Sampling-based Techniques Research Articles

Learning complex predicates for cardinality estimation using recursive neural networks

Cardinality estimation is one of the most vital components in the query optimizer, which has been extensively studied recently. On one hand, traditional cardinality estimators, such as histograms and sampling methods, struggle to capture the correlations between multiple tables. On the other hand, current learning-based methods still suffer from the feature extraction of complex predicates and join relations, which will lead to inaccurate cost estimation, eventually a sub-optimal execution plan. To address these challenges, we present a novel end-to-end architecture leveraging deep learning to provide high-quality cardinality estimation. We exploit an effective feature extraction technique, which can fully make use of the structure of tables, join conditions and predicates. Besides, we use sampling-based technique to construct sample bitmaps for the tables and join conditions respectively. We also utilize the characteristics of predicate tree combined with recursive neural network to extract deep-level features of complex predicates. Finally, we embed these feature vectors into the model, which consists of three components: a recursive neural network, a graph convolutional neural network (GCN) and a multi-set convolutional neural network, to obtain the estimated cardinality. Extensive results conducted on real-world workloads demonstrate that our approach can achieve significant improvement in accuracy and be extended to queries with complex semantics.

On the Influence of Data Imbalance on Supervised Gaussian Mixture Models

Imbalanced data present a pervasive challenge in many real-world applications of statistical and machine learning, where the instances of one class significantly outnumber those of the other. This paper examines the impact of class imbalance on the performance of Gaussian mixture models in classification tasks and establishes the need for a strategy to reduce the adverse effects of imbalanced data on the accuracy and reliability of classification outcomes. We explore various strategies to address this problem, including cost-sensitive learning, threshold adjustments, and sampling-based techniques. Through extensive experiments on synthetic and real-world datasets, we evaluate the effectiveness of these methods. Our findings emphasize the need for effective mitigation strategies for class imbalance in supervised Gaussian mixtures, offering valuable insights for practitioners and researchers in improving classification outcomes.

PiP-X: Online feedback motion planning/replanning in dynamic environments using invariant funnels

Computing kinodynamically feasible motion plans and repairing them on-the-fly as the environment changes is a challenging, yet relevant problem in robot navigation. We propose an online single-query sampling-based motion re-planning algorithm using finite-time invariant sets, commonly referred to as “ funnels”. We combine concepts from nonlinear systems analysis, sampling-based techniques, and graph-search methods to create a single framework that enables feedback motion re-planning for any general nonlinear dynamical system in dynamic workspaces. A volumetric network of funnels is constructed in the configuration space using sampling-based methods and invariant set theory; and an optimal sequencing of funnels from robot configuration to a desired goal region is then determined by computing the shortest-path subgraph (tree) in the network. Analyzing and formally quantifying the stability of trajectories using Lyapunov level-sets ensures kinodynamic feasibility and guaranteed set-invariance of the solution paths. Though not required, our method is capable of using a pre-computed library of motion primitives to speedup online computation of controllable motion plans that are volumetric in nature. We introduce a novel directed-graph data structure to represent the funnel-network and its inter-sequencibility; helping us leverage discrete graph-based incremental search to quickly rewire feasible and controllable motion plans on-the-fly in response to changes in the environment. We validate our approach on a simulated cart-pole, car-like robot, and 6DOF quadrotor platform in a variety of scenarios within a maze and a random forest environment. Using Monte Carlo methods, we evaluate the performance in terms of algorithm success, length of traversed trajectory, and runtime.

Trust-Region Approximation of Extreme Trajectories in Power System Dynamics

In this work we present a novel technique, based on a trust-region optimization algorithm and second-order trajectory sensitivities, to compute the extreme trajectories of power system dynamic simulations given a bounded set that represents parametric uncertainty. We show how this method, while remaining computationally efficient compared with sampling-based techniques, overcomes the limitations of previous sensitivity-based techniques to approximate the bounds of the trajectories, when the local approximation loses validity because of the nonlinearity. In addition, we show how this method can be adapted to account for those cases in which the initial conditions depend on the uncertain parameter. To conclude, we present several numerical experiments that showcase the accuracy and scalability of the technique, including a demonstration on the IEEE New England test system.

Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5.

