Proposed Sampling Algorithm Research Articles

Bayesian mixed-effect higher-order hidden Markov models with applications to predictive healthcare using electronic health records

The disease progression dynamics in electronic health records often reflect patients’ health condition evolution, holding the promise of enabling the development of clinical predictive models. These dynamics, however, generally exist significant variability among patients due to some critical factors (e.g., gender and age) and patient-level heterogeneity. Moreover, future health state may not only depend on the current state but also more distant history states due to the complicated disease progression. To capture this complex transition behavior and address mixed effects in clinical prediction problems, we propose a novel and flexible Bayesian mixed-effect higher-order hidden Markov model (MHOHMM), and develop a classifier based on MHOHMMs. A range of MHOHMMs are designed to capture different data structures and the optimal one is identified by using the k-fold cross-validation. An effective two-stage Markov chain Monte Carlo (MCMC) sampling algorithm is designed for model inference. A simulation study is conducted to evaluate the performance of the proposed sampling algorithm and the MHOHMM-based classification method. The practical utility of the proposed framework is demonstrated by a case study on the acute hypotensive episode prediction for intensive care unit patients. Our results show that the MHOHMM-based framework provides good prediction performance.

A rapidly mixing Markov chain from any gapped quantum many-body system

We consider the computational task of sampling a bit string x from a distribution π(x)=|⟨x|ψ⟩|2, where ψ is the unique ground state of a local Hamiltonian H. Our main result describes a direct link between the inverse spectral gap of H and the mixing time of an associated continuous-time Markov Chain with steady state π. The Markov Chain can be implemented efficiently whenever ratios of ground state amplitudes ⟨y|ψ⟩/⟨x|ψ⟩ are efficiently computable, the spectral gap of H is at least inverse polynomial in the system size, and the starting state of the chain satisfies a mild technical condition that can be efficiently checked. This extends a previously known relationship between sign-problem free Hamiltonians and Markov chains. The tool which enables this generalization is the so-called fixed-node Hamiltonian construction, previously used in Quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. We observe empirically that our Markov chain based on the fixed-node Hamiltonian mixes more rapidly than the standard Metropolis-Hastings Markov chain.

Active Learning: Encoder-Decoder-Outlayer and Vector Space Diversification Sampling

This study introduces a training pipeline comprising two components: the Encoder-Decoder-Outlayer framework and the Vector Space Diversification Sampling method. This framework efficiently separates the pre-training and fine-tuning stages, while the sampling method employs pivot nodes to divide the subvector space and selectively choose unlabeled data, thereby reducing the reliance on human labeling. The pipeline offers numerous advantages, including rapid training, parallelization, buffer capability, flexibility, low GPU memory usage, and a sample method with nearly linear time complexity. Experimental results demonstrate that models trained with the proposed sampling algorithm generally outperform those trained with random sampling on small datasets. These characteristics make it a highly efficient and effective training approach for machine learning models. Further details can be found in the project repository on GitHub.

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.

The taxicab sampler: MCMC for discrete spaces with application to tree models

Motivated by the problem of exploring discrete but very complex state spaces in Bayesian models, we propose a novel Markov Chain Monte Carlo search algorithm: the taxicab sampler. We describe the construction of this sampler and discuss how its interpretation and usage differs from that of standard Metropolis-Hastings as well as the related Hamming ball sampler. The proposed sampling algorithm is then shown to demonstrate substantial improvement in computation time without any loss of efficiency relative to a naïve Metropolis–Hastings search in a motivating Bayesian regression tree count model, in which we leverage the discrete state space assumption to construct a novel likelihood function that allows for flexibly describing different mean-variance relationships while preserving parameter interpretability compared to existing likelihood functions for count data.

Prostate cancer classification using radiomics and machine learning on mp-MRI validated using co-registered histology

BackgroundMulti-parametric magnetic resonance imaging (mp-MRI) is emerging as a useful tool for prostate cancer (PCa) detection but currently has unaddressed limitations. Computer aided diagnosis (CAD) systems have been developed to address these needs, but many approaches used to generate and validate the models have inherent biases. MethodAll clinically significant PCa on histology was mapped to mp-MRI using a previously validated registration algorithm. Shape and size matched non-PCa regions were selected using a proposed sampling algorithm to eliminate biases towards shape and size. Further analysis was performed to assess biases regarding inter-zonal variability. ResultsA 5-feature Naïve-Bayes classifier produced an area under the receiver operating characteristic curve (AUC) of 0.80 validated using leave-one-patient-out cross-validation. As mean inter-class area mismatch increased, median AUC trended towards positively biasing classifiers to producing higher AUCs. Classifiers were invariant to differences in shape between PCa and non-PCa lesions (AUC: 0.82 vs 0.82). Performance for models trained and tested only in the peripheral zone was found to be lower than in the central gland (AUC: 0.75 vs 0.95). ConclusionWe developed a radiomics based machine learning system to classify PCa vs non-PCa tissue on mp-MRI validated on accurately co-registered mid-gland histology with a measured target registration error. Potential biases involved in model development were interrogated to provide considerations for future work in this area.

