Partial Regularization Research Articles

Developing equity-aware safety performance functions for identifying hotspots of pedestrian-involved crashes

Crashes are frequently disproportionally observed in disadvantaged areas. Despite the evident disparities in transportation safety, there has been limited exploration of quantitative approaches to incorporating equity considerations into road safety management. This study proposes a novel concept of equity-aware safety performance functions (SPFs), enabling a distinct treatment of equity-related variables such as race and income. Equity-aware SPFs introduce a fairness distance and integrate it into the log-likelihood function of the negative binomial regression as a form of partial lasso regularization. A parameter λ is used to control the importance of the regularization term. Equity-aware SPFs are developed for pedestrian-involved crashes at the census tract level in Virginia, USA, and then employed to compute the potential for safety improvement (PSI), a prevalent metric used in hotspot identification. Results show that equity-aware SPFs can diminish the effects of equity-related variables, including poverty ratio, black ratio, Asian ratio, and the ratio of households without vehicles, on the expected crash frequencies, generating higher PSIs for disadvantaged areas. Based on the results of Wilcoxon signed-rank tests, it is evident that there are significant differences in the rankings of PSIs when equity awareness is considered, especially for disadvantaged areas. This study adds to the literature a new quantitative approach to harmonize equity and effectiveness considerations, empowering more equitable decision-making in safety management, such as allocating resources for safety enhancement.

Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems

We revisit a class of integer optimal control problems for which a trust-region method has been proposed and analyzed in arXiv:2106.13453v3 [math.OC]. While the algorithm proposed in arXiv:2106.13453v3 [math.OC] successfully solves the class of optimization problems under consideration, its convergence analysis requires restrictive regularity assumptions. There are many examples of integer optimal control problems involving partial differential equations where these regularity assumptions are not satisfied. In this article we provide a way to bypass the restrictive regularity assumptions by introducing an additional partial regularization of the control inputs by means of mollification and proving a $\Gamma$-convergence-type result when the support parameter of the mollification is driven to zero. We highlight the applicability of this theory in the case of fluid flows through deformable porous media equations that arise in biomechanics. We show that the regularity assumptions are violated in the case of poro-visco-elastic systems, and thus one needs to use the regularization of the control input introduced in this article. Associated numerical results show that while the homotopy can help to find better objective values and points of lower instationarity, the practical performance of the algorithm without the input regularization may be on par with the homotopy.

Controller-Guided Partial Label Consistency Regularization with Unlabeled Data

Partial label learning (PLL) learns from training examples each associated with multiple candidate labels, among which only one is valid. In recent years, benefiting from the strong capability of dealing with ambiguous supervision and the impetus of modern data augmentation methods, consistency regularization-based PLL methods have achieved a series of successes and become mainstream. However, as the partial annotation becomes insufficient, their performances drop significantly. In this paper, we leverage easily accessible unlabeled examples to facilitate the partial label consistency regularization. In addition to a partial supervised loss, our method performs a controller-guided consistency regularization at both the label-level and representation-level with the help of unlabeled data. To minimize the disadvantages of insufficient capabilities of the initial supervised model, we use the controller to estimate the confidence of each current prediction to guide the subsequent consistency regularization. Furthermore, we dynamically adjust the confidence thresholds so that the number of samples of each class participating in consistency regularization remains roughly equal to alleviate the problem of class-imbalance. Experiments show that our method achieves satisfactory performances in more practical situations, and its modules can be applied to existing PLL methods to enhance their capabilities.

Computationally efficient techniques for spatial regression with differential regularization

We investigate some computational aspects of an innovative class of PDE-regularized statistical models: Spatial Regression with Partial Differential Equation regularization (SR-PDE). These physics-informed regression methods can account for the physics of the underlying phenomena and handle data observed over spatial domains with nontrivial shapes, such as domains with concavities and holes or curved domains. The computational bottleneck in SR-PDE estimation is the solution of a computationally demanding linear system involving a low-rank but dense block. We address this aspect by innovatively using Sherman–Morrison–Woodbury identity. We also investigate the efficient selection of the smoothing parameter in SR-PDE estimates. Specifically, we propose ad hoc optimization methods to perform Generalized Cross-Validation, coupling suitable reformulation of key matrices, e.g. those based on Sherman–Morrison–Woodbury formula, with stochastic trace estimation, to approximate the equivalent degrees of freedom of the problem. These solutions permit high computational efficiency also in the context of massive data.

