We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters. The strategy is based on the extraction of conditional distribution from the joint distribution of parameters and data, via the estimation of structured (e.g., block triangular) transport maps. This gives explicit surrogate models for the likelihood functions and their gradients. This allow gradient-based characterizations of posterior density via transport maps in a model-free, online phase. This framework is well suited for parameter estimation in case of complex noise models including nuisance parameters and when the forward model is only known as a black box. The numerical application of this method is performed in the context of characterization of ice thickness with conductivity measurements.
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective solution. However, despite their wide use, a rigorous performance characterization, as well as a principled way to preprocess the data, are available only for unstructured (i.i.d.\ Gaussian and Haar orthogonal) designs. In contrast, real-world data matrices are highly structured and exhibit non-trivial correlations. To address the problem, we consider correlated Gaussian designs capturing the anisotropic nature of the features via a covariance matrix $\Sigma$. Our main result is a precise asymptotic characterization of the performance of spectral estimators. This allows us to identify the optimal preprocessing that minimizes the number of samples needed for parameter estimation. Surprisingly, such preprocessing is universal across a broad set of designs, which partly addresses a conjecture on optimal spectral estimators for rotationally invariant models. Our principled approach vastly improves upon previous heuristic methods, including for designs common in computational imaging and genetics. The proposed methodology, based on approximate message passing, is broadly applicable and opens the way to the precise characterization of spiked matrices and of the corresponding spectral methods in a variety of settings.
Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps into deep learning's abilities to uncover parameters governing intricate behaviors in nonlinear equations. We validate our approach using synthetic data and predefined functions that model system dynamics. By training the neural network with noisy time series data, it fine-tunes the Huber loss function to converge to accurate parameters. We apply our method to damped oscillators, Van der Pol oscillators, Lotka-Volterra systems, and Lorenz systems under multiplicative noise. The trained neural network accurately estimates parameters, evident from closely matching latent dynamics. Comparing true and estimated trajectories visually reinforces our method's precision and robustness. Our study underscores the Huber loss-guided neural network as a versatile tool for parameter estimation, effectively uncovering complex relationships in nonlinear systems. The method navigates noise and uncertainty adeptly, showcasing its adaptability to real-world challenges.
This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression. This approach has the additional practical advantage of requiring no a priori knowledge of the source of the excitation (or, alternatively, the initial conditions). By using training data, we devise a coarse regression procedure to recover different PDE parameters from the PDE solution measured at a single location. Numerical experiments show that the proposed regression procedure is capable of detecting and estimating PDE parameters with superior accuracy compared to a number of recently developed machine learning methods. Furthermore, a damage identification experiment conducted on a publicly available dataset provides strong evidence of the proposed method's effectiveness in structural health monitoring (SHM) applications. The Python implementation of the proposed system identification technique is integrated as a part of the software package PyTransKit (https://github.com/rohdelab/PyTransKit).
Computerized Adaptive Testing (CAT) is a widely used, efficient test mode that adapts to the examinee's proficiency level in the test domain. CAT requires pre-trained item profiles, for CAT iteratively assesses the student real-time based on the registered items' profiles, and selects the next item to administer using candidate items' profiles. However, obtaining such item profiles is a costly process that involves gathering a large, dense item-response data, then training a diagnostic model on the collected data. In this paper, we explore the possibility of leveraging response data collected in the CAT service. We first show that this poses a unique challenge due to the inherent selection bias introduced by CAT, i.e., more proficient students will receive harder questions. Indeed, when naively training the diagnostic model using CAT response data, we observe that item profiles deviate significantly from the ground-truth. To tackle the selection bias issue, we propose the user-wise aggregate influence function method. Our intuition is to filter out users whose response data is heavily biased in an aggregate manner, as judged by how much perturbation the added data will introduce during parameter estimation. This way, we may enhance the performance of CAT while introducing minimal bias to the item profiles. We provide extensive experiments to demonstrate the superiority of our proposed method based on the three public datasets and one dataset that contains real-world CAT response data.
In many parameter estimation problems, the exact model is unknown and is assumed to belong to a set of candidate models. In such cases, a predetermined data-based selection rule selects a parametric model from a set of candidates before the parameter estimation. The existing framework for estimation under model misspecification does not account for the selection process that led to the misspecified model. Moreover, in post-model-selection estimation, there are multiple candidate models chosen based on the observations, making the interpretation of the assumed model in the misspecified setting non-trivial. In this work, we present three interpretations to address the problem of non-Bayesian post-model-selection estimation as an estimation under model misspecification problem: the naive interpretation, the normalized interpretation, and the selective inference interpretation, and discuss their properties. For each of these interpretations, we developed the corresponding misspecified maximum likelihood estimator and the misspecified Cram$\acute{\text{e}}$r-Rao-type lower bound. The relations between the estimators and the performance bounds, as well as their properties, are discussed. Finally, we demonstrate the performance of the proposed estimators and bounds via simulations of estimation after channel selection. We show that the proposed performance bounds are more informative than the oracle Cram$\acute{\text{e}}$r-Rao Bound (CRB), where the third interpretation (selective inference) results in the lowest mean-squared-error (MSE) among the estimators.
