1. Predicting Primary Myocardial Infarction from Electronic Health Records
-Jitong Lou

2. Objective
Myocardial infarctions(MIs), known as heart attacks, are commonly and deadly, causing one in six deaths overall in the U.S. totaling 400,000 per year
Longitudinal methods such as case-control studies, cross-sectional studies, cohort studies, and randomized controlled trials have limitations
Expensive
Provide the risk assessment for just one particular variable
Baseline variables are important to determine risk
Make measurements at fixed points in time
Conduct fewer studies, analyze the effects of many variables, make reliable predictions without the regular checkups and baseline variables.

3. Electronic Health Records(EHRs) Data
EHRs are an emerging relational domain with large potential to improve clinical outcomes
The EHR database consists of tables including patient information such as diagnoses, drugs, labs, and genetic information.

4. Electronic Health Records(EHRs) Data
For example, Framingham Heat Study (FRS) data is recalculated every two years, where one based on the HER would be updated as new clinical event occurs

5. Relational Data
Relational data violate two assumptions of conventional classification techniques.
First, algorithms designed for propositional data assume the data are independent and identically distributed (i.i.d.). Relational data, on the other hand, have dependencies both as a result of direct relations (e.g. a patient is using a certain treatment) and through chaining multiple relations together (e.g. all the records of the same patient).
Second, algorithms for propositional data assume that the data instances are recorded in homogeneous structures (a fixed set of fields for each object), but relational data “instances” are usually more varied and complex. For example, some patients may take 2 kinds of medicine and others may take 10.
A relational classification technique needs to contend with dependent, heterogeneous data instances for both learning and inference.

6. Relational Data
A relational classification model takes collection of subgraphs as input, that is, single target object to be classified and other objects/links in the related neighborhood.
Construct a classifier to predict target class label(MI or not) given:
The attributes(such as cholesterol levels, gender, smoking status, blood pressure, history of alcoholism and valve replacement) of target object
The attributes(such as treatment effect, price) of other objects in neighborhood(cardiac drugs the patient is using)
The degree attributes/summary statistics counting object and neighborhood objects

7. Relational Functional Gradient Boosting(RFGB)
Assume that the training examples are of the form (𝑥 𝑖 , 𝑦 𝑖 ) for 𝑖 = 1, ..., 𝑁 and y i ∈{0,1} where 𝑦 𝑖 = 1 indicates MI and x represents the set of all observations about the current patient 𝑖.
The goal is to fit a model 𝑃 𝑦 𝑥 𝑖 ∝ e Ψ(y,x)
The standard method of supervised learning is based on gradient descent directly on the parameters where the learning algorithm starts with initial parameters and computes the gradient of the likelihood function
The key difference between RFGB and the standard method is that the gradients are computed directly on the functions instead of parameters

8. Relational Functional Gradient Boosting(RFGB)
RFGB starts with an initial potential Ψ 0 and iteratively adds gradients Δ 𝑖 . After 𝑚 iterations, the potential is given by
Ψ 𝑚 = Ψ 0 + Δ 1 +…+ Δ 𝑚
Δ 𝑚 is the functional gradient at iteration 𝑚 and
Δ 𝑚 = 𝜂 𝑚 × 𝐸 𝑥,𝑦 [ 𝜕𝑙𝑜𝑔𝑃 𝑦 𝑥; Ψ 𝑚−1 𝜕Ψ ​ Ψ= Ψ 𝑚−1 ]
The expectation 𝐸 𝑥,𝑦 cannot be computed as the joint distribution 𝑃(𝑥,𝑦) is unknown, so the functional gradient are computed for each training example 𝑖 given as ( 𝑥 𝑖 , 𝑦 𝑖 ). Now this set of local gradients forms a set of training samples for the gradient at iteration 𝑚.
The direction of (relational) regression tree ℎ 𝑚 on the training samples [( 𝑥 𝑖 , 𝑦 𝑖 ), Δ 𝑚 ( 𝑦 𝑖 ; 𝑥 𝑖 )] will approximate the true function gradient
The functional gradient with respect to Ψ 𝑦 𝑖 =1; 𝑥 𝑖 of the likelihood for each example ( 𝑥 𝑖 , 𝑦 𝑖 ) can be shown to be
𝜕𝑙𝑜𝑔𝑃 𝑦 𝑖 ; 𝑥 𝑖 𝜕Ψ( 𝑦 𝑖 =1; 𝑥 𝑖 ) =𝐼 𝑦 𝑖 =1; 𝑥 𝑖 −𝑃( 𝑦 𝑖 =1; 𝑥 𝑖 )

9. Relational Functional Gradient Boosting(RFGB)
𝐹 𝑚 𝑘 : model for predicate 𝑘 at iteration 𝑚
𝑆 𝑘 : training samples for Δ(𝑘)
Δ 𝑚 𝑘 : components of the functional gradient at iteration 𝑚
𝐿: number of leaves in each functional gradient Δ 𝑚 (𝑘)

10. Model Comparisons
The paper compared RFGB models to boosted decision trees (AdaBoostM1 (Ada); default parameters) and RPTs with decision tree learners (J48; C=0.25, M=2).
Other common models were also included: Naive Bayes (NB; default parameters), tree-augmented naive Bayes (TAN; Simple Estimator), support vector machines (SVMs; linear kernel, C=1.0; radial basis function kernel, C=250007, G=0.01), and random forests (RF; 10 trees, default parameters).

11. Results
The best cross-validated predictor of primary MI according to AUC-ROC was the RFGB model
The RPT model did not score as well, ranking in the middle of the propositional learners.
RFGB and RPT models significantly outperformed their direct propositional analogs (Boosted Tree and Tree models, respectively).
The Bayesian model (NB; TAN) scores may be somewhat inflated because only features known to be CHD risk factors were specifically chosen for this analysis.

12. Results
A false negative incurs the costs of untreated human morbidity, and usually expensive, delayed treatments, so models with many false negatives (that is, low recall) cannot be accepted
In the high-recall region, RFGB gives the highest precision.

13. References
Weiss, J. C., Natarajan, S., Peissig, P. L., McCarty, C. A., & Page, D. (2012). Machine learning for personalized medicine: Predicting primary myocardial infarction from electronic health records. AI Magazine, 33(4),
Natarajan, S.; Khot, T.; Kersting, K.; Guttmann, B.; and Shavlik, J. 2011b. Gradient-Based Boosting for Statistical Relational Learning: The Relational Dependency Network Case. Machine Learning 86(1): 25–56.
Neville, J.; Jensen, D.; Friedland, L.; and Hay, M Learning Relational Probability Trees. In Proceedings of the 9th Knowledge Discovery and Data Mining (KDD) Conference. New York: Association for Computing Machinery.

14. Thank you!