+ All Categories
Home > Documents > Quantum-Classical Hybrid Machine Learning for Gene ... · 1 01 10 2 Radhakrishnan Balu: Quantum...

Quantum-Classical Hybrid Machine Learning for Gene ... · 1 01 10 2 Radhakrishnan Balu: Quantum...

Date post: 23-Mar-2019
Category:
Upload: lexuyen
View: 214 times
Download: 0 times
Share this document with a friend
24
UNCLASSIFIED UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces UNCLASSIFIED Quantum-Classical Hybrid Machine Learning for Gene Regulatory Pathways Radhakrishnan Balu , CISD-ARL Qubits North America, 09/26/2018, Knoxville, TN
Transcript

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land ForcesUNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

UNCLASSIFIED

Quantum-Classical Hybrid Machine Learning for Gene Regulatory Pathways

Radhakrishnan Balu , CISD-ARL

Qubits North America, 09/26/2018, Knoxville, TN

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Outline of the Talk

o A Brief introduction to the problem

o Review of Bayesian Networks

o Embedding challenges

o Probabilistic Logic Programming (ML)

o Solution Architecture and Results

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

MAPK/Raf Pathway

MAPK/Ras pathway. Source: Discovery Medicine

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Sachs, K.; Perez, O.; Pe’er, D.; Laughenburger, A. D.; Nolan, P. G. Causal Protein-Signaling Networks

Derived from Multiparameter Single-Cell Data. Science 2005, 308.

Bio Signaling Pathways

A Bayesian Network based Causal Relationship Elucidation

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

o BN is a pair (Bs, Bp).

o Bs is directed acyclic graph representing the model

o Bp is the set of conditional probabilities

o Xi state of node – gene is activated or not

o Probability of Xi conditioned on the joint state of its parents πi(BS)

o Parents: Arcs in the structure to Xi

Bayesian Networks

Coin Toss

Weather

Visit Zoo

Spend Money

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Proteomics data from flow cytometry

Concentrations of proteins as probabilities

Bayesian networks for hypothetical proteins X, Y, Z, and W. In this

model, X influences Y, which, in turn, influences both Z and W.

Bayesian Networks

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Acyclic directed graphs

o Biological pathways may contain cycles

o BN May miss some dependencies

Bayesian Networks

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

PRISM Generated BN

Nand Kishore, Radhakrishnan Balu, and Shashi P. Karna, “Modeling Genetic Regulatory Networks Using First-Order Probabilistic Logic”, ARL-TR-6354, 2013.

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

(Quantum) Probabilistic Logic9

• Non-commutative Probability

• Quantum Probability Space

• Attach Probability Amplitudes to H-interpretations

• Projections of H

• ρ - State

Denotational Semantics

Distribution Semantics (PRISM)

Entanglement Semantics

PHPQP ,,

H-I

10012

1

Radhakrishnan Balu: Quantum probabilistic logic programming, Proc. SPIE-DSS, quantum information and computation, Baltimore MD (2015)

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Hybrid Architecture

BNProteomics PRISM (MLE)

D-Wave

SuprvisedLearning

PRISM (MAP)

Un

sup

rvisedLearn

ing

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Quantum Annealing

o 2000 qubit processor

o Restricted class of optimization problems

o Quadratic Unconstrained Binary Optimization (QUBO)

O’Gorman, B. A., Perdomo-Ortiz, A., Babbush, R., Aspuru-Guzik, A. &

Smelyanskiy, V. Bayesian network structure learning using quantum

annealing. European Physics Journal Special Topics 224, 163–188 (2015)

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces12

Current Implementation

o Number of nodes of BN = 8

o Number of parents allowed = 3

o Number of logical qubits = 230

o Number of Physical qubits ~ 2000

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

2

1

3

45

6

7

8

Embedding Challenge

o Denny’s help with manual embedding

o Routine based embedding also worked

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

MAPK/Raf Pathway

Bayesian Network encoding the causal relationship in MAPK/Raf signal transduction pathway in human T-cells. Only eight of the units are considered here.

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Bayesian Theorem

D – Data

BS – BN

α – Dirichlet priors (assumed uniform here)

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

QUBO

o Htotal = Hscore + Hmax + Hcycle

o QUBO conversion

O’Gorman, B. A., Perdomo-Ortiz, A., Babbush, R., Aspuru-Guzik, A.

and Smelyanskiy, V.: Bayesian network structure learning using

quantum annealing, European Physics Journal Special Topics 224,

163-188 (2015).

o BN with at most three parents constraint

o No cycles constraint

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Expt. vs PRISM Score

Legend :

Black arcs : Correct edges (True Positives)

Dotted arcs : Missed edges (False Negatives)

Red arcs : Wrong edges (False Positives)

Green arcs : Reversed edges (False Positive + False

Negative)

TRUE POSITIVE : 12

FALSE POSITIVES : 2

FALSE NEGATIVES : 2

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

R vs PRISM Legend :

Black arcs : Correct edges (True Positives)

Dotted arcs : Missed edges (False Negatives)

Red arcs : Wrong edges (False Positives)

Green arcs : Reversed edges (False Positive + False Negative)

TRUE POSITIVE : 11FALSE POSITIVES : 2FALSE NEGATIVES : 3

TRUE POSITIVE : 12

FALSE POSITIVES : 2

FALSE NEGATIVES : 2

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Expt. vs R SCORE

Legend :

Black arcs : Correct edges (True Positives)

Dotted arcs : Missed edges (False Negatives)

Red arcs : Wrong edges (False Positives)

Green arcs : Reversed edges (False Positive +

False Negative)

TRUE POSITIVE : 11

FALSE POSITIVES : 2

FALSE NEGATIVES : 3

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

Expt. VS D-Wave II

LEGEND:

BLACK EDGES : CORRECT

DOTTED : MISSING

RED : EXTRA EDGES

GREEN : REVERSED

True Positives : 11

False Positives : 4

False Negatives : 3

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces

MAPK/Raf Pathway

Results from 30 annealing schedules for the MAPK/Raf BN with 14 arcs.

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces22

Summary and Future Plans

o Real world application embedded

o Limited error correction applied

o Essential features of BN captured

o Scalability beyond 8-nodes BN

o ML applied to QUBOs (U. Calgary)

o Benchmarking against classical solutions

o Dynamic BN and Bayesian Neural Networks

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces23

Acknowledgements

Annealings: Ajinkya Borle

Graduate Student, UMBC

D-Wave technical support team

Denny, Murray, and Rene

UNCLASSIFIED

UNCLASSIFIED The Nation’s Premier Laboratory for Land Forces24

Thank you for your attention


Recommended