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Predictive Health Analytics

A Potential Role for Quantum Annealing in the Enhancement of Patient Outcomes?

David Sahner, [email protected]

APRIL 2018

Presentation Outline

• Why do we need AI in medicine?

• Lightning overview of some tools of the trade, upsides and challenges*

• Specific examples of means to which those tools have been put

• “Precision Quantum Medicine Algorithm”• Rationale and differentiation from existing techniques• Method• Preliminary results using a quantum simulation and mock clinical data

State of the art

*Support vector machines, although useful, omitted for several reasons. Will not cover topological data analysis either for lack of time.

AI in Medicine: Why Now?

• The complexity of biology and medicine is outstripping even the most powerful human intellect, while an increasing premium is being placed upon quality healthcare outcomes at lower cost.

o Physicians, nurses, and NPs will always be a critical part of health care, but need help, particularly in the primary care setting.

o What is the best preventive health strategy for John Q. Patient? How can I avoid a 30 day hospital readmission? What is the diagnosis? What is the best therapeutic choice? We need to act with precision, remaining cognizant of an exploding medical literature.

• The era of Big Data is upon us, and we are developing access to vast integrated troves of clinical, laboratory, imaging, and –omic data.

o These enormous data sets allow us to use the most powerful and informative of machine learning algorithms with minimal risk of overfitting. And we now have the computational firepower to do so.

Simple Linear Regression Model to Predict One of Two Binary Outcomes (e.g., Survival at 30 Days in Septic Shock Y/N)

Variable x1

Variable x2

Variable x3 . . .

Variable xn

Patient 1 Yes Yes Yes No

Patient 2 ...

No Yes No Yes

Patient N Yes No No Yes

Multiply each variable value for a patient by a specific weight (w) and sum up*

This sum (z) isput through a sigmoid “activation” or “output” function to produce a number between 0 and 1. If this is ≥ 0.5, predict death

Mortality at 30 d(For Real)

Patient 1: Yes

Patient 2: No...

Patient N: No

Right Answers?(Y/N)

Compute Cost(Wrong answers costly)

Optimize weights to minimize cost (i.e., increase accuracy)

Compareprediction and reality

*Technically, a biasterm is added, but we will ignore that

Computation of cost function; model parameter optimization to improve accuracy• This happens iteratively over time. Typically, there are multiple swipes through the

entire training data set.

• Typical cost function for logistic regression based on “maximum log likelihood.” Each training example classification (right/wrong) contributes to the cost.

o First calculate probability of actual outcome given the model’s prediction leveraging the sigmoid output shown on the last slide.*

o Cost = the negative log value of that probability (thus, higher cost if the likelihood of the actual outcome given the prediction is low).

• Weight adjustments for each variable dictated by rate of change of cost with respect to that weight (i.e., a partial derivative).

o If cost increasing with respect to weight, then decrease that weight o If cost rapidly decreasing with respect to weight then increase that weight o This is gradient descent

*Actually, we use a “Bernoulli distribution” controlled by this sigmoid output

Gradient Descent-Based Weight Adjustment: A Critical Component of Much Machine Learning

• Again, weight adjustment based on rate of change of cost with respect to the weight• This rate of change is multiplied

by a constant (“step size”), and that product is added to (or subtracted from) the weight for the next swipe through the data• Step size can be modulated during

training to increase chance of efficiently finding an optimum (or near-optimum) set of weight values minimizing cost

J (θ0 θ1) = cost; θ0 = weight for one variable (feature) and θ1 = weight for another feature. Ski down gradient to lowest cost by optimizing weights

What if we have multiple classes or outcomes that we would like to predict?*

• Analogous to prior example, but now we use what are known as softmax (instead of sigmoid) output units to estimate the probability of actual outcome given the prediction*

• In this case, the softmax output function exponentiates “z” (recall “z” is just the raw sum of the products of weights and features, plus bias)• Softmax(z) simply equals ez (normalized, actually) = probability of actual

outcome (or class) given the prediction of that outcome (or class)

• KEY POINT: Both the sigmoid output function and softmax output function lend themselves well to cost functions based on maximum log likelihood• Log and exponent “cancel out, preventing “saturation,” which

can flatten the gradient making it hard to train the algorithm • A mean squared error-based cost function lacks this advantage!

*Actually, we use a “multinoulli distribution” controlled by this softmax output

The Twin Banes of “Overfitting” and “Underfitting” a Model

• Overfitting: With a powerful enough model, you can predict or classify anything in a training set!

o But you may have packed “spurious” features into a powerful model that do not have true bearing on whether or not, for example, a Delicious Apple is a Delicious Apple.

o Models that have been overfitted do not generalize well to independent datasets.

• Underfitting: You can also choose a model that is too feeble given the task. That is to say, it is simply incapable of reliably making a distinction between, for example, Delicious apples and Fuji apples.

