We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy minimization on the space of probability distributions equipped with the Wasserstein metric. We outline the general method and show its competitiveness in posterior representation and parameter estimation on two state-space models for which Gaussian approximations typically fail: systems with multiplicative noise and multi-modal state distributions.
Achieving optimal statistical performance while ensuring the privacy of personal data is a challenging yet crucial objective in modern data analysis. However, characterizing the optimality, particularly the minimax lower bound, under privacy constraints is technically difficult. To address this issue, we propose a novel approach called the score attack, which provides a lower bound on the differential-privacy-constrained minimax risk of parameter estimation. The score attack method is based on the tracing attack concept in differential privacy and can be applied to any statistical model with a well-defined score statistic. It can optimally lower bound the minimax risk of estimating unknown model parameters, up to a logarithmic factor, while ensuring differential privacy for a range of statistical problems. We demonstrate the effectiveness and optimality of this general method in various examples, such as the generalized linear model in both classical and high-dimensional sparse settings, the Bradley-Terry-Luce model for pairwise comparisons, and nonparametric regression over the Sobolev class.
Quantitative MRI (qMRI) aims to map tissue properties non-invasively via models that relate these unknown quantities to measured MRI signals. Estimating these unknowns, which has traditionally required model fitting - an often iterative procedure, can now be done with one-shot machine learning (ML) approaches. Such parameter estimation may be complicated by intrinsic qMRI signal model degeneracy: different combinations of tissue properties produce the same signal. Despite their many advantages, it remains unclear whether ML approaches can resolve this issue. Growing empirical evidence appears to suggest ML approaches remain susceptible to model degeneracy. Here we demonstrate under the right circumstances ML can address this issue. Inspired by recent works on the impact of training data distributions on ML-based parameter estimation, we propose to resolve model degeneracy by designing training data distributions. We put forward a classification of model degeneracies and identify one particular kind of degeneracies amenable to the proposed attack. The strategy is demonstrated successfully using the Revised NODDI model with standard multi-shell diffusion MRI data as an exemplar. Our results illustrate the importance of training set design which has the potential to allow accurate estimation of tissue properties with ML.
Existing approaches to system identification (estimating the physical parameters of an object) from videos assume known object geometries. This precludes their applicability in a vast majority of scenes where object geometries are complex or unknown. In this work, we aim to identify parameters characterizing a physical system from a set of multi-view videos without any assumption on object geometry or topology. To this end, we propose "Physics Augmented Continuum Neural Radiance Fields" (PAC-NeRF), to estimate both the unknown geometry and physical parameters of highly dynamic objects from multi-view videos. We design PAC-NeRF to only ever produce physically plausible states by enforcing the neural radiance field to follow the conservation laws of continuum mechanics. For this, we design a hybrid Eulerian-Lagrangian representation of the neural radiance field, i.e., we use the Eulerian grid representation for NeRF density and color fields, while advecting the neural radiance fields via Lagrangian particles. This hybrid Eulerian-Lagrangian representation seamlessly blends efficient neural rendering with the material point method (MPM) for robust differentiable physics simulation. We validate the effectiveness of our proposed framework on geometry and physical parameter estimation over a vast range of materials, including elastic bodies, plasticine, sand, Newtonian and non-Newtonian fluids, and demonstrate significant performance gain on most tasks.
SAR technology has been intensively implemented for geo-sensing and mapping purposes due to its advantages of high azimuthal resolution and weather-independent operation compared to other remote sensing technologies. Modelling SAR image data consequently becomes a prominent topic of interest, especially for data populations with impulsive signal features, which are common in SAR images of urban areas. A recently proposed model named Cauchy-Rician has manifested great potential in modelling extremely heterogeneous SAR images, yet the work only provided a MCMC-based parameter estimator that demands considerable computational power. In this work, a novel analytical parameter estimation method based on algebraic moments is proposed to provide stable and accurate estimation of the parameters of the Cauchy-Rician model with significant improvement on computation speed.
