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We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

Mendelian randomization uses genetic variants as instrumental variables to make causal inferences about the effects of modifiable risk factors on diseases from observational data. One of the major challenges in Mendelian randomization is that many genetic variants are only modestly or even weakly associated with the risk factor of interest, a setting known as many weak instruments. Many existing methods, such as the popular inverse-variance weighted (IVW) method, could be biased when the instrument strength is weak. To address this issue, the debiased IVW (dIVW) estimator, which is shown to be robust to many weak instruments, was recently proposed. However, this estimator still has non-ignorable bias when the effective sample size is small. In this paper, we propose a modified debiased IVW (mdIVW) estimator by multiplying a modification factor to the original dIVW estimator. After this simple correction, we show that the bias of the mdIVW estimator converges to zero at a faster rate than that of the dIVW estimator under some regularity conditions. Moreover, the mdIVW estimator has smaller variance than the dIVW estimator.We further extend the proposed method to account for the presence of instrumental variable selection and balanced horizontal pleiotropy. We demonstrate the improvement of the mdIVW estimator over the dIVW estimator through extensive simulation studies and real data analysis.

In observational studies, covariates with substantial missing data are often omitted, despite their strong predictive capabilities. These excluded covariates are generally believed not to simultaneously affect both treatment and outcome, indicating that they are not genuine confounders and do not impact the identification of the average treatment effect (ATE). In this paper, we introduce an alternative doubly robust (DR) estimator that fully leverages non-confounding predictive covariates to enhance efficiency, while also allowing missing values in such covariates. Beyond the double robustness property, our proposed estimator is designed to be more efficient than the standard DR estimator. Specifically, when the propensity score model is correctly specified, it achieves the smallest asymptotic variance among the class of DR estimators, and brings additional efficiency gains by further integrating predictive covariates. Simulation studies demonstrate the notable performance of the proposed estimator over current popular methods. An illustrative example is provided to assess the effectiveness of right heart catheterization (RHC) for critically ill patients.

Vessel segmentation and centerline extraction are two crucial preliminary tasks for many computer-aided diagnosis tools dealing with vascular diseases. Recently, deep-learning based methods have been widely applied to these tasks. However, classic deep-learning approaches struggle to capture the complex geometry and specific topology of vascular networks, which is of the utmost importance in most applications. To overcome these limitations, the clDice loss, a topological loss that focuses on the vessel centerlines, has been recently proposed. This loss requires computing, with a proposed soft-skeleton algorithm, the skeletons of both the ground truth and the predicted segmentation. However, the soft-skeleton algorithm provides suboptimal results on 3D images, which makes the clDice hardly suitable on 3D images. In this paper, we propose to replace the soft-skeleton algorithm by a U-Net which computes the vascular skeleton directly from the segmentation. We show that our method provides more accurate skeletons than the soft-skeleton algorithm. We then build upon this network a cascaded U-Net trained with the clDice loss to embed topological constraints during the segmentation. The resulting model is able to predict both the vessel segmentation and centerlines with a more accurate topology.

Autoencoders (AE) are simple yet powerful class of neural networks that compress data by projecting input into low-dimensional latent space (LS). Whereas LS is formed according to the loss function minimization during training, its properties and topology are not controlled directly. In this paper we focus on AE LS properties and propose two methods for obtaining LS with desired topology, called LS configuration. The proposed methods include loss configuration using a geometric loss term that acts directly in LS, and encoder configuration. We show that the former allows to reliably obtain LS with desired configuration by defining the positions and shapes of LS clusters for supervised AE (SAE). Knowing LS configuration allows to define similarity measure in LS to predict labels or estimate similarity for multiple inputs without using decoders or classifiers. We also show that this leads to more stable and interpretable training. We show that SAE trained for clothes texture classification using the proposed method generalizes well to unseen data from LIP, Market1501, and WildTrack datasets without fine-tuning, and even allows to evaluate similarity for unseen classes. We further illustrate the advantages of pre-configured LS similarity estimation with cross-dataset searches and text-based search using a text query without language models.

