Dataset Information

Optimal clustering under uncertainty.

ABSTRACT: Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point processes and characterizing a Bayes clusterer that minimizes the number of misclustered points. The Bayes clusterer is analogous to the Bayes classifier. Whereas determining a Bayes classifier requires full knowledge of the feature-label distribution, deriving a Bayes clusterer requires full knowledge of the point process. When uncertain of the point process, one would like to find a robust clusterer that is optimal over the uncertainty, just as one may find optimal robust classifiers with uncertain feature-label distributions. Herein, we derive an optimal robust clusterer by first finding an effective random point process that incorporates all randomness within its own probabilistic structure and from which a Bayes clusterer can be derived that provides an optimal robust clusterer relative to the uncertainty. This is analogous to the use of effective class-conditional distributions in robust classification. After evaluating the performance of robust clusterers in synthetic mixtures of Gaussians models, we apply the framework to granular imaging, where we make use of the asymptotic granulometric moment theory for granular images to relate robust clustering theory to the application.

SUBMITTER: Dalton LA

PROVIDER: S-EPMC6168142 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Optimal clustering under uncertainty.

Dalton Lori A LA Benalcázar Marco E ME Dougherty Edward R ER

PloS one 20181002 10

Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point processes and characterizing a Bayes clusterer that minimizes the number of misclustered points. The Bayes clusterer is analogous to the Bayes classifier. Whereas determining a Ba ...[more]

PMID: 30278063

Similar Datasets

Project description:This study presents a new risk-averse multi-stage stochastic epidemics-ventilator-logistics compartmental model to address the resource allocation challenges of mitigating COVID-19. This epidemiological logistics model involves the uncertainty of untested asymptomatic infections and incorporates short-term human migration. Disease transmission is also forecasted through a new formulation of transmission rates that evolve over space and time with respect to various non-pharmaceutical interventions, such as wearing masks, social distancing, and lockdown. The proposed multi-stage stochastic model overviews different scenarios on the number of asymptomatic individuals while optimizing the distribution of resources, such as ventilators, to minimize the total expected number of newly infected and deceased people. The Conditional Value at Risk (CVaR) is also incorporated into the multi-stage mean-risk model to allow for a trade-off between the weighted expected loss due to the outbreak and the expected risks associated with experiencing disastrous pandemic scenarios. We apply our multi-stage mean-risk epidemics-ventilator-logistics model to the case of controlling COVID-19 in highly-impacted counties of New York and New Jersey. We calibrate, validate, and test our model using actual infection, population, and migration data. We also define a new region-based sub-problem and bounds on the problem and then show their computational benefits in terms of the optimality and relaxation gaps. The computational results indicate that short-term migration influences the transmission of the disease significantly. The optimal number of ventilators allocated to each region depends on various factors, including the number of initial infections, disease transmission rates, initial ICU capacity, the population of a geographical location, and the availability of ventilator supply. Our data-driven modeling framework can be adapted to study the disease transmission dynamics and logistics of other similar epidemics and pandemics.

Project description:Experience is known to facilitate our ability to interpret sequences of events and make predictions about the future by extracting temporal regularities in our environments. Here, we ask whether uncertainty in dynamic environments affects our ability to learn predictive structures. We exposed participants to sequences of symbols determined by first-order Markov models and asked them to indicate which symbol they expected to follow each sequence. We introduced uncertainty in this prediction task by manipulating the: (a) probability of symbol co-occurrence, (b) stimulus presentation rate. Further, we manipulated feedback, as it is known to play a key role in resolving uncertainty. Our results demonstrate that increasing the similarity in the probabilities of symbol co-occurrence impaired performance on the prediction task. In contrast, increasing uncertainty in stimulus presentation rate by introducing temporal jitter resulted in participants adopting a strategy closer to probability maximization than matching and improving in the prediction tasks. Next, we show that feedback plays a key role in learning predictive statistics. Trial-by-trial feedback yielded stronger improvement than block feedback or no feedback; that is, participants adopted a strategy closer to probability maximization and showed stronger improvement when trained with trial-by-trial feedback. Further, correlating individual strategy with learning performance showed better performance in structure learning for observers who adopted a strategy closer to maximization. Our results indicate that executive cognitive functions (i.e., selective attention) may account for this individual variability in strategy and structure learning ability. Taken together, our results provide evidence for flexible structure learning; individuals adapt their decision strategy closer to probability maximization, reducing uncertainty in temporal sequences and improving their ability to learn predictive statistics in variable environments.

Dataset Information

Optimal clustering under uncertainty.

Publications

Optimal clustering under uncertainty.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets