Deep Learning in Hamiltonian Space on iPad

Screen Shot 2016-12-09 at 12.11.22 AM.png

Large Data Analytics – on your iPad 

[Big Data In Your Mini Space] 

Combinatorial Explosion !!! 

Hermitian Conjugates and Billion Tags

Hamiltonian Space Offering Deep Learning 

The™ Platform

The™offers a comprehensive bio-statistical reasoning experience in the application of the data science that blends descriptive and inferential statistical studies. Progressing further it will also blend NLP and AI to create a holistic Cognitive Experience.

The™; is a High Performance Cloud Computing Platformdelivering HealthCare Large-Data Analytics capability derived from an ensemble of bio-statistical computations. The automated bio-statistical reasoning is a combination of “deterministic” and “probabilistic” methods employed against both structured and unstructured large data sets leading into Cognitive Reasoning.

The figure below depicts the healthcare analytics challenge as the order complexity is scaled.

Given the challenge of analyzing against the large data sets both structured (EHR data) and unstructured data; the emerging Healthcare analytics are around below discussed methods E (multivariate regression) and F (multivariate probabilistic inference); Ingine is unique in the Hyperbolic Dirac Net proposition for probabilistic inference.

The basic premise in engineering The™ is in acknowledging the fact that in solving knowledge extraction from the large data sets (both structured and unstructured), one is confronted by very large data sets riddled with high-dimensionality and uncertainty.

Generally in solving insights from the large data sets the order in complexity is scaled as follows.

A)   Descriptive Statistics :- Insights around :- “what”

For large data sets, descriptive statistics are adequate to extract a “what” perspective. Descriptive statistics generally delivers statistical summary of the ecosystem and the probabilistic distribution.

Descriptive statistics : Raw data often takes the form of a massive list, array, or database of labels and numbers. To make sense of the data, we can calculate summary statistics like the mean, median, and interquartile range. We can also visualize the data using graphical devices like histograms, scatterplots, and the empirical cdf. These methods are useful for both communicating and exploring the data to gain insight into its structure, such as whether it might follow a familiar probability distribution. 

i)   Univariate Problem :- “what”

Considering some simplicity in the variables relationships or is cumulative effects between the independent variables (causing) and the dependent variables (outcomes):-

Univariate regression (simple independent variables to dependent variables analysis)

ii)    Bivariate Problem :- “what”

Correlation Cluster – shows impact of set of variables or segment analysis.

From above link :- In machine learningcorrelation clustering or cluster editing operates in a scenario where the relationships between the objects are known instead of the actual representations of the objects. For example, given a weighted graph G = (V,E), where the edge weight indicates whether two nodes are similar (positive edge weight) or different (negative edge weight), the task is to find a clustering that either maximizes agreements (sum of positive edge weights within a cluster plus the absolute value of the sum of negative edge weights between clusters) or minimizes disagreements (absolute value of the sum of negative edge weights within a cluster plus the sum of positive edge weights across clusters). Unlike other clustering algorithms this does not require choosing the number of clusters k in advance because the objective, to minimize the sum of weights of the cut edges, is independent of the number of clusters.

From above link. :- Correlation is a bivariate analysis that measures the strengths of association between two variables. In statistics, the value of the correlation coefficient varies between +1 and -1. When the value of the correlation coefficient lies around ± 1, then it is said to be a perfect degree of association between the two variables. As the correlation coefficient value goes towards 0, the relationship between the two variables will be weaker. Usually, in statistics, we measure three types of correlations: Pearson correlation, Kendall rank correlation and Spearman correlation

iii)   Multivariate Analysis (Complexity increases) :- “what”

§ Multiple regression (considering multiple univariate to analyze the effect of the independent variables on the outcomes)

Multivariate regression – where multiple causes and multiple outcomes exists

iv)   Neural Net :- “what”

The above discussed challenges of analyzing multivariate pushes us into techniques such as Neural Net; which is the next level to Multivariate Regression Statistical Approach…. where multiple regression models are feeding into the next level of clusters, again an array of multiple regression models.The above Neural Net method still remains inadequate in depicting “how” probably the human mind is operates. In discerning the health ecosystem for diagnostic purposes, for which “how”, “why” and “when” interrogatives becomes imperative to arrive at accurate diagnosis and target outcomes effectively. Its learning is “smudged out”. A little more precisely put: it is hard to interrogate a Neural Net because it is far from easy to see what are the weights mixed up in different pooled contributions, or where they come from.

“We Enter Probabilistic Computations which is as such Combinatorial Explosion Problem”.

B)    Inferential Statistics : – Deeper Insights “how”, “why”, “when” in addition to “what”.

Hyperbolic Dirac Net (Inverse or Dual Bayesian technique)

All the above are still discussing the “what” aspect. When the complexity increases the notion of independent and dependent variables become non-deterministic, since it is difficult to establish given the interactions, potentially including cyclic paths of influence in a network of interactions, amongst the variables. A very simple example in just a simple case is that obesity causes diabetes, but the also converse is true, and we may also suspect that obesity causes type 2 diabetes cause obesity. In such situation what is best as “subject” and what is best as “object” becomes difficult to establish. Existing inference network methods typically assume that the world can be represented by a Directional Acyclic Graph, more like a tree, but the real world is more complex than that that: metabolism, neural pathways, road maps, subway maps, concept maps, are not unidirectional, and they are more interactive, with cyclic routes. Furthermore, discovering the “how” aspect becomes important in the diagnosis of the episodes and to establish correct pathways, while also extracting the severe cases (chronic cases which is a multivariate problem). Indeterminism also creates an ontology that can be probabilistic, not crisp.

Note: From Healthcare Analytics perspective most Accountable Care Organization (ACO) analytics addresses the above based on the PQRS clinical factors, which are all quantitative. Barely useful for advancing the ACO into solving performance driven or value driven outcomes most of which are qualitative.

Notes On Statistics :-

Generally one enters Inferential Statistics an inductive reasoning when there is no clear distinction between independent and dependent variables, furthermore this problem is accentuated by multivariate condition. As such the problem becomes irreducible. Please refer to below MIT course work to gain better understanding on statistics, different statistical methods, descriptive and inferential. Particularly pay attention to Bayesian Statistics. HDN Inferential Statistics being introduced in The is an advancement to Bayesian Statistics

Introduction to Statistics Class 10, 18.05, 

Spring 2014 Jeremy Orloff and Jonathan Bloom 

Click to access MIT18_05S14_Reading10a.pdf

From above link

a)   What is a Statistics?

We give a simple definition whose meaning is best elucidated by examples. Definition. A statistic is anything that can be computed from the collected data.

The mathematical study of the likelihood and probability of events occurring based on known information and inferred by taking a limited number of samples. Statistics plays an extremely important role in many aspects of economics and science, allowing educated guesses to be made with a minimum of expensive or difficult-to-obtain data. A joke told about statistics (or, more precisely, about statisticians), runs as follows. Two statisticians are out hunting when one of them sees a duck. The first takes aim and shoots, but the bullet goes sailing past six inches too high. The second statistician also takes aim and shoots, but this time the bullet goes sailing past six inches too low. The two statisticians then give one another high fives and exclaim, “Got him!” (This joke plays on the fact that the mean of -6 and 6 is 0, so “on average, ” the two shots hit the duck.) Approximately 73.8474% of extant statistical jokes are maintained by Ramseyer.

b)   Descriptive statistics

Raw data often takes the form of a massive list, array, or database of labels and numbers. To make sense of the data, we can calculate summary statistics like the mean, median, and interquartile range. We can also visualize the data using graphical devices like histograms, scatterplots, and the empirical cdf. These methods are useful for both communicating and exploring the data to gain insight into its structure, such as whether it might follow a familiar probability distribution.

c)    Inferential statistics

Are concerned with making inferences based on relations found in the sample, to relations in the population. Inferential statistics help us decide, for example, whether the differences between groups that we see in our data are strong enough to provide support for our hypothesis that group differences exist in general, in the entire population.

d)    Types of Inferential Statistics

i)     Frequentist – 19th Century

Hypothesis Stable – Evaluating Data

Frequentist inference is a type of statistical inference that draws conclusions from sample data by emphasizing the frequency or proportion of the data. An alternative name is frequentist statistics. This is the inference framework in which the well-established methodologies of statistical hypothesis testing and confidence intervals are based.

ii)   Bayesian Inference – 20th Century

Data Held Stable – Evaluating Hypothesis 2014/readings/MIT18_05S14_Reading10a.pdf

In scientific experiments we start with a hypothesis and collect data to test the hypothesis. We will often let H represent the event ‘our hypothesis is true’ and let D be the collected data. In these words Bayes theorem says

The left-hand term is the probability our hypothesis is true given the data we collected. This is precisely what we’d like to know. When all the probabilities on the right are known exactly, we can compute the probability on the left exactly. This will be our focus next week. Unfortunately, in practice we rarely know the exact values of all the terms on the right. Statisticians have developed a number of ways to cope with this lack of knowledge and still make useful inferences. We will be exploring these methods for the rest of the course.

A. Conditional Probability

P (A|B) is the probability of event A occurring, given that event B occurs.

In probability theoryconditional probability is a measure of the probability of an event given that (by assumption, presumption, assertion or evidence) another event has occurred.[1] If the event of interest is A and the event B is known or assumed to have occurred, “the conditional probability of A given B“, or “the probability of A under the condition B“, is usually written as P(A|B), or sometimes PB(A). For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person has a cold, then they are much more likely to be coughing. The conditional probability of coughing given that you have a cold might be a much higher 75%.

The concept of conditional probability is one of the most fundamental and one of the most important concepts in probability theory.[2] But conditional probabilities can be quite slippery and require careful interpretation.[3] For example, there need not be a causal or temporal relationship between A and B.

B. Joint Probability

P (A,B) The probability of two or more events occurring together.

In the study of probability, given at least two random variables XY, …, that are defined on a probability space, the joint probability distribution for XY, … is a probability distribution that gives the probability that each of XY, … falls in any particular range or discrete set of values specified for that variable. In the case of only two random variables, this is called a bivariate distribution, but the concept generalizes to any number of random variables, giving a multivariate distribution.

Bayesian Rules 

P(A | B) = P(A,B) / P(B)

P(B | A) = P(B,A) / P(A)

P(B | A) = P(A,B) / P(A)

P(A | B) P(B) = P(A,B)

P(B | A) P(A) = P(A,B)

P(A | B) P(B) = P(A,B) = P(B | A) P(A)

P(A | B) = P(B | A) P(A) / P(B)

iii)  C. Hyperbolic Dirac Net (HDN) – 21st Century

Non – Hypothesis driven unsupervised machine learning. Independent of both data and hypothesis.


Data-mining to build a knowledge representation store for clinical decision support. Studies on curation and validation based on machine performance in multiple choice medical licensing examinations

Barry Robson Srinidhi Boray

The differences between a BN and an HDN are as follows. A BN is essentially an estimate of a complicated joint or conditional probability, complicated because it considers many factors, states, events, measurements etc., that by analogy with XML tags and hence Q-UEL tags, we call attributes in the HDN context. In a BN, the complicated probability is seen as a probabilistic-algebraic expansion into many simpler conditional probabilities of general form P(x | y) = P(x, y)/P(y), simpler because each have fewer attributes. For example, one such may be of more specific form P(G | B, D, F, H), where B, D, F, G, H are attributes and the vertical bar ‘|’ is effectively a logical operator that has the sense of “conditional upon” or “if”, “derived from the sample of”, “is a set with members” or sometimes “is caused by”. Along with simple, self or prior probabilities such as P(D) all these probabilities multiply together, which implies use of logical AND between the statements they represent, to give the estimate. It is an estimate because the use of probabilities with fewer attributes assumes that attributes separated by being in different probabilities are statistically independent of each other. As previously described [2], one key difference in an HDN is that the individual probabilities are bidirectional, using a dual probability (P(x|y), P(y|x)), say (P(B, G | D, F, H), P(D, F, H|B, G)) which is a complex value, i.e., with an imaginary part [1, 2]. Another, the subject of the present report, is that for these probabilities to serve as semantic triples such as subject-verb-object as the Semantic Web requires, the vertical bar must be replaced by many other kinds of relationship. Yet another, which will be described in great deal elsewhere, is that there can be other kinds of operator between probabilities as statements than just logical AND. All these aspects, and the notation used including for the format of Q-UEL, have direct analogies in the Dirac notation and algebra [8] developed in the 1920s and 1930s for quantum mechanics (QM). It is a widely accepted standard, the capabilities of which are described in Refs. [9-12] that are also excellent introductions. The primary difference between QM and Q-UEL and HDN methodologies is that the complex value in the latter cases is purely h-complex where is the hyperbolic imaginary number such that hh = +1. The significance of this is that it avoids a description of the world in terms of waves and so behaves in an essentially classical way.

