scholarly journals A Possible World-Based Fusion Estimation Model for Uncertain Data Clustering in WBNs

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 875
Author(s):  
Chao Li ◽  
Zhenjiang Zhang ◽  
Wei Wei ◽  
Han-Chieh Chao ◽  
Xuejun Liu
Keyword(s):  
Data Clustering ◽  
Possible Worlds ◽  
Probability Distributions ◽  
Uncertain Data ◽  
Estimation Algorithm ◽  
Measured Data ◽  
Possible World ◽  
Estimation Model ◽  
Leibler Divergence ◽  
Multiple Measurements

In data clustering, the measured data are usually regarded as uncertain data. As a probability-based clustering technique, possible world can easily cluster the uncertain data. However, the method of possible world needs to satisfy two conditions: determine the data of different possible worlds and determine the corresponding probability of occurrence. The existing methods mostly make multiple measurements and treat each measurement as deterministic data of a possible world. In this paper, a possible world-based fusion estimation model is proposed, which changes the deterministic data into probability distribution according to the estimation algorithm, and the corresponding probability can be confirmed naturally. Further, in the clustering stage, the Kullback–Leibler divergence is introduced to describe the relationships of probability distributions among different possible worlds. Then, an application in wearable body networks (WBNs) is given, and some interesting conclusions are shown. Finally, simulations show better performance when the relationships between features in measured data are more complex.

scholarly journals On the Connections between Relational and XML Probabilistic Data Models

2017 ◽  
Author(s):  
Antoine Amarilli ◽  
Pierre Senellart
Keyword(s):  
Relational Databases ◽  
Possible Worlds ◽  
Probability Distributions ◽  
Uncertain Data ◽  
Data Models ◽  
Query Complexity ◽  
Probabilistic Data ◽  
Probabilistic Xml ◽  
Compact Representations ◽  
The Impact

A number of uncertain data models have been proposed,based on the notion of compact representations of probability distributionsover possible worlds. In probabilistic relational models, tuples areannotated with probabilities or formulae over Boolean random variables.In probabilistic XML models, XML trees are augmented with nodesthat specify probability distributions over their children. Both kinds ofmodels have been extensively studied, with respect to their expressivepower, compactness, and query efficiency, among other things. Probabilisticdatabase systems have also been implemented, in both relationaland XML settings. However, these studies have mostly been carried outindependently and the translations between relational and XML models,as well as the impact for probabilistic relational databases of resultsabout query complexity in probabilistic XML and vice versa, have notbeen made explicit: we detail such translations in this article, in bothdirections, study their impact in terms of complexity results, and presentinteresting open issues about the connections between relational andXML probabilistic data models.

scholarly journals A nonlinear updating algorithm captures suboptimal inference in the presence of signal-dependent noise

2018 ◽  
Author(s):  
Seth W. Egger ◽  
Mehrdad Jazayeri
Keyword(s):  
Probability Distributions ◽  
Nonlinear Function ◽  
Alternative View ◽  
Time Interval ◽  
Prior Beliefs ◽  
Optimal Behavior ◽  
Multiple Measurements ◽  
The Brain ◽  
Full Probability ◽  
Sequential Measurements

AbstractBayesian models of behavior have advanced the idea that humans combine prior beliefs and sensory observations to minimize uncertainty. How the brain implements Bayes-optimal inference, however, remains poorly understood. Simple behavioral tasks suggest that the brain can flexibly represent and manipulate probability distributions. An alternative view is that brain relies on simple algorithms that can implement Bayes-optimal behavior only when the computational demands are low. To distinguish between these alternatives, we devised a task in which Bayes-optimal performance could not be matched by simple algorithms. We asked subjects to estimate and reproduce a time interval by combining prior information with one or two sequential measurements. In the domain of time, measurement noise increases with duration. This property makes the integration of multiple measurements beyond the reach of simple algorithms. We found that subjects were able to update their estimates using the second measurement but their performance was suboptimal, suggesting that they were unable to update full probability distributions. Instead, subjects’ behavior was consistent with an algorithm that predicts upcoming sensory signals, and applies a nonlinear function to errors in prediction to update estimates. These results indicate that inference strategies humans deploy may deviate from Bayes-optimal integration when the computational demands are high.

