Efficient Algorithm Research Articles

Differential Privacy-Preserving IoT Data Sharing Through Enhanced PSO

ABSTRACT With the proliferation of Internet of Things (IoT) devices and the generation of massive amounts of sensitive data, preserving privacy while enabling data sharing has become a critical concern. In this research, we propose a novel approach for achieving differential privacy in IoT data sharing through an improved Particle Swarm Optimization (PSO) algorithm. Our objective is to find the optimal configuration of privacy-preserving mechanisms that maximizes privacy while maintaining data utility. The research begins with a comprehensive overview of differential privacy in IoT data sharing, highlighting the limitations of existing optimization algorithms. We then present our proposed improvements to the traditional PSO algorithm, including the design of a suitable fitness function, the use of a dynamic inertia weight, exploration of different neighborhood topologies, and adaptive acceleration coefficients. We define a set of performance metrics, including privacy metrics (e.g. ε-differential privacy parameter) and utility measures (e.g. accuracy, utility loss), to assess the algorithm’s effectiveness. The results of our experiments demonstrate that the improved PSO algorithm achieves higher privacy guarantees while maintaining competitive levels of data utility compared to existing approaches. The proposed algorithm exhibits faster convergence, better exploration of the search space, and improved scalability. Our research contributes to the field of privacy-preserving IoT data sharing by providing an efficient and effective optimization algorithm that enables secure and privacy-aware data sharing while facilitating valuable insights and analysis.

Learning Motion and Temporal Cues for Unsupervised Video Object Segmentation.

In this article, we address the challenges in unsupervised video object segmentation (UVOS) by proposing an efficient algorithm, termed MTNet, which concurrently exploits motion and temporal cues. Unlike previous methods that focus solely on integrating appearance with motion or on modeling temporal relations, our method combines both aspects by integrating them within a unified framework. MTNet is devised by effectively merging appearance and motion features during the feature extraction process within encoders, promoting a more complementary representation. To capture the intricate long-range contextual dynamics and information embedded within videos, a temporal transformer module is introduced, facilitating efficacious interframe interactions throughout a video clip. Furthermore, we employ a cascade of decoders all feature levels across all feature levels to optimally exploit the derived features, aiming to generate increasingly precise segmentation masks. As a result, MTNet provides a strong and compact framework that explores both temporal and cross-modality knowledge to robustly localize and track the primary object accurately in various challenging scenarios efficiently. Extensive experiments across diverse benchmarks conclusively show that our method not only attains state-of-the-art performance in UVOS but also delivers competitive results in video salient object detection (VSOD). These findings highlight the method's robust versatility and its adeptness in adapting to a range of segmentation tasks. The source code is available at https://github.com/hy0523/MTNet.

Adaptive analysis of the heteroscedastic multivariate regression modeling

Multivariate regression is a widely used technique for large-scale statistical applications. In this paper, we propose a novel method for the multivariate regression model, called multivariate weighted lasso (MWL). We consider the heteroscedasticity in the noise matrix and introduce an adjustable weight to calibrate the fitting residuals of different responses. The proposed method shows an advantage in complex multivariate regressions with heteroscedasticity. To implement the procedure, an efficient algorithm is provided based on the multivariate coordinate descent. We provide theoretical guarantees for the proposed method. Numerical simulations and financial applications are conducted using the proposed and other existing methods. The results indicate that the proposed method performs well in both variable selection and coefficient estimation.

An Improved Porosity Calculation Algorithm for Particle Flow Code

The widely used discrete-element particle flow software PFC’s (PFC 7.0 and previous versions) algorithm for calculating porosity is not sufficiently accurate. Because of this, when the particles are densely packed, the solution to the equation produces an algorithm exception for odd calculations of porosity, which results in the inability to calculate the results. This paper, based on a Darcy seepage model of fluid flow through a granular bed, analyzed the shortcomings of the two porosity calculation methods of PFC and the function analysis method. Combining this analysis with the theory of computer graphics, a new and efficient porosity calculation algorithm was proposed. The result showed that the new proposed porosity calculation algorithm calculated a more accurate and reasonable porosity field and made the iterative solution of the CFD equation more stable. This method makes porosity-related models of PFC more accurate. The algorithm can be not only used to calculate porosity, but also applied to other fields.