Exact penalization for cardinality and rank-constrained optimization problems via partial regularization

In this paper, we consider a class of constrained optimization problems whose constraints involve a cardinality or rank constraint. The penalty formulation based on a partial regularization has recently been promoted in the literature to approximate these problems, which usually outperforms the penalty formulation based on a full regularization in terms of solution quality. Nevertheless, the relation between the penalty formulation with a partial regularizer and the original problem was not much studied yet. Under some suitable assumptions, we show that the penalty formulation based on a partial regularization is an exact reformulation of the original problem in the sense that they both share the same global minimizers. We also show that a local minimizer of the original problem is that of the penalty reformulation. These results provide some theoretical justification for the often-observed superior performance of the penalty model based on a partial regularizer over a corresponding full regularizer.

Generalization error bounds of dynamic treatment regimes in penalized regression-based learning

A dynamic treatment regime (DTR) is a sequence of decision rules, one per stage of intervention, that maps up-to-date patient information to a recommended treatment. Discovering an appropriate DTR for a given disease is a challenging issue especially when a large set of prognostic variables are observed. To address this problem, we propose penalized regression-based learning methods with l1 penalty to estimate the optimal DTR that would maximize the expected outcome if implemented. We also provide generalization error bounds of the estimated DTR in the setting of finite number of stages with multiple treatment options. We first examine the relationship between value and Q-functions and derive a finite sample upper bound on the difference in values between the optimal and the estimated DTRs. For practical implementation, we develop an algorithm with partial regularization via orthogonality to construct the optimal DTR. The advantages of the proposed methods are demonstrated with extensive simulation studies and data analysis of depression clinical trials.

The Impact of Epithelial Remodeling on Surgical Techniques Used in Topography-guided Surface Ablation in Irregular Corneas.

To analyze the optical consequences of epithelial remodeling in irregular corneas and their impact on the choice of different surface ablation techniques. Anterior corneal and stromal surface topographies and epithelial thickness maps were analyzed in 24 eyes with irregular corneal optics. On two of the eyes, four different surface ablation techniques were simulated: (1) conventional anterior topography-guided photorefractive keratectomy (PRK), (2) transepithelial phototherapeutic keratectomy (PTK), (3) transepithelial anterior topography-guided PRK, and (4) stromal topography-guided PRK. Stromal surface topographies showed higher keratometric values, astigmatism, asphericity, and corneal higher order aberrations compared to topographies of anterior corneas covered by epithelium. Transepithelial anterior topography-guided PRK and stromal topography-guided PRK both resulted in regularized stromal surface, transepithelial PTK achieved partial regularization corresponding to the smoothing effect of the epithelial remodeling, and conventional anterior topography-guided PRK delivered after epithelial removal resulted in residual stromal surface irregularities. The difference in optical landscapes between the stromal and anterior surfaces in irregular corneas will represent a source of error when anterior topography-guided treatments are delivered on the deepithelialized stroma, as in conventional PRK. In contrast, anterior topography-guided ablations performed as transepithelial PRK and stromal topography-guided PRK delivered after epithelial removal address the full stromal irregularity, whereas transepithelial PTK alone may be used when topography-guided treatments are not possible. The authors conclude topography-guided PRK of irregular corneas should lead to significantly improved regularization only if it includes the effect of epithelial remodeling. [J Refract Surg. 2022;38(8):529-537.].

Asymptotic analysis of deformation behavior in high-contrast fiber-reinforced materials: Rigidity and anisotropy

We identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. In mathematical terms, we characterize the weak limits of sequences of Sobolev maps whose gradients on the fibers lie in the set of rotations. These limits are determined by an anisotropic constraint in the sense that they locally preserve length in the fiber direction. Our proof of the necessity emerges as a natural generalization and modification of the recently established asymptotic rigidity analysis for composites with layered reinforcements. However, the construction of approximating sequences is more delicate here due to the higher flexibility and connectedness of the soft material component. We overcome these technical challenges by a careful approximation of the identity that is constant on the rigid components, combined with a lifting in fiber bundles for Sobolev functions. The results are illustrated with several examples of attainable effective deformations. If an additional partial second-order regularization is introduced into the material model, only rigid body motions can occur macroscopically.

