Introduction to High-Dimensional Statistics

Giraud, Christophe

doi:10.1201/b17895

Cited by 169 publications

(169 citation statements)

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“…MDL and STACT have lower model fidelity and confidence when compared to AGSS and Heuristic, indicating they penalize model complexity too severely and terminate the splitting too early. This is in agreement with the fact that MDL and STACT assume a data size much larger than the number of model parameters [15] [24],…”

Section: Empirical Experimental Resultssupporting

confidence: 86%

Medical Workflow Modeling Using Alignment-Guided State-Splitting HMM

Yang

Zhou

Chen

et al. 2017

2017 IEEE International Conference on Healthcare Informatics (ICHI)

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Process mining techniques have been used to discover and analyze workflows in various fields, ranging from business management to healthcare. Much of this research, however, has overlooked the potential of hidden Markov models (HMMs) for workflow discovery. We present a novel alignment-guided state-splitting HMM inference algorithm (AGSS) for discovering workflow models based on observed traces of process executions. We compared the AGSS to existing methods using four real-world medical workflow datasets and a more detailed case study on one of them. Our numerical results show that AGSS not only generates more accurate workflow models, but also better represents the underlying process. In addition, with trace alignment to guide state splitting, AGSS is significantly more efficient (by a factor of O(n)) than previous HMM inference algorithms. Our case study results show that our approach produces a more readable and accurate workflow model that existing algorithms. Comparing the discovered model to the hand-made expert model of the same process, we found three discrepancies. These three discrepancies were reconsidered by medical experts and used for enhancing the expert model.

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Section: Empirical Experimental Resultssupporting

confidence: 86%

Medical Workflow Modeling Using Alignment-Guided State-Splitting HMM

Yang

Zhou

Chen

et al. 2017

2017 IEEE International Conference on Healthcare Informatics (ICHI)

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“…Estimating the parameters of Gaussian models (or GMM) in such high dimensional spaces is complex. When p is large, patches seen as points in R p are essentially isolated, the euclidean distance and the notion of nearest neighbor become much less reliable than in low dimensional spaces [9]. These phenomena, known as the curse of dimensionality, cause difficulties to decide which patches should be grouped together in a common Gaussian model.…”

Section: Inference In High Dimensionmentioning

confidence: 99%

Gaussian Priors for Image Denoising

Delon

Houdard

2018

Denoising of Photographic Images and Video

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This chapter is dedicated to the study of Gaussian priors for patch-based image denoising. In the last twelve years, patch priors have been widely used for image restoration. In a Bayesian framework, such priors on patches can be used for instance to estimate a clean patch from its noisy version, via classical estimators such as the conditional expectation or the maximum a posteriori. As we will recall, in the case of Gaussian white noise, simply assuming Gaussian (or Mixture of Gaussians) priors on patches leads to very simple closed-form expressions for some of these estimators. Nevertheless, the convenience of such models should not prevail over their relevance. For this reason, we also discuss how these models represent patches and what kind of information they encode. The end of the chapter focuses on the different ways in which these models can be learned on real data. This stage is particularly challenging because of the curse of dimensionality. Through these different questions, we compare and connect several denoising methods using this framework.

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“…Such forms of data are too much bigger in size and hence are called as high-dimensional data. Unfortunately, in such form of high-dimensional data, the distance and locations of the data points are more disperse and scattered in order to take the shape of sparsity [3][4] [5]. Therefore, clustering is the only alternative technique to solve such classification problem.…”

Section: Introduction (Heading 1)mentioning

confidence: 99%

RMSC: Robust modeling of subspace clustering for high dimensional data

Radhika

et al. 2017

2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI)

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Abstract-Subspace clustering is one of the active research problem associated with high-dimensional data. Here some of the standard techniques are reviewed to investigate existing methodologies. Although, there have been various forms of research techniques evolved recently, they do not completely mitigate the problems pertaining to noise sustainability and optimization of clustering accuracy. Hence, a novel technique called as Robust Modeling of Subspace Clustering (RMSC) presented to solve the above problem. An analytical research methodology is used to formulate two algorithms for computing outliers and for extracting elite subspace from the highdimensional data inflicted by different forms of noise. RMSC was found to offer higher accuracy and lower error rate both in presence of noise and absence of noise over high-dimensional data.

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Introduction to High-Dimensional Statistics

Cited by 169 publications

References 0 publications

Medical Workflow Modeling Using Alignment-Guided State-Splitting HMM

Medical Workflow Modeling Using Alignment-Guided State-Splitting HMM

Gaussian Priors for Image Denoising

RMSC: Robust modeling of subspace clustering for high dimensional data

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