The problem of state reconstruction is considered for uncertain linear time-invariant systems with overparameterization, arbitrary state-space matrices and unknown additive perturbation described by an exosystem. A novel adaptive observer is proposed to solve it, which, unlike known solutions, simultaneously: (i) reconstructs the physical state of the original system rather than the virtual state of its observer canonical form, (ii) ensures exponential convergence of the reconstruction error to zero when the condition of finite excitation is satisfied, (iii) is applicable to systems, in which mentioned perturbation is generated by an exosystem with fully uncertain constant parameters. The proposed solution uses a recently published parametrization of uncertain linear systems with unknown additive perturbations, the dynamic regressor extension and mixing procedure, as well as a method of physical states reconstruction developed by the authors. Detailed analysis for stability and convergence has been provided along with simulation results to validate the theoretical analysis.
We address the problem of aligning real-world 3D data of garments, which benefits many applications such as texture learning, physical parameter estimation, generative modeling of garments, etc. Existing extrinsic methods typically perform non-rigid iterative closest point and struggle to align details due to incorrect closest matches and rigidity constraints. While intrinsic methods based on functional maps can produce high-quality correspondences, they work under isometric assumptions and become unreliable for garment deformations which are highly non-isometric. To achieve wrinkle-level as well as texture-level alignment, we present a novel coarse-to-fine two-stage method that leverages intrinsic manifold properties with two neural deformation fields, in the 3D space and the intrinsic space, respectively. The coarse stage performs a 3D fitting, where we leverage intrinsic manifold properties to define a manifold deformation field. The coarse fitting then induces a functional map that produces an alignment of intrinsic embeddings. We further refine the intrinsic alignment with a second neural deformation field for higher accuracy. We evaluate our method with our captured garment dataset, GarmCap. The method achieves accurate wrinkle-level and texture-level alignment and works for difficult garment types such as long coats. Our project page is https://jsnln.github.io/iccv2023_intrinsic/index.html.
We investigate radar parameter estimation and beam tracking with a hybrid digital-analog (HDA) architecture in a multi-block measurement framework using an extended target model. In the considered setup, the backscattered data signal is utilized to predict the user position in the next time slots. Specifically, a simplified maximum likelihood framework is adopted for parameter estimation, based on which a simple tracking scheme is also developed. Furthermore, the proposed framework supports adaptive transmitter beamwidth selection, whose effects on the communication performance are also studied. Finally, we verify the effectiveness of the proposed framework via numerical simulations over complex motion patterns that emulate a realistic integrated sensing and communication (ISAC) scenario.
We address the task of simultaneous part-level reconstruction and motion parameter estimation for articulated objects. Given two sets of multi-view images of an object in two static articulation states, we decouple the movable part from the static part and reconstruct shape and appearance while predicting the motion parameters. To tackle this problem, we present PARIS: a self-supervised, end-to-end architecture that learns part-level implicit shape and appearance models and optimizes motion parameters jointly without any 3D supervision, motion, or semantic annotation. Our experiments show that our method generalizes better across object categories, and outperforms baselines and prior work that are given 3D point clouds as input. Our approach improves reconstruction relative to state-of-the-art baselines with a Chamfer-L1 distance reduction of 3.94 (45.2%) for objects and 26.79 (84.5%) for parts, and achieves 5% error rate for motion estimation across 10 object categories. Video summary at: https://youtu.be/tDSrROPCgUc
In this paper, we address the problem of online parameter estimation of a Proton Exchange Membrane Fuel Cell (PEMFC) polarization curve, that is the static relation between the voltage and the current of the PEMFC. The task of designing this estimator -- even off-line -- is complicated by the fact that the uncertain parameters enter the curve in a highly nonlinear fashion, namely in the form of nonseparable nonlinearities. We consider several scenarios for the model of the polarization curve, starting from the standard full model and including several popular simplifications to this complicated mathematical function. In all cases, we derive separable regression equations -- either linearly or nonlinearly parameterized -- which are instrumental for the implementation of the parameter estimators. We concentrate our attention on on-line estimation schemes for which, under suitable excitation conditions, global parameter convergence is ensured. Due to these global convergence properties, the estimators are robust to unavoidable additive noise and structural uncertainty. Moreover, their on-line nature endows the schemes with the ability to track (slow) parameter variations, that occur during the operation of the PEMFC. These two features -- unavailable in time-consuming off-line data-fitting procedures -- make the proposed estimators helpful for on-line time-saving characterization of a given PEMFC, and the implementation of fault-detection procedures and model-based adaptive control strategies. Simulation and experimental results that validate the theoretical claims are presented.