A Network Sampling Strategy Inspired by Epidemic Spreading

Nowadays, network sampling has become an indispensable premise and foundation for large-scale network analysis, and its effectiveness determines to a large extent the reliability and practicability of the subsequent network analysis results. In this paper, we propose a network sampling algorithm inspired by an epidemic spreading model named the contact process. The contact process is similar to the random walk process but different from it in two key points. First, at each time step, a randomly selected sampled node rather than the latest sampled node is responsible for recruiting a new node from its neighborhood. Second, the responsible node recruits one of its neighbor nodes with a probability inversely proportional to the degree of this neighbor node, instead of equal probability. Experiments on nine indiscriminately selected real-world networks show that our proposed sampling algorithm has a significant advantage in preserving two basic network properties, the degree distributions and clustering coefficient distributions of original networks, compared with seven classical sampling methods.

Curvature-Variation-Inspired Sampling for Point Cloud Classification and Segmentation

Point cloud is a discrete and unordered expression of 3D data. A lot of methods have been proposed to solve the problem in 3D object classification and scene recognition. To handle the huge amount of unordered point cloud, down-sampling before processing is needed. The shortage of existing sampling methods is the lack of geometry information consideration, which is essential for point cloud classification and segmentation tasks. Our method is mainly motivated by the observation that points with a high curvature variation can depict the outlines of objects. Thus, we propose a curvature variation based sampling method for point cloud classification and segmentation tasks. We aim to sample points with high curvature variations, which are considered to be more suitable for classification and segmentation tasks than the traditional sampling method. We combine the proposed sampling algorithm with the existing sampling method for multiple information fusion, and a higher accuracy and mean IoU can be achieved. The experimental results verify the advantage of considering curvature variation in classification and segmentation tasks.

Learning adaptive criteria weights for active semi-supervised learning

Batch mode active learning (BMAL) is devoted to training trustful learning models with scarce labeled samples by efficiently asking the ground truth annotations of the most beneficial unlabeled points for supervision with the feedback of an expert. Particularly, BMAL algorithms always sample points based on the decent-designed criteria, such as (un)certainty and representativeness, etc. However, present BMAL approaches consistently are afflicted with one limitation: They simply integrate the sampling criteria with fixed weights to select instances for supervised training, which may yield suboptimal batch acquisition since the criteria values of the plentiful candidate unlabeled samples would fluctuate after retraining the classifier with the newly augmented training set. Instead, the weights of sampling criteria should be allocated appropriately. To overcome this problem, this work proposes a novel Adaptive Criteria Weights batch selection algorithm, abbreviated ACW, which dynamically adjusts the importance of (un)certainty and representativeness to choose critical instances for semi-supervised learning. A submodular function is employed to recognize a diverse mini-batch from the selected batch of samples. We apply our proposed ACW batch sampling algorithm to two types of essential semi-supervised tasks, i.e., semi-supervised classification and semi-supervised clustering. To the best of our knowledge, this work is the first devoted attempt to explore adaptive mechanism of criteria weights in the context of active learning. The superiority and effectiveness of ACW against the present state-of-the-art BMAL approaches have also been demonstrated by the encouraging experimental results.

A dynamic sampling algorithm based on learning automata for stochastic trust networks

Trust is known as an important social concept and an effective factor in all human interactions in social networks. Users tend to interact with trusted people with whom they have had positive experiences. Trust is updated over time as a result of these repeated interactions. Even though dynamicity is a universally accepted property of the social trust, trust networks are often modeled as static digraphs. In this paper, we first propose that a stochastic graph model, where the weights associated with edges are random variables with unknown distributions, may be a better candidate for representing trust networks. Then, we review the literature on analyzing complex networks and determine graph measures which are most appropriate with respect to the special properties of the concept of trust. Considering trust-specific measures, we finally propose a dynamic algorithm for sampling from stochastic trust networks, which is an extension of Frontier sampling. Even though there exist a few sampling methods which address edge weights and their variations over time through the sampling process, these methods are unable to accurately preserve the properties of trust networks. The proposed algorithm in this paper uses learning automata to tackle the disconnectivity problem of sampled subgraphs by Frontier sampling and, at the same time, capture the changes of edge weights through the sampling process. Our experimental results on the well-known trust network datasets indicate that the proposed sampling algorithm preserves more accurately the trust-specific measures of trust networks compared to existing sampling methods.

Sliced Lattice Gaussian Sampling: Convergence Improvement and Decoding Optimization

Sampling from the lattice Gaussian distribution has emerged as a key problem in coding and decoding while Markov chain Monte Carlo (MCMC) methods from statistics offer an effective way to solve it. In this paper, the sliced lattice Gaussian sampling algorithm is proposed to further improve the convergence performance of the Markov chain targeting at lattice Gaussian sampling. We demonstrate that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution. Meanwhile, the convergence rate of the underlying Markov chain is also investigated, and we show the proposed sliced sampling algorithm entails a better convergence performance than the independent Metropolis-Hastings-Klein (IMHK) sampling algorithm. On the other hand, the decoding performance based on the proposed sampling algorithm is analyzed, where the optimization with respect to the standard deviation σ > 0 of the target lattice Gaussian distribution is given. After that, a judicious mechanism based on distance judgement and dynamic updating for choosing σ is proposed for a better decoding performance. Finally, simulation results based on multiple-input multiple-output (MIMO) detection are presented to confirm the performance gain by the convergence enhancement and the parameter optimization.

Efficient approximate dynamic programming based on design and analysis of computer experiments for infinite-horizon optimization

The approximate dynamic programming (ADP) method based on the design and analysis of computer experiments (DACE) approach has been demonstrated as an effective method to solve multistage decision-making problems in the literature. However, this method is still not efficient for infinite-horizon optimization considering the required large volume of sampling in the state space and high-quality value function identification. Therefore, we propose a sequential sampling algorithm and embed it into a DACE-based ADP method to obtain a high-quality value function approximation. Considering the limitations of the traditional stopping criterion (Bellman error bound), we further propose a 45-degree line stopping criterion to terminate value iteration early by identifying an optimally equivalent value function. A comparison of the computational results with those of other three existing policies indicates that the proposed sampling algorithm and stopping criterion can determine a high-quality ADP policy. Finally, we discuss the extrapolation issue of the value function approximated by multivariate adaptive regression splines, the results of which further demonstrate the quality of the ADP policy generated in this study.

Optimal allocation of Monte Carlo simulations to multiple hypothesis tests

Multiple hypothesis tests are often carried out in practice using p-value estimates obtained with bootstrap or permutation tests since the analytical p-values underlying all hypotheses are usually unknown. This article considers the allocation of a pre-specified total number of Monte Carlo simulations $$K \in \mathbb {N}$$ (i.e., permutations or draws from a bootstrap distribution) to a given number of $$m \in \mathbb {N}$$ hypotheses in order to approximate their p-values $$p \in [0,1]^m$$ in an optimal way, in the sense that the allocation minimises the total expected number of misclassified hypotheses. A misclassification occurs if a decision on a single hypothesis, obtained with an approximated p-value, differs from the one obtained if its p-value was known analytically. The contribution of this article is threefold: under the assumption that p is known and $$K \in \mathbb {R}$$, and using a normal approximation of the Binomial distribution, the optimal real-valued allocation of K simulations to m hypotheses is derived when correcting for multiplicity with the Bonferroni correction, both when computing the p-value estimates with or without a pseudo-count. Computational subtleties arising in the former case will be discussed. Second, with the help of an algorithm based on simulated annealing, empirical evidence is given that the optimal integer allocation is likely of the same form as the optimal real-valued allocation, and that both seem to coincide asympotically. Third, an empirical study on simulated and real data demonstrates that a recently proposed sampling algorithm based on Thompson sampling asympotically mimics the optimal (real-valued) allocation when the p-values are unknown and thus estimated at runtime.

Anomaly detection method for sensor network data streams based on sliding window sampling and optimized clustering

When detecting abnormal data in the sensor network data stream, it is necessary to accurately obtain the source of the abnormal data. The traditional data stream clustering algorithm has the disadvantages of large clustering information loss and low accuracy. Therefore, this paper proposes a sensor network data stream anomaly detection method based on optimized clustering. Firstly, the proposed sampling algorithm is used to sample the data stream. The sampling result is used as a sample set. Use dynamic data histogram to divide the data dimension into different dimension groups, calculate the maximum entropy division dimension space cluster of each dimension, and aggregate the data of the same dimension cluster into the micro cluster. The abnormality detection of the data stream is realized by comparing the information entropy size of the micro cluster and its distribution characteristics. The experimental results show that the proposed algorithm can improve the accuracy and effectiveness of data stream anomaly detection.