Herein, we propose a novel computational protocol that enables calculating free energies with improved accuracy by combining the best available techniques for enthalpy and entropy calculation. While the entropy is described by enhanced sampling molecular dynamics techniques, the energy is calculated using ab initio methods. We apply the method to assess the stability of isobutene adsorption intermediates in the zeolite H-SSZ-13, a prototypical problem that is computationally extremely challenging in terms of calculating enthalpy and entropy. We find that at typical operating conditions for zeolite catalysis (400 °C), the physisorbed π-complex, and not the tertiary carbenium ion as often reported, is the most stable intermediate. This method paves the way for sampling-based techniques to calculate the accurate free energies in a broad range of chemistry-related disciplines, thus presenting a big step forward toward predictive modeling.

Kinodynamic on-orbit inspection path planning for full-coverage inspection in close proximity of space structures

In this paper, a kinodynamic inspection path planner, called Random Kinodynamic Inspection Tree algorithm, is presented to perform in-close proximity full-coverage on-orbit inspection for the space structures, under kinematic/dynamic motion constraints in deep space environments. Inspection, as one of the key elements of proximity operations, would make a significant breakthrough in on-orbit servicing and, therefore, space exploration missions. The presented approach combines a novel coverage planning scheme with a kinodynamic motion planner to quickly and effectively solve the inspection path planning problem while at the same time handling both holonomic and non-holonomic constraints of the environment and the inspector robot. Our planner avoids the previous decoupled two steps method, which usually has been used to solve coverage planning problems, namely the Art Gallery and Traveling salesman problems, which are difficult or infeasible to be applied to a robot with differential constraints working in a high-dimensional environment. By contrast, our planner employs the Rapidly Exploring Random Tree algorithm as an asymptotically-optimal sampling-based technique in cooperation with a Linear Quadratic Minimum Time controller to generate an optimal and smooth inspection trajectory for any space structures, given complete knowledge of the structure and inspector’s dynamics. The algorithm guarantees probabilistic completeness. Simulations are provided as a validation of the achieved inspection performance.

Credit Card Fraud Detection Using Selective Class Sampling and Random Forest Classifier

The incidences of credit card fraud are increasing. It puts the hard-earned money of users at risk. The financial institutions and governing bodies are looking forward to some robust and reliable ways of detecting credit card fraudulent transactions. The task is challenging due to non-availability of enough data, high class imbalance, and high stake on false negative rates (FNR). Most of the methods available in literature perform well on the accuracy-based performance metrics. However, they fail to yield satisfactory ROC-AUC performance due to the high false positive or false negative rates. Mitigating this issue is the real challenge for the task of fraudulent credit card transaction detection. This paper investigates the problem of credit card fraudulent transaction detection and proposes a technique for it. The proposed method uses a custom selective class sampling-based class balancing technique, and subsequently, it uses random forest for classification. The experimental results show that the proposed technique has better AUC score, accuracy, precision, and recall values as compared with other similar approaches.

Comparative analysis on path planning of ATR using RRT*, PSO, and modified APF in CG-Space

Path planning of All-Terrain Rover over 3D terrains is one of the most challenging robotics problems. Prior research has been carried out over 2D static and dynamic configuration space. Currently, all available algorithms for 3D path planning of articulated rover require optimization for wheel-terrain interaction. In this comparative analysis, the path planning is carried out over the 10 degrees of freedom Rover CG-Space instead of ground. CG-Space is the collection of all possible center of gravity locations of the Rover while traversing on terrain. The introduction of preobtained CG-Space eliminates the need for optimization during the planning stage. In this work, a comprehensive path planning comparison has been obtained among modified artificial potential field (APF) method, sampling-based technique (RRT*), and particle swarm optimization (PSO) algorithm based on path length, path smoothness, and computational time. All algorithms are applied over CG-Space associated with two categories of terrains: even and uneven. Even terrains have a well-defined surface equation, while uneven terrains are generated using Kinect V2 sensor mounted over the sand arena. A continuous surface from CG-Space is generated using cubic spline interpolation. The simulation results show that all three algorithms generate obstacle-free paths in a different time span. Although sampling-based and APF-based techniques take about five times lesser time, the obtained paths have moderate smoothness. PSO performs better than RRT* and modified APF for the requirements of optimal path length and smoothness. Thus, PSO is the optimal way to plan the path if the computational cost associated is acceptable. On the other hand, if time is the major planning concern, then RRT* is the best because the path smoothening takes very little time when using separate cubic spline techniques after obtaining the path nodes. This comparative analysis is useful in selecting an appropriate algorithm depending on the terrain complexity and obstacle conditions.