Methods to Avoid Overfitting and Underfitting

• Overfitting avoidanceo Increase size of training dataset

o Don’t choose a hyper-powerful classifier (deep neural net or complex polynomial classifier) if you have a tiny data set

o Use “regularization” techniques that exact a penalty for unduly complex models

o Use “dimensionality reduction” to limit yourself to key features

• Underfitting avoidanceo Don’t choose a simple linear model

if you are attempting to learn distinctions that depend on non-linear factors

o Consider adding featureso If a simple model doesn’t cut it

(poor accuracy), increase the size of your training dataset so that you can exploit a more potent model type

Cross-validation (creation of mock independent test sets using “reserved” training examples)is a critical means of detecting underfitting and overfitting, and tweaking “hyper-parameters”

Regularization and Dimensionality Reduction Techniques to Prevent Overfitting

• L1 regularization to put your “feature list” on a healthy diet. Less model fat (fewer features), less overfitting*

• L2 regularization, which penalizes for larger weights with preferential reduction in weights of variables that have minimal effect on model performance*

• Principal Component Analysis to identify key independent drivers of model strength in lower dimensional space

*L1 and L2 regularization require anotherHyperparameter we need to select

Regularization and Dimensionality Reduction to Prevent Overfitting (continued)

• Sequential Backward Selection: Select a tolerance limit for erosion of model performance when a feature is removed. Cut hairs one by one until you hit that tolerance limit.

• Linear discriminant analysis

• Mathematically “match” the Vapnik-Chervonenkis dimension (i.e., power) of model to training sample size.

o Enables calculation of the likely upper bound of the test error on an independent sample (i.e., how well the model would generalize).

• Other techniques mentioned later in the context of discussion of Decision Tree analysis and in a back-up slide for “Deep Learning.”

Polynomial Classifiers: More Muscular

• What if the “decision boundary” between two classes is not linear, and a linear model therefore underfits the data (i.e., it is too weak)?

• Well, we can use a polynomial classifier (with more features because a polynomial classifier let’s us exponentiate feature values to create “new features”)

• Example: instead of an algorithm that uses a function like z = w1x1 + w2x2 + w3x3 + bias (b) term, we could try:z = w1x1 + w2(x1)2 + w3x2 + w4(x2)3 + w5x3 + w6(x3)2 + b • More features means a greater risk of overfitting.

We buy model power at the expense of this risk.

Bayesian Classifiers

• Bayesian classifiers are based on conditional probabilities• That is, what is the probability of x given y? • This is written: P(x|y)

• Bayes rule, where ci = class “i” and x = vector (or “list”) of feature attributes for the example we are attempting to classify:• P(ci|x) = P(x|ci) times P(ci) divided by P(x)

• If the features of an example are thought to be independent(i.e., uncorrelated) we are making the “Naïve Bayes” assumption• Prior expectations, based on expert opinion, can be used to

“leaven” predictions (based on what we observe) with what we believe to be the case at the outset

Thomas Bayes (perhaps)

k-Nearest Neighbor (k-NN) Classifier*

• Extremely simple intuition: You are likely to belong to the same group as a known neighbor in “feature (i.e., attribute) space”• Think of each feature for a given example as a

coordinate value in a graph (i.e., a value for the x, y, z, etc. coordinates). Collectively, the coordinates define a point in (potentially hyperdimensional) space• The algorithm evaluates distance of a new example

from other points. Classification can be based on the single closest neighbor, a “vote” among the three closest neighbors, etc.*

*The number of nearest neighbors who weigh in on the class of a newcomer affects model fitting (over versus under versus just right).

k-NN Classifier (concluded)

• Important to scale attributes if using Euclidean distance, because those with larger values can dominate the distance estimate between examples

• Can also weight attributes based on their discriminative importance

• Performance enhanced by removing outliers surrounded by another class, and “borderline” cases on the cusp of two classes

• Exclusion of examples in feature space that do not affect classification performance can decrease computational burden

Decision Tree Separating Six Classes (one per terminal leaf of an inverted tree)

Attribute 1(Root Node)

Attribute 2 Attribute 3

Attribute 4 Leaf 1 Leaf 2Attribute 5

Leaf 3 Leaf 4 Leaf 5 Leaf 6

Increasing information (and, by corollary, decreasing “entropy”) as we descend from root to leaves. First branch provides greatest amt. of information*, second branch provides second greatest amt., etc.

*Information is assessed mathematically as a difference in entropy between levels. Tree “pruning “ and “Random Forrest” approach mitigate risk of overfitting and decrease error rate.

Yes

YesYes

Yes

Yes

No

No

No

No

No

Feedforward Neural Nets

• Each input is a feature from an example (e.g., in training data set)

• Each input provides a weighted output to the hidden layer, and each hidden layer provides weighted outputs to next

• Weighted inputs at each hidden node summed, and we apply an activation function*

• Output layer provides class probabilities for a given example

• Gradient descent to optimize (usu.)*Sigmoid or softmax activation function common for output layer, but now we tend to favor “ReLu” or “Maxout” activation function for hidden layers to avoid loss of gradient. Maxout units also offer computational efficiency and protection from “catastrophic forgetting.”

