Hyperbolic Dirac Net (HDN) + Data Mining to Map Clinical Pathways (The Tacit Knowledge)

 

Bioingine.com employs algorithmic approach based on Hyperbolic Dirac Net that allows inference nets that are a general graph (GC), including cyclic paths, thus surpassing the limitation in the Bayes Net that is traditionally a Directed Acyclic Graph (DAG) by definition.

The Bioingine.com approach thus more fundamentally reflects the nature of probabilistic knowledge in the real world, which has the potential for taking account of the interaction between all things without limitation, and ironically this more explicitly makes use of Bayes rule far more than does a Bayes Net.

It also allows more elaborate relationships than mere conditional dependencies, as a probabilistic semantics analogous to natural human language but with a more detailed sense of probability. To identify the things and their relationships that are important and provide the required probabilities, the Bioingine.com scouts the large complex data of both structured and also information of unstructured textual character.

It treats initial raw extracted knowledge rather in the manner of potentially erroneous or ambiguous prior knowledge, and validated and curated knowledge as posterior knowledge, and enables the refinement of knowledge extracted from authoritative scientific texts into an intuitive canonical “deep structure” mental-algebraic form that the Bioingine.com can more readily manipulate.

Discussion on employing HDN to map Clinical Pathways (The Tacit Knowledge)

Screenshot 2016-01-05 21.04.17

In the below referenced articles on the employ of Bayesian Net to model Clinical Pathways as probabilistic inference net, replace Bayesian Net to achieve stress tested Hyperbolic Dirac Net (HDN) which is a non-acyclic Bayesian resolving both correlation and causation in both the direction; etymology –> outcomes and outcomes –> etymology

1. Elements of Q-UEL 

Q-UEL is based on the Dirac Notation and associated algebra The notation was introduced into later editions of Dirac’s book to facilitate understanding and use of quantum mechanics (QM) and it has been a standard notation in physics and theoretical chemistry since the 1940s

a) Dirac Notation

In the early days of quantum theory, P. A. M. (Paul Adrian Maurice) Dirac created a powerful and concise formalism for it which is now referred to as Dirac notation or bra-ket (bracket ) notation

<bra vector exprn* | operator exprn* | ket vector exprn*> 

[ exprn* is expression]

It  is an  algebra for observations and measurements, and probabilistic inference from  them

 QM is a system for representing observations and measurements, and drawing probabilistic inference from them.

In Dirac’s notation what is known is put in a ket, “|>” . So, for example, “|p >” expresses the fact that a particle has momentum p. It could also be more explicit: |p = 2> , the particle has momentum equal to 2; | x = 1.23 , the particle has position 1.23 |Ψ > represents a system in the state and is therefore called the state vector. 

The ket |> can also be interpreted as the initial state in some transition or event.

The bra <| represents the final state or the language in which you wish to express the content of the ket

Hyperbolic Dirac Net, has ket |> as row vector, and bra <| as column vector

b) hh = +1 Imaginary Number

QM is a system for representing observations and measurements, and drawing probabilistic inference from them. The Q in Q-UEL refers to QM, but a simple mathematical transformation of QM gives classical everyday behavior. Q-UEL inherits the machinery of QM by replacing the more familiar imaginary number i (such that ii = -1), responsible for QM as wave mechanics, by the hyperbolic imaginary number h (such that hh=+1). Hence our inference net in general is called the Hyperbolic Dirac Net (HDN)

In probability theory A, B, C, etc. represent things, states, events, observations, measurements, qualities etc. In this paper we mean medical factors, including demographic factors such as age and clinical factors such as systolic blood pressure value or history of diabetes.

They can also stand for expressions containing many factors, so note that by e.g.

P(A|B) we would usually mean that it also applies to, say, P(A, B | C, D, E). In text, P(A,B, C,…) with ellipsis ‘…’ means all combinatorial possibilities, P(A), P(B), P(A, C), P(B, D, H) etc.

2) Employing Q-UEL  preliminary inference net as the query can be created.

“Will my female patient age 50-59 taking diabetes medication and having a body mass index of 30-39 have very high cholesterol if the systolic BP is 130-139 mmHg and HDL is 50-59 mg/dL and non-HDL is 120-129 mg/dL?”.

