We investigate novel parameter estimation and goodness-of-fit (GOF) assessment methods for large-scale confirmatory item factor analysis (IFA) with many respondents, items, and latent factors. For parameter estimation, we extend Urban and Bauer's (2021) deep learning algorithm for exploratory IFA to the confirmatory setting by showing how to handle constraints on loadings and factor correlations. For GOF assessment, we explore simulation-based tests and indices that extend the classifier two-sample test (C2ST), a method that tests whether a deep neural network can distinguish between observed data and synthetic data sampled from a fitted IFA model. Proposed extensions include a test of approximate fit wherein the user specifies what percentage of observed and synthetic data should be distinguishable as well as a relative fit index (RFI) that is similar in spirit to the RFIs used in structural equation modeling. Via simulation studies, we show that: (1) the confirmatory extension of Urban and Bauer's (2021) algorithm obtains comparable estimates to a state-of-the-art estimation procedure in less time; (2) C2ST-based GOF tests control the empirical type I error rate and detect when the latent dimensionality is misspecified; and (3) the sampling distribution of the C2ST-based RFI depends on the sample size.
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly growing literature of differentiable physics techniques and highlight methods for parameter estimation, learning representations, solving differential equations, and developing what we call scientific foundation models using data and inductive priors. We argue that differentiable physics offers a new paradigm for modeling physical phenomena by combining classical analytic solutions with numerical methodology using the bridge of differentiable programming.
Kidney DCE-MRI aims at both qualitative assessment of kidney anatomy and quantitative assessment of kidney function by estimating the tracer kinetic (TK) model parameters. Accurate estimation of TK model parameters requires an accurate measurement of the arterial input function (AIF) with high temporal resolution. Accelerated imaging is used to achieve high temporal resolution, which yields under-sampling artifacts in the reconstructed images. Compressed sensing (CS) methods offer a variety of reconstruction options. Most commonly, sparsity of temporal differences is encouraged for regularization to reduce artifacts. Increasing regularization in CS methods removes the ambient artifacts but also over-smooths the signal temporally which reduces the parameter estimation accuracy. In this work, we propose a single image trained deep neural network to reduce MRI under-sampling artifacts without reducing the accuracy of functional imaging markers. Instead of regularizing with a penalty term in optimization, we promote regularization by generating images from a lower dimensional representation. In this manuscript we motivate and explain the lower dimensional input design. We compare our approach to CS reconstructions with multiple regularization weights. Proposed approach results in kidney biomarkers that are highly correlated with the ground truth markers estimated using the CS reconstruction which was optimized for functional analysis. At the same time, the proposed approach reduces the artifacts in the reconstructed images.
The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique of parameter estimation of PDEs that is robust against high levels of noise nearly 100 %, by simultaneously fitting basis functions to the measured response and estimating the parameters of both ordinary and partial differential equations. The domain knowledge of the general multidimensional process is used as a constraint in the formulation of the optimization framework. SNAPE not only demonstrates its applicability on various complex dynamic systems that encompass wide scientific domains including Schr\"odinger equation, chaotic duffing oscillator, and Navier-Stokes equation but also estimates an analytical approximation to the process response. The method systematically combines the knowledge of well-established scientific theories and the concepts of data science to infer the properties of the process from the observed data.
This paper introduces V-SysId, a novel method that enables simultaneous keypoint discovery, 3D system identification, and extrinsic camera calibration from an unlabeled video taken from a static camera, using only the family of equations of motion of the object of interest as weak supervision. V-SysId takes keypoint trajectory proposals and alternates between maximum likelihood parameter estimation and extrinsic camera calibration, before applying a suitable selection criterion to identify the track of interest. This is then used to train a keypoint tracking model using supervised learning. Results on a range of settings (robotics, physics, physiology) highlight the utility of this approach.
Computational fluid dynamics (CFD) is a valuable tool for personalised, non-invasive evaluation of hemodynamics in arteries, but its complexity and time-consuming nature prohibit large-scale use in practice. Recently, the use of deep learning for rapid estimation of CFD parameters like wall shear stress (WSS) on surface meshes has been investigated. However, existing approaches typically depend on a hand-crafted re-parametrisation of the surface mesh to match convolutional neural network architectures. In this work, we propose to instead use mesh convolutional neural networks that directly operate on the same finite-element surface mesh as used in CFD. We train and evaluate our method on two datasets of synthetic coronary artery models with and without bifurcation, using a ground truth obtained from CFD simulation. We show that our flexible deep learning model can accurately predict 3D WSS vectors on this surface mesh. Our method processes new meshes in less than 5 [s], consistently achieves a normalised mean absolute error of $\leq$ 1.6 [%], and peaks at 90.5 [%] median approximation accuracy over the held-out test set, comparing favourably to previously published work. This demonstrates the feasibility of CFD surrogate modelling using mesh convolutional neural networks for hemodynamic parameter estimation in artery models.