Deep Learning: Weight Optimization during Learning – Hot Topic and an Evolving Art

• Gradient descent* is largely the “go-to” approach, but here we need to use the chain rule to compute our partial derivatives of cost with respect to weight, because there are multiple layers

• Gradient descent on “mini-batches” of training examples improves efficiency and generalization

• Use of second-order derivatives (analogous to monitoring “acceleration” of the skier on the slope) may offer benefits, but computationally costly• Takes curvature into account when deciding on step size during

descent – preferentially pursue paths of greater downward curvature. Better efficiency in theory but can gravitate to “saddle points”

• New “saddle free” method may be helpful

• Momentum method to “plow down” noisy/craggy landscape*Can also average weights over repetitions of a trajectory to obtain a best guess Continuation methods tackle progressively more rugged cost functions, but have drawbacks

Saddle Point: Cost minimal in onedimension but maximal in another

Deep Learning: Regularization to Enhance Generalizability of Model to Novel Datasets

• Typical regularization techniques • Dataset augmentation (e.g., rotating or rescaling images to be

recognized, injection of noise) • Early stopping during training (before the clothes shrink and you overfit)• Sparse representation within hidden layers – can penalize “non-sparsity”• Dropout as a computationally inexpensive means of “hiring” an ensemble

of nets• “Tangent prop” and “double backprop,” which coax the same

classification from similar inputs

Current Deep Learning Challenges

• Goal is to arrive at or near global minimum of cost function, one but can get trapped in “local minima” • Not thought to be as large of a problem as it once was• Can follow “norm” of gradient over time to rule this out

• Exploding and vanishing gradients• With exploding gradient (and cliffs), can overshoot minimum*• With vanishing gradient, can take forever to learn

• Ideal initialization of weights? Implications for model performance and learning rate• Random scaled initialization • Normalization technique developed to foster preservation of

variance of gradients and forward outputs across layers• Ideal weight initializations may lie only near predicted optimum

*Gradient clipping can help to prevent this

Deep Learning: Recent/Modern Innovations are Proliferating

• Adversarial Training: One net tries to “hoodwink” the other by producing “perturbed” ambiguous examples to be classified. Learn to avoid being fooled.

• Recurrent/Recursive neural nets for sequence modeling (not new, per se)• Retention of info a challenge. “Skip” connections across layers, connection removal and leaky

units are not new but “long short-term memory” is a recent tactic promoting retention of information re. long-term dependencies in time-series data. “Memory networks” also new.

• Supervised pretraining: Short squat neural nets teach more “difficult-to-train” tall (i.e., deep) lanky nets. Latter obtains hints from former. May aid generalization.

• Batch normalization to address coordination of weight updates across many layers. Learning concentrated in upper layers (although lower layers still contribute). Can maintain expressive power of network.

• Multiple adaptive learning rate algorithms• Curriculum learning – start with easy classification examples, then up the game• Capsule nets; advanced convolutional nets; generative (e.g., modern Boltzmann)

models

Voting Assemblies (“Ensemble Learning”)

• Basic idea: Train multiple learning algorithms with complementary strengths to tap into collective wisdom of the ensemble

• Tally a vote among members of the learning ensemble for your answer

• Individual votes can be weighted

Some Companies in Predictive Health Analytics (not a comprehensive list)*

Company Stated capabilities include . . . Publication Examples

Ambient Clinical Analytics

AWARE Critical Care to reduce information overload and AWARE Sepsis Dart for identification of potential sepsis and decision support. MAYO clinic YES board – workflow management tool for ED.

A sepsis tool was 80% sensitive and 96% specific in a 2015 study.

Unable to find a published study using acontemporaneous control group for AWARE system, but some historical control ICU data (2017 publication).

Ayasdi Grouping of patients into clinically relevant phenotype/genotype classes using topological data analysis

Several publications, including studies in type 2 diabetes, TBI

Evidation Health Collection and analysis of behavioral and traditional healthcare data

Health trackers associated with weight loss using linear model. A recent (very small) crowdsourcing study.

*For example, companies primarily involved in linking/cleansing EHR records omitted, as well as those (e.g., Calico) with recent pubs concentrated in basic research. Companies for which a PubMed search revealed no full publically accessible manuscripts that have bearing on predictive health analytics in the last ~5-7 years omitted (search over last ~2 years largely restricted to freely available pubs). Not always possible to determine if a study with a company author used a company algorithm. Compiled 3/2018. Contact me for citations if desired.

Some Companies in Predictive Health Analytics (not a comprehensive list)


BaseHealth “. . . picture of financial liability and health risk for member populations.” Curated articles used to identify risk factors for machine learning.

Prediction of type 2 diabetes risk in a Swedish cohort using environmental and genetic (SNP) risk factors.

Early Sense Monitor heart and respiratory rate to detect early trends (rather than threshold alerts) suggesting deterioration. Monitor nocturnal movement and compliance with turn protocols to assess pressure ulcer risk

“Under the mattress” sensor to algorithmically monitor sleep. Retrospective analysis of HR and RR trend data as a correlate of deterioration suggesting complementary sensitivity and specificity (78% and 90% for HR versus 100% and 64% for RR).

Flashback Technologies

Emphasize importance of better awareness of response to resuscitation. Methods include “classification, regression, clustering, semi-supervised learning, reinforcement learning . . . with feature extraction techniques derived from robotics and computer vision.”

Compensatory reserve index based on arterial waveform features as a marker of reduced circulating blood volume.



GNS Healthcare “We reverse engineer the complex causal mechanisms that determine which therapies will produce the best outcomesfor each patient.” “REFS” platform relies on an ensemble of models and Bayesian methods.

Medication discontinuation, adherence and remission in schizophrenic patients. Prediction of Parkinson’s disease outcomes, progression to T2DM

Humedica(acquired by UnitedHealth)

Large health care database. Risk stratification and predictive population-based algorithms with models of multiple diseases

Impact of co-morbidity clusters on outcomes in diabetics using logistic regression. Prediction of 30-day hospital readmission in T2DM.