Inductive (Inferential Statistics) Reasoning: – Hyperbolic Dirac Net Reference :- Notes on Synthesis of Forms by Christopher Alexander on Inductive Logic

The search for causal relations of this sort cannot be mechanically experimental or statistical; it requires interpretation: to practice it we must adopt the same kind of common sense that we have to make use of all the time in the inductive part of science. The data of scientific method never go further than to display regularities. We put structure into them only by inference and interpretation. In just the same way, the structural facts about a system of variables in an ensemble will come only from the thoughtful interpretation of observations.

We shall say that two variables interact if and only if the designer can find some reason (or conceptual model), which makes sense to him and tells him why they should do so.

But, in speaking of logic, we do not need to be concerned with processes of inference at all. While it is true that a great deal of what is generally understood to be logic is concerned with deduction, logic, in the widest sense, refers to something far more general. It is concerned with the form of abstract structures, and is involved the moment we make pictures of reality and then seek to manipulate these pictures so that we may look further into the reality itself. It is the business of logic to invent purely artificial structures of elements and relations.

Christopher Alexander: – Sometimes one of these structures is close enough to a real situation to be allowed to represent it. And then, because the logic is so tightly drawn, we gain insight into the reality, which was previously withheld from us.

Study Descriptive Statistics (Univariate – Bibariate – Multivariate)

Transformed Data Set

Univariate – Statistical Summary

Univariate – Probability Summary

Bivariate – Correlation Cluster

Correlation Cluster Varying the Pearson’s Coefficient

Scatter (Cluster) Plot – Linear Regression

Scatter (Cluster) Plot and Pearson Correlation Coefficient

What values can the Pearson correlation coefficient take?

The Pearson correlation coefficient, r, a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation)

Multivariate Regression

HDN Multivariate Probabilistic Inference – Computing in Hamiltonian System

Hyperbolic Dirac Net (HDN) – This computation is against Billion Tags in the Semantic Lake

What is the relative risk of needing to take BP medication if you are diabetic as opposed to not diabetic?

Note: – To conduct HDN Inference, bear in mind that getting all the combinations of factors by data mining is “ combinatorial explosion ” problem, which lies behind the difficulty of Big Data as high dimensional data.

It applies in any kind of data mining, though it is most clearly apparent when mining structured data, a kind of spreadsheet with many columns, each of which are our different dimensions. In considering combinations of demographic and clinical factors, say A, B, C, D, E.., we ideally have to count the number of combinations (A), (A,B) (A, C) …(B, C, E)…and so on. Though sometimes assumptions can be made, you cannot always deduce a combination with many factors from those with fewer, nor vice versa. In the case of the number N of factors A,B,C,D,E,… etc. the answer is that there are 2N-1 possible combinations. So data with 100 columns as factors would imply about 


combinations, each of which we want to observe several times and so count them, to obtain probabilities. To find what we need without knowing what exactly it is in advance, distinguishes unsupervised data mining from statistics in which traditionally we test a hunch, a hypothesis. But worse still, in our spreadsheet the A, B, C, D, E are really to be seen as column headings with say about n possible different values in the columns below them, and so roughly we are speaking of potentially needing to count not just, say, males and females but each of nN different kinds of patient or thing. This results in truly astronomic number of different things, each to observe many time. If merely n=10, then nN is


There is a further implied difficulty, which in a strange way lifts much the above challenge from the shoulders of researchers and of their computers. In most cases of the above, must of the things we are counting contain many of the factors A,B,C,D, E..etc. Such concurrences of so many things is typically rare, so many of the things we would like to count will never be seen at all, and most of the rest will just be seen 1, 2, or 3 times. Indeed, any reasonably rich patient record with lots of data will probably be unique on this planet. However, most approaches are unable to make proper use of that sparse data, since it seems that it would need to be weighted and taken into account in the balance of evidence according to the information it contains, and it is not evident how. The zeta approach tells us how to do that. In short, the real curse of high dimensionality is in practice not that our computers lack sufficient memory to hold all the different probabilities, but that this is also true for the universe: even in principle we do not have all the data to work to determine probabilities by counting with even if we could count and use them. Note that probabilities of things that are never observed are, in the usual interpretation of zeta theory and of Q-UEL, assumed to have probability 1. In a purely multiplicative inference net, multiplying by probability 1 will have no effect. Information I = –log(P) for P = 1 means that information I = 0. Most statements of knowledge are, as philosopher Karl Popper argued, assertions awaiting refutation.

Nonetheless the general approach in the fields of semantics, knowledge representation, and reasoning from it is to gather all the knowledge that can be got into a kind of vast and ever growing encyclopedia. 

In The™ the native data sets have been transformed into Semantic Lake or Knowledge Representation Store (KRS) based on Q-UEL Notational Language such that they are now amenable to HDN based Inferences. Where possible, probabilities are assigned, if not, the default probabilities are again 1. 