Markov chain Monte Carlo sampling using a reservoir method

Markov chain Monte Carlo methods are widely used to draw a sample from a target distribution which is hard to characterize analytically, and reservoir sampling is developed to obtain a sample from a data stream sequentially in a single pass. A stochastic thinning algorithm using reservoir sampling is proposed, and it can be embedded in most Markov chain Monte Carlo methods to reduce the autocorrelation among the generated sample. The distribution of the sample generated by the proposed sampling algorithm converges in total variation to the target distribution in probability under mild conditions. A practical method is introduced to detect the convergence of the proposed sampling algorithm. Two simulation studies are conducted to compare the proposed sampling algorithm and the corresponding Markov chain Monte Carlo methods without thinning, and results show that the estimation bias of the proposed sampling algorithm is approximately the same as the corresponding Markov chain Monte Carlo method, but the proposed sampling algorithm has a smaller Monte Carlo variance. The proposed sampling algorithm saves computer memory in the sense that the storage of a small portion of the Markov chain is required in each iteration.

Cost-Effective Extreme Case-Control Design Using a Resampling Method.

Nested case-control sampling design is a popular method in a cohort study whose events are often rare. The controls are randomly selected with or without the matching variable fully observed across all cohort samples to control confounding factors. In this article, we propose a new nested case-control sampling design incorporating both extreme case-control design and a resampling technique. This new algorithm has two main advantages with respect to the conventional nested case-control design. First, it inherits the strength of extreme case-control design such that it does not require the risk sets in each event time to be specified. Second, the target number of controls can only be determined by the budget and time constraints and the resampling method allows an under sampling design, which means that the total number of sampled controls can be smaller than the number of cases. A simulation study demonstrated that the proposed algorithm performs well even when we have a smaller number of controls compared with the number of cases. The proposed sampling algorithm is applied to a public data collected for “Thorotrast Study.”

ROI-Based LiDAR Sampling Algorithm in on-Road Environment for Autonomous Driving

As the acquisition of laser range measurements such as those from light detection and ranging (LiDAR) sensors requires a considerable amount of time, to design an effective sampling algorithm is a critical task in numerous laser range applications. The state-of-the-art adaptive methods such as two-step sampling are highly effective at handling less complex scenes such as indoor environments with a moderately low sampling rate. However, their performance is relatively low in complex on-road environments, particularly when the sampling rate of the measuring equipment is low. To address this problem, this paper proposes a region-of-interest (ROI)-based sampling algorithm in on-road environments for autonomous driving. With the aid of fast and accurate road and object detection algorithms, particularly those based on convolutional neural networks, the proposed sampling algorithm utilizes the semantic information and effectively distributes samples in the road, object, and background areas. The experimental results demonstrate that the proposed algorithm significantly reduces the mean-absolute-error in the object area by at most 52.8% compared to two-step sampling; moreover, it achieves robust reconstruction quality even at a very low sampling rate of 1%.

Stochastic leaching analysis on cementitious materials considering the influence of material uncertainty

Uncertainties significantly influence the durability-related experiments and field studies, which can hardly be addressed by deterministic approaches. This work aims at developing a stochastic numerical framework to disentangle the influence of material uncertainty on the case of leaching. To ensure the robustness of the numerical framework, a realistic stochastic reactive-transportation model is developed, which consists of a novel sampling algorithm and a comprehensive deterministic model. By using the proposed sampling algorithm, a more effective and efficient sampling process can be achieved without compromising the randomness of the uncertain properties. Besides, realistic mechanisms of leaching are considered by the deterministic model, including the simultaneous processes of ionic transportation, chemical reactions and material degradation. By performing the stochastic leaching analyses, numerical results suggest the overwhelming influence of the physical uncertainty on long-term leaching, while the impact of chemical uncertainty is more evident in terms of short-term leaching. It is also revealed that the root-time relation as determined from short-term experiments is inappropriate for long-term predictions. Thus, a modified relation is developed based on the stochastic leaching analysis, which generates accurate predictions for both the short-term and long-term leaching.

Random Node Pair Sampling-Based Estimation of Average Path Lengths in Networks

This article describes how the average path length (APL) of a network is an important metric that provides insights on the interconnectivity in a network and how much time and effort would be required for search and navigation on that network. However, the estimation of APL is time-consuming as its computational complexity scales nonlinearly with the network size. In this article, the authors develop a computationally efficient random node pair sampling algorithm that enables the estimation of APL with a specified precision and confidence. The proposed sampling algorithms provide a speed-up factor ranging from 240-750 for networks with more than 100,000 nodes. The authors also find that the computational time required for estimation APL does not necessarily increase with the network size; it shows an inverted U shape instead.

Random Node Pair Sampling-Based Estimation of Average Path Lengths in Networks

The average path length (APL) of a network is an important metric that provides insights on the interconnectivity in a network and how much time and effort would be required for search and navigation on that network. However, the estimation of APL is time-consuming as its computational complexity scales nonlinearly with the network size. In this paper, we develop a computationally efficient random node pair sampling algorithm that enables the estimation of APL with a specified precision and confidence. The proposed sampling algorithms provide a speed-up factor ranging from 240-750 for networks with more than 100,000 nodes. We also find that the computational time required for estimation APL does not necessarily increase with the network size; it shows an inverted U shape instead.