This paper explores the potential of near-field beamforming (NFBF) in integrated sensing and communication (ISAC) systems with extremely large-scale arrays (XL-arrays). The large-scale antenna arrays increase the possibility of having communication users and targets of interest in the near field of the base station (BS). The paper first establishes the models of electromagnetic (EM) near-field spherical waves and far-field plane waves. With the models, we analyze the near-field beam focusing ability and the far-field beam steering ability by finding the gain-loss mathematical expression caused by the far-field steering vector mismatch in the near-field case. We formulate the NFBF design problem as minimizing the weighted summation of radar and the communication beamforming errors under a total power constraint and solve this quadratically constrained quadratic programming (QCQP) problem using the least squares (LS) method. Moreover, the Cram\'er-Rao bound (CRB) for target parameter estimation is derived to verify the performance of NFBF. Furthermore, we also perform power minimization using convex optimization while ensuring the required communication and sensing quality-of-service (QoS). The simulation results show the influence of model mismatch on near-field ISAC and the performance gain of transmit beamforming from the additional distance dimension of near-field.
This work presents generalized forgetting recursive least squares (GF-RLS), a generalization of recursive least squares (RLS) that encompasses many extensions of RLS as special cases. First, sufficient conditions are presented for the 1) Lyapunov stability, 2) uniform Lyapunov stability, 3) global asymptotic stability, and 4) global uniform exponential stability of parameter estimation error in GF-RLS when estimating fixed parameters without noise. Second, robustness guarantees are derived for the estimation of time-varying parameters in the presence of measurement noise and regressor noise. These robustness guarantees are presented in terms of global uniform ultimate boundedness of the parameter estimation error. A specialization of this result gives a bound to the asymptotic bias of least squares estimators in the errors-in-variables problem. Lastly, a survey is presented to show how GF-RLS can be used to analyze various extensions of RLS from the literature.
The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter estimation from the tool remains an open question. To address this, we propose a neural network model to map persistence images to cosmological parameters. Through a parameter recovery test, we demonstrate that our model makes accurate and precise estimates, considerably outperforming conventional Bayesian inference approaches.
Recent works have shown that imposing tensor structures on the coefficient tensor in regression problems can lead to more reliable parameter estimation and lower sample complexity compared to vector-based methods. This work investigates a new low-rank tensor model, called Low Separation Rank (LSR), in Generalized Linear Model (GLM) problems. The LSR model -- which generalizes the well-known Tucker and CANDECOMP/PARAFAC (CP) models, and is a special case of the Block Tensor Decomposition (BTD) model -- is imposed onto the coefficient tensor in the GLM model. This work proposes a block coordinate descent algorithm for parameter estimation in LSR-structured tensor GLMs. Most importantly, it derives a minimax lower bound on the error threshold on estimating the coefficient tensor in LSR tensor GLM problems. The minimax bound is proportional to the intrinsic degrees of freedom in the LSR tensor GLM problem, suggesting that its sample complexity may be significantly lower than that of vectorized GLMs. This result can also be specialised to lower bound the estimation error in CP and Tucker-structured GLMs. The derived bounds are comparable to tight bounds in the literature for Tucker linear regression, and the tightness of the minimax lower bound is further assessed numerically. Finally, numerical experiments on synthetic datasets demonstrate the efficacy of the proposed LSR tensor model for three regression types (linear, logistic and Poisson). Experiments on a collection of medical imaging datasets demonstrate the usefulness of the LSR model over other tensor models (Tucker and CP) on real, imbalanced data with limited available samples.
We summarise popular methods used for skill rating in competitive sports, along with their inferential paradigms and introduce new approaches based on sequential Monte Carlo and discrete hidden Markov models. We advocate for a state-space model perspective, wherein players' skills are represented as time-varying, and match results serve as observed quantities. We explore the steps to construct the model and the three stages of inference: filtering, smoothing and parameter estimation. We examine the challenges of scaling up to numerous players and matches, highlighting the main approximations and reductions which facilitate statistical and computational efficiency. We additionally compare approaches in a realistic experimental pipeline that can be easily reproduced and extended with our open-source Python package, https://github.com/SamDuffield/abile.
