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Visual Tools for explaining Machine Learning Models

Leonardo Auslender, profile picture
Leonardo Auslender

The presentation discusses visual tools for interpreting statistical and data science models, focusing on partial dependency plots and their variants to aid model interpretation. It emphasizes the objectives of interpretation, like identifying important attributes and understanding model errors, while introducing novel visual concepts derived from these plots. The document serves as a guide for those with some insight into model creation and aims to clarify the complexities of model interpretation in practical terms.

Data & Analytics
Related topics:
Data Science Insights • Logistic Regression
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Visual Tools for explaining Machine Learning Models
Abstract Statistical and data science models are considered to be, somewhat pejoratively, black-boxes, interpretation of which has not been systematically studied. Molnar’s “Interpretable Machine Learning” is a big effort in finding solutions. Our presentation is humbler. We aim at presenting visual tools for model interpretation based on partial dependency plots and their variants, such as collapsed PDPs created by the presenter, some of which may be polemical and debatable. The audience should be versed in models creation, and at least some insight into partial dependency plots. The presentation will be based on a simple working example with 6 predictors and one binary target variable for ease of exposition. Not possible to detail exhaustively every method described in this presentation. Extensive document in preparation. Presentation requires 3 hours and wide awake audience. Double if not awake. Slides Marked **** can be skipped for easier first reading.
Visual Tools for explaining Machine Learning Models
Overall comments and introduction. Presentation by way of example focusing on Fraud/Default Data sets and continuing previous chapters. Aim: study interpretation/diagnosis mostly via Partial Dependency Plots of logistic regression, Classification Trees and Regression Boosting. Presentation available at https://www.slideshare.net/LeonardoAuslender/visual- tools-for-interpretation-of-machine-learning-models At present, lots of written opinions and distinctions about topic. No time to discuss them all. See Molnar’s (2018) recent book for an overall view.
Overall comments and introduction (cont 1). No discussion about imbalanced data set modeling or other modeling issues. No discussion on literature, all due to time constraints. This presentation introduces novel visual concepts as well as tools derived from Partial Dependency Plots (PDP): -Overall PDP -Collapsed PDP -Marginal PDP and how they assist in model interpretation.
Objectives of Interpretation. Why does the model make mistakes (large residuals, outliers, etc.)? Which attributes (alone / group) end up being important? Why is this attribute/s not important? Why is this observation predicted with high probability score? However, immediate aim is NOT explanations at observation level (why predicted sick/churner/innocent…) but
Objectives of Interpretation (cont. 1) Why not directly at observation level? Suppose model to predict entertainment type preference for database of families in large cities. Since not possible to obtain updated family preferences consistently, since data is ‘soft’, models necessarily are not created at specific family levels. Contrariwise, disease diagnostic prediction is closer to individual explanation and interpretablity.
Visual Tools for explaining Machine Learning Models
Model Interpretation categorization. Just as in EDA (but on model results, not on initial data), three types: Univariate Model Interpretation (UMI): One variable at a type. EASIEST to understand and huge source of “makes sense”. E.g., Classical linear models interpretations. E.g., reasons to decline a loan. Bivariate Model Interpretation (BMI): Looking at pairs of variables to interpret model results. Multivariate Model Interpreation (MMI): Overall model interpretation, most difficult. Typically, most work results in UMI and perhaps BMI.
Visual Tools for explaining Machine Learning Models