An Improved Porosity Calculation Algorithm for Particle Flow Code

The widely used discrete-element particle flow software PFC’s (PFC 7.0 and previous versions) algorithm for calculating porosity is not sufficiently accurate. Because of this, when the particles are densely packed, the solution to the equation produces an algorithm exception for odd calculations of porosity, which results in the inability to calculate the results. This paper, based on a Darcy seepage model of fluid flow through a granular bed, analyzed the shortcomings of the two porosity calculation methods of PFC and the function analysis method. Combining this analysis with the theory of computer graphics, a new and efficient porosity calculation algorithm was proposed. The result showed that the new proposed porosity calculation algorithm calculated a more accurate and reasonable porosity field and made the iterative solution of the CFD equation more stable. This method makes porosity-related models of PFC more accurate. The algorithm can be not only used to calculate porosity, but also applied to other fields.

A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. From a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

Maximum principle preserving time implicit DGSEM for linear scalar hyperbolic conservation laws

The properties of the high-order discontinuous Galerkin spectral element method (DGSEM) with implicit backward Euler time stepping are investigated for the approximation of hyperbolic linear scalar conservation equation in multiple space dimensions. We first prove that the DGSEM scheme in one space dimension preserves a maximum principle for the cell-averaged solution when the time step is large enough. This property however no longer holds in multiple space dimensions and we propose to use the flux-corrected transport (FCT) limiting [5] based on a low-order approximation using graph viscosity to impose a maximum principle on the cell-averaged solution. These results allow us to use a linear scaling limiter [58] in order to impose a maximum principle at nodal values within elements, while limiting the cell average with the FCT limiter improves the accuracy of the limited solution. Then, we investigate the inversion of the linear systems resulting from the time implicit discretization at each time step. We prove that the diagonal blocks are invertible and provide efficient algorithms for their inversion. Numerical experiments in one and two space dimensions are presented to illustrate the conclusions of the present analyses.

Intramedullary Screw versus Locking Plate Fixation for Traumatic Displaced Proximal Fifth Metatarsal Fractures: A Systematic Review.

Background/Objectives: Intramedullary screw fixation (IMS) and locking plate fixation (LPF) are currently recommended treatments for proximal fifth metatarsal fractures (PFMF). However, treating comminuted or small displaced avulsion PFMF with IMS poses challenges due to complications. A novel alternative fixation method, the locking compression plate for distal ulna hook plate fixation (LPF), has been introduced recently for distal ulna fractures and has shown improved clinical results. This scoping review aims to assess whether LPF yields superior outcomes, such as postoperative AOFAS scores and rate of postoperative complications, compared to IMS in PFMF treatment. Methods: This review included randomized controlled trials (RCTs), prospective cohort studies, retrospective cohort studies, or case series involving patients with PFMF who underwent plate fixation or screw fixation. The primary outcome was the postoperative American Orthopedic Foot and Ankle Society (AOFAS) score. Studies were sourced from databases including PubMed, Embase, and Scopus, with the search conducted up to February 2024. The Systematic Review protocol was registered in the CRD PROSPERO database (CRD42024532593). Results: Ten studies were included, comprising 3 cohort studies, 1 case-control study, and 6 case series, with a total of 309 patients (158 with LPF and 142 with IMS). The postoperative AOFAS scores showed no significant difference between LPF and IMS in treating PFMF. However, LPF demonstrated efficient surgical procedures and enhanced functional outcomes. Complications were minimal in both groups, with no significant difference in the rate of postoperative complications. Conclusions: Although there was no significant difference in AOFAS scores between LPF and IMS, LPF demonstrated efficient surgical procedures and enhanced functional outcomes, making it a reasonable alternative method for PFMF. Effective shared decision-making (SDM) with patients becomes paramount in choosing the optimal surgical approach. In the surgical landscape, thoughtful deliberation, patient engagement, and adherence to biomechanical principles are crucial for achieving successful outcomes in the treatment of PFMF.

