Patent Application: US-201414216021-A

Abstract:
the present invention addresses two ubiquitous and pressing problems of modern data analytics technology . many modern pattern recognition technologies produce models with excellent predictivity but they are “ black boxes ”, that is they are opaque to the user ; they are too large , and / or expensive to execute in less powerful computing platforms . the invention “ opens up ” a black box model by converting it to a compact and understandable model that is functionally equivalent . the invention also converts a predictive model into a functionally equivalent model into a form that can be implemented and deployed more easily or efficiently in practice . the benefits include : model understandability and defensibility of modeling . a particularly interesting application is that of understanding the decision making of humans , comparison of the behavior of a human or computerized decision process against another and use to enhance education and guideline compliance / adherence detection and improvement . the invention can be applied to practically any field where predictive modeling is desired because it relies on extremely broad distributional assumptions that are valid in numerous fields .

Description:
1 . learn a model m1 from dataset d . 2 . generate a model b1 of the distribution of input variables in d ( using any method that can model a joint probability distribution ; a prototypical method being state of the art bayesian network induction techniques such as method mmhc [ 6 ] or hiton - bach [ 7 - 9 ]). 3 . generate input patterns from b1 or d using statistical sampling , eg : a . resampling from d with uniform probability with or without replacement ; or b . sample joint patterns of input variables proportionately to the pattern probability ; or c . generate all high probability input patterns and sample over remaining ones proportionately to their probability ; or d . using logic sampling on b1 ( i . e ., uniformly randomly over space of joint input patterns ); or any of a number of sampling methods that are commonly employed in statistics , engineering or pattern recognition to sample from a joint distribution . 4 . create new data d1 that comprises of the generated inputs followed by the corresponding m1 model - estimated outputs . input patterns are instantiations of the variables , and feeding input patterns to m1 produces new outputs . 5 . derive all or multiple markov boundaries ( mb 1 , . . . , mb n ) of the response variable ( eg by application of appropriately instantiated tie * method on d1 ). 6 . from each markov boundary ( i . e ., mb i ), learn a decision tree dt i using standard decision tree induction ( e . g ., using cart , id3 or other decision tree learning method [ 10 , 11 ]). optionally , prune each tree using standard pruning methods . verify and fine tune each decision tree ( i . e ., dt i ) to capture the outputs of m1 within acceptable accuracy e . keep only the markov boundaries that satisfy this condition . 7 . the catalogue of all validated models dt i comprises of the complete final set of equivalent explanations of the function contained in model m1 . the model trained in step 1 is the model that we would like to explain or convert into a more easily understandable format . an example classifier is support vector machine ( svm ) models , but the method can be used with practically all modeling methods . steps 2 and 3 facilitate generation of new data d1 . data can be generated using other procedures besides bayesian networks , which were mentioned as a preferred example method . d1 is created ( step 4 ) on one hand to increase the sample size and on the other hand to provide a more general description of the underlying function that is modeled , beyond the finite set of original training inputs . when the training data is small , however , it may not have enough samples to fully illustrate the underlying function or relationship between the inputs and target variable . in this case , it is not possible to learn a fully representative model . generating new data also provides more examples so that the underlying function can be learned more accurately . step 5 performs feature selection to reduce the dimensionality of the input space for decision tree learning . the markov boundary of a variable is typically a very small subset of the original input variables but is mathematically guaranteed to contain all predictive information about the variable that is contained in the full data . thus the markov boundary compresses the data by feature selection in an optimal manner . tie * is an example of a markov boundary induction method . feature selection can be performed in this step with other suitable feature selection methods , and tie * was used as a preferred example . step 6 produces decision trees that yield similar outputs to those produced by m1 and have similar performance . in step 7 , the decision tree models can be combined to provide an explanation of model m1 . one example method is converting the decision trees to a boolean expression each decision tree leaf represents a path from the root that maps to a distinct boolean expression . for binary trees , the juncture at a tree node represents the presence or absence of a variable . for continuous values , the node represents whether a value is greater than or less than a threshold value . one of the primary benefits of the novel method is that it learns and combines multiple markov boundaries and decision trees so that it does not throw away significant parts of the learnt function . techniques that use a single markov boundary ( or a single selected feature set more broadly ) suffer from this limitation . another benefit of the inventive method is that it probes the learnt model m1 and examines its behavior outside the narrow scope of previously encountered cases . it simulates cases that range from mildly unexpected to greatly unexpected cases relative to the training cases . as a result , it can identify the limits and potential breaking points of the learnt black box model . a final benefit is that we can elect to use all or a subset of induced markov boundaries according to the intended use of the converted model when simplifying or converting the black box model to a simpler model . there are a number of possible variations of the method . a highly simplified version of the method can use the original data without generating new cases . also , learning a single markov boundary can be performed instead of learning multiple markov boundaries . another modification involves performing feature selection before training model m1 so that model training would use the feature subset rather than all features . a simplified instantiation of the general method which has the practical benefits of higher speed and higher implementation simplicity over the full method comprises of the following series of steps : 1 . learn a model m1 from data d . 