scholarly journals Mínimo e máximo em estruturas nominais – uma análise semântica

2019 ◽  
pp. 250-264
Author(s):  
Rui Marques
Keyword(s):  
Possible Worlds ◽  
Modal Operator ◽  
Possible World

This paper is concerned with the semantics of the portuguese phrases with the form o mínimo/máximo N (‘the minimum N’) and o mínimo/máximo de N (‘the minimum/maximum of N’). Some nouns may occur in both of these constructions, while others might occur in only one of them, and still other nouns might occur only if accompanied by a modal operator. The proposal is made that these facts can be straightforwardly explained by the hypothesis that the first and the second of these syntactic constructions have, respectively, an extensional and an intensional meaning, together with the fact that some nouns have the same denotation in any possible world, while others denote different sets of entities in different possible worlds.

scholarly journals Duality Theorem for a Minimax Vector Optimization Problem

2021 ◽  
Author(s):  
Jacob Atticus Armstrong Goodall
Keyword(s):  
Vector Optimization ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Optimal Transport ◽  
Probability Distributions ◽  
Vector Optimization Problem ◽  
Complexity Science ◽  
Polish Spaces ◽  
Leibler Divergence ◽  
Mathematical Optimisation

Abstract A duality theorem is stated and proved for a minimax vector optimization problem where the vectors are elements of the set of products of compact Polish spaces. A special case of this theorem is derived to show that two metrics on the space of probability distributions on countable products of Polish spaces are identical. The appendix includes a proof that, under the appropriate conditions, the function studied in the optimisation problem is indeed a metric. The optimisation problem is comparable to multi-commodity optimal transport where there is dependence between commodities. This paper builds on the work of R.S. MacKay who introduced the metrics in the context of complexity science in [4] and [5]. The metrics have the advantage of measuring distance uniformly over the whole network while other metrics on probability distributions fail to do so (e.g total variation, Kullback–Leibler divergence, see [5]). This opens up the potential of mathematical optimisation in the setting of complexity science.

scholarly journals Nonexistence, Vague Existence, Merely Possible Existence

Disputatio ◽  
2012 ◽  
Vol 4 (33) ◽  
pp. 427-443
Author(s):  
Iris Einheuser
Keyword(s):  
Possible Worlds ◽  
Target Object ◽  
Possible World ◽  
Plausible Assumption ◽  
De Re ◽  
Modal Semantics ◽  
Vague Existence

Abstract This paper explores a new non-deflationary approach to the puzzle of nonexistence and its cousins. On this approach, we can, under a plausible assumption, express true de re propositions about certain objects that don’t exist, exist indeterminately or exist merely possibly. The defense involves two steps: First, to argue that if we can actually designate what individuates a nonexistent target object with respect to possible worlds in which that object does exist, then we can express a de re proposition about “it”. Second, to adapt the concept of outer truth with respect to a possible world – a concept familiar from actualist modal semantics – for use in representing the actual world.

Introduction to Information Theory

2014 ◽  
Author(s):  
M. Vidyasagar
Keyword(s):  
Information Theory ◽  
Probability Distribution ◽  
Relative Entropy ◽  
Probability Distributions ◽  
Random Variables ◽  
Conditional Entropy ◽  
Random Variable ◽  
Entropy Function ◽  
Concave Functions ◽  
Leibler Divergence

This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random variable (or more precisely, the probability distribution of the random variable). When there are two or more random variables, it is worthwhile to study the conditional entropy of one random variable with respect to another. The last concept is relative entropy, also known as the Kullback–Leibler divergence, which measures the “disparity” between two probability distributions. The chapter first considers convex and concave functions before discussing the properties of the entropy function, conditional entropy, uniqueness of the entropy function, and the Kullback–Leibler divergence.