We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually orthogonal subspaces of latent vectors. This insight allows us to construct new algorithms for community detection and parameter estimation for the PABM, as well as improve an existing algorithm that relies on Sparse Subspace Clustering. Using established asymptotic properties of Adjacency Spectral Embedding for the GRDPG, we derive asymptotic properties of these algorithms. In particular, we demonstrate that the absolute number of community detection errors tends to zero as the number of graph vertices tends to infinity. Simulation experiments illustrate these properties.
Physics-informed Machine Learning has recently become attractive for learning physical parameters and features from simulation and observation data. However, most existing methods do not ensure that the physics, such as balance laws (e.g., mass, momentum, energy conservation), are constrained. Some recent works (e.g., physics-informed neural networks) softly enforce physics constraints by including partial differential equation (PDE)-based loss functions but need re-discretization of the PDEs using auto-differentiation. Training these neural nets on observational data showed that one could solve forward and inverse problems in one shot. They evaluate the state variables and the parameters in a PDE. This re-discretization of PDEs is not necessarily an attractive option for domain scientists that work with physics-based codes that have been developed for decades with sophisticated discretization techniques to solve complex process models and advanced equations of state. This paper proposes a physics constrained machine learning framework, AdjointNet, allowing domain scientists to embed their physics code in neural network training workflows. This embedding ensures that physics is constrained everywhere in the domain. Additionally, the mathematical properties such as consistency, stability, and convergence vital to the numerical solution of a PDE are still satisfied. We show that the proposed AdjointNet framework can be used for parameter estimation (and uncertainty quantification by extension) and experimental design using active learning. The applicability of our framework is demonstrated for four flow cases. Results show that AdjointNet-based inversion can estimate process model parameters with reasonable accuracy. These examples demonstrate the applicability of using existing software with no changes in source code to perform accurate and reliable inversion of model parameters.
Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of the numerical schemes determining the evolution of humidity and temperature, but large contributions are due to the parametrization of microphysics and the parametrization of processes in the surface and boundary layers. These schemes typically contain several tunable parameters that are either not physical or only crudely known, leading to model errors. Traditionally, the numerical values of these model parameters are chosen by manual model tuning. More objectively, they can be estimated from observations by the augmented state approach during the data assimilation. Alternatively, in this work, we look at the problem of parameter estimation through an artificial intelligence lens by training two types of artificial neural networks (ANNs) to estimate several parameters of the one-dimensional modified shallow-water model as a function of the observations or analysis of the atmospheric state. Through perfect model experiments, we show that Bayesian neural networks (BNNs) and Bayesian approximations of point estimate neural networks (NNs) are able to estimate model parameters and their relevant statistics. The estimation of parameters combined with data assimilation for the state decreases the initial state errors even when assimilating sparse and noisy observations. The sensitivity to the number of ensemble members, observation coverage, and neural network size is shown. Additionally, we use the method of layer-wise relevance propagation to gain insight into how the ANNs are learning and discover that they naturally select only a few gridpoints that are subject to strong winds and rain to make their predictions of chosen parameters.
Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and system realization to obtain a state space model. In both sub-problems it is implicitly assumed that standard numerical algorithms such as the singular value decomposition (SVD) can be easily and reliably computed. When trying to fit a high-dimensional model to data, for example in the cyber-physical system setting, even computing an SVD is intractable. In this work we show that an approximate matrix factorization obtained using randomized methods can replace the standard SVD in the realization algorithm while maintaining the non-asymptotic (in data-set size) performance and robustness guarantees of classical methods. Numerical examples illustrate that for large system models, this is the only method capable of producing a model.
We propose a detailed analysis of the online-learning problem for Independent Cascade (IC) models under node-level feedback. These models have widespread applications in modern social networks. Existing works for IC models have only shed light on edge-level feedback models, where the agent knows the explicit outcome of every observed edge. Little is known about node-level feedback models, where only combined outcomes for sets of edges are observed; in other words, the realization of each edge is censored. This censored information, together with the nonlinear form of the aggregated influence probability, make both parameter estimation and algorithm design challenging. We establish the first confidence-region result under this setting. We also develop an online algorithm achieving a cumulative regret of $\mathcal{O}( \sqrt{T})$, matching the theoretical regret bound for IC models with edge-level feedback.