Q-UEL Toolkit for Medical Decision Making :- Science of Uncertainty and Probabilities

Screen Shot 2016-08-24 at 11.07.49 AM

Quantum Universal Exchange Language

Emergent | Interoperability | Knowledge Mining | Blockchain


  1. It is a toolkit / framework
  2. Is an Algorithmic Language for constructing Complex System
  3. Results into a Inferential Statistical mechanism suitable for a highly complex system – “Hyperbolic Dirac Net”
  4. Involves an approach that is based on the premise that a Highly Complex System driven by the human social structures continuously strives to achieve a higher order in the entropic journey by continuos discerning the knowledge hidden in the system that is in continuum.
  5. A System in Continuum seeking Higher and Higher Order is a Generative System.
  6. A Generative System; Brings System itself as a Method to achieve Transformation. Similar is the case for National Learning Health System.
  7. A Generative System; as such is based on Distributed Autonomous Agents / Organization; achieving Syndication driven by Self Regulation or Swarming behavior.
  8. Essentially Q-UEL as a toolkit / framework algorithmically addresses interoperability, knowledge mining and blockchain; while driving the Healthcare Eco-system into Generative Transformation achieving higher nd higher orders in the National Learning Health System.
  9. It has capabilities to facilitate medical workflow, continuity of care, medical knowledge extraction and representation from vast large sets of structured and unstructured data, automating bio-statistical reasoning leading into large data driven evidence based medicine, that further leads into clinical decision support system including knowledge management and Artificial Intelligence; and public health and epidemiological analysis.


A Large Chaotic System driven by Human Social Structures has two contending ways.

a. Natural Selection – Adaptive – Darwinian – Natural Selection – Survival Of Fittest – Dominance

b. Self Regulation – Generative – Innovation – Diversity – Cambrian Explosion – Unique Peculiarities – Co Existence – Emergent

Accountable Care Organization (ACO) driven by Affordability Care Act transforms the present Healthcare System that is adaptive (competitive) into generative (collaborative / co-ordinated) to achieve inclusive success and partake in the savings achieved. This is a generative systemic response contrasting the functional and competitive response of an adaptive system.

Natural selection seems to have resulted in functional transformation, where adaptive is the mode; does not account for diversity.

Self Regulation – seems like is a systemic outcome due to integrative influence (ecosystem), responding to the system constraints. Accounts for rich diversity.

The observer learns generatively from the system constraints for the type of reflexive response required (Refer – Generative Grammar – Immune System –

From the above observation, should the theory in self regulation seem more correct and that adheres to laws of nature, in which generative learning occurs. Then, the assertion is “method” is offered by the system itself. System’s ontology has an implicate knowledge of the processes required for transformation (David Bohm – Implicate Order)

For very large complex system,

System itself is the method – impetus is the “constraint”.

In the video below, the ability for the cells to creatively create the script is discussed which makes the case for self regulated and generative complex system in addition to complex adaptive system.


Further Notes on Q-UEL / HDN :-

  1. That brings Quantum Mechanics (QM) machinery to Medical Science.
  2. Is derived from Dirac Notation that helped in defining the framework for describing the QM. The resulting framework or language is Q-UEL and it delivers a mechanism for inferential statistics – “Hyperbolic Dirac Net”
  3. Created from System Dynamics and Systems Thinking Perspective.
  4. It is Systemic in approach; where System is itself the Method.
  5. Engages probabilistic ontology and semantics.
  6. Creates a mathematical framework to advance Inferential Statistics to study highly chaotic complex system.
  7. Is an algorithmic approach that creates Semantic Architecture of the problem or phenomena under study.
  8. The algorithmic approach is a blend of linguistics semantics, artificial intelligence and systems theory.
  9. The algorithm creates the Semantic Architecture defined by Probabilistic Ontology :- representing the Ecosystem Knowledge distribution based on Graph Theory

To make a decision in any domain, first of all the knowledge compendium of the domain or the system knowledge is imperative.

System Riddled with Complexity is generally a Multivariate System, as such creating much uncertainty

A highly complex system being non-deterministic, requires probabilistic approaches to discern, study and model the system.

General Characteristics of Complex System Methods

  • Descriptive statistics are employed to study “WHAT” aspects of the System
  • Inferential Statistics are applied to study “HOW”, “WHEN”, “WHY” and “WHERE” probing both spatial and temporal aspects.
  • In a highly complex system; the causality becomes indeterminable; meaning the correlation or relationships between the independent and dependent variables are not obviously established. Also, they seem to interchange the position. This creates dilemma between :- subject vs object, causes vs outcomes.
  • Approaching a highly complex system, since the priori and posterior are not definable; inferential techniques where hypothesis are fixed before the beginning the study of the system become enviable technique.

Review of Inferential Techniques as the Complexity is Scaled

Step 1:- Simple System (turbulence level:-1)

Frequentist :- simplest classical or traditional statistics; employed treating data random with a steady state hypothesis – system is considered not uncertain (simple system). In Frequentist notions of statistics, probability is dealt as classical measures based only on the idea of counting and proportion. This technique is applied to probability to data, where the data sets are rather small.

Increase complexity: Larger data sets, multivariate, hypothesis model is not established, large variety of variables; each can combine (conditional and joint) in many different ways to produce the effect.

Step 2:- Complex System (turbulence level:-2)

Bayesian :- hypothesis is considered probabilistic, while data is held at steady state. In Bayesian notions of statistics, probability is of the hypothesis for a given sets of data that is fixed. That is, hypothesis is random and data is fixed. The knowledge extracted contains the more subjectivist notions of uncertainty, belief, reliability, or confidence often used in automated inference and decision support systems.

Additionally the hypothesis can be explored only in an acyclic fashion creating Directed Acyclic Graphs (DAG)

Increase the throttle on the complexity: Very large data sets, both structured and unstructured,  Hypothesis random, multiple Hypothesis possible, Anomalies can exist, There are hidden conditions, need arises to discover the “probabilistic ontology” as they represent the system and the behavior within.

Step 3: Highly Chaotic Complex System (turbulence level:-3)

Certainly DAG is now inadequate, since we need to check probabilities as correlations and also causations of the variables, and if they conform to a hypothesis producing pattern, meaning some ontology is discovered which describes the peculiar intrinsic behavior among a specific combinations of the variables to represent a hypothesis condition. And, there are many such possibilities within the system, hence  very chaotic and complex system.