A Comparison of the Effectiveness of the RRT, PRM, and Novel Hybrid RRT-PRM Path Planners

Abstract: Sampling-based path planners develop paths for robots to journey to their destinations. The two main types of sampling-based techniques are the probabilistic roadmap (PRM) and the Rapidly Exploring Random Tree (RRT). PRMs are multi-query methods that construct roadmaps to find routes, while RRTs are single-query techniques that grow search trees to find paths. This investigation evaluated the effectiveness of the PRM, the RRT, and the novel Hybrid RRT-PRM methods. This novel path planner was developed to improve the performance of the RRT and PRM techniques. It is a fusion of the RRT and PRM methods, and its goal is to reduce the path length. Experiments were conducted to evaluate the effectiveness of these path planners. The performance metrics included the path length, runtime, number of nodes in the path, number of nodes in the search tree or roadmap, and the number of iterations required to obtain the path. Results showed that the Hybrid RRT-PRM method was more effective than the PRM and RRT techniques because of the shorter path length. This new technique searched for a path in the convex hull region, which is a subset of the search area near to the start and end locations. The roadmap for the Hybrid RRT-PRM could also be re-used to find pathways for other sets of initial and final positions. Keywords: Path Planning, Sampling-based algorithms, search tree, roadmap, single-query planners, multi-query planners, Rapidly Exploring Random Tree (RRT), Probabilistic Roadmap (PRM), Hybrid RRT-PRM

ATLANTIC

Differential privacy promises to enable data sharing and general data analytics while protecting individual privacy. Because the private data is often stored in the form of relational database that supports SQL queries, making SQL-based analytics differentially private is thus critical. However, the existing SQL-based differentially private systems either only focus on specific type of SQL queries such as COUNT or substantially modify the database engine, thus obstructing adoption in practice. Worse yet, these systems often do not guarantee the desired accuracy by the applications. In this demonstration, using the driving trace workload from Cambridge Mobile Telematics (CMT), we show that our ATLANTIC system, as a database middleware, enforces differential privacy for real-world SQL queries with provable accuracy guarantees and is compatible with existing databases. Moreover, using a sampling-based technique, ATLANTIC significantly speeds up the query execution, yet effectively amplifying the privacy guarantee.

An efficient sampling-based visualization technique for big data clustering with crisp partitions

The data cluster tendency is an emerging need for exploring the big data cluster analysis tasks. The data are evaluated based on the number of clusters is known as cluster tendency. Many visualization techniques have been developed for the detection of cluster tendency. Some of the existing techniques include Visual Assessment Tendency (VAT), spectral-based VAT (SpecVAT), and improved VAT (iVAT), are considerably succeeded for an assessment of cluster tendency for small datasets. A bigVAT is another method that was recently developed for the estimation of cluster tendency of big data. It is perfect for deriving the clustering tendency in visual form for big data. However, it is intractable to explore the data clusters for large volumes of data objects. The proposed work addresses the clustering problem of bigVAT with the derivation of sampling-based crisp partitions. The crisp partitions will accurately predict the cluster labels of data objects. This research is based on big synthetic and big real-life datasets for demonstrating the performance efficiency of the proposed work.

Sampling-based tolerance analysis: the key to establish tolerance-cost optimization in the product development process

Tolerance allocation during detail design aims to identify a combination of tolerances which are tight enough to ensure total product functionality but also as wide as possible to minimize the resultant manufacturing costs. Optimization techniques automatize and thus significantly accelerate the complex search for suitable tolerance values taking both the design and manufacturing perspective into account. While sampling techniques became well-established for tolerance analysis, statistical approximative approaches, e.g. the root sum square method, are still commonly used for tolerance-cost optimization. However, this leads to a limited applicability and validity of the optimization which currently prevents its successful implementation in industry. Thus, the article discusses the direct and indirect effects of sampling methods on the definition and solution of the optimization problem and reveals the benefits and drawbacks of sampling-based tolerance-cost optimization in terms of effectiveness and efficiency using an illustrative case study. In addition, guidelines as well as recommendations for its proper application in research and industry are given. In doing so, this article shows that the use of sampling-based techniques can significantly contribute to a shift of tolerance-cost optimization from an expert tool for tolerance specialists with in-depth knowledge in statistics, optimization and programming, to a user-friendly engineering design tool with an enhanced usability, which enables solving problems of industrial complexity.