In recent years, single image dehazing models (SIDM) based on atmospheric scattering model (ASM) have achieved remarkable results. However, it is noted that ASM-based SIDM degrades its performance in dehazing real world hazy images due to the limited modelling ability of ASM where the atmospheric light factor (ALF) and the angular scattering coefficient (ASC) are assumed as constants for one image. Obviously, the hazy images taken in real world cannot always satisfy this assumption. Such generating modelling mismatch between the real-world images and ASM sets up the upper bound of trained ASM-based SIDM for dehazing. Bearing this in mind, in this study, a new fully non-homogeneous atmospheric scattering model (FNH-ASM) is proposed for well modeling the hazy images under complex conditions where ALF and ASC are pixel dependent. However, FNH-ASM brings difficulty in practical application. In FNH-ASM based SIDM, the estimation bias of parameters at different positions lead to different distortion of dehazing result. Hence, in order to reduce the influence of parameter estimation bias on dehazing results, two new cost sensitive loss functions, beta-Loss and D-Loss, are innovatively developed for limiting the parameter bias of sensitive positions that have a greater impact on the dehazing result. In the end, based on FNH-ASM, an end-to-end CNN-based dehazing network, FNHD-Net, is developed, which applies beta-Loss and D-Loss. Experimental results demonstrate the effectiveness and superiority of our proposed FNHD-Net for dehazing on both synthetic and real-world images. And the performance improvement of our method increases more obviously in dense and heterogeneous haze scenes.
This paper provides an exponential stability result for the adaptive anti-unwinding attitude tracking control problem of a rigid body with uncertain but constant inertia parameters, without requiring the satisfaction of persistent excitation (PE) condition. Specifically, a composite immersion and invariance (I&I) adaptive controller is derived by integrating a prediction-error-driven learning law into the dynamically scaled I&I adaptive control framework, wherein we modify the scaling factor so that the algorithm design does not involve any dynamic gains. To avoid the unwinding problem, a barrier function is introduced as the attitude error function, along with the tactful establishment of two crucial algebra properties for exponential stability analysis. The regressor filtering method is adopted in combination with the dynamic regressor extension and mixing (DREM) procedure to acquire the prediction error using only easily obtainable signals. In particular, aiding by a constructive liner time-varying filter, the scalar regressor of DREM is extended to generate a new exciting counterpart. In this way, the derived controller is shown to permit closed-loop exponential stability without PE, in the sense that both output-tracking and parameter estimation errors exponentially converge to zero. Further, the composite learning law is augmented with a power term to achieve synchronized finite/fixed-time parameter convergence. Numerical simulations are performed to verify the theoretical findings.
In this paper, we propose a convex formulation for learning logistic regression model (logit) with latent heterogeneous effect on sub-population. In transportation, logistic regression and its variants are often interpreted as discrete choice models under utility theory (McFadden, 2001). Two prominent applications of logit models in the transportation domain are traffic accident analysis and choice modeling. In these applications, researchers often want to understand and capture the individual variation under the same accident or choice scenario. The mixed effect logistic regression (mixed logit) is a popular model employed by transportation researchers. To estimate the distribution of mixed logit parameters, a non-convex optimization problem with nested high-dimensional integrals needs to be solved. Simulation-based optimization is typically applied to solve the mixed logit parameter estimation problem. Despite its popularity, the mixed logit approach for learning individual heterogeneity has several downsides. First, the parametric form of the distribution requires domain knowledge and assumptions imposed by users, although this issue can be addressed to some extent by using a non-parametric approach. Second, the optimization problems arise from parameter estimation for mixed logit and the non-parametric extensions are non-convex, which leads to unstable model interpretation. Third, the simulation size in simulation-assisted estimation lacks finite-sample theoretical guarantees and is chosen somewhat arbitrarily in practice. To address these issues, we are motivated to develop a formulation that models the latent individual heterogeneity while preserving convexity, and avoids the need for simulation-based approximation. Our setup is based on decomposing the parameters into a sparse homogeneous component in the population and low-rank heterogeneous parts for each individual.
In counterfactual learning to rank (CLTR) user interactions are used as a source of supervision. Since user interactions come with bias, an important focus of research in this field lies in developing methods to correct for the bias of interactions. Inverse propensity scoring (IPS) is a popular method suitable for correcting position bias. Affine correction (AC) is a generalization of IPS that corrects for position bias and trust bias. IPS and AC provably remove bias, conditioned on an accurate estimation of the bias parameters. Estimating the bias parameters, in turn, requires an accurate estimation of the relevance probabilities. This cyclic dependency introduces practical limitations in terms of sensitivity, convergence and efficiency. We propose a new correction method for position and trust bias in CLTR in which, unlike the existing methods, the correction does not rely on relevance estimation. Our proposed method, mixture-based correction (MBC), is based on the assumption that the distribution of the CTRs over the items being ranked is a mixture of two distributions: the distribution of CTRs for relevant items and the distribution of CTRs for non-relevant items. We prove that our method is unbiased. The validity of our proof is not conditioned on accurate bias parameter estimation. Our experiments show that MBC, when used in different bias settings and accompanied by different LTR algorithms, outperforms AC, the state-of-the-art method for correcting position and trust bias, in some settings, while performing on par in other settings. Furthermore, MBC is orders of magnitude more efficient than AC in terms of the training time.