IBM AI for drug development support and treatment recommendations.

Concordance with oncologist Rx recom-mendations; prediction of statin response, ICU stay

Jointly Health (now Sentrian)

Rules-based remote patient monitoring. Feasibility study of home monitoring of patients with NYHA Class 2-4 CHF

Lumiata Structure time series data and then subject data to AI-based prediction. Provides clinical rationale for predictions

Tool for ED triage – probabilistic graphical model



Pascal Metrics Help identifying, avoiding, and ameliorating patient harm using insights from real-time EHR data. System fires “automated clinical triggers.”

Multiple, including several involving“trigger tools” retrospectively characterized/evaluated

Perigen Perinatal decision support. Detection of worrisome fetal HR trends. Labor progress. Shoulder dystocia assessment.

Eval. of associations between fetal HRdeceleration subtypes and metabolic acidemia using computerized pattern recognition. Multifactorial model to predict labor complications.

RxAnte Identification of risk of patient non-adherence. Collaboration with Pharma and health care sectors to evaluate disease prevalence & outcomes, utilization, etc.

Demographic factors influencing non-urgent ED visits in Medicaid population in which Poisson regression model used. Prediction of future insulin use. Breast cancer prognosis (Cox regression).


Company Stated capabilities include . . . Publications

SVBio (now Lifecode)

“Combining . . . health economics, econometric outcomes research, agent-based computation, disease decision algorithms . . . Lifecode gives . . . access to models that determine health outcomes and economic consequences within any disease area.”

Simulation of ramifications (QoL, survival, economic) of cerebral palsy following preventable obstetric complications. Recent abstract mentions determination of “appropriate cost-effectiveness thresholds to inform the Cancer Drug Fund’s decision making.” Latter manuscript not free.

Valence Health (recently acquired by Evolent)

Population health, utilization, risk adjustment, quality, financial performance. Analytical/improvement-oriented support.

Impact of computerized order entry on pneumonia outcomes. Recenthypertension manuscript in which a VH representative was 4th author. Standard statistical tests used in both.

PrecisionQuantumMedicineConcept:“FillintheBlanks”inaGraphicalModelQuestion:GiventheavailabledataforJohnQ.Patient(e.g.,history,SNPs,labs,meds,etc.),whatarethe likeliesttruthvalueassignmentsforscores/hundredsof“unknownnodes”?ProblemReframed: Howdowe“optimize”truthvalueassignmentsforunknownnodes,gainingbroadinsightintotheprobabilitiesofmanypotentialco-morbidities,risks,&outcomesforJohnQ.Patient?• Suchknowledgewouldassistindiagnosticscreeningand

preventivecare,improvingoutcomes,butthis“optimizationproblem”rapidlybecomesintractablebasedon(classical)computationaldemands

BackgroundandBroadVision:Ø Predictiveanalyticsarepromisingandtopical,but

solutionstypicallyenablefocusedprediction(of,e.g.,readmission,adherence,singlediseaseoutcome,etc.)

Ø Whatifwecouldsimultaneouslydetectaperson’sriskofhundredsofillnessesandoutcomesbyleveragingahugegraphicalmedicalknowledgedatabasethatcapturesnumerouslogicalinterdependencies?

D.

Circulatingcurrentinaqubitloopenablestwospinstatesalongzaxistoexistinsuperposition.

PossibleSolution:AnovelformulationasproblemHamiltonian(H)enablesaquantumsolutiontothe“nodaltruthvalue”optimizationproblem,lettinguspopulatethelikeliesttruthvalueassignments(T/F)forJohn’s“unknownnodes”• Quantumannealingnudges“initial”H to“problemH”• GroundstateofproblemH encodessolution• Withaccretionofnewclinicaldatainagivencase,thealgorithm

canberecursivelyappliedtoobtainevendeeperknowledge.

MarkovNetwork:Lines(edges)existbetweennodesthatarelinkedmechanistically(and/orbasedonpublisheddata).EdgeweightsestablishedbyBigData.ForJohnQ.Patient,onlysomenodaltruthvaluesknown.Q:Whataremostlikelytruthvaluesfortheothernodes?

Aren’tthereefficientclassicalalgorithmsthatsolvetheseMAPinferenceproblems?

• Yes,ifyouhave,perhaps,scoresofnodesthatarenottoodenselyconnected– integerprogramming– graph-cutmethods– combinatorialsearch– beliefpropagation– linearprogrammingrelaxation– messagepassing,jumpflooding,move&swap,etc.

• Butnotifyouhavehundredsofdenselyconnectednodes– couldtakeaneternity

29

ExecutePQMAlgorithmonDWaveMachine(atHealthCareSystemorCentralHub)towhichaMarkovNetwork(MN)hasbeenMapped

MNInformedbyAbundantLongitudinalPopulation-BasedData

ElectronicHealthRecorddata:medicalhistory,medications,imagingandlabresults,immunizationdates,allergies,demographicinformation,etc.

LikelytodevelopdiseaseXwithin1year

PersonalizedInputLikelytoenjoy5-yearcancer-freesurvivalonregimenA,butnotregimensBorC*

PersonalizedOutput

Panomic biomarkerdata

CurrentundiagnosedconditionsYandZlikely,considerscreening

Likelytoexperience75%improvementinpsoriasisscore(e.g.,PASI)ondrugD*

*Starredoutputsaremerelyexampleswithintwotherapeuticareas.