Objective: Most deep neural network-based diffusion tensor imaging methods require the diffusion gradients' number and directions in the data to be reconstructed to match those in the training data. This work aims to develop and evaluate a novel dynamic-convolution-based method called FlexDTI for highly efficient diffusion tensor reconstruction with flexible diffusion encoding gradient scheme. Approach: FlexDTI was developed to achieve high-quality DTI parametric mapping with flexible number and directions of diffusion encoding gradients. The method used dynamic convolution kernels to embed diffusion gradient direction information into feature maps of the corresponding diffusion signal. Furthermore, it realized the generalization of a flexible number of diffusion gradient directions by setting the maximum number of input channels of the network. The network was trained and tested using datasets from the Human Connectome Project and local hospitals. Results from FlexDTI and other advanced tensor parameter estimation methods were compared. Main results: Compared to other methods, FlexDTI successfully achieves high-quality diffusion tensor-derived parameters even if the number and directions of diffusion encoding gradients change. It reduces normalized root mean squared error (NRMSE) by about 50% on fractional anisotropy (FA) and 15% on mean diffusivity (MD), compared with the state-of-the-art deep learning method with flexible diffusion encoding gradient scheme. Significance: FlexDTI can well learn diffusion gradient direction information to achieve generalized DTI reconstruction with flexible diffusion gradient scheme. Both flexibility and reconstruction quality can be taken into account in this network.
The maximum likelihood principle advocates parameter estimation via optimization of the data likelihood function. Models estimated in this way can exhibit a variety of generalization characteristics dictated by, e.g. architecture, parameterization, and optimization bias. This work addresses model learning in a setting where there further exists side-information in the form of an oracle that can label samples as being outside the support of the true data generating distribution. Specifically we develop a new denoising diffusion probabilistic modeling (DDPM) methodology, Gen-neG, that leverages this additional side-information. Our approach builds on generative adversarial networks (GANs) and discriminator guidance in diffusion models to guide the generation process towards the positive support region indicated by the oracle. We empirically establish the utility of Gen-neG in applications including collision avoidance in self-driving simulators and safety-guarded human motion generation.
Malnutrition poses a significant threat to global health, resulting from an inadequate intake of essential nutrients that adversely impacts vital organs and overall bodily functioning. Periodic examinations and mass screenings, incorporating both conventional and non-invasive techniques, have been employed to combat this challenge. However, these approaches suffer from critical limitations, such as the need for additional equipment, lack of comprehensive feature representation, absence of suitable health indicators, and the unavailability of smartphone implementations for precise estimations of Body Fat Percentage (BFP), Basal Metabolic Rate (BMR), and Body Mass Index (BMI) to enable efficient smart-malnutrition monitoring. To address these constraints, this study presents a groundbreaking, scalable, and robust smart malnutrition-monitoring system that leverages a single full-body image of an individual to estimate height, weight, and other crucial health parameters within a multi-modal learning framework. Our proposed methodology involves the reconstruction of a highly precise 3D point cloud, from which 512-dimensional feature embeddings are extracted using a headless-3D classification network. Concurrently, facial and body embeddings are also extracted, and through the application of learnable parameters, these features are then utilized to estimate weight accurately. Furthermore, essential health metrics, including BMR, BFP, and BMI, are computed to conduct a comprehensive analysis of the subject's health, subsequently facilitating the provision of personalized nutrition plans. While being robust to a wide range of lighting conditions across multiple devices, our model achieves a low Mean Absolute Error (MAE) of $\pm$ 4.7 cm and $\pm$ 5.3 kg in estimating height and weight.
Over the past decades, hemodynamics simulators have steadily evolved and have become tools of choice for studying cardiovascular systems in-silico. While such tools are routinely used to simulate whole-body hemodynamics from physiological parameters, solving the corresponding inverse problem of mapping waveforms back to plausible physiological parameters remains both promising and challenging. Motivated by advances in simulation-based inference (SBI), we cast this inverse problem as statistical inference. In contrast to alternative approaches, SBI provides \textit{posterior distributions} for the parameters of interest, providing a \textit{multi-dimensional} representation of uncertainty for \textit{individual} measurements. We showcase this ability by performing an in-silico uncertainty analysis of five biomarkers of clinical interest comparing several measurement modalities. Beyond the corroboration of known facts, such as the feasibility of estimating heart rate, our study highlights the potential of estimating new biomarkers from standard-of-care measurements. SBI reveals practically relevant findings that cannot be captured by standard sensitivity analyses, such as the existence of sub-populations for which parameter estimation exhibits distinct uncertainty regimes. Finally, we study the gap between in-vivo and in-silico with the MIMIC-III waveform database and critically discuss how cardiovascular simulations can inform real-world data analysis.