In this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation,which we show is equivalent to interval excitation of the regressor vector. Continuous and discrete-time versions of the estimators are given. An extension to--separable and monotonic--non-linear parameterizations is also given. The estimators are shown to be robust to additive measurement noise and--not necessarily slow--parameter variations. Moreover, a version of the continuous-time estimator that rejects sinusoidal disturbances with unknown internal model is given. The estimator is shown to be applicable to the classical model reference adaptive control problem relaxing the conspicuous assumption of known sign of the high-frequency gain. Simulation results that illustrate the performance of the estimator are given.
Accurately modeling power distribution grids is crucial for designing effective monitoring and decision making algorithms. This paper addresses the partial observability issue of data-driven distribution modeling in order to improve the accuracy of line parameter estimation. Inspired by the sparse changes in residential loads, we advocate to regularize the group sparsity of the unobservable injections in a bi-linear estimation problem. The alternating minimization scheme of guaranteed convergence is proposed to take advantage of convex subproblems with efficient solutions. Numerical results using real-world load data on the single-phase equivalent of the IEEE 123-bus test case have demonstrated the accuracy improvements of the proposed solution over existing work for both parameter estimation and voltage modeling.
This paper presents Bayesian parameter estimation for first order Grey system models' parameters (or sometimes referred to as hyperparameters). There are different forms of first-order Grey System Models. These include $GM(1,1)$, $GM(1,1| \cos(\omega t)$, $GM(1,1| \sin(\omega t)$, and $GM(1,1| \cos(\omega t), \sin(\omega t)$. The whitenization equation of these models is a first-order linear differential equation of the form \[ \frac{dx}{dt} + a x = f(t) \] where $a$ is a parameter and $f(t) = b$ in $GM(1,1|)$ , $f(t) = b_1\cos(\omega t) + b_2$ in $GM(1,1| cos(\omega t)$, $f(t) = b_1\sin(\omega t)+b_2$ in $GM(1,1| \sin(\omega t)$, $f(t) = b_1\sin(\omega t) + b_2\cos(\omega t) + b_3$ in $GM(1,1| \cos(\omega t), \sin(\omega t)$, $f(t) = b x^2$ in Grey Verhulst model (GVM), and where $b, b_1, b_2$, and $b_3$ are parameters. The results from Bayesian estimations are compared to the least square estimated models with fixed $\omega$. We found that using rolling Bayesian estimations for GM parameters can allow us to estimate the parameters in all possible forms. Based on the data used for the comparison, the numerical results showed that models with Bayesian parameter estimations are up to 45\% more accurate in mean squared errors.
This paper reports a reduced-order modeling framework of bladed disks on a rotating shaft to simulate the vibration signature of faults like cracks in different components aiming towards simulated data-driven machine learning. We have employed lumped and one-dimensional analytical models of the subcomponents for better insight into the complex dynamic response. The framework seeks to address some of the challenges encountered in analyzing and optimizing fault detection and identification schemes for health monitoring of rotating turbomachinery, including aero-engines. We model the bladed disks and shafts by combining lumped elements and one-dimensional finite elements, leading to a coupled system. The simulation results are in good agreement with previously published data. We model the cracks in a blade analytically with their effective reduced stiffness approximation. Multiple types of faults are modeled, including cracks in the blades of single and two-stage bladed disks, Fan Blade Off (FBO), and Foreign Object Damage (FOD). We have applied aero-engine operational loading conditions to simulate realistic scenarios of online health monitoring. The proposed reduced-order simulation framework will have applications in probabilistic signal modeling, machine learning toward fault signature identification, and parameter estimation with measured vibration signals.
The traditional Capacitated Vehicle Routing Problem (CVRP) minimizes the total distance of the routes under the capacity constraints of the vehicles. But more often, the objective involves multiple criteria including not only the total distance of the tour but also other factors such as travel costs, travel time, and fuel consumption.Moreover, in reality, there are numerous implicit preferences ingrained in the minds of the route planners and the drivers. Drivers, for instance, have familiarity with certain neighborhoods and knowledge of the state of roads, and often consider the best places for rest and lunch breaks. This knowledge is difficult to formulate and balance when operational routing decisions have to be made. This motivates us to learn the implicit preferences from past solutions and to incorporate these learned preferences in the optimization process. These preferences are in the form of arc probabilities, i.e., the more preferred a route is, the higher is the joint probability. The novelty of this work is the use of a neural network model to estimate the arc probabilities, which allows for additional features and automatic parameter estimation. This first requires identifying suitable features, neural architectures and loss functions, taking into account that there is typically few data available. We investigate the difference with a prior weighted Markov counting approach, and study the applicability of neural networks in this setting.