ОБ ОПЕРАТОРЕ ТЕПЛИЦА НА ТОРЕ В НЕКОТОРЫХ ТОПОЛОГИЧЕСКИХ ПРОСТРАНСТВАХ

In countably-normed spaces of functions on a torus that are smooth in one or both variables, we study Toeplitz operators with symbols that ensure that the operators are bounded in these spaces. To study operators of bisingular type in the spaces of summable and Ho¨lder functions, the method of partial regularization was used. Using this method, we obtain the construction of a regularizer and the condition for the Toeplitz operator to be Noetherian in a countably-normed space of functions that are smooth in one of the variables. Despite the fact that the set of Noetherian operators in this space, unlike in the case of Banach spaces, contains operators with symbols vanishing on the torus, these results are quite analogous to the case of Banach spaces. The situation is different in the space of functions that are smooth in both variables. It is shown that the partial regularization method is inapplicable in this space.

Image-to-image translation of label-free molecular vibrational images for a histopathological review using the UNet+/seg-cGAN model.

Translating images generated by label-free microscopy imaging, such as Coherent Anti-Stokes Raman Scattering (CARS), into more familiar clinical presentations of histopathological images will help the adoption of real-time, spectrally resolved label-free imaging in clinical diagnosis. Generative adversarial networks (GAN) have made great progress in image generation and translation, but have been criticized for lacking precision. In particular, GAN has often misinterpreted image information and identified incorrect content categories during image translation of microscopy scans. To alleviate this problem, we developed a new Pix2pix GAN model that simultaneously learns classifying contents in the images from a segmentation dataset during the image translation training. Our model integrates UNet+ with seg-cGAN, conditional generative adversarial networks with partial regularization of segmentation. Technical innovations of the UNet+/seg-cGAN model include: (1) replacing UNet with UNet+ as the Pix2pix cGAN's generator to enhance pattern extraction and richness of the gradient, and (2) applying the partial regularization strategy to train a part of the generator network as the segmentation sub-model on a separate segmentation dataset, thus enabling the model to identify correct content categories during image translation. The quality of histopathological-like images generated based on label-free CARS images has been improved significantly.

Some first results on the consistency of spatial regression with partial differential equation regularization

Some first results on the consistency of spatial regression with partial differential equation regularization

Smoothing spatio-temporal data with complex missing data patterns

We consider spatio-temporal data and functional data with spatial dependence, characterized by complicated missing data patterns. We propose a new method capable to efficiently handle these data structures, including the case where data are missing over large portions of the spatio-temporal domain. The method is based on regression with partial differential equation regularization. The proposed model can accurately deal with data scattered over domains with irregular shapes and can accurately estimate fields exhibiting complicated local features. We demonstrate the consistency and asymptotic normality of the estimators. Moreover, we illustrate the good performances of the method in simulations studies, considering different missing data scenarios, from sparse data to more challenging scenarios where the data are missing over large portions of the spatial and temporal domains and the missing data are clustered in space and/or in time. The proposed method is compared to competing techniques, considering predictive accuracy and uncertainty quantification measures. Finally, we show an application to the analysis of lake surface water temperature data, that further illustrates the ability of the method to handle data featuring complicated patterns of missingness and highlights its potentiality for environmental studies.

Lifting propositional proof compression algorithms to first-order logic

Abstract Proofs are a key feature of modern propositional and first-order theorem provers. Proofs generated by such tools serve as explanations for unsatisfiability of statements. However, these explanations are complicated by proofs which are not necessarily as concise as possible. There are a wide variety of compression techniques for propositional resolution proofs but fewer compression techniques for first-order resolution proofs generated by automated theorem provers. This paper describes an approach to compressing first-order logic proofs based on lifting proof compression ideas used in propositional logic to first-order logic. The first approach lifted from propositional logic delays resolution with unit clauses, which are clauses that have a single literal. The second approach is partial regularization, which removes an inference $\eta $ when it is redundant in the sense that its pivot literal already occurs as the pivot of another inference in every path from $\eta $ to the root of the proof. This paper describes the generalization of the algorithms LowerUnits and RecyclePivotsWithIntersection (Fontaine et al.. Compression of propositional resolution proofs via partial regularization. In Automated Deduction—CADE-23—23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31–August 5, 2011, p. 237--251. Springer, 2011) from propositional logic to first-order logic. The generalized algorithms compresses resolution proofs containing resolution and factoring inferences with unification. An empirical evaluation of these approaches is included.