Analysing Modality

2020 ◽  
pp. 22-73
Author(s):  
Alastair Wilson
Keyword(s):  
Actual World ◽  
Possible Worlds ◽  
Modal Realism ◽  
Possible World ◽  
Metaphysical Modality ◽  
Novel Theory ◽  
Reductive Theory

This chapter presents and defends the basic tenets of quantum modal realism. The first of these principles, Individualism, states that Everett worlds are metaphysically possible worlds. The converse of this principle, Generality, states that metaphysically possible worlds are Everett worlds. Combining Individualism and Generality yields Alignment, a conjecture about the nature of possible worlds that is closely analogous to Lewisian modal realism. Like Lewisian modal realism, Alignment entails that each possible world is a real concrete individual of the same basic kind as the actual world. These similarities render EQM suitable for grounding a novel theory of the nature of metaphysical modality with some unique properties. Also like Lewisian modal realism, quantum modal realism is a reductive theory: it accounts for modality in fundamentally non-modal terms. But quantum modal realism also has unique epistemological advantages over Lewisian modal realism and other extant realist approaches to modality.

Counterfactual conditionals

2018 ◽  
Author(s):  
Frank Doring
Keyword(s):  
Possible Worlds ◽  
Laws Of Nature ◽  
Possible World ◽  
Counterfactual Conditional ◽  
Counterfactual Conditionals

‘If bats were deaf, they would hunt during the day.’ What you have just read is called a ‘counterfactual’ conditional; it is an ‘If…then…’ statement the components of which are ‘counter to fact’, in this case counter to the fact that bats hear well and sleep during the day. Among the analyses proposed for such statements, two have been especially prominent. According to the first, a counterfactual asserts that there is a sound argument from the antecedent (‘bats are deaf’) to the consequent (‘bats hunt during the day’). The argument uses certain implicit background conditions and laws of nature as additional premises. A variant of this analysis says that a counterfactual is itself a condensed version of such an argument. The analysis is called ‘metalinguistic’ because of its reference to linguistic items such as premises and arguments. The second analysis refers instead to possible worlds. (One may think of possible worlds as ways things might have gone.) This analysis says that the example is true just in case bats hunt during the day in the closest possible world(s) where they are deaf

Modal logic, philosophical issues in

2018 ◽  
Author(s):  
Thomas J. McKay
Keyword(s):  
Modal Logic ◽  
Natural Language ◽  
Possible Worlds ◽  
Possible World ◽  
Modal Claim ◽  
Knowing That ◽  
Modal Semantics ◽  
Bull's Eye ◽  
Modal Systems ◽  
Richard Montague

In reasoning we often use words such as ‘necessarily’, ‘possibly’, ‘can’, ‘could’, ‘must’ and so on. For example, if we know that an argument is valid, then we know that it is necessarily true that if the premises are true, then the conclusion is true. Modal logic starts with such modal words and the inferences involving them. The exploration of these inferences has led to a variety of formal systems, and their interpretation is now most often built on the concept of a possible world. Standard non-modal logic shows us how to understand logical words such as ‘not’, ‘and’ and ‘or’, which are truth-functional. The modal concepts are not truth-functional: knowing that p is true (and what ‘necessarily’ means) does not automatically enable one to determine whether ‘Necessarily p’ is true. (‘It is necessary that all people have been people’ is true, but ‘It is necessary that no English monarch was born in Montana’ is false, even though the simpler constituents – ‘All people have been people’ and ‘No English monarch was born in Montana’– are both true.) The study of modal logic has helped in the understanding of many other contexts for sentences that are not truth-functional, such as ‘ought’ (‘It ought to be the case that p’) and ‘believes’ (‘Alice believes that p’); and also in the consideration of the interaction between quantifiers and non-truth-functional contexts. In fact, much work in modern semantics has benefited from the extension of modal semantics introduced by Richard Montague in beginning the development of a systematic semantics for natural language. The framework of possible worlds developed for modal logic has been fruitful in the analysis of many concepts. For example, by introducing the concept of relative possibility, Kripke showed how to model a variety of modal systems: a proposition is necessarily true at a possible world w if and only if it is true at every world that is possible relative to w. To achieve a better analysis of statements of ability, Mark Brown adapted the framework by modelling actions with sets of possible outcomes. John has the ability to hit the bull’s-eye reliably if there is some action of John’s such that every possible outcome of that action includes John’s hitting the bull’s-eye. Modal logic and its semantics also raise many puzzles. What makes a modal claim true? How do we tell what is possible and what is necessary? Are there any possible things that do not exist (and what could that mean anyway)? Does the use of modal logic involve a commitment to essentialism? How can an individual exist in many different possible worlds?

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