Efficient Sampling Algorithm Research Articles

Efficient Environment Map Rendering Based on Decomposition

AbstractThis paper presents an efficient environment map sampling algorithm designed to render high‐quality, low‐noise images with only a few light samples, making it ideal for real‐time applications. We observe that bright pixels in the environment map produce high‐frequency shading effects, such as sharp shadows and shading, while the rest influence the overall tone of the scene. Building on this insight, our approach differs from existing techniques by categorizing the pixels in an environment map into emissive and non‐emissive regions and developing specialized algorithms tailored to the distinct properties of each region. By decomposing the environment lighting, we ensure that light sources are deposited on bright pixels, leading to more accurate shadows and specular highlights. Additionally, this strategy allows us to exploit the smoothness in the low‐frequency component by rendering a smaller image with more lights, thereby enhancing shading accuracy. Extensive experiments demonstrate that our method significantly reduces shadow artefacts and image noise compared to previous techniques, while also achieving lower numerical errors across a range of illumination types, particularly under limited sample conditions.

Sigmoni: classification of nanopore signal with a compressed pangenome index.

Improvements in nanopore sequencing necessitate efficient classification methods, including pre-filtering and adaptive sampling algorithms that enrich for reads of interest. Signal-based approaches circumvent the computational bottleneck of basecalling. But past methods for signal-based classification do not scale efficiently to large, repetitive references like pangenomes, limiting their utility to partial references or individual genomes. We introduce Sigmoni: a rapid, multiclass classification method based on the r-index that scales to references of hundreds of Gbps. Sigmoni quantizes nanopore signal into a discrete alphabet of picoamp ranges. It performs rapid, approximate matching using matching statistics, classifying reads based on distributions of picoamp matching statistics and co-linearity statistics, all in linear query time without the need for seed-chain-extend. Sigmoni is 10-100× faster than previous methods for adaptive sampling in host depletion experiments with improved accuracy, and can query reads against large microbial or human pangenomes. Sigmoni is the first signal-based tool to scale to a complete human genome and pangenome while remaining fast enough for adaptive sampling applications. Sigmoni is implemented in Python, and is available open-source at https://github.com/vshiv18/sigmoni.

A Semiparametric Bayesian Approach to Heterogeneous Spatial Autoregressive Models.

Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis-Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method.

Prediction of 3D RNA Structures from Sequence Using Energy Landscapes of RNA Dimers: Application to RNA Tetraloops.

Access to the three-dimensional structure of RNA enables an ability to gain a more profound understanding of its biological mechanisms, as well as the ability to design RNA-targeting drugs, which can take advantage of the unique chemical environment imposed by a folded RNA structure. Due to the dynamic and structurally complex properties of RNA, both experimental and traditional computational methods have difficulty in determining RNA's 3D structure. Herein, we introduce TAPERSS (Theoretical Analyses, Prediction, and Evaluation of RNA Structures from Sequence), a physics-based fragment assembly method for predicting 3D RNA structures from sequence. Using a fragment library created using discrete path sampling calculations of RNA dinucleoside monophosphates, TAPERSS can sample the physics-based energy landscapes of any RNA sequence with relatively low computational complexity. We have benchmarked TAPERSS on 21 RNA tetraloops, using a combinatorial algorithm as a proof-of-concept. We show that TAPERSS was successfully able to predict the apo-state structures of all 21 RNA hairpins, with 16 of those structures also having low predicted energies as well. We demonstrate that TAPERSS performs most accurately on GNRA-like tetraloops with mostly stacked loop-nucleotides, while having limited success with more dynamic UNCG and CUYG tetraloops, most likely due to the influence of the RNA force field used to create the fragment library. Moreover, we show that TAPERSS can successfully predict the majority of the experimental non-apo states, highlighting its potential in anticipating biologically significant yet unobserved states. This holds great promise for future applications in drug design and related studies. With discussed improvements and implementation of more efficient sampling algorithms, we believe TAPERSS may serve as a useful tool for a physics-based conformational sampling of large RNA structures.

Heisenberg-limited metrology with perturbing interactions

We show that it is possible to perform Heisenberg-limited metrology on GHZ-like states, in the presence of generic spatially local, possibly strong interactions during the measurement process. An explicit protocol, which relies on single-qubit measurements and feedback based on polynomial-time classical computation, achieves the Heisenberg limit. In one dimension, matrix product state methods can be used to perform this classical calculation, while in higher dimensions the cluster expansion underlies the efficient calculations. The latter approach is based on an efficient classical sampling algorithm for short-time quantum dynamics, which may be of independent interest.