Learning Sparse Low-Precision Neural Networks With Learnable Regularization

We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed with high-precision weights while quantized low-precision weights and activations are used in the forward pass to calculate the loss function for training. Thus, the gradient descent becomes suboptimal, and accuracy loss follows. In order to reduce the mismatch in the forward and backward passes, we utilize mean squared quantization error (MSQE) regularization. In particular, we propose using a learnable regularization coefficient with the MSQE regularizer to reinforce the convergence of high-precision weights to their quantized values. We also investigate how partial L2 regularization can be employed for weight pruning in a similar manner. Finally, combining weight pruning, quantization, and entropy coding, we establish a low-precision DNN compression pipeline. In our experiments, the proposed method yields low-precision MobileNet and ShuffleNet models on ImageNet classification with the state-of-the-art compression ratios of 7.13 and 6.79, respectively. Moreover, we examine our method for image super resolution networks to produce 8-bit low-precision models at negligible performance loss.

Synergetic interpretation of bifurcations of open systems

Introduction . In order to establish the causes of unexpected bifurcations of open systems, this work is presented. It is based on the corporate interaction of unidirectional open systems, an assumption is made about the reasons for their self-improvement. Main part. The identification of bifurcations of closed and open systems is considered. The prerequisites for the occurrence of incorrect bifurcations of open systems are given. In studies of closed systems, it is imperative that the conditions of structural stability to relatively small perturbations, which cannot be satisfied when identifying open systems, are met. Self-improvement of open systems occurs due to the exchange of information with the external environment. Based on the assumption that the long-term memory of an open system can be considered as an external environment, the exchange of information can be considered through the cooperative interaction of an open single focus the most open system and its long-term memory. The latter leads to the formation of targeted actions that contribute to the self-improvement of an open system. An admissible regularization of a problem identified by an incorrect bifurcation of an open system is shown. The task is regularized in two stages. At the first stage, an operator is defined that regularizes the problem in the format of thinking corresponding to incorrect bifurcation. At the second stage, the solution obtained at the first stage is applied to the problem in the original format. Conclusions. It has been suggested that the occurrence of incorrect bifurcations of open systems is a result of the cooperation of the previously existing long-term memory with its present memory. These reasons indicate the incorrectness of such tasks. It is shown that the use of the logical operator allows partial regularization of such problems by identifying incorrect bifurcations. Due to the wide variety of open systems, the probability of an adequate identification of their bifurcations is obvious.

A cosparse analysis model with combined redundant systems for MRI reconstruction.

Magnetic resonance imaging (MRI) is widely used due to its noninvasive and nonionizing properties. However, MRI requires a long scanning time. In this paper, our goal is to reconstruct a high-quality MR image from its sampled k-space data to accelerate the data acquisition in MRI. We propose a cosparse analysis model with combined redundant systems to fully exploit the sparsity of MR images. Two fixed redundant systems are used to characterize different structures, namely, the wavelet tight frame and Gabor frame. An alternating iteration scheme is used for reconstruction with simple implementation and good performance. The proposed method is tested on two MR images under three sampling patterns with sampling ratios ranging from 10% to 60%. The results show that the proposed method outperforms other state-of-the-art MRI reconstruction methods in terms of both subjective visual quality and objective quantitative measurement. For instance, for brain images under random sampling with a ratio of 10%, compared to the other three methods, the proposed method improves the peak signal-to-noise ratio (PSNR) by more than 9dB. To better characterize different sparsities of different structures of MRI, a cosparse analysis model combining the wavelet tight frame and Gabor frame is proposed. A partial norm regularization is leveraged to obtain the optimal solution in a lower dimension. Compared to other state-of-the-art MRI reconstruction methods, the proposed method improves the reconstruction quality of MRI, especially highly undersampled MRI.

LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS.

This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central χ2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.

Finite element simulation of complex dense granular flows using a well-posed regularization of the μ(I)-rheology

Dense granular flows play an important role in industry and nature. Numerical simulation is a helpful tool to understand their behavior. The high particle concentration in a particle-laden flow leads to non-Newtonian fluid properties. The μ(I)-rheology is a constitutive model to describe a complex, unconventional viscoplastic, shear-thinning flow behavior that agrees well with experiments of dense granular flow. This constitutive model is based on the Coulomb [1] friction and assumes that the pressure is proportional to the tangential stress and related to it by a friction parameter. The friction parameter depends on a dimensionless inertial number I which describes the macroscopic and microscopic timescales of the particle rearrangement. Barker et al. [2] showed that the constitutive equations of the μ(I)-rheology are ill-posed for low and high inertial number regimes. This often results in instabilities, oscillations and high sensitivity of the solution to input parameters. We apply a partial regularization proposed by Barker and Gray [3] for a finite element simulation of a 2D and 3D column collapse with the intention to get stable results and show the disadvantageous outcome of ill-posed constitutive equations. Here, we use a Navier-Stokes solver and the volume-of-fluid method to describe the interface between a dense granular column and a light surrounding fluid. The implementation is done in libMesh using the residual-based variational multiscale method. The objective of this study is to analyze the effects of the partial regularization on the computational simulation of a column collapse using the finite element method. We observe that the viscosity field using the partially well-posed regularized formulation of the μ(I)-rheology by Barker and Gray [3] has a smoother distribution and no spurious oscillations or shear bands, even in simulations with high density and viscosity contrasts.

Multiple Partial Regularized Nonnegative Matrix Factorization for Predicting Ontological Functions of lncRNAs

Long non-coding RNAs (LncRNA) are critical regulators for biological processes, which are highly related to complex diseases. Even though the next generation sequence technology facilitates the discovery of a great number of lncRNAs, the knowledge about the functions of lncRNAs is limited. Thus, it is promising to predict the functions of lncRNAs, which shed light on revealing the mechanisms of complex diseases. The current algorithms predict the functions of lncRNA by using the features of protein-coding genes. Generally speaking, these algorithms fuse heterogeneous genomic data to construct lncRNA-gene associations via a linear combination, which cannot fully characterize the function-lncRNA relations. To overcome this issue, we present an nonnegative matrix factorization algorithm with multiple partial regularization (aka MPrNMF) to predict the functions of lncRNAs without fusing the heterogeneous genomic data. In details, for each type of genomic data, we construct the lncRNA-gene associations, resulting in multiple associations. The proposed method integrates separately them via regularization strategy, rather than fuse them into a single type of associations. The results demonstrate that the proposed algorithm outperforms state-of-the-art methods based network-analysis. The model and algorithm provide an effective way to explore the functions of lncRNAs.

Регуляризация и построение асимптотических решений в методе пограничных функций

In his brief article published in 1977, S.A. Lomov noted that the asymptotics of Vasil'eva—Butuzov’s type boundary layer for a singularly perturbed problem can be obtained by the method of transition to a space of higher dimension or regularization of the original differential operator using a fast independent variable. Unfortunately, a detailed algorithm for constructing such asymptotics is not given in the article, and it remains to be answered whether the asymptotics obtained in it will actually coincide with a boundary-layer type asymptotics. In the present paper, this question is solved positively. However, the regularization itself is divided into two stages: partial regularization and complete regularization. In the course of partial regularization, it is not possible to obtain an "extended" problem the iterative systems of which admit solutions in the form of the sum of two functions with separated independent variables (one of which is an ordinary variable, and the other is a regularizing variable) The complete regularization has at its heart the procedure for constructing an "extended" system, which was applied by the authors in their papers devoted to regularization of integral operators, the essence of which consists in regularizing the original problem in the class of formal asymptotic series in powers of a small parameter with coefficients in the form of the sum of functions with separated variables. The asymptotics obtained using such procedure coincides completely with the boundary-layer type asymptotics, a result that confirms S.A. Lomov’s hypothesis.