Now the System itself seems probabilistic; regardless of the hypothesis and the data. This demands Multi-Lateral Cognitive approach

Telandic …. “Point – equilibrium – steady state – periodic (oscillatory) – quasiperiodic – Chaotic – and telandic (goal seeking behavior) are examples of behavior here placed in order of increasing complexity”

A Highly Complex System, demands a Dragon Slayer – Hyperbolic Dirac Net (HDN) driven Statistics (BI-directional Bayesian) for extracting the Knowledge from a Chaotic Uncertain System. :- High Performance Cloud Computing Platform

Screenshot 2016-08-03 17.51.37

Non-Hypothesis driven Unsupervised Machine Learning Platform delivering Medical Automated Reasoning Programming Language Environment (MARPLE)

Evidence Based Medicine Decision Process is based on PICO

From above link “Using medical evidence to effectively guide medical practice is an important skill for all physicians to learn. The purpose of this article is to understand how to ask and evaluate questions of diagnosis, and then apply this knowledge to the new diagnostic test of CT colonography to demonstrate its applicability. Sackett and colleagues1 have developed a step-wise approach to answering questions of diagnosis:”

Uncertainties in the Healthcare Ecosystem Platform

Is High Performance Cloud Computing Platform delivering both probabilistic and deterministic computations; while combining HDN Inferential Statistics and Descriptive Statics.

The bio-statistical reasoning algorithm have been implemented in the Wolfram Language; which is a knowledge based programming unified symbolic language. As such symbolic language has a good synergy in implementing Dirac Notational Algebra.

The; brings the Quantum Mechanics machinery to Healthcare analytics; delivering a comprehensive data science experience that covers both Patient Health and Public Health analytics driven by a range of bio-statistical methods from descriptive to inferential statistics, leading into evidence driven medical reasoning.

The transforms the large clinical data sets generated by interoperability architectures, such as in Health Information Exchange (HIE) into semantic lake representing the Health ecosystem that is more amenable to bio-statistical reasoning and knowledge representation. This capability delivers evidence based knowledge needed for Clinical Decision Support System better achieving Clinical Efficacy by helping to reduce medical errors.

Algorithm based on Hyperbolic Dirac Net (HDN)

An HDN is a dualization procedure performed on a given inference net that consists of a pair of split-complex number factorizations of the joint probability and its dual (adjoint, reverse direction of conditionality). Hyperbolic Dirac Net is derived from Dirac Notational Algebra that forms the mechanism to define Quantum Mechanics.

A Hyperbolic Dirac Net (HDN) is a truly Bayesian model and a probabilistic general graph model that includes cause and effect as players of equal importance. It is taken from the mathematics of Nobel Laureate Paul A. M. Dirac that has become standard notation and algebra in physics for some 70 years.  It includes but goes beyond the Bayes Net that is seen as a special and (arguably) usually misleading case. In attune with nature, the HDN does not constrain interactions and may contain cyclic paths in the graphs representing the probabilistic relationships between all things (states, events, observations, measurements etc.).  In the larger picture, HDNs define a probabilistic semantics and so are not confined to conditional relationships, and they can evolve under logical, grammatical, definitional and other relationships. It is also, in its larger context, a model of the nature of natural language and human reasoning based on it that takes account of uncertainty.

Explanation: An HDN is an inference net, but it is also best explained by showing that it stands in sharp contrast to the current notion of an inference net that, for historical reasons, is today often taken as meaning the same thing as a  Bayes Net. “A Bayesian network, Bayes network, belief network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.”  [ wiki/Bayesian_ network].  In practice, such nets have little to do with Bayes, nor Bayes’ rule, law, theorem or equation that  allows verification that probabilities used are consistent with each other and all other probabilities that can be derived from data. Most importantly, in reality, all things interact in the manner of a general graph, and a DAG is in general a poor model of reality since it consequently may miss key interactions.


Is a machine learning based biostatistical algorithm that transforms Large Data Sets such as Millions of Patient Records  into Semantic Lake as defined by HDN driven computations that is a mix of Numbers theory (Riemann Zeta) and Information Theory (Dual Bayesian or HDN)

The HDN – Semantic Lake, represents the health-ecosystem as captured in Knowledge Representation Store (KRS) consisting of Billions of Tags (Q-UEL Tags).


Send an HDN query to KRS to seek HDN probabilistic inference / estimate. The Query for the inference contains the HDN that the user would like to have, and DiracBuilder helps get the best similar dual net by looking at what Billions of QUEL tags and joint probabilities are available.

High Performance Cloud Computing

The Platform computes (probabilistic computations) against the billions of Q-UEL tags employing extended in-memory processing technique. The creation of the billions of Q-UEL tags and querying against them is combinatorial explosionproblem.

The Bioingine platform working against large clinical data sets or while residing within the large Patient Health Information Exchange (HIE) works in creating opportunity for Clinical Efficacy and also facilitates in the better achievement of “Efficiencies in the Healthcare Management” that ACO seeks.

Our endeavors have resulted in the development of revolutionary Data Science to deliver Health Knowledge by Probabilistic Inference. The solution developed addresses critical areas both scientific and technical, notably the healthcare interoperability challenges of delivering semantically relevant knowledge both at patient health (clinical) and public health level (Accountable Care Organization).

Multivariate Cognitive Inference from Uncertainty

Solving High-dimentional Multivariate Inference involving variables factors excess of factor 4 representing the high-dimentioanlity that characteristics of the healthcare domain.

EBM Diagnostic Risk Factors and Calculating Predictive Odds

Q-UEL tags of form

< A Pfwd:=x |  assoc:=y | B Pbwd:=z >

Say A = disease, B = cause,  drug,  or diagnostic prediction of disease, are designed to imply the following, knowing numbers x, y, and z.

P(A|B) = x

K(A; B) = P(A,B) / (P(A)P(B))   = y

P(BIA) = z

From which we can calculate the following….