Lifted algorithms for symmetric weighted first-order model sampling

Weighted model counting (WMC) is the task of computing the weighted sum of all satisfying assignments (i.e., models) of a propositional formula. Similarly, weighted model sampling (WMS) aims to randomly generate models with probability proportional to their respective weights. Both WMC and WMS are hard to solve exactly, falling under the #P-hard complexity class. However, it is known that the counting problem may sometimes be tractable, if the propositional formula can be compactly represented and expressed in first-order logic. In such cases, model counting problems can be solved in time polynomial in the domain size, and are known as domain-liftable. The following question then arises: Is it also the case for WMS? This paper addresses this question and answers it affirmatively. Specifically, we prove the domain-liftability under sampling for the two-variables fragment of first-order logic with counting quantifiers in this paper, by devising an efficient sampling algorithm for this fragment that runs in time polynomial in the domain size. We then further show that this result continues to hold even in the presence of cardinality constraints. To empirically validate our approach, we conduct experiments over various first-order formulas designed for the uniform generation of combinatorial structures and sampling in statistical-relational models. The results demonstrate that our algorithm outperforms a state-of-the-art WMS sampler by a substantial margin, confirming the theoretical results.

Beyond windability: Approximability of the four-vertex model

We study the approximability of the four-vertex model, a special case of the six-vertex model. We prove that, despite being NP-hard to approximate in the worst case, the four-vertex model admits a fully polynomial randomized approximation scheme (FPRAS) when the input satisfies certain linear equation system over GF(2). The FPRAS is given by a Markov chain known as the worm process, whose state space and rapid mixing rely on the solution of the linear equation system. This is the first attempt to design an FPRAS for the six-vertex model with unwindable constraint functions. Additionally, we explore the applications of this technique on planar graphs, providing efficient sampling algorithms.

Sparse Bayesian Inference on Gamma-Distributed Observations Using Shape-Scale Inverse-Gamma Mixtures

In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where most of the underlying means are concentrated around a certain value. Unlike existing shrinkage priors, our new prior is a shape-scale mixture of inverse-gamma distributions, which has a desirable interpretation of the form of posterior mean and admits flexible shrinkage. We show that the proposed prior has two desirable theoretical properties; Kullback-Leibler super-efficiency under sparsity and robust shrinkage rules for large observations. We propose an efficient sampling algorithm for posterior inference. The performance of the proposed method is illustrated through simulation and two real data examples, the average length of hospital stay for COVID-19 in South Korea and adaptive variance estimation of gene expression data.

Bayesian semi-parametric inference for clustered recurrent events with zero inflation and a terminal event.

Recurrent events are common in clinical studies and are often subject to terminal events. In pragmatic trials, participants are often nested in clinics and can be susceptible or structurally unsusceptible to the recurrent events. We develop a Bayesian shared random effects model to accommodate this complex data structure. To achieve robustness, we consider the Dirichlet processes to model the residual of the accelerated failure time model for the survival process as well as the cluster-specific shared frailty distribution, along with an efficient sampling algorithm for posterior inference. Our method is applied to a recent cluster randomized trial on fall injury prevention.

Accounting for network noise in graph-guided Bayesian modeling of structured high-dimensional data.

There is a growing body of literature on knowledge-guided statistical learning methods for analysis of structured high-dimensional data (such as genomic and transcriptomic data) that can incorporate knowledge of underlying networks derived from functional genomics and functional proteomics. These methods have been shown to improve variable selection and prediction accuracy and yield more interpretable results. However, these methods typically use graphs extracted from existing databases or rely on subject matter expertise, which are known to be incomplete and may contain false edges. To address this gap, we propose a graph-guided Bayesian modeling framework to account for network noise in regression models involving structured high-dimensional predictors. Specifically, we use 2 sources of network information, including the noisy graph extracted from existing databases and the estimated graph from observed predictors in the dataset at hand, to inform the model for the true underlying network via a latent scale modeling framework. This model is coupled with the Bayesian regression model with structured high-dimensional predictors involving an adaptive structured shrinkage prior. We develop an efficient Markov chain Monte Carlo algorithm for posterior sampling. We demonstrate the advantages of our method over existing methods in simulations, and through analyses of a genomics dataset and another proteomics dataset for Alzheimer's disease.

Fast and Perfect Sampling of Subgraphs and Polymer Systems

We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets ) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and works under a percolation subcriticality condition. We show that this condition is optimal in the sense that the task of (approximately) sampling weighted rooted graphlets becomes impossible in finite expected time for infinite graphs and intractable for finite graphs when the condition does not hold. We apply our sampling algorithm as a subroutine to give near linear-time perfect sampling algorithms for polymer models and weighted non-rooted graphlets in finite graphs, two widely studied yet very different problems. This new perfect sampling algorithm for polymer models gives improved sampling algorithms for spin systems at low temperatures on expander graphs and unbalanced bipartite graphs, among other applications.