This paper presents an adaptive control approach for uncertain nonlinear systems subject to safety constraints that allows for modularity in the selection of the parameter estimation algorithm. Such modularity is achieved by unifying the concepts of input-to-state stability (ISS) and input-to-state safety (ISSf) via control Lyapunov functions (CLFs) and control barrier functions (CBFs), respectively. In particular, we propose a class of exponential ISS-CLFs and ISSf high order CBFs that can be combined with a general class of parameter estimation algorithms akin to those found in the literature on concurrent learning adaptive control. We demonstrate that the unification of ISS and ISSf in an adaptive control setting allows for maintaining a single set of parameter estimates for both the CLF and CBF that can be generated by a class of update laws satisfying a few general properties. The modularity of our approach is demonstrated via numerical examples by comparing performance in terms of stability and safety across different parameter estimation algorithms.
For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is not chosen carefully, models with either large variance or large bias would be resulted, which is one of the obstacles to further improve the modeling and tracking performances of data-driven ILC in practice. An emerging trend in the system identification community to deal with this issue is using regularization instead of the statistical tests, e.g., AIC, BIC, and one of the representatives is the so-called kernel-based regularization method (KRM). In this paper, we integrate KRM into data-driven ILC to handle a class of repetitive linear time-varying systems, and moreover, we show that the proposed method has ultimately bounded tracking error in the iteration domain. The numerical simulation results show that in contrast with the least squares method and some existing data-driven ILC methods, the proposed one can give faster convergence speed, better accuracy and robustness in terms of the tracking performance.
We investigate an optimization problem in a queueing system where the service provider selects the optimal service fee p and service capacity \mu to maximize the cumulative expected profit (the service revenue minus the capacity cost and delay penalty). The conventional predict-then-optimize (PTO) approach takes two steps: first, it estimates the model parameters (e.g., arrival rate and service-time distribution) from data; second, it optimizes a model based on the estimated parameters. A major drawback of PTO is that its solution accuracy can often be highly sensitive to the parameter estimation errors because PTO is unable to properly link these errors (step 1) to the quality of the optimized solutions (step 2). To remedy this issue, we develop an online learning framework that automatically incorporates the aforementioned parameter estimation errors in the solution prescription process; it is an integrated method that can "learn" the optimal solution without needing to set up the parameter estimation as a separate step as in PTO. Effectiveness of our online learning approach is substantiated by (i) theoretical results including the algorithm convergence and analysis of the regret ("cost" to pay over time for the algorithm to learn the optimal policy), and (ii) engineering confirmation via simulation experiments of a variety of representative examples. We also provide careful comparisons for PTO and the online learning method.
In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case. Bayesian inference has been very successful because this technique provides a representation of the parameters as a posterior probability distribution, with uncertainties informed by the precision of the experimental measurements. During the last couple of decades, many specific advances have been proposed and employed in order to solve a large variety of different problems. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm that integrates many of those concepts into a single MCMC package. For this purpose, we have built {\tt Eryn}, a user-friendly and multipurpose toolbox for Bayesian inference, which can be utilized for solving parameter estimation and model selection problems, ranging from simple inference questions, to those with large-scale model variation requiring trans-dimensional MCMC methods, like the LISA global fit problem. In this paper, we describe this sampler package and illustrate its capabilities on a variety of use cases.
Physics-informed deep learning is a popular trend in the modeling and control of dynamical systems. This paper presents a novel method for rapid online identification of vehicle cornering stiffness coefficient, a crucial parameter in vehicle stability control models and control algorithms. The new method enables designers to rapidly identify the vehicle front and rear cornering stiffness parameters so that the controller reference gains can be re-adjusted under varying road and vehicle conditions to improve the reference tracking performance of the control system during operation. The proposed method based on vehicle model-based deep learning is compared to other alternatives such as traditional neural network training and identification, and Pacejka model estimation with regression. Our initial findings show that, in comparison to these classical methods, high fidelity estimations can be done with much smaller data sets simple enough to be obtained from a lane-changing or vehicle overtake maneuver. In order to conduct experiments, and collect sensor data, a custom-built 1:8 scaled test vehicle platform is used real-time wireless networking capabilities. The proposed method is applicable to predict derived vehicle parameters such as the understeering coefficient so it can be used in parallel with conventional MIMO controllers. Our $H_{\infty}$ yaw rate regulation controller test results show that the reference gains updated with the proposed online estimation method improve the tracking performance in both simulations and vehicle experiments.