Consensus and discriminative non-negative matrix factorization for multi-view unsupervised feature selection

Multi-view unsupervised feature selection (MUFS) has been proven to be an efficient dimensionality reduction technique for multi-view data. Existing methods have two main challenges: (1) The consistency information from different views is not fully exploited. (2) The cluster structure of the original data is not well utilized. To settle these problems, we propose a novel consensus and discriminative non-negative matrix factorization (CDNMF) for multi-view unsupervised feature selection. Specifically, CDNMF obtains a robust low-dimensional latent space by NMF with an ℓ2,1-norm constraint. To select more discriminative features, we further impose a sparsity constraint on the learned latent features. Moreover, CDNMF performs k-means clustering on all views separately to obtain the pseudo-labels of each view, which are used to guide the learning of consensus information among views. To solve our model, we develop an efficient iterative optimization algorithm. Extensive experimental results on ten benchmark datasets demonstrate that the proposed significantly outperforms several existing feature selection methods in clustering tasks.

A Co-evolutionary Multi-population Evolutionary Algorithm for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization problems (DMOPs) widely appear in various real-world applications and have attracted increasing attention worldwide. However, how to obtain both good population diversity and fast convergence speed to efficiently solve DMOPs are two challenging issues. Inspired by that the multiple populations for multiple objectives (MPMO) framework can provide algorithms with good population diversity and fast convergence speed, this paper proposes a new efficient algorithm called a co-evolutionary multi-population evolutionary algorithm (CMEA) based on the MPMO framework together with three novel strategies, which are helpful for solving DMOPs efficiently from two aspects. First, in the evolution control aspect, a convergence-based population evolution strategy is proposed to select the suitable population for executing the evolution in different generations, so as to accelerate the convergence speed of the algorithm. Second, in the dynamic control aspect, a multi-population-based dynamic detection strategy and a multi-population-based dynamic response strategy are proposed to help the algorithm maintain the population diversity, which are efficient for detecting and responding to the dynamic changes of environments. Integrating with the above strategies, the CMEA is proposed to solve the DMOP efficiently. The superiority of the proposed CMEA is validated in experiments on widely-used DMOP benchmark problems.

Propagation of Modelling Uncertainties for Seismic Risk Assessment: The Effect of Sampling Techniques on Low-Rise Non-Ductile RC Frames

ABSTRACT Quantifying the impact of modelling uncertainty on seismic performance assessment of existing buildings is non-trivial when considering the partial information available on material properties, construction details, and the uncertainty in the capacity models. This task is further complicated when uncertainty related to ground motion representation is considered. To address this issue, record-to-record variability, uncertainties in structural model parameters, and fragility model parameters due to limited sample size are propagated herein by employing a nonlinear dynamic analysis procedure based on recorded ground motions. A one-to-one sampling approach is adopted in which each recorded ground motion is paired up with a different structural model realization. Uncertainty propagation is explored by measuring the impact of different sampling techniques, such as Monte Carlo simulation with standard random sampling and Latin Hypercube sampling (with Simulated Annealing) in the presence of three alternative nonlinear dynamic analysis procedures: Incremental Dynamic Analysis (IDA), Modified Cloud Analysis (MCA), and Cloud to IDA (a highly efficient IDA-like procedure). This is all illustrated through application to an existing reinforced-concrete school building in southern Italy. It is shown that with a small subset of records, both MCA and Cloud to IDA can provide reliable structural fragility (and risk) estimates for three considered limit states, comparable to the results of more resource-intensive schemes.

MERCI: Mixed curvature-based elements for computing equilibria of thin elastic ribbons

Thin elastic ribbons represent a class of intermediary objects lying in-between thin elastic plates and thin elastic rods. Although the two latter families of thin structures have received much interest from the Computer Graphics community over the last decades, ribbons have seldom been considered and modelled numerically so far, in spite of a growing number of applications in Computer Design. In this paper, starting from the reduced developable ribbon models [Sadowsky 1929; Wunderlich 1962] recently popularised in Soft Matter Physics, we propose a both accurate and efficient algorithm for computing the statics of thin elastic ribbons. Inspired by the super-clothoid model for thin elastic rods, our method relies on compact ribbon elements whose normal curvature varies linearly with respect to arc length s , while their geodesic torsion is quadratic in s . In contrast however, for the sake of efficiency, our algorithm avoids building a fully reduced kinematic chain and instead treats each element independently, gluing them only at the final solving stage through well-chosen bilateral constraints. Thanks to this mixed variational strategy, which yields a banded Hessian, our algorithm recovers the linear complexity of low-order models while preserving the quadratic convergence of curvature-based models. As a result, our approach is scalable to a large number of elements, and suitable for various boundary conditions and unilateral contact constraints, making it possible to handle challenging scenarios such as confined buckling experiments or Möbius bands with contact. Remarkably, our mixed algorithm proves an order of magnitude faster compared to Discrete Elastic Ribbon models of the literature while achieving, in a few seconds only, high accuracy levels that remain out of reach for such low-order models. Additionally, our numerical model can incorporate various ribbon energies, including the RibExt model for quasi-developable ribbons recently introduced in Physics [Audoly and Neukirch 2021], which allows to transition smoothly between a rectangular Kirchhoff rod and a (developable) Sadowsky ribbon. Our numerical scheme is carefully validated against demanding experiments of the Physics literature, which demonstrates its accuracy, efficiency, robustness, and versatility. Our Merci code is publicly available at https://gitlab.inria.fr/elan-public-code/merci for the sake of reproducibility and future benchmarking.