Contextualized Trajectory Parsing with Spatio-Temporal Graph

This work investigates how to automatically parse object trajectories in surveillance videos, which aims at jointly solving three subproblems: 1) spatial segmentation, 2) temporal tracking, and 3) object categorization. We present a novel representation spatiotemporal graph (ST-Graph) in which: 1) Graph nodes express the motion primitives, each representing a short sequence of small-size patches over consecutive images, and 2) every two neighbor nodes are linked with either a positive edge or a negative edge to describe their collaborative or exclusive relationship of belonging to the same object trajectory. Phrasing the trajectory parsing as a graph multicoloring problem, we propose a unified probabilistic formulation to integrate various types of context knowledge as informative priors. An efficient composite cluster sampling algorithm is employed in search of the optimal solution by exploiting both the collaborative and the exclusive relationships between nodes. The proposed framework is evaluated over challenging videos from public datasets, and results show that it can achieve state-of-the-art tracking accuracy.

Bayesian variable selection and estimation in binary quantile regression using global-local shrinkage priors

In this paper, we construct a Bayesian hierarchical model with global-local shrinkage priors for the regression coefficients, which includes the horseshoe prior and normal-gamma prior. This model is used for high-dimensional quantile regression models with dichotomous response data. We have developed an efficient sampling algorithm to generate posterior samplings for making posterior inference. We use a location-scale mixture representation of the asymmetric Laplace distribution. We assess the performance of the proposed methods through Monte Carlo simulations and two real-data applications in terms of parameter estimation and variable selection. Numerical results demonstrate that the proposed methods perform comparably with existing Bayesian methods under a variety of scenarios.

Galerkin–Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds

A new numerical approximation method for a class of Gaussian random fields on compact connected oriented Riemannian manifolds is introduced. This class of random fields is characterized by the Laplace–Beltrami operator on the manifold. A Galerkin approximation is combined with a polynomial approximation using Chebyshev series. This so-called Galerkin–Chebyshev approximation scheme yields efficient and generic sampling algorithms for Gaussian random fields on manifolds. Strong and weak orders of convergence for the Galerkin approximation and strong convergence orders for the Galerkin–Chebyshev approximation are shown and confirmed through numerical experiments.

Real options analysis for valuation of climate adaptation pathways with application to transit infrastructure.

Climate change and sea-level rise (SLR) are expected to increase the frequency and intensity of coastal flood events, posing risks to coastal communities and infrastructure. While regional climate adaptation investments can provide substantive flood protection, existing plans often neglect uncertainty in future climate conditions and adaptation performance, consequently neglecting the option value of flexibly implementing proposed projects. Addressing this gap, we develop and employ a generalizable real options analysis (ROA) valuation framework that considers how uncertainty in adaptation project costs, SLR, flood severity, and flood losses inform the full range of adaptation performance outcomes. We further propose and apply a novel, computationally efficient flood loss sampling algorithm to estimate the consequences of randomly arriving coastal flood events. We apply this ROA framework to assess the option value of flexibly timing adaptation investments over time, investigating an adaptation pathway proposed by the City of Boston from the perspective of the regional transit system manager. Our results suggest that flexible implementation can provide significant option value in the near- to mid-term (>30 years), with the highest option values under low-probability, high-consequence scenarios. Our results also suggest adaptation pathway performance in the latter half of the 21st century is most sensitive to uncertainty in SLR, flood loss estimates, and flood frequency, underscoring the importance of uncertainty quantification in the long-term valuation of adaptation investments.

A latent functional approach for modeling the effects of multidimensional exposures on disease risk.

Understanding the relationships between exposure and disease incidence is an important problem in environmental epidemiology. Typically, a large number of these exposures are measured, and it is found either that a few exposures transmit risk or that each exposure transmits a small amount of risk, but, taken together, these may pose a substantial disease risk. Further, these exposure effects can be nonlinear. We develop a latent functional approach, which assumes that the individual effect of each exposure can be characterized as one of a series of unobserved functions, where the number of latent functions is less than or equal to the number of exposures. We propose Bayesian methodology to fit models with a large number of exposures and show that existing Bayesian group LASSO approaches are a special case of the proposed model. An efficient Markov chain Monte Carlo sampling algorithm is developed for carrying out Bayesian inference. The deviance information criterion is used to choose an appropriate number of nonlinear latent functions. We demonstrate the good properties of the approach using simulation studies. Further, we show that complex exposure relationships can be represented with only a few latent functional curves. The proposed methodology is illustrated with an analysis of the effect of cumulative pesticide exposure on cancer risk in a large cohort of farmers.