LargehealthcaresystemsmaybeequippedwiththeirownDWavemachinesmappedtoMarkovNetworksinformedbylongitudinalpopulation-baseddatafromthathealthsystem.Centralizeddataentryanddataimportationwouldleadtobriefactionableoutputsforhealthcareprovidersinthesystem(seeexamplesabove)basedonanalgorithm-enabledintegratedanalysisofthatspecificpatient’sdata.

Canrecursivelyapplyafteracquisitionofmoredatatodeepeninsights

PrecisionQuantumMedicine(PQM)

PythonAPIinterface(SAPI)withDWave

FindObjectiveFunctionthatInformsProblemHamiltonianNeededforAlgorithm

• Foranindividualpatient,thenodaltruthvalueassignments(Dy′) determinethespecificvaluesofinternodalweightfunctions(φ),whichcharacterizetheprobabilitiesoftruthvaluecombinationsforeachofthenodepairs

• Byprobabilitytheory,𝑃(Dy′|E)α productofallφij values• Byextension,thesetofnodaltruthvalueassignmentscorrespondingtoDy* (i.e.,themostlikelyvalues)yieldsthemaximalsumofall(i.e.,m)φvalues:§ argmax∑ φ𝑖𝑗*

+,- =Dy*

• Tocreate“objectivefunction”tobeminimized,takeinverseornegativeofabove

31Localoptimumnotnecessarilypartofglobaloptimalnetworksolution

ObjectiveFunctiontobeMinimized(toobtainoptimalsolutiontothe“fill-in-the-blanks”problem)

•Objectivefunction=∑ 1/φij*+,- (or∑ −φij

*+,- )

•Next,wemustexpressφ𝑖 asafunctionofthetruthvaluesofthetwonodesitjoins

Node1

Node2

Φ1,2

TruthValue Weight/Potential Function TruthValue

1(i.e.,true) Φ1,2a=3 1

1 Φ1,2b=5 0(false)

0 Φ1,2c=6 1

0 Φ1,2d=2 0

Canregardthesevaluesaspre-specifiedconstantsgroundedinempiricalpopulation-baseddata.Thesetof4constantsisspecifictoeachedgeinthegraph&canbeupdatedasneededbasedonaccretionof(big)data.

32

Onewaytoexpressφ𝑖𝑗 asafunctionofthetruthvaluesofthenodesitjoins

Node1(x1)

Node2(x2)

Cvalue (Unity) multiplierof CthatyieldsC(i.e.,correspondingΦ value)IFtruthconditionshold(andzerootherwise)

1 1 ca x1x2

1 0 cb x1[(x2+1)mod2]

0 1 cc x2[(x1+1)mod2]

0 0 cd [(x1+1)mod2][(x2+1)mod2]

Thereforeφ1,2 isequalto:

cax1x2 +cbx1[(x2+1)mod2]+ccx2[(x1+1)mod2]+cd[(x1+1)mod2][(x2+1)mod2]33

Finally:TheProblemHamiltonianandtheFruitsThereof(OnceitsGroundStateisKnown)

• Toreiterate,the“objectivefunction”tobeminimizedinordertoobtaintheoptimal(mostprobable)truthvalueassignments forthe“vacantnodes”canbeexpressedas:

∑ 1/*+,- (caxixj +cbxi[(xj+1)mod2]+ccxj[(xi+1)mod2]+cd[(xi+1)mod2][(xj+1)mod2])

• ForthosefamiliarwiththeIsing/Hamiltonianmodelusedinquantumannealing,whichreliesuponqubitspinsinthezaxisthatareelementsof{-1,1},thequadraticequationabovecanbeconvertedtoaHamiltonian/Ising formulation

ThegroundstateoftheproblemHamiltonian,whichisthetargetofquantumannealing,correspondstothestatethatminimizestheenergyfunction.Inotherwords,theeigenvalues(quibit spins)ofthegroundstateHamiltonianencodetheoptimaltruthvalueassignmentsforthepatient’s“unknownnodes.”

34

(NB:Insteadofinverse,insertionofnegativesignbeforesumaboveacceptableandmayimproveprecision)

Theobjectivefunctioncanalsoberepresentedsomewhatdifferently,enablingustoleveragetheQuadraticUnconstrainedBinaryOptimizationforminaD-Wavemachinesimulationtooptimizenodevalues.Weusedadifferentquadraticformtoexpressφ𝒊𝒋 asafunctionofthetruthvaluesofthenodesitjoinsinoursimulationtesting...

a*n1+b*n2+c*n1*n2+dNode1(n1)

Node2(n2)

PolynomialthatyieldsΦ valueIFtruthconditionshold(andzerootherwise)

1 1 a*n1+b*n2+c*n1*n2+d

1 0 a*n1+b*n2+c*n1*n2+dREDUCESTO:a*n1+d

0 1 a*n1+b*n2+c*n1*n2+dREDUCESTO:b*n2+d

0 0 a*n1+b*n2+c*n1*n2+dREDUCESTO:d

Task:Solvefortheconstantsa,b,c,anddtocompletethemappingtothenewquadraticformsofthepossiblepotentialfunctionvalues.ThenoptimizetoidentifystatewithlowestnegativesumofΦ valuesinMarkovnetwork.