Several mixed-effects models for longitudinal data have been proposed to accommodate the non-linearity of late-life cognitive trajectories and assess the putative influence of covariates on it. No prior research provides a side-by-side examination of these models to offer guidance on their proper application and interpretation. In this work, we examined five statistical approaches previously used to answer research questions related to non-linear changes in cognitive aging: the linear mixed model (LMM) with a quadratic term, LMM with splines, the functional mixed model, the piecewise linear mixed model, and the sigmoidal mixed model. We first theoretically describe the models. Next, using data from two prospective cohorts with annual cognitive testing, we compared the interpretation of the models by investigating associations of education on cognitive change before death. Lastly, we performed a simulation study to empirically evaluate the models and provide practical recommendations. Except for the LMM-quadratic, the fit of all models was generally adequate to capture non-linearity of cognitive change and models were relatively robust. Although spline-based models have no interpretable nonlinearity parameters, their convergence was easier to achieve, and they allow graphical interpretation. In contrast, piecewise and sigmoidal models, with interpretable non-linear parameters, may require more data to achieve convergence.

By computing a feedback control via the linear quadratic regulator (LQR) approach and simulating a non-linear non-autonomous closed-loop system using this feedback, we combine two numerically challenging tasks. For the first task, the computation of the feedback control, we use the non-autonomous generalized differential Riccati equation (DRE), whose solution determines the time-varying feedback gain matrix. Regarding the second task, we want to be able to simulate non-linear closed-loop systems for which it is known that the regulator is only valid for sufficiently small perturbations. Thus, one easily runs into numerical issues in the integrators when the closed-loop control varies greatly. For these systems, e.g., the A-stable implicit Euler methods fails.\newline On the one hand, we implement non-autonomous versions of splitting schemes and BDF methods for the solution of our non-autonomous DREs. These are well-established DRE solvers in the autonomous case. On the other hand, to tackle the numerical issues in the simulation of the non-linear closed-loop system, we apply a fractional-step-theta scheme with time-adaptivity tuned specifically to this kind of challenge. That is, we additionally base the time-adaptivity on the activity of the control. We compare this approach to the more classical error-based time-adaptivity.\newline We describe techniques to make these two tasks computable in a reasonable amount of time and are able to simulate closed-loop systems with strongly varying controls, while avoiding numerical issues. Our time-adaptivity approach requires fewer time steps than the error-based alternative and is more reliable.

This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an $M$-matrix) on Voronoi polygonal meshes, provided their duals are Delaunay triangulations with acute angles. Furthermore, the study outlines a comprehensive framework for EAVE methodologies, introducing another variant that integrates with the stiffness matrix derived from the lowest-order virtual element method for the Poisson equation. Numerical experiments confirm the theoretical advantages of the monotonicity property and demonstrate an optimal convergence rate across various mesh configurations.

Time-series models typically assume untainted and legitimate streams of data. However, a self-interested adversary may have incentive to corrupt this data, thereby altering a decision maker's inference. Within the broader field of adversarial machine learning, this research provides a novel, probabilistic perspective toward the manipulation of hidden Markov model inferences via corrupted data. In particular, we provision a suite of corruption problems for filtering, smoothing, and decoding inferences leveraging an adversarial risk analysis approach. Multiple stochastic programming models are set forth that incorporate realistic uncertainties and varied attacker objectives. Three general solution methods are developed by alternatively viewing the problem from frequentist and Bayesian perspectives. The efficacy of each method is illustrated via extensive, empirical testing. The developed methods are characterized by their solution quality and computational effort, resulting in a stratification of techniques across varying problem-instance architectures. This research highlights the weaknesses of hidden Markov models under adversarial activity, thereby motivating the need for robustification techniques to ensure their security.

Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.