This forms a preliminary inference net as the query, which may be refined and to which probabilities must be assigned

The real answers of interest here are not qualitative statements, but the final probabilities. The protocols involved map to what data miners often seem to see as two main options in mining, although we see them as the two ends of a continuum.

Method (A) may be recognized as Unsupervised (or unrestricted) data mining and post-filtering, and is the method mainly used here. In this approach

we (1) mine data (“observe”),(2) compute a very large number of the more significant probabilities and render them as tags and maintained as Knowledge Representative Store (KRS) or Semantic Lake (“evaluate”), (3) use a propose inference net as a query to search amongst the probabilities represented by those tags, but only looking for those relevant to complete the net and assign probabilities to it, assessing what is available, and seeing what can be substituted (“interpret”), and (4) compute the overall probability of the final inference net in order to make a decision (“decide”). Unsupervised data mining is preferred because it generates many tags for an SW-like approach, and may uncover new unexpected relationships that could be included in the net.

Method (B) uses supervised (or restricted) data mining and prefiltering. Data mining considers only what appears in the net. The down-stream user interested in inference always accesses the raw database, while in (A) he or she may never see it.

The advantage of (B) is that mining is far less computationally demanding both in terms of processing and memory. Useful to computing HDN for a specified Hypothesis.

The Popular Bayes Net BN Compared with our Hyperbolic Dirac Net HDN.

Each probabilities of any kind can also be manipulated for inference in a variety of ways, according to philosophy (which is a matter of concern ). The BN is probably the most popular method, perhaps because it does seem to be based on traditional, conservative, principles of probability. However, the BN is traditionally (and, strictly speaking, by definition) confined to a probability network that is a directed acyclic graph (DAG).

In general, reversibility, cyclic paths and feedback abound in the real world, and we need probabilistic knowledge networks that are general graphs, or even more diffuse fields of influence, not DAGs. In our response as the Hyperbolic Dirac Net (HDN), “Dirac” relates to use of Paul A. M. Dirac’s view of quantum mechanics (QM).

QM is not only a standard system for representing probabilistic observation and inference from it in physics, but also it manages and even promotes concepts like reversibility and cycles. The significance of “hyperbolic” is that it relates to a particular type of imaginary number rediscovered by Dirac. Dirac notation entities, Q-UEL tags, and the analogous building blocks of an HDN all have complex probabilities better described as probability amplitudes. This means that they have the form x + jy where x and y are real numbers and j is an imaginary number, though they can also be vectors or matrices with such forms as elements.

Q-UEL is seen as a Lorentz rotation i → h of QM as wave mechanics. The imaginary number involved is now no longer the familiar i such that ii = -1, but the hyperbolic imaginary number, called h in Q-UEL, such that hh = +1.

This renders the HDN to behave classically. A basic HDN is an h-complex BN.

Both BN and basic HDN may use Predictive Odds in which conditional probabilities (or the HDN’s comparable h-complex notions) are replaced by ratios of these.

Discussions on Employing Bayesian Net to Model Clinical Pathways (Replace BN by HDN to achieve Hyperbolic BN)

Development of a Clinical Pathways Analysis System with Adaptive Bayesian Nets and Data Mining Techniques 

D. KOPEC*, G. SHAGAS*, D. REINHARTH**, S. TAMANG

 

Pathway analysis of high-throughput biological data within a Bayesian network framework

Senol IsciCengizhan OzturkJon Jones and Hasan H. Otu

Are Standardized Clinical Pathways Stymying Drug Innovation?

HDN :- Need for Agile Clinical Pathways that do not impede Drug Innovation

Oncologists Say Clinical Pathways Are Too Confining

Creating fixed plans for treating common malignancies promises to make the work of nurses and other staff more predictable and practiced, increasing efficiency and reducing errors that could lead to poor outcomes and hospitalization. For payers, pathways also gave them another way to insert awareness of costs directly into the examining room.

“The way the pathways are constructed does promote consideration of value-driven practice, which is to say that the pathways vendors all take into account cost of care, but only after considering efficacy and toxicity,” said Michael Kolodziej, MD, national medical director of oncology solutions at Aetna, and a former medical director at US Oncology. “So there is an element here of reduction of cost of care, by trying to encourage physicians to consider the relative value of various treatment options. This has now become the mantra in oncology.”

Studies found that using pathways can indeed cut costs substantially without hurting outcomes.

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