(Notethatn1andn2areanalogoustox1 andx2 onslide15.Theprincipleisthesameinthatweexpressthepotential/weightfunctionsintermsofthetruthvaluesandconstants.) 35

Challenge:Whatarethemostlikelytruthvaluesfornodes2,4,5,6,7,9,11,and14?

Node4?DiagnosisC

Node2?DiagnosisB(withno

symptoms)

Node5?DiagnosisD(withno

symptoms)

Node3TRUE

African-Americanmale>65

yearsofage

Node6?5yearrisk

ofCatastrophicEventX>

10%

Node1TRUESingle

NucleotideGeneticVariantX

Node7?Bloodplasma

levelofY>clinicallyrelevantthreshold

Φ5,6

Φ3,7

Φ6,7

Φ2,6

Φ3,4

Φ4,6

Φ2,4

Φ1,2

36

Node8TRUESignsandSymptoms

XYZ

Φ2,8

Node15FALSE

DiagnosisF

Node14 ?High

expressionoftranscript

Xinbiopsy

Node9?Single

NucleotideGeneticVariantY

Node13FALSE

DiagnosisE

Node10TRUE

Exposuretoasbestos

Node11?>75%likelytorespondtoRxA

Node12TRUESingle

NucleotideGeneticVariantZ

Φ14,15

Φ12,14

Φ12,13

Φ12,2Φ11,1

Φ11,12Φ10,11

Φ9,11

Φ9,8

MockPotentialFunctionValuesforChallengeProblemTruthValue

Weight/PotentialFunction

TruthValue

1(i.e.,true)

Φ1,2a=3 1

1 Φ1,2b=5 0(false)

0 Φ1,2c=6 1

0 Φ1,2d=2 0

37

TruthValue


TruthValue

1(i.e.,true)

Φ2,4a=2 1

1 Φ2,4b=7 0(false)

0(false) Φ2,4c=1 1

0 Φ2,4d=2 0TruthValue


TruthValue

1(i.e.,true)

Φ2,6a=7 1

1 Φ2,6b=1 0(false)

0 Φ2,6c=3 1

0 Φ2,6d=1 0

TruthValue


TruthValue

1(i.e.,true)

Φ6,7a=3 1

1 Φ6,7b=2 0(false)

0 Φ6,7c=3 1

0 Φ6,7d=2 0

TruthValue


TruthValue

1(i.e.,true)

Φ3,7a=4 1

1 Φ3,7b=1 0(false)

0 Φ3,7c=2 1

0 Φ3,7d=5 0

TruthValue


TruthValue

1(i.e.,true)

Φ2,8a=1 1

1 Φ2,8b=2 0(false)

0 Φ2,8c=6 1

0 Φ2,8d=2 0

TruthValue


TruthValue

1(i.e.,true)

Φ5,6a=2 1

1 Φ5,6b=4 0(false)

0 Φ5,6c=4 1

0 Φ5,6d=6 0

TruthValue


TruthValue

1(i.e.,true)

Φ4,6a=1 1

1 Φ4,6b=9 0(false)

0 Φ4,6c=3 1

0 Φ4,6d=2 0

TruthValue


TruthValue

1(i.e.,true)

Φ3,4a=3 1

1 Φ3,4b=3 0(false)

0 Φ3,4c=8 1

0 Φ3,4d=2 0

MockPotentialFunctionValuesforChallengeProblemTruthValue


TruthValue

1(i.e.,true)

Φ10,11a=4 1

1 Φ10,11b=9 0(false)

0 Φ10,11c=2 1

0 Φ10,11d=2 0

38

TruthValue


TruthValue

1(i.e.,true)

Φ9,11a=3 1

1 Φ9,11b=3 0(false)

0(false) Φ9,11c=7 1

0 Φ9,11d=2 0TruthValue


TruthValue

1(i.e.,true)

Φ12,2a=7 1

1 Φ12,2b=1 0(false)

0 Φ12,2c=5 1

0 Φ12,2d=2 0

TruthValue


TruthValue

1(i.e.,true)

Φ11,12a=3 1

1 Φ11,12b=8 0(false)

0 Φ11,12c=2 1

0 Φ11,12d=4 0

TruthValue


TruthValue

1(i.e.,true)

Φ11,1a=2 1

1 Φ11,1b=5 0(false)

0 Φ11,1c=2 1

0 Φ11,1d=1 0

TruthValue


TruthValue

1(i.e.,true)

Φ14,15a=1 1

1 Φ14,15b=1 0(false)

0 Φ14,15c=6 1

0 Φ14,15d=3 0

TruthValue


TruthValue

1(i.e.,true)

Φ12,14a=2 1

1 Φ12,14b=4 0(false)

0 Φ12,14c=4 1

0 Φ12,14d=8 0

TruthValue


TruthValue

1(i.e.,true)

Φ12,13a=9 1

1 Φ12,13b=1 0(false)

0 Φ12,13c=3 1

0 Φ12,13d=2 0

TruthValue


TruthValue

1(i.e.,true)

Φ9,8a=5 1

1 Φ9,8b=3 0(false)

0 Φ9,8c=1 1

0 Φ9,8d=8 0

Challenge:Whatarethemostlikelytruthvaluesfornodes2,4,5,6,7,9,11,and14?AnswersinyellowobtainedusingDWavequantumsimulatorandappropriatebiases