P(A) = P(A|B)/K(A;B)

P(B) = P(B|A)/K(A;B)

P( NOT A) = 1 – P(A)

P(NOT B) = 1 – P(B)

P(A, B) = P(A|B)P(B) = P(B|A) P(A)

P(NOT A,  B)= P(B) – P(A B)

P(A, NOT B) = P(A) – P(A B)

P(NOT A, NOT B) = 1 – P(A, B) – P(NOT A, B) – P(A NOT B)

P(NOT A | B)  = 1  – P(A|B)

P(NOT B | A) = 1 –  P(B|A)

P(A | NOT B) =  P(A, NOT B)/P(NOT B)

P(B | NOT A) =  P(NOT A, B)/P(NOT A)

Positive Predictive Value P+ = P(A | B)

Negative Predictive value  P- = P(NOTA | NOT B)

Sensitivity = P(B | A)

Specificity = P(NOT B | NOT A)

Accuracy A =   P(A | B) + P(NOT A | NOT B)

Predictive odds PO = P(A | B) / P(NOT A | B)

Relative Risk RR = Positive likelihood ratio  LR+ =  P(A | B) / P(A | NOT B)

Negative  likelihood ratio  LR- =  P(NOT A | B) /  NOT A | NOT B)

Odds ratio OR = P(A, B)P(NOT A, NOT B)  /  (  P(NOT A,  B)P(A, NOT B) )

Absolute risk reduction ARR =  P(NOT A | B) – P(A | B) (where A is disease and B is drug etc).

Number  Needed to Treat NNT = +1 / ARR if ARR > 0 (giving positive result)

Number  Needed to Harm  NNH = -1 / ARR  if ARR > 0 (giving positive result)


BP = blood pressure (high)

This case is very similar, because high BP and diabetes are each comorbidities with high BMI and hence to some extent with each other.  Consequently we just substitute diabetes by BP throughout.

(0) We can in f act test the strength of the above  with the following RR, which in effect reads as “What is the relative risk of needing to take BP medication if you are diabetic as opposed to not diabetic?

<‘Taking BP  medication’:=’1’  |  ‘Taking diabetes medication’:= ‘1’>

/<‘Taking BP  medication’:=’1’  | ‘Taking diabetes medication’:= ‘0’>

The following predictive odds  PO make sense and are useful here:-

<‘Taking BP  medication’:=’1’  |  ‘BMI’:= ’50-59’  >

/<‘Taking BP  medication’:=’0’  |  ‘BMI’:= ’50-59’  >

and (separately entered)

<‘Taking diabets medication’:=’1’  |  ‘BMI’:= ’50-59’  >

/<‘Taking diabetes  medication’:=’0’  |  ‘BMI’:= ’50-59’  >

And the odds ratio OR would be a good measure here (as it works in both directions). Note Pfwd = Pbw theoretically for an odds ratio.

<‘Taking BP  medication’:=’1’  | ‘Taking diabetes medication’:= ‘1’>

<‘Taking BP  medication’:=’0’  | ‘Taking diabetes medication’:= ‘0’>

/<‘Taking BP  medication’:=’1’  | ‘Taking diabetes medication’:= ‘0’>

/<‘Taking BP  medication’:=’0’  | ‘Taking diabetes medication’:= ‘1’>

Value Added Partners Invited –; Cognitive Computing Platform democratizing Medical Knowledge at Point of Care.

Screenshot 2016-06-24 10.59.09

Commoditization of Data Science and unleashing Democratized Medical Knowledge.

The mission of Ingine Inc as a startup is to bring advancement in data science as applicable to medical knowledge extraction from large data sets.

Screenshot 2016-06-24 11.29.39

Particularly following are the differentiators owing to which Ingine Inc is a candidate startup in hope of advancing science in difficult to solve areas; driven by decades of research by Dr. Barry Robson.

  1. Introducing Hyperbolic Dirac Net (HDN); a machinery created borrowing from Quantum Mechanics to advance data mining and deep learning beyond what Bayesian could deliver; against the backdrop of very large data sets riddled with uncertainty and high-dimentionality. Most importantly, HDN based non-hypothesis approach allows us to create a learning system workbench that is also amenable to research and discovery related efforts based on deep learning techniques.
  2. Create large data driven evidence based medicine (EBM). This means creating scientifically curated medical knowledge having gone through a process akin to systematic review.
  3. Integrate Patient centric studies with epidemiological studies to achieve a comprehensive framework to advance integrated large data driven bio-statistical approach which addresses both systemic and also functional concerns. This means blending both descriptive and inferential (HDN) statistical approaches.
  4. Introduce a comprehensive notational and symbolic programming framework that allows us to create a unified mathematical framework to deliver both probabilistic and deterministic methods of reasoning which allows us to create varieties of cognitive experience from large sets of data riddled with uncertainty.
  5. Use all of the above in creating a Point of Care platform experience that delivers EBM in a PICO format as followed by the industry as a gold standard.

While PICO is employed as a framework to create EBM driven diagnosis process as a consequence of both qualitative and quantitative methods that better achieves systematic review; medical exam setting is used as a specification to define the template for enacting the EBM process. This is based on the caveat that for a system to qualify as an expert system in the medical area, it should also be able to pass medical exams based on the knowledge the learning system has acquired that is scientifically curated by both automated machine learning and manual intervention efforts.

As part of the overall architecture, that employs some ingenious design techniques such as non-predicated, non -hypothesis driven and schema-less design; semantic lake a tag driven knowledge repository is created from which the cognitive experience is created employing inferential statistics. Furthermore the capability can be delivered as a cloud computing platform where parallelization, in-memmory processing, high performance computing (HPC) and elastic scaling are addressed.

Precision Medicine: With new program from White House; also comes redundant grant funding and waste – How does all these escape in high science areas?


Recently announced Precision Medicine a fantastic mission to bring all the research institutions country wide to collaborate together and holistically solve the civilization’s most complex and pressing problem Cancer, employing genomics while engaging science in an integrative discipline approach.

While the Precision Medicine mission is grand and certainly requires much attention and focus; that many new tools are now available for medical research such as complex algorithms in the areas of cognitive science (data mining, deep learning, etc), bigdata processing, cloud computing, etc; we also need efforts to arrest redundant spend and grants.  

