance across various room parameter estimation tasks, especially with the help of dedicated pretraining and data augmentation schemes. Additionally, the model demonstrates more advantageous adaptability and robustness when handling variable-length audio inputs compared to existing methods.
Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state estimation, however can have difficulty learning the parameters accurately. On the other hand, machine learning based approaches can naturally learn the state and parameters, but their applicability can be limited, or produce uncertainties that are hard to interpret. Inspired by the Integrated Nested Laplace Approximation (INLA) method in spatial statistics, we propose an alternative approach to DA based on iteratively linearising the dynamical model. This produces a Gaussian Markov random field at each iteration, enabling one to use INLA to infer the state and parameters. Our approach can be used for arbitrary nonlinear systems, while retaining interpretability, and is furthermore demonstrated to outperform existing methods on the DA task. By providing a more nuanced approach to handling nonlinear PDE priors, our methodology offers improved accuracy and robustness in predictions, especially where data sparsity is prevalent.
What does it take to build mobile manipulation systems that can competently operate on previously unseen objects in previously unseen environments? This work answers this question using opening of articulated structures as a mobile manipulation testbed. Specifically, our focus is on the end-to-end performance on this task without any privileged information, i.e. the robot starts at a location with the novel target articulated object in view, and has to approach the object and successfully open it. We first develop a system for this task, and then conduct 100+ end-to-end system tests across 13 real world test sites. Our large-scale study reveals a number of surprising findings: a) modular systems outperform end-to-end learned systems for this task, even when the end-to-end learned systems are trained on 1000+ demonstrations, b) perception, and not precise end-effector control, is the primary bottleneck to task success, and c) state-of-the-art articulation parameter estimation models developed in isolation struggle when faced with robot-centric viewpoints. Overall, our findings highlight the limitations of developing components of the pipeline in isolation and underscore the need for system-level research, providing a pragmatic roadmap for building generalizable mobile manipulation systems. Videos, code, and models are available on the project website: https://arjung128.github.io/opening-articulated-structures/