Improving tail accuracy of the predicted cumulative distribution function of time of failure

Prognostic information is used to make decisions such as when to perform maintenance or - in time sensitive and safety critical applications - when to change operational settings. Where distributions about expected end of life (EOL) are available, these decisions are often based on risk-informed thresholds, for example a 2σ or 3σ criterion which considers the probability of making a bad decision at 5% or 0.3%, respectively, as tolerable. Sampling-based techniques such as Monte Carlo Sampling (MCS) and Latin Hypercube Sampling (LHS) can provide effective approaches to the propagation and analysis of uncertainty. Due to its efficient manner of stratifying across the range of each sampled variable, LHS requires less computational effort than MCS and is therefore more often used. However, since the focus is placed on accurately predicting the tails of the Cumulative Distribution Function (CDF) of Time of Failure (ToF) sampling-base techniques may not properly represent these areas. Although one might be tempted to use a brute force approach and simply increase the number of samples, some safety-critical applications may be computationally constrained. Such applications include electric UAV where the decision making process has to be fast in order to take action as soon as possible. This paper explores the ability of MCS and LHS to perform tail prediction with small sample sizes. The results show that LHS does not provide a significant advantage over MCS in terms of characterizing the tails of the CDF of the battery End of Discharge (EOD) prediction. Then, a methodology that combines MCS and Kernel Density Estimation (KDE) is investigated. The advantages of KDE in terms of reducing sample size while improving tail accuracy are demonstrated on battery end-of-discharge data.

Direct Solution of Scattering Problems Using Generalized Source Integral Equations

A class of inherently compressible integral equation formulations for problems of scattering by impenetrable objects, which makes use of generalized directional sources, is presented. The new formulation effectively reduces the problem's dimensionality and, thus, allows for efficient low-rank compression of moment matrices' off-diagonal blocks. When the formulation is used with a hierarchical matrix compression and factorization algorithm, a fast direct solver is obtained. The computational bottlenecks introduced by the proposed generalized formulation, in both the matrix-fill and matrix compression stages, are alleviated by using nonuniform sampling-based techniques. These techniques are described in detail for one choice of generalized sources, which use absorbing equivalent source shields, and can be extended to other shield types. The formulation's properties and limitations are studied and its enhanced compressibility is used for the development of a fast direct solver.

Properties of the bridge sampler with a focus on splitting the MCMC sample

Computation of normalizing constants is a fundamental mathematical problem in various disciplines, particularly in Bayesian model selection problems. A sampling-based technique known as bridge sampling (Meng and Wong in Stat Sin 6(4):831–860, 1996) has been found to produce accurate estimates of normalizing constants and is shown to possess good asymptotic properties. For small to moderate sample sizes (as in situations with limited computational resources), we demonstrate that the (optimal) bridge sampler produces biased estimates. Specifically, when one density (we denote as $$p_2$$) is constructed to be close to the target density (we denote as $$p_1$$) using method of moments, our simulation-based results indicate that the correlation-induced bias through the moment-matching procedure is non-negligible. More crucially, the bias amplifies as the dimensionality of the problem increases. Thus, a series of theoretical as well as empirical investigations is carried out to identify the nature and origin of the bias. We then examine the effect of sample size allocation on the accuracy of bridge sampling estimates and discovered that one possibility of reducing both the bias and standard error with a small increase in computational effort is by drawing extra samples from the moment-matched density $$p_2$$ (which we assume easy to sample from), provided that the evaluation of $$p_1$$ is not too expensive. We proceed to show how the simple adaptive approach we termed “splitting” manages to alleviate the correlation-induced bias at the expense of a higher standard error, irrespective of the dimensionality involved. We also slightly modified the strategy suggested by Wang et al. (Warp bridge sampling: the next generation, Preprint, 2019. arXiv:1609.07690) to address the issue of the increase in standard error due to splitting, which is later generalized to further improve the efficiency. We conclude the paper by offering our insights of the application of a combination of these adaptive methods to improve the accuracy of bridge sampling estimates in Bayesian applications (where posterior samples are typically expensive to generate) based on the preceding investigations, with an application to a practical example.

SPPOLAP: Computing Privacy-Preserving OLAP Data Cubes Effectively and Efficiently Algorithms, Complexity Analysis and Experimental Evaluation.