Node4‘TRUE

DiagnosisC

Node2FALSE

DiagnosisB(withno

symptoms)

Node5TRUE

DiagnosisD(withno

symptoms)

Node3TRUE

African-Americanmale>65

yearsofage

Node6TRUE5yearriskofCatastrophicEventX>10%

Node1TRUESingle

NucleotideGeneticVariantX

Node7FALSE

BloodplasmalevelofY>clinicallyrelevantthreshold

Φ5,6

Φ3,7

Φ6,7

Φ2,6

Φ3,4

Φ4,6

Φ2,4

Φ1,2

39

Node8TRUESignsandSymptoms

XYZ

Φ2,8

Node15FALSE

DiagnosisF

Node14TRUEHigh

expressionoftranscriptXinbiopsy

Node9FALSESingle

NucleotideGeneticVariantY

Node13FALSE

DiagnosisE

Node10TRUE

Exposuretoasbestos

Node11FALSE

>75%likelytorespondtoRxA

Node12TRUESingle

NucleotideGeneticVariantZ

Φ14,15

Φ12,14

Φ12,13

Φ12,2Φ11,1

Φ11,12Φ10,11

Φ9,11

Φ9,8

Predictedtruthvalueassignmentsfornodeswereconsistentwithresultsofaclassicalsolver.Plantooptimizeimplementationtoharmonizeobjectivefunctionoutputs.Notethattheembeddingforthisproblem

requiredonly21qubits(currentDWavemachinehas~2000qubits)

IsthereaPossibleRoleforQuantumAnnealinginPredictiveHealthAnalytics?NextSteps?

• Yes– theremaybearole.Proofofprincipledemonstratedusingagraphicalmodel,mockdataandquantumsimulation– Potentialfunctionalcapabilityofthisholisticandbroadlypredictiveapproachmaybefavorablydifferentiatedfromothereffortsinthisarea

• NextSteps:–Wehaveidentifiedtwosourcesofclinicaldata– Developingideasregardinggraphicuserinterfaceforclinicians– Preliminarilyexploringpossibleprivatefundingsources

40

Acknowledgements

• MichaelBoothandSteveReinhardt(D-Wave)

41

Back-Up Slides

Machine Learning: What is It?

• Machine learning is a branch of Artificial Intelligence that uses algorithms and models to:o Classify objects and entities based on features. For

example, patient X is likely to have diagnosis Y.o Predict outcomes. The likelihood of 5 year survival

given this patient’s clinical characteristics, tumor genome, etc. is 75% if I use this regimen.

• Many other applications in non-medical areas, but not to be covered today (computer vision, natural language processing, machine translation, robotics, etc.)

Species of Machine Learning

• Supervised Learningo I know what an apple is, but this model does not.o I show the system 10,000 pieces of fruit with many different features.o The system is told when its classification is right and when it is wrong.oWhen it errs, it learns by adjusting, for example, the emphasis it

places on certain discriminative features.

• Unsupervised Learningo The system is not told when its classification is right or wrong; it

looks, for example, for patterns (cluster analysis, e.g.)

• Reinforcement Learning

Focus today

Machine Learning 101: A Few Major Members of the Cast (we Will Meet Each in Turn)

• Feature matrix: Resembles a simple spreadsheet. Features in columns (e.g., clinical findings, labs, imaging results, etc.) and patients in rows. One entry for each feature per patient.

• Target vector (or “labels”): Provides “ground truth answers” that a learning algorithm seeks to predict. One column, with one entry (label) per patient (e.g., a unifying diagnosis).

• Algorithm itself: (logistic regression, Bayesian, random forest, deep neural net, etc.). This is the character who makes predictions: What is the likely answer for patient X based on his/her features?

• Cost or “performance function”: Algorithm is dinged for wrong answers and then modifies itself (e.g., through “weight” adjustments) to improve it’s performance (“optimize” itself).

Typical Flow for Machine Learning Algorithm: Hyper-Simple Overview of “Training” Phase

Localized infiltrate on CXR

Fever ElevatedWBC count . . .

Feature N

Patient 1 Yes Yes Yes No

Patient 2 ...

No Yes No Yes

Patient N Yes No No Yes

Algorithm PredictionPneumonia (Y/N)

Pneumonia (For Real)

Patient 1: Yes

Patient 2: No...

Patient N: No

Right Answers?(Y/N)

Compute Cost(Wrong answers costly)

Optimize algorithm to minimize cost (i.e., increase accuracy)

Feature matrix

Target Vector

Compare

How to Train an Algorithm in Five Steps

• Choose your (potentially predictive) features carefully – more is not necessarily better.

• Assemble a “training set.” This is feature data for a sufficient number of training “examples” (one patient = one example).

• Select your pupil, i.e., the algorithm type (make sure he or she is appropriate given the task you expect him/her to master).

• Decide on a “cost function” which will assess model performance (e.g., predictive prowess) as it evolves during training.

• Settle on an “optimization technique” that will, for example, upwardly adjust the “weights” of features that the model discovers to “really count” in detecting differences.*

*Optimization requires selection of a key “hyperparameter” called “step size.” We will discuss this and another hyperparameter briefly.

You Have just Trained your Pupil (Algorithm). Is it OK to let him Loose in the World?