P-464 Patients satisfaction with Hypnosis during Oocyte Retrieval

Abstract Study question Are patients receiving hypnosis during oocyte retrieval (OR) satisfied with this support? Summary answer Three-quarters of the women receiving hypnosis during OR were satisfied with this support, considering it beneficial for both pain and anxiety. What is known already OR is a crucial component in the management of assisted reproductive technology (ART). Despite being a safe and efficient procedure, OR is often perceived as the most stressful and painful aspect of ART. OR can be performed under local anesthesia with a paracervical block analgesia but may still cause discomfort for some patients (pain, anxiety related to the procedure). Therefore, exploring non-pharmacological approaches, such as hypnosis, to enhance anesthesia is of major interest. Hypnosis has demonstrated efficacy in pain management across various medical indications, prompting an investigation into its potential benefits during OR. Study design, size, duration A cohort study involving women undergoing an OR under local anesthesia combined with hypnosis at our institution between November 2022 to November 2023. A questionnaire was distributed to patients just after the OR, assessing women’s satisfaction with hypnosis support, along with their experiences of pain (Visual Analogic scale (VAS)) and anxiety (State-Trait Anxiety Inventory (STAI) questionnaire) during the OR procedure. Participants/materials, setting, methods Women for whom hypnosis was administered during the entire OR procedure, using either a virtual reality headset or with a hypnotherapist were included. Exclusions comprised incomplete questionnaires and patients unable to communicate in French. Objectives were (i) to assess the women satisfaction concerning hypnosis during OR on pain and anxiety through specific questions of the survey, (ii) to evaluate pain (VAS) and anxiety (STAI) during the procedure and (iii) to compare the two hypnosis techniques. Main results and the role of chance Two hundred and nine women undergoing OR under local anesthesia fully responded to the questionnaire out of six hundred surveyed. The mean population age was 34.4±4.1 years. Hypnosis support was provided by a hypnotherapist for 79.9% (167/209) of women and using a virtual reality headset for 20.1% (42/209). 73.7% were satisfied of hypnosis for pain, and 86.1% for anxiety. A higher proportion found hypnosis beneficial for anxiety in the therapist group compared to the virtual reality headset group (88.6% (148/167) versus 76.2% (32/42) respectively, p:0.037). For a new oocyte retrieval, 70.8% of women preferred undergoing the procedure under local anesthesia with hypnosis. The mean VAS score was 5.3 ± 2.6 and the mean STAI score was 36.7± 17.8 during oocyte retrieval. No significant differences concerning VAS and STAI scores were found between the therapist and virtual reality headset groups. Limitations, reasons for caution The study evaluates the satisfaction of women with hypnosis support; hence, there is no assessment of long-term benefits on pregnancy chances. Additionally, a potential selection bias exists as not all surveyed women returned the questionnaire. Wider implications of the findings Positive feedback suggests a potential role for hypnosis in enhancing patient well-being during oocyte retrieval, warranting further research and clinical exploration to improve the overall patient experience during what is often perceived as a stressful procedure. Trial registration number NA

Suppressing Protodeboronation in Cu-Mediated 19F/18F-Fluorination of Arylboronic Acids: A Mechanistically Guided Approach Towards Optimized PET Probe Development.