Baseband processing algorithms often require knowledge of the noise power, signal power, or signal-to-noise ratio (SNR). In practice, these parameters are typically unknown and must be estimated. Furthermore, the mean-square error (MSE) is a desirable metric to be minimized in a variety of estimation and signal recovery algorithms. However, the MSE cannot directly be used as it depends on the true signal that is generally unknown to the estimator. In this paper, we propose novel blind estimators for the average noise power, average receive signal power, SNR, and MSE. The proposed estimators can be computed at low complexity and solely rely on the large-dimensional and sparse nature of the processed data. Our estimators can be used (i) to quickly track some of the key system parameters while avoiding additional pilot overhead, (ii) to design low-complexity nonparametric algorithms that require such quantities, and (iii) to accelerate more sophisticated estimation or recovery algorithms. We conduct a theoretical analysis of the proposed estimators for a Bernoulli complex Gaussian (BCG) prior, and we demonstrate their efficacy via synthetic experiments. We also provide three application examples that deviate from the BCG prior in millimeter-wave multi-antenna and cell-free wireless systems for which we develop nonparametric denoising algorithms that improve channel-estimation accuracy with a performance comparable to denoisers that assume perfect knowledge of the system parameters.
In this paper, we propose a novel symbol-level precoding (SLP) method for a multi-user multi-input multi-output (MU-MIMO) downlink Integrated Sensing and Communications (ISAC) system based on faster-than-Nyquist (FTN) signaling. Our method minimizes the minimum mean squared error (MMSE) for target parameter estimation while guaranteeing per-user quality-of-service by exploiting constructive interference (CI) techniques. We tackle the non-convex problem using an efficient successive convex approximation (SCA) method. Numerical results demonstrate that our FTN-ISAC-SLP design significantly outperforms conventional benchmarks in both communication and sensing performance.
In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its current level and, possibly, the parameters governing its dynamics have to be estimated from the observable time series of asset prices. To complicate matters further, recent research has analyzed the rough behavior of volatility time series to challenge the common assumption that the volatility process is a Brownian semimartingale. In order to tackle the arising inferential task efficiently in this setting, we use the fact that a fractional Brownian motion can be represented as a superposition of Markovian semimartingales (Ornstein-Uhlenbeck processes) and we solve the filtering (and parameter estimation) problem by resorting to more standard techniques, such as particle methods.
We consider a class of uncertain linear time-invariant overparametrized systems affected by bounded disturbances, which are described by a known exosystem with unknown initial conditions. For such systems an exponentially stable extended adaptive observer is proposed, which, unlike existing solutions, simultaneously: (i) allows one to reconstruct original (physical) states of the system represented in arbitrarily chosen state-space form rather than virtual states of the observer canonical form; (ii) ensures convergence of the state observation error to zero under weak requirement of the regressor finite excitation; (iii) does not include Luenberger correction gain and forms states estimate using algebraic rather than differential equation; (iv) additionally reconstructs the unmeasured external disturbance. The proposed solution is based on the new parametrizations to identify the observer parameters obtained with the help of the heterogeneous mappings and the dynamic regressor extension and mixing procedure. Illustrative simulations support obtained theoretical results.
State estimation from measured data is crucial for robotic applications as autonomous systems rely on sensors to capture the motion and localize in the 3D world. Among sensors that are designed for measuring a robot's pose, or for soft robots, their shape, vision sensors are favorable because they are information-rich, easy to set up, and cost-effective. With recent advancements in computer vision, deep learning-based methods no longer require markers for identifying feature points on the robot. However, learning-based methods are data-hungry and hence not suitable for soft and prototyping robots, as building such bench-marking datasets is usually infeasible. In this work, we achieve image-based robot pose estimation and shape reconstruction from camera images. Our method requires no precise robot meshes, but rather utilizes a differentiable renderer and primitive shapes. It hence can be applied to robots for which CAD models might not be available or are crude. Our parameter estimation pipeline is fully differentiable. The robot shape and pose are estimated iteratively by back-propagating the image loss to update the parameters. We demonstrate that our method of using geometrical shape primitives can achieve high accuracy in shape reconstruction for a soft continuum robot and pose estimation for a robot manipulator.
A study is presented in which a contrastive learning approach is used to extract low-dimensional representations of the acoustic environment from single-channel, reverberant speech signals. Convolution of room impulse responses (RIRs) with anechoic source signals is leveraged as a data augmentation technique that offers considerable flexibility in the design of the upstream task. We evaluate the embeddings across three different downstream tasks, which include the regression of acoustic parameters reverberation time RT60 and clarity index C50, and the classification into small and large rooms. We demonstrate that the learned representations generalize well to unseen data and perform similarly to a fully-supervised baseline.