This paper provides significant contributions in the line of the so-called privacy-preserving OLAP research area, via extending the previous SPPOLAP’s results provided recently. SPPOLAP is a state-of-the-art algorithm whose main goal consists in computing privacy-preserving OLAP data cubes effectively and efficiently. The main innovations carried-out by SPPOLAP are represented by the novel privacy OLAP notion and the flexible adoption of sampling-based techniques in order to achieve the final privacy-preserving data cube. In line with the main SPPOLAP’s results, this paper significantly extends the previous research efforts by means of the following contributions: (i) complete algorithms of the whole SPPOLAP algorithmic framework; (ii) complexity analysis and results; (iii) comprehensive experimental analysis of SPPOLAP against real-life multidimensional data cubes, according to several experimental parameters. These contributions nice-fully complete the state-of-the-art SPPOLAP’s results.

A Proper Generalized Decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties

Understanding the failure of brittle heterogeneous materials is essential in many applications. Heterogeneities in material properties are frequently modeled through random fields, which typically induces the need to solve finite element problems for a large number of realizations. In this context, we make use of reduced order modeling to solve these problems at an affordable computational cost. This paper proposes a reduced order modeling framework to predict crack propagation in brittle materials with random heterogeneities. The framework is based on a combination of the Proper Generalized Decomposition (PGD) method with Griffith’s global energy criterion. The PGD framework provides an explicit parametric solution for the physical response of the system. We illustrate that a non-intrusive sampling-based technique can be applied as a post-processing operation on the explicit solution provided by PGD. We first validate the framework using a global energy approach on a deterministic two-dimensional linear elastic fracture mechanics benchmark. Subsequently, we apply the reduced order modeling approach to a stochastic fracture propagation problem.

On Numerical Simulations of Ultra-Wideband Long-Haul Optical Communication Systems

This paper discusses the key issues in reliable modeling and numerical simulation of ultra-wideband (UWB) long-haul fiber-optic systems, such as those spanning the C+L band. We analyze the complexity of the split-step Fourier method (SSFM), including modern scenarios based on graphical processing units (GPU), and its numerical setup for accurate simulations. We explain why using the Manakov equation in the nonlinear step of the SSFM remains a good solution also in the UWB scenario, even though the underlying assumptions may be violated. We next propose a technique, called virtual channel grouping, to speed up SSFM simulations in the UWB regime. Importance sampling-based techniques are proposed to speed up the computation of the enhanced Gaussian noise (EGN) model, with computational times of the order of seconds. With such novel solutions, accurate simulations are feasible even for UWB systems.

Control of Magnetic Microrobot Teams for Temporal Micromanipulation Tasks

In this paper, we present a control framework that allows magnetic microrobot teams to accomplish complex micromanipulation tasks captured by global linear temporal logic (LTL) formulas. To address this problem, we propose an optimal control synthesis method that constructs discrete plans for the robots that satisfy both the assigned tasks as well as proximity constraints between the robots due to the physics of the problem. The proposed algorithm relies on an existing optimal control synthesis approach combined with a novel sampling-based technique to reduce the state-space of the product automaton that is associated with the LTL specifications. The synthesized discrete plans are executed by the microrobots independently using local magnetic fields. Simulation studies show that the proposed algorithm can address large-scale planning problems that cannot be solved using existing optimal control synthesis approaches. Moreover, we present experimental results that also illustrate the potential of the method in practice. To the best of our knowledge, this is the first control framework that allows independent control of teams of magnetic microrobots for temporal micromanipulation tasks.

Propagation of Parametric Uncertainty in Aliev-Panfilov Model of Cardiac Excitation.

Models of cardiac electrophysiology are useful for studying heart functions and cardiac disease mechanisms. However, cardiac models often have a great level of complexity, and it is often computationally prohibitive to simulate tissue and organ activities in a real-time fashion. To address the challenge, simplified models such as Aliev-Panfilov model are developed to reduce model complexity, while providing necessary details of cardiac functions. Simplified models may induce uncertainty, which can deteriorate the accuracy and reliability of cardiac models. In addition, model parameters are calibrated with noisy data and cannot be known with certainty. It is important to assess the effect of parametric uncertainty on model predictions. For the probabilistic, time-invariant parametric uncertainty, a generalized polynomial chaos (gPC) expansion-based method is presented in this work to quantify and propagate uncertainty onto model predictions. Using gPC, a measure of confidence in model predictions can be quickly estimated. As compared with sampling-based uncertainty propagation techniques, e.g., Monte Carlo (MC) simulations, the gPC-based method in this work shows its advantages in terms of computational efficiency and accuracy, which has the potentials for dealing with complicated cardiac models, e.g., 2D tissue and 3D organ models.