Fluorinated arenes play a crucial role in drug discovery, specialty materials, and medical imaging. Although several variants for Cu-mediated nucleophilic fluorination of arylboronic acids and derivatives have been developed, these protocols rarely address the occurrence and control of protodeboronation, which greatly complicates product separation and can compromise the effectiveness of a radiotracer for in vivo imaging. Consequently, simpler and more efficient procedures are needed to allow rapid 18F/19F-fluorination of both arylboronic acids and esters while minimizing protodeboronation. Mechanistic controls revealed that in addition to a high temperature, strong donor ligands such as acetonitrile and pyridine accentuate a Cu-mediated protodeboronation. This observation guided the optimization of a ligandless procedure with t-BuOH as solvent to enhance the nucleophilicity of fluoride under milder conditions at lower temperatures minimizing protodeboronation. Additionally, a new copper salt, Cu(ONf)2 was employed to further improve the fluorination efficiency. A large range of functional groups are tolerated under the new procedure, which is complete within 30 minutes at a temperature of 60 °C, and affords fluorinated arenes and heteroarenes in 39% to 84% yield. With minimal modifications, the protocol can also be applied in 18F-radiofluorination, affording radiochemical conversions (RCCs) between 17-54% with minimal protodeboronation compared to previously established protocols.

Prime Time Tactics—Sieve Tweaks and Boosters

In a landscape where interest in prime sieving has waned and practitioners are few, we are still hoping for a domain renaissance, fueled by a resurgence of interest and a fresh wave of innovation. Building upon years of extensive research and experimentation, this article aims to contribute by presenting a heterogeneous compilation of generic tweaks and boosters aimed at revitalizing prime sieving methodologies. Drawing from a wealth of resurfaced knowledge and refined sieving algorithms, techniques, and optimizations, we unveil a diverse array of strategies designed to elevate the efficiency, accuracy, and scalability of prime sieving algorithms; these tweaks and boosters represent a synthesis of old wisdom and new discoveries, offering practical guidance for researchers and practitioners alike.

P-227 Blastocyst rate prediction by artificial intelligence: evaluation of static oocyte images in patients and donors

Abstract Study question Can a deep learning tool accurately predict blastocyst development from single static oocyte images across diverse patient populations? Summary answer The automatic oocyte score was directly correlated with the blastocyst formation rate in conventional treatments using patient oocytes and in the egg donation program. What is known already The implementation of artificial intelligence (AI)-based algorithms has revolutionized gamete and embryo evaluation in assisted reproduction, providing a standardized basis for clinical decisions. Despite these advances, the implementation of AI algorithms in oocyte evaluation has faced unique challenges. This study explores the predictive ability of an AI algorithm on the actual blastocyst arrival rate from static oocyte images, focusing on finding differences or similarities in these predictions between patients and donors. Study design, size, duration This retrospective cohort study analyzed 1092 static images of oocytes before ICSI. The sample included 791 donor and 301 patient oocyte images. A deep learning algorithm was employed to assess oocyte scores, categorizing them into quartiles. The study explored the correlation between oocyte scores and the actual rate of blastocyst arrival for all oocytes. The rates were also compared between patients and donors, assessing an effective cut-off point to improve the accuracy of the predictions. Participants/materials, setting, methods The oocyte images analyzed were captured with cameras connected to microinjection microscopes immediately before the ICSI procedure. Oocyte images and oocyte age were used as input data for the blind analysis performed by the deep learning-based algorithm. The algorithm predicted blastocyst arrival probability for each oocyte, and these predictions were compared with actual outcomes. This evaluation assessed the algorithm’s performance across patient and donor populations, providing valuable insights into its predictive accuracy for blastocyst arrival. Main results and the role of chance Significant differences in blastocyst formation rates were observed between quartiles of scores assigned by the artificial intelligence (AI) algorithm. Oocytes classified in Quartile 1 showed a significantly lower blastocyst arrival rate (54.63±49.99, n = 216) compared to Quartiles 3 (71.88±45.06, n = 224) and 4 (66.82±47.19, n = 220)*. In general, each increased unit in the algorithm was significantly associated with an increased probability of blastocyst formation (OR = 1.10 [95% CI: 1.02-1.16])*. The algorithm successfully predicted the blastocyst arrival rate, with an area under the curve (AUC) of 0.60 (95% CI: 0.56-0.65). When assessing differences between patients and donors, both groups exhibited similar rates in the first quartile (59.68% and 52.60%, respectively) and the three last quartiles combined (67.55% and 66.02%, respectively). However, an effective cutoff point was identified at 2.8 (between first and second quartile), where both populations experienced a notable increase in blastocyst formation rates. (*p<.05) Limitations, reasons for caution This project is limited by its retrospective, single-center nature and small sample size. Consequently, it would be advisable to conduct a large-scale multicenter study to confirm the conclusions of this study. Wider implications of the findings This study highlights the efficiency of the artificial intelligence algorithm in predicting blastocyst arrival from oocyte images. Establishing a cutoff point in oocyte scoring could enhance the management of the egg donation program and provide individualized guidance to patients based on the quality of their gametes. Trial registration number not applicable