Speaking of precision medicine such waste what an irony.

The White House Hosts a Precision Medicine Initiative Summit

Grand Initiative Redundant Research Grants for Same Methods

$1,399,997 :- Study Description: We propose to develop Bayesian double-robust causal inference methods that are accurate, vigorous, and efficient for evaluating the clinical effectiveness of ATSs, utilizing electronic health records and registry studies, through working closely with our stakeholder advisory panel. The proposed “PCATS” R package will allow easy application of our methods without requiring R programming skills. We will assess clinical effectiveness of the expert-recommended ATSs for the pJIA patient population using a multicenter new-patient registry study design. The study outcomes are clinical responses and the health-related quality of life after a year of treatment.

$832,703 :- Bayesian statistical approach in contrary try to use present as well as historical trial data in a combined framework and can provide better precision for CER. Bayesian methods also flexible in capturing subjecting prior opinion about multiple treatment options and tend to be robust. Despite these advantages, the Bayesian method for CER is underused and underdeveloped (see PCORI Methodology Report, pg. 64, 2013). The primary reasons being a lack of understanding about the role, the lack of methodological development, and the unavailability of easy-to-use software to design and conduct such analysis.

$839,943 :- We propose to use a method of analysis called Bayes method, in which data on the frequency of a disease in a population is combined with data taken from an individual patient (for example, the result of a diagnostic test) to calculate the chance that the patient has the disease given his or her test result. Clinicians currently use Bayes method when screening patients for disease, but we believe the utility of this methodology extends far beyond its current use.

$535,277 Specific Aims:

  1. To encourage Bayesian analysis of HTE:
  • To develop recommendations on how to study HTE using Bayesian statistical models
  • To develop a user-friendly, free, validated software for Bayesian methods for HTE analysis

2. To develop recommendations about the choice of treatment effect scale for the assessment of HTE in PCOR. The main products of this study will be:

  • recommendations or guidance on how to do Bayesian analysis of HTE in PCOR
  • software to do the Bayesian methods
  • recommendations or guidance on choosing appropriate treatment effect scale for HTE analysis in PCOR, and
  • demonstration of our products using data from large comparative effectiveness trials.; Integrated Platform for Population Health and EBM based Patient Health Analytics

Ingine Inc;

Deductive Logic to Inductive Logic

Notational Algebra & Symbolic Programming

Deductive – What | Inductive – Why, How

Deductive:- Statistical Summary of the Population by each Variable Recorded

Deductive:- Statistical Distribution of a Variable

Deductive:- Partitioning Data into Clusters

Cluster analysis is an unsupervised learning technique used for classification of data. Data elements are partitioned into groups called clusters that represent proximate collections of data elements based on a distance or dissimilarity function. Identical element pairs have zero distance or dissimilarity, and all others have positive distance or dissimilarity.

Click to access CCtuto_kdd14.pdf


correlation coefficient is a coefficient that illustrates a quantitative measure of some type of correlation and dependence, meaning statistical relationships between two or more random variables or observed data values.

The regression equation can be thought of as a mathematical model for a relationship between the two variables. The natural question is how good is the model, how good is the fit. That is where r comes in, the correlation coefficient (technically Pearson’s correlation coefficient for linear regression).

Inductive :- Hyperbolic Dirac Net 

Notes on Synthesis of Forms :-

Christopher Alexander on Inductive Logic

The search for causal relations of this sort cannot be mechanically experimental or statistical; it requires interpretation: to practice it we must adopt the same kind of common sense that we have to make use of all the time in the inductive part of science. The data of scientific method never go further than to display regularities. We put structure into them only by inference and interpretation. In just the same way, the structural facts about a system of variables in an ensemble will come only from the thoughtful interpretation of observations.

We shall say that two variables interact if and only if the designer can find some reason (or conceptual model) which makes sense to him and tells him why they should do so.

But, in speaking of logic, we do not need to be concerned with processes of inference at all. While it is true that a great deal of what is generally understood to be logic is concerned with deduction, logic, in the widest sense, refers to something far more general . It is concerned with the form of abstract structures, and is involved the moment we make pictures of reality and then seek to manipulate these pictures so that we may look further into the reality itself . It is the business of logic to invent purely artificial structures of elements and relations. 

Christopher Alexander:- Sometimes one of these structures is close enough to a real situation to be allowed to represent it. And then, because the logic is so tightly drawn, we gain insight into the reality which was previously withheld from us.

Quantum Mechanics Driven Knowledge Inference for Medical Diagnosis

HDN Inference

HDN Results :- Inverse Bayesian Probability


Platform for BigData Driven Medicine and Public Health Studies [ Deep Learning & Biostatistics ]

Panel_Logo; Platform for comprehensive statistical and probability studies for BigData Driven Medicine and Public Health.

Importantly helps redefine Data driven Medicine as:-

Ontology (Semantics) Driven Medicine

Comprehensive Platform that covers Descriptive Statistics and Inferential Probabilities.

Beta Platform on the anvil. Signup for Demo by sending mail to

“” 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 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 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 can more readily manipulate.

BigData Driven Medicine Program :-

Objectives and Goals

Informatics & Data-Driven Medicine (IDDM) is a foundation area within the Scholarly Concentration program that explores the new transformative paradigm called BIG DATA that is revolutionizing medicine. The proliferation of huge databases of clinical, imaging, and molecular data are driving new biomedical discoveries and informing and enabling precision medical care. The IDDM Scholarly Concentration will provide students insights into this important emerging area of medicine, and introducing fundamental topics such as information management, computational methods of structuring and analyzing biomedical data, and large-scale data analysis along the biomedical research pipeline, from the analysis and interpretation of new biological datasets to the integration and management of this information in the context of clinical care.