2 . use a markov boundary induction method to derive a markov boundary of the response variable . 3 . from the markov boundary , learn a decision tree dt using standard decision tree induction on the original data d . optionally , prune the tree using standard pruning methods . verify that the decision tree closely captures the outputs of m1 . 4 . convert the decision tree into the final explanation of the function contained in model m1 . fig1 is an example of a decision tree produced by the new method when applied on data from a biomedical predictive modeling application . the purpose of the predictive modeling was to identify high quality content - specific articles in the domain of internal medicine [ 12 ]. the original set of input features was over 20000 variables . after performing feature selection using a markov boundary induction method , the number of features was reduced to 13 features . a decision tree with 4 features was then learned . fig2 shows performance of the decision tree compared to an svm ( i . e ., the original black box model in this example ). the results show that it is possible to create an explainable model that produces similar outputs to a black box model or classifier . both the original black box svm model and the converted decision tree evaluate articles based on the occurrence of terms in the articles . to understand the decision tree , we start from the top ( root node ) and move to the bottom ( to a leaf node ). the left branch at a node means that a term is absent , and the right branch means that a term is present . in cases where the nodes represent numerical values , the left branch means that a variable is less than a threshold value while the right branch means the variable is greater than or equal to the threshold value . in other words , each path from the root to a leaf node corresponds to a rule that can be applied to a document to classify it . the whole tree is a set of rules that can be collectively used to classify the documents . the leaves indicate the probability of a high quality treatment related document . the leaf can also be a continuous value or classification . fig3 shows application of the method to another biomedical predictive modeling example . in this example , svms were trained to model clinical decision making of dermatologists in diagnosing malignant melanomas . by application of the inventive method the svm black box for each dermatologist is converted to an equivalent decision tree which is easily understood by physicians ( who are very familiar with clinical decision trees by training ). it was verified that decision trees closely captured the outputs of the svms by analyzing the coefficient of determination ( r 2 ) between svm and decision tree output for all physicians . it was very high for all the physician &# 39 ; s decision tree models ( average : 0 . 99 , range [ 0 . 94 , 1 . 00 ]). this decision tree represents the decision making process for an individual dermatologist . in the presented example a dermatologist classifies a lesion as malignant if blue veil and streaks are present . hiton - bach — a state of the art method for learning a causal graph from data ; it combines local causal learning and edge orientation by bach &# 39 ; s scoring function . mmhc ( max - min hill climbing )— a state of the art method for learning a causal graph from data . svm ( support vector machines ): a state of the art method for classification and regression . tie * ( target information equivalency )— a state of the art method for multiple markov boundary discovery from data ; it is also used to find all local causal pathways that are statistically indistinguishable from the data . the relationships , correlations , and significance ( thereof ) discovered by application of the method of this invention may be output as graphic displays ( multidimensional as required ), probability plots , linkage / pathway maps , data tables , and other methods as are well known to those skilled in the art . for instance , the structured data stream of the method &# 39 ; s output can be routed to a number of presentation , data / format conversion , data storage , and analysis devices including but not limited to the following : ( a ) electronic graphical displays such as crt , led , plasma , and lcd screens capable of displaying text and images ; ( b ) printed graphs , maps , plots , and reports produced by printer devices and printer control software ; ( c ) electronic data files stored and manipulated in a general purpose digital computer or other device with data storage and / or processing capabilities ; ( d ) digital or analog network connections capable of transmitting data ; ( e ) electronic databases and file systems . the data output is transmitted or stored after data conversion and formatting steps appropriate for the receiving device have been executed . due to large numbers of data elements in the datasets , which the present invention is designed to analyze , the invention is best practiced by means of a general purpose digital computer with suitable software programming ( i . e ., hardware instruction set ) ( fig4 describes the architecture of modern digital computer systems ). such computer systems are needed to handle the large datasets and to practice the method in realistic time frames . based on the complete disclosure of the method in this patent document , software code to implement the invention may be written by those reasonably skilled in the software programming arts in any one of several standard programming languages including , but not limited to , c , java , and python . in addition , where applicable , appropriate commercially available software programs or routines may be incorporated . the software program may be stored on a computer readable medium and implemented on a single computer system or across a network of parallel or distributed computers linked to work as one . to implement parts of the software code , the inventors have used mathworks matlab ® and a personal computer with an intel xeon cpu 2 . 4 ghz with 24 gb of ram and 2 tb hard disk . 1 . davenport t h , harris j g : competing on analytics : the new science of winning : harvard 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