An Adaptive Frequency Sampling Algorithm for Dynamic Condensation-Based Frequency Response Analysis

This paper proposed an efficient and adaptive frequency sampling algorithm for frequency response analysis using dynamic condensation-based reduced-order modeling. For the degree of freedom-based model reduction method, the reduced-order basis becomes a frequency-dependent matrix since the relationship between master and slave degrees of freedom stems from partial equations of a second-order dynamical system. Such frequency-dependency makes the analysis inefficient for investigating the frequency response of the system. Considering that the coverage of a local reduced-order basis at a single frequency varies depending on the frequency, a new frequency sampling algorithm was proposed with a strategy of constructing multiple local reduced-order models (ROMs) at sample frequencies. For adaptive sampling, the frequency range of a local ROM was evaluated, and a new sample was added if there was a gap between two adjacent ROMs. As a result, the accuracy of the local ROM can be estimated, and the efficiency in the online stage was greatly enhanced. The proposed method was verified by performing frequency response analysis with several numerical examples, including a large-scale structural and dynamic system.

Sampling from the Gibbs Distribution in Congestion Games

Logit dynamics is a form of randomized game dynamics in which players have a bias toward strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converge to the so-called Gibbs distribution over the set of all strategy profiles when interpreted as a Markov chain. In general, logit dynamics can converge slowly to the Gibbs distribution, but beyond that, not much is known about its algorithmic aspects, nor that of the Gibbs distribution. In this work, we are interested in the following two questions for congestion games: (i) Is there an efficient algorithm for sampling from the Gibbs distribution? (ii) If yes, does there also exist natural randomized dynamics that converge quickly to the Gibbs distribution? We first study these questions in extension parallel congestion games, a well-studied special case of symmetric network congestion games. As our main result, we show that there is a simple variation on the logit dynamics that converges quickly to the Gibbs distribution in such games. We also address the first question for the class of so-called capacitated uniform congestion games and the second question for max cut games played on a complete graph. To prove our results, we rely on the recent breakthrough work of Anari et al. (2019) regarding the approximate sampling of a base of a matroid according to a strongly log-concave probability distribution.

Efficient Langevin and Monte Carlo sampling algorithms: The case of field-theoretic simulations.

We introduce Langevin sampling algorithms to field-theoretic simulations (FTSs) of polymers that, for the same accuracy, are ∼10× more efficient than a previously used Brownian dynamics algorithm that used predictor corrector for such simulations, over 10× more efficient than the smart Monte Carlo (SMC) algorithm, and typically over 1000× more efficient than a simple Monte Carlo (MC) algorithm. These algorithms are known as the Leimkuhler-Matthews (the BAOAB-limited) method and the BAOAB method. Furthermore, the FTS allows for an improved MC algorithm based on the Ornstein-Uhlenbeck process (OU MC), which is 2× more efficient than SMC. The system-size dependence of the efficiency for the sampling algorithms is presented, and it is shown that the aforementioned MC algorithms do not scale well with system sizes. Hence, for larger sizes, the efficiency difference between the Langevin and MC algorithms is even greater, although, for SMC and OU MC, the scaling is less unfavorable than for the simple MC.

Efficient sampling using feature matching and variable minimal structure size

Greedy search-based guided sampling is a promising research field in model fitting to data with multiple structures in the presence of a large number of outliers. However, these greedy search-based guided sampling algorithms are sensitive to the fixed minimal (acceptable) structure size and the initial model hypothesis: when the fixed minimal structure size is too small, data subsets sampled by these algorithms are not representative. In contrast, when it is too large, data subsets might be contaminated by outliers. Furthermore, these algorithms may fail to obtain an accurate model hypothesis, if the initial model hypothesis is far from the true model. In this paper, we address the above-mentioned two issues by proposing two greedy search-based strategies: one aims to adaptively estimate minimal structure sizes and the other aims to generate effective initial model hypotheses. Specifically, on one hand, to avoid using the fixed minimal structure size, a strategy is proposed to adaptively estimate minimal structure sizes by using previously obtained ones. On the other hand, to reduce the impact of outliers, a strategy is proposed to filter out outliers to obtain a reduced data subset by using a feature matching algorithm. Then, this strategy generates promising initial model hypotheses by using a proximity sampling on the reduced data subset. Finally, an efficient sampling algorithm based on the two proposed greedy search-based strategies is applied to three vision tasks, i.e., fundamental matrix estimation, homography plane detection and 3D motion segmentation. Extensive experimental results demonstrate the effectiveness of the proposed sampling algorithm.