Students who pursue Informatics & Data-Driven Medicine in conjunction with an application area, such as Immunology, are required to complete 6 units including:

Biomedin 205: Precision Practice with Big Data :- Quantum Mechanics Machinery for Healthcare Ecosystem Analytics

Screenshot 2016-04-01 10.25.05

Notational – Symbolic Programming Introduced for Healthcare Analytics

Quantum Mechanics Firepower for Healthcare Ecosystem Studies        

Interoperability Analytics

Public Health and Patient Health

Quantum Mechanics Driven A.I Experience

Deep Machine Learning

Descriptive and Inferential Statistics

Definite and Probabilistic Reasoning and Cognitive Experience

Know Your Health Ecosystem (Semantic Lake) :- Deep Learning from Healthcare Interoperability BigData – Descriptive and Inferential Statistics

Screenshot 2016-04-01 11.28.31; Platform for Healthcare Interoperability (large data sets) Analytics

Deep Learning from Millions of EHR Records

1. Payer – Provider:- (Mostly Descriptive Statistics)

Mostly answers “What”

  • Healthcare Management Analysis (Systemic Efficiencies)
  • Opportunities for cost reduction
  • Chronic patient management
  • Pathway analysis for cost insights
  • Service based to Performance Based – Outcome Analysis (+Inferential)

2. Provider – Clinical Data – (Mostly Inferential Statistics)

Reasoning to understand “Why”, “How”, “Where” (Spatial) and “When” (Temporal)

  • Healthcare Delivery Analysis (Clinical Efficacies)
  • EBM – Clinical Decision Support – Hypothesis Analysis
  • Pathways and Outcome (+Descriptive)

Health Information Exchange :- Interoperability Large BigData


Sample Descriptive Statistics:-

Inferential Statistics:-

Computing Cardiovascular Risk Score – BioIngine (HDN)

Mar 21, 2016

Hyperbolic Dirac Net :- Dual Bayesian Probabilities Computations.

Below is Screen Shots of the BioIngine – HDN Ingine; that creates a semantic lake and from which computes the probabilistic risk; as one of the use case.; in its first attempt is being implemented employing the Wolfram Symbolic Programming Language, where the Bioingine’s algorithm is developed based on Q-UEL (a Notional Language Framework to express Probabilistic Semantics – derived from the Dirac Notation a Framework to describe Quantum Mechanics). As such the Wolfram Language is designed based on deterministic system providing definite answers based on deductive methods.

Introduction of Q-UEL / HDN introduces probabilistic system, where knowledge by inference can be extracted employing inductive techniques.

A typical query below; which is a Dirac Notational Expression (semantic algebra) queries the semantic lake (the health ecosystem as HDN representation)

HDN Inference Results

Pay attention to notational expression and HDN computations in Section B.

Section A
‘HEART ATTACK’ | ‘Age(years)’:=’50-59′> ‘HEART ATTACK’ | ‘History of BP’:=’1′ and ‘Taking BP medication’:=’1′ and ‘History of high cholesterol’:=’1′>/’HEART ATTACK’ | ? >’History of BP’:=’1′ and ‘Taking BP medication’:=’1′ | ‘Total cholesterol(mg/dl)’:=’180-229′> ‘History of high cholesterol’:=’1′ | ‘Male’:=’0′ and ‘Systolic BP(mmHg)’:=’170-179′ and ‘Taking diabetes medication’:=’0′>  /’History of BP’:=’1′ | ? > /’Taking BP medication’:=’1′ | ? >/’History of high cholesterol’:=’1′ | ? >

Got Following Results:- Pay attention to how all the probabilistic estimates contributed by each contending factors add to the risk. Eventually we have HDN as a forward and backward computed results.

Section B

  1. ‘HEART ATTACK’ | ‘Age(years)’:=’50-59′>=0.0404, 0.2805
  2. ‘HEART ATTACK’ | ‘History of BP’:=’1′ and ‘Taking BP medication’:=’1′ and ‘History of high cholesterol’:=’1′>=0.1171,0.2927
  3. /’HEART ATTACK’ | ? >=0.0860,1
  4. /’History of BP’:=’1′ | ? >=0.3904,1
  5. /’Taking BP medication’:=’1′ | ? >=0.2910,1
  6. /’History of high cholesterol’:=’1′ | ? >=0.2911,1
  7. #    NET = {166.34%,8.21%}
  8. #        = iota(166.34%) + iota*(8.21%)
  9. #    where real part = existential joint probability component = 87.275%
  10. #    where imaginary part = universal purely conditional component = h*79.065%

 WHAT IS THE PROBABILITY OF not having a history of high cholesterol, for a female patient age 50-59 taking diabetes medication and having a BMI of 30-39 and HDL 50-59, GIVEN THAT the systolic BP is 130-139 and Non-HDL is 120-129? Also implies the question with the lower case parts of the first and fourth lines switched.

The above is easily translated into Dirac brakets, manually or automatically, as shown below. To get the probabilities for those brakets, the DiracBuilder module looks for tags outputted from DiracMiner into Semantic Lake that carry the required information. Here it finds four relevant tags. One corresponds to the complex conjugate of the implied corresponding query tag, e.g. we looked for A, B | C> and found C | B, A>, but we merely imagine switching the Pfwd and Pbwd that it presents. The Query as HDN would be as:-

‘History of high cholesterol’:=’0′ |’BMI’:=’30-39′ and ‘HDL(mg/dl)’:=’50-59′> = Pfwd 70.87, Pbwd 6.65

‘BMI’:=’30-39′ | ‘Systolic BP(mmHg)’:=’130-139′>

= Pfwd 46.44, Pbwd 28.51

‘HDL(mg/dl)’:=’50-59′ | ‘Taking diabetes medication’:=’1′>

= Pfwd 25.11, Pbwd 14.92

‘Taking diabetes medication’:=’1′ | ‘Male’:=’0′ and ‘Age(years)’:=’50-59′>

= Pfwd 11.69, Pbwd 22.91

‘Male’:=’0′ and ‘Age(years)’:=’50-59′ | ‘Non-HDL(mg/dl)’:=’120-129′>

= Pfwd 20.81, Pbwd 8.09

We multiply the probabilities in each direction, 70.87 x 46.44 etc. to the left, and 6.65 x 28.51 etc. to the right. The answers are 0.2010%, 0.0052% respectively, i.e. the dual – {Pfwd 0.2010%, Pbwd 0.0052%}.