PDE-Based Two-Dimensional Radiomagnetotelluric Forward Modelling Using Vertex-Centered Finite-Volume Scheme

An efficient finite-volume algorithm, based on the vertex-centered technique, is proposed for solving two-dimensional radiomagnetotelluric forward modeling. Firstly, we derive the discrete expressions of the radiomagnetotelluric Helmholtz-type equation and the corresponding mixed boundary conditions using the vertex-centered finite-volume technique. Then, the corresponding approximate solutions of the radiomagnetotelluric forward problem can be calculated by applying the finite-volume scheme to treat the boundary conditions. Secondly, we apply the finite-volume algorithm to solve two-dimensional Helmholtz equations and the resistivity half-space model. Numerical experiments demonstrate the high accuracy of the proposed approach. Finally, we summarize the radiomagnetotelluric responses through a numerical simulation of a two-dimensional model, which enables qualitative interpretation of field data. Furthermore, our numerical method can be extended and implemented for three-dimensional radiomagnetotelluric forward modeling to achieve more accurate computation.

A privacy-preserving image retrieval scheme with access control based on searchable encryption in media cloud

With the popularity of the media cloud computing industry, individuals and organizations outsource image computation and storage to the media cloud server to reduce the storage burden. Media images usually contain a large amount of private information. To prevent disclosure of privacy of the image owners, media images are encrypted before uploading to the server. However, this operation will greatly limit the utilization of the image for the user, such as content-based image retrieval. We propose an efficient similarity query algorithm with access control based on Bkd-tree in this paper, in which a searchable encryption scheme is designed for similarity image retrieval, and the encrypted image is used to extract image features by a pre-trained CNN model. The Bkd-tree is utilized to generate an index tree for the image features to speed up retrieval and make it faster than linear indexing. Finally, the security performances of the proposed scheme is analyzed and the performance of this scheme is evaluated by experiments. The results show that the security of the image content and image features can be ensured, and it has a shorter retrieval time and higher retrieval efficiency.

Robust Matrix Completion with Heavy-tailed Noise

This paper studies noisy low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion problem has attracted much attention in the past decade, there is still lack of theoretical understanding when the observations are contaminated by heavy-tailed noises. Prior theory falls short of explaining the empirical results and is unable to capture the optimal dependence of the estimation error on the noise level. In this paper, we adopt an adaptive Huber loss to accommodate heavy-tailed noise, which is robust against large and possibly asymmetric errors when the parameter in the Huber loss function is carefully designed to balance the Huberization biases and robustness to outliers. Then, we propose an efficient nonconvex algorithm via a balanced low-rank Burer-Monteiro matrix factorization and gradient descent with robust spectral initialization. We prove that under merely a bounded second-moment condition on the error distributions, rather than the sub-Gaussian assumption, the Euclidean errors of the iterates generated by the proposed algorithm decrease geometrically fast until achieving a minimax-optimal statistical estimation error, which has the same order as that in the sub-Gaussian case. The key technique behind this significant advancement is a powerful leave-one-out analysis framework. The theoretical results are corroborated by our numerical studies.

Rule learning by modularity

AbstractIn this paper, we present a modular methodology that combines state-of-the-art methods in (stochastic) machine learning with well-established methods in inductive logic programming (ILP) and rule induction to provide efficient and scalable algorithms for the classification of vast data sets. By construction, these classifications are based on the synthesis of simple rules, thus providing direct explanations of the obtained classifications. Apart from evaluating our approach on the common large scale data sets MNIST, Fashion-MNIST and IMDB, we present novel results on explainable classifications of dental bills. The latter case study stems from an industrial collaboration with Allianz Private Krankenversicherung which is an insurance company offering diverse services in Germany.