3D single-photon LiDAR imaging has an important role in many applications. However, full deployment of this modality will require the analysis of low signal to noise ratio target returns and a very high volume of data. This is particularly evident when imaging through obscurants or in high ambient background light conditions. This paper proposes a multiscale approach for 3D surface detection from the photon timing histogram to permit a significant reduction in data volume. The resulting surfaces are background-free and can be used to infer depth and reflectivity information about the target. We demonstrate this by proposing a hierarchical Bayesian model for 3D reconstruction and spectral classification of multispectral single-photon LiDAR data. The reconstruction method promotes spatial correlation between point-cloud estimates and uses a coordinate gradient descent algorithm for parameter estimation. Results on simulated and real data show the benefits of the proposed target detection and reconstruction approaches when compared to state-of-the-art processing algorithms
Distributed MIMO radar is known to achieve superior sensing performance by employing widely separated antennas. However, it is challenging to implement a low-complexity distributed MIMO radar due to the complex operations at both the receivers and the fusion center. This work proposed a low-bit quantized distributed MIMO (LiQuiD-MIMO) radar to significantly reduce the burden of signal acquisition and data transmission. In the LiQuiD-MIMO radar, the widely-separated receivers are restricted to operating with low-resolution ADCs and deliver the low-bit quantized data to the fusion center. At the fusion center, the induced quantization distortion is explicitly compensated via digital processing. By exploiting the inherent structure of our problem, a quantized version of the robust principal component analysis (RPCA) problem is formulated to simultaneously recover the low-rank target information matrices as well as the sparse data transmission errors. The least squares-based method is then employed to estimate the targets' positions and velocities from the recovered target information matrices. Numerical experiments demonstrate that the proposed LiQuiD-MIMO radar, configured with the developed algorithm, can achieve accurate target parameter estimation.
Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their sampling process is slow due to a need for many (\eg, $2000$) iterations of sequential computations. An intuitive acceleration method is to reduce the sampling iterations which however causes severe performance degradation. We assault this problem to the ill-conditioned issues of the Langevin dynamics and reverse diffusion in the sampling process. Under this insight, we propose a model-agnostic {\bf\em preconditioned diffusion sampling} (PDS) method that leverages matrix preconditioning to alleviate the aforementioned problem. PDS alters the sampling process of a vanilla SGM at marginal extra computation cost, and without model retraining. Theoretically, we prove that PDS preserves the output distribution of the SGM, no risk of inducing systematical bias to the original sampling process. We further theoretically reveal a relation between the parameter of PDS and the sampling iterations,easing the parameter estimation under varying sampling iterations. Extensive experiments on various image datasets with a variety of resolutions and diversity validate that our PDS consistently accelerates off-the-shelf SGMs whilst maintaining the synthesis quality. In particular, PDS can accelerate by up to $29\times$ on more challenging high resolution (1024$\times$1024) image generation. Compared with the latest generative models (\eg, CLD-SGM, DDIM, and Analytic-DDIM), PDS can achieve the best sampling quality on CIFAR-10 at a FID score of 1.99. Our code is made publicly available to foster any further research https://github.com/fudan-zvg/PDS.
Mixture models of Plackett-Luce (PL) -- one of the most fundamental ranking models -- are an active research area of both theoretical and practical significance. Most previously proposed parameter estimation algorithms instantiate the EM algorithm, often with random initialization. However, such an initialization scheme may not yield a good initial estimate and the algorithms require multiple restarts, incurring a large time complexity. As for the EM procedure, while the E-step can be performed efficiently, maximizing the log-likelihood in the M-step is difficult due to the combinatorial nature of the PL likelihood function (Gormley and Murphy 2008). Therefore, previous authors favor algorithms that maximize surrogate likelihood functions (Zhao et al. 2018, 2020). However, the final estimate may deviate from the true maximum likelihood estimate as a consequence. In this paper, we address these known limitations. We propose an initialization algorithm that can provide a provably accurate initial estimate and an EM algorithm that maximizes the true log-likelihood function efficiently. Experiments on both synthetic and real datasets show that our algorithm is competitive in terms of accuracy and speed to baseline algorithms, especially on datasets with a large number of items.