Bayesian generalized probability calculus for density matrices

Warmuth, Manfred K.; Kuzmin, Dima

doi:10.1007/s10994-009-5133-7

Cited by 32 publications

(20 citation statements)

References 18 publications

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“…This is probably the most obvious but not the only approach to model a quantum system. Other possible frameworks exist (for instance, [17] and [23]). …”

Section: Discussionmentioning

confidence: 99%

A Probabilistic Graphical Model of Quantum Systems

Yeang

2010

2010 Ninth International Conference on Machine Learning and Applications

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Abstract-Quantum systems are promising candidates of future computing and information processing devices. In a large system, information about the quantum states and processes may be incomplete and scattered. To integrate the distributed information we propose a quantum version of probabilistic graphical models. Variables in the model (quantum states and measurement outcomes) are linked by several types of operators (unitary, measurement, and merge/split operators). We propose algorithms for three machine learning tasks in quantum probabilistic graphical models: a belief propagation algorithm for inference of unknown states, an iterative algorithm for simultaneous estimation of parameter values and hidden states, and an active learning algorithm to select measurement operators based on observed evidence. We validate these algorithms on simulated data and point out future extensions toward a more comprehensive theory of quantum probabilistic graphical models.

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“…This is probably the most obvious but not the only approach to model a quantum system. Other possible frameworks exist (for instance, [17] and [23]). …”

Section: Discussionmentioning

confidence: 99%

A Probabilistic Graphical Model of Quantum Systems

Yeang

2010

2010 Ninth International Conference on Machine Learning and Applications

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“…However, we know that it represents some constant. We can easily see that the adopted probability measure fulfils the two conditions that are required for probability function fix) (in our case p(x)) to be considered as a modified generalized probability measure [26]:…”

Section: Fig 2 a 3-d Examplementioning

confidence: 95%

Probabilistic principal component analysis based on JoyStick Probability Selector

Janković

Sugiyama

2009

2009 International Joint Conference on Neural Networks

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Principal component analysis (PCA) is a commonly applied technique for data analysis and processing, e.g, compression or clustering. In this paper we propose a probabilistic PCA model based on the Born rule. In off-line realization it can be seen as a successive optimization problem. In the on-line realization it will be solved by introduction of two different time scales. It will be shown that recently proposed time oriented hierarchical method, used for realization of biologically plausible peA neural networks, represents a special case of the proposed model. The proposed model gives a general framework for creating different PCA realizations/algorithms. A particular realization can optimize locality of calculation, convergence speed, preciseness or some other parameter of interest. We will present some experimental results to illustrate effectiveness of the proposed model.

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“…Suma u imeniocu predstavlja ukupnu snagu odbiraka koji se analiziraju -ta vrednost nije poznata sve do uzimanja poslednjeg odbirka. Jednostavno se može ustanoviti da usvojena mera verovatnoće zadovoljava dva uslova koja se zahtevaju od funkcije verovatnoće f(z) (u našem slučaju p(z)) [8]:…”

Section: Kvantni Probabilistički Model I Bornovo Pravilounclassified

Analysis of possibilities of early diagnostics criteria for Parkinson's disease based on analysis of the input-output curve

Janković¹,

Kačar²

2013

Zb EI Nikola Tesla

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Parkinsonove bolesti. Prvi metod je baziran na analizi pojačanja, a drugi na izračunavanju Calisove entropije UI krive koji je baziran na osnovnim konceptima iz kvantne mehanike.Ključne reči: Parkinsonova bolest, kriva regrutacije, Calisova entropija, transkranijalna magnetna stimulacija UvodParkinsonova bolest (PB) je progresivno i neurodegenerativno oboljenje koje nastaje usled propadanja dopaminergičkih neurona u kompaktnom delu substancije nigre (SN) i njihovih nigrostrijatnih veza kao dela bazalnih ganglija. Klinički se karakteriše: bradikinezijom, rigorom, tremorom u miru i posturalnom nestabilnošću. Bazalne ganglije (BG) su centri engrama za izvođenje motornih programa. Njihove integrativne aktivnosti se ostvaruju preko motornih kortikalnih područja, dok se egzekutivna funkcija BG realizuje putem kortikospinalnog (KS) puta. Kao model motorne disfunkcije PB je dugo vremena aktuelan problem ispitivanja stepena kortikalne ekscitabilnosti. Nivo kortikalne ekscitabilnosti se može objektivizirati primenom različitih neuromodulatornih procedura, od kojih je posebno značajna primena 199

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Bayesian generalized probability calculus for density matrices

Cited by 32 publications

References 18 publications

A Probabilistic Graphical Model of Quantum Systems

A Probabilistic Graphical Model of Quantum Systems

Probabilistic principal component analysis based on JoyStick Probability Selector

Analysis of possibilities of early diagnostics criteria for Parkinson's disease based on analysis of the input-output curve

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