• Look! I’ve trained an algorithm on 250 medical records, and I can now reliably determine who, in this training set, was at risk for 30-day hospital readmission! Can I roll this out to the clinic?

• Answer: I’m sorry, but “no.”

• Regulatory considerations aside, the objective of training a machine learning algorithm is not perfect performance on a training set, butgood/excellent performance on a training set that can be generalized to other independent data sets on which it has not been trained.

Two Overfitting Examples? Quiz: You tell me.

I have an algorithm that can reliably “tell the difference” between these two applevarieties in a training set mainlybecause all of the Ambrosia apples (on the left) were bruised.

Bayesian Classifiers (concluded)

• Prior expectations, based on expert opinion, can be used to “leaven the loaf” of predictions (based on what we observe) with what we believe to be the case at the outset (our “prior beliefs”).o Pretend we are flipping a coin that we do not believe to be “unfair,” so we think the

probability of heads is 0.5 and the probability of tails is 0.5.

o A simple formula for calculating the probability of heads based on both what has been observed and what we would expect (i.e., 0.5) is provided below, where the parameter “m” can be adjusted to reflect our confidence level:

Pheads = (Observed # heads +m times 0.5)/(# of tosses + m)

“Priors” (i.e., our prior beliefs) can be updated.We can also handle continuous (as opposed to discrete) attributes.

Deep Learning (and Neural Nets): Powerful!

DEPTH

WIDTH

What makes Deep Learning deep?

Hidden layers. Think of each hidden layer as housing a new abstract representation of the input (i.e., feature) data. There can be many layers.

Hierarchical learning architecture.

Geoff Hinton has said it is “quite obvious that we should stop training radiologists.”

(Personally, I don’t think radiologists will be entirely replaced by Deep Learning algorithms within 5-10 years, but there are potential near term uses).

Context

• Given the increasing complexity of medicine/biology, spiraling health care costs, and an emphasis on value-based care, we must use every tool at hand to enhance quality & efficiency when ministering to our patients.

• AI in medicine has arrived and is here to stay. Let’s embrace it and help to ensure it provides us with the support we need.

• Machine learning is a tool that must be fit-to-task. Success depends on both science and art. The right expertise is essential.

• To harness the full power of modern machine learning, we need large, integrated and reconciled, high quality, multidimensional datasets with reliable patient linking

• All stakeholders have an instrument to play: physicians, nurses, NPs, PAs, clinical pharmacists, the supply chain, and C-suites across health care systems, academia, government, payers, and Pharma

The Data “Quilt”

Images Used (classified as free to share and use commercially per Bing)

• https://i.stack.imgur.com/bFu3C.jpghttps://i.stack.imgur.com/lqW7s.png

• https://s.iha.com/5423900019194/Short-term-rentals-Umhausen-Apartment-Isak_19.jpeg

• http://i.stack.imgur.com/yhkx4.jpg

• https://upload.wikimedia.org/wikipedia/commons/4/4a/1937-Wheat-Penny-Front-Back.jpg

• https://i.stack.imgur.com/nSZ7k.png

• http://1.bp.blogspot.com/_u6j9yYGzu0A/TKKDEMkFfoI/AAAAAAAAD9s/aYXBUJHnUTM/s1600/tree.jpg

• https://d3n8a8pro7vhmx.cloudfront.net/sortitionfoundation/pages/194/attachments/original/1505118334/AR-160619960.jpg?1505118334

• http://www.texample.net/media/tikz/examples/PNG/neural-network.png

• https://c.mql5.com/18/20/NN1__1.gif

• https://upload.wikimedia.org/wikipedia/commons/b/be/Australian_Saddle_No_Horn.jpg

• https://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Maxima_and_Minima.svg/325px-Maxima_and_Minima.svg.png

• https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/White_Cliffs_of_Dover_02.JPG/1200px-White_Cliffs_of_Dover_02.JPG

• https://www.med-ed.virginia.edu/courses/rad/cxr/web%20images/rul-pneumonia-pa.jpg

• https://d.ibtimes.co.uk/en/full/1408328/artificial-intelligence-deepmind-google.jpg• http://3.bp.blogspot.com/-qsh_B8vmwjE/VcbZ-HjeeHI/AAAAAAAAQJg/G73rLeS-

mQk/s1600/any-genuine-psychics-out-thereor-are-they-all-just-out-there.jpg• http://www.gooddogspot.net/wp-content/uploads/2015/01/positive-training.jpeg• http://crunchfitness.ie/media/diet.jpg• https://upload.wikimedia.org/wikipedia/commons/thumb/9/96/GillrayBritannia.jpg

/325px-GillrayBritannia.jpg• http://2.bp.blogspot.com/_9GAwD8C7wBw/Sk6cVpyfa5I/AAAAAAAAAfs/TkWenz3poL

o/s320/219229-caduceus01_large.jpg• https://farm6.staticflickr.com/5802/22784647459_ae37c9e23d_c.jpg• http://moldvictim.org/wp-content/uploads/2012/12/doctor-patient-mold-

sickness.jpg• http://www.sumsar.net/images/posts/2013-12-26-the-mascots-of-bayesian-

statistics/bayes.jpeg

Documents

Predictive Health Analytics - D-Wave Systems › sites › default › files › Sahner.2018.pdf · Predictive Health Analytics A Potential Role for Quantum Annealing in the Enhancement