Days of Linear Regression Interpretation *** Based on “ceteris paribus” assumption that fails In case of Even relatively small VIFs. At present, rule of thumb VIF >= 10 (R-sq = .90 among predictors)  unstable model. “Ceteris paribus” exercise: Keeping all other predictors Constant, an increase in …. But if R-sq among predictors is Even 10%, not possible to keep all predictors constant while Increasing by 1 the variable of interest. Advantages: EASY to conceptualize because practice Follows notion of bivariate correlation. But notion is generally wrong in multivariate case..
Corr (X,Y) = if SD(Y) = SD(X). E.g., if both Standardized, otherwise same sign at least, and interpretation from correlation holds in simple regression case. Notice that regression of X on Y is NOT inverse of regression of Y on X because of SD(X) and SD(Y). / Confusion on signs of coefficients and interpretation. ( ) ˆ { ( ) } ˆ( ) ( )yi xy xy xi xy Y X sY Y r r sX X sg r sg                2 1 2 2
13 2019-06-14 In multiple linear regression, previous relationship does not hold because predictors can be correlated (rxz) weighted by ryz, hinting at co-linearity and/or relationships of supression/enhancement  . . . 2 2 But in multivariate, e.g.: , estimated equation (emphasizing "partial") and for example: ˆ ˆ ˆ , ˆ 1 ˆ( ) ( ) ( ) ( ) and 1 YX Z YZ X Y YX YZ XZ YX Z X XZ YX YX YZ XZ XZ Y X Z Y a X Z s r r r s r sg sg r abs r abs r r r                        
Comment on Linear Model Interpretation Even in traditional UMI land, we find that multivariate relations given by Partial- and semi- partial correlations must be part of the interpretation. Note that while correlation is a bivariate relationship, partial and semipartial corrs can be extended to multivariate setting. However, even BMI and certainly MMI not so often performed.
Visual Tools for explaining Machine Learning Models
Searching for Important variables en route to answering modeling question. Case study: minimum components to make a car go along highway. 1) Engine 2) Tires 3) Steering wheel 4) Transmission 5) Gas 6) ….. Other MMI aspects and interrelations. Take just one of them out, and the car won’t drive. There is no SINGLE most important variable but a minimum irreducible set of them. In Data Science case with n  ∞, possibly many subsets of ‘important’ variables. But “suspect VARS” good starting point of research.
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
Model Name Item Information M2 TRN DATA set train . TRN num obs 3595 VAL DATA set validata . VAL num obs 2365 TST DATA set . TST num obs 0 Dep. Var fraud TRN % Events 20.389 VAL % Events 19.281 TST % Events
Original Vars + Labels Model Name M2 Variable Label ** DOCTOR_VISITS Total visits to a doctor MEMBER_DURATION Membership duration ** NO_CLAIMS No of claims made recently ** NUM_MEMBERS Number of members covered ** OPTOM_PRESC Number of opticals claimed ** TOTAL_SPEND Total spent on opticals **
Requested Models: Names & Descriptions. Full Model Name Model Description Overall Models M2 20 pct prior M2_BY_DEPVAR Inference 01_M2_GB_TRN_TREES Tree Repr. for Gradient Boosting 02_M2_TRN_GRAD_BOOSTING Gradient Boosting 03_M2_TRN_LOGISTIC_STEPWISE Logistic TRN STEPWISE 04_M2_VAL_GRAD_BOOSTING Gradient Boosting 05_M2_VAL_LOGISTIC_STEPWISE Logistic VAL STEPWISE
— 22 — Data set: Definition by way of Example • Health insurance company: Ophtamologic Insurance Claims • Is claim valid or fraudulent? Binary target. • No transformations created to have simple data set. • Full description and analysis of this data set in https://www.slideshare.net/LeonardoAuslender (lectures at Principal Analytics Prep).
Ch. 1.1-23 Alphabetic List of Variables and Attributes # Variable Type Len Format Informa t Label 3 DOCTOR_VISITS Num 8 BEST12 . F12. Total visits to a doctor 1 FRAUD Num 8 BEST12 . F12. Fraudulent Activity yes/no 5 MEMBER_DURAT ION Num 8 Membership duration 4 NO_CLAIMS Num 8 BEST12 . F12. No of claims made recently 7 NUM_MEMBERS Num 8 Number of members covered 6 OPTOM_PRESC Num 8 BEST12 . F12. Number of opticals claimed 2 TOTAL_SPEND Num 8 BEST12 . F12. Total spent on opticals Note: No nominal predictors. No transformations to keep presentation simple but not simpler than necessary
.... Reporting area for all Model.s coefficients Importance, etc. and Selected Variables.
Vars * Models * Coeffs Model Name M2_TRN_GRAD_BO OSTING M2_TRN_LOGIS TIC_STEPWISE M2_VAL_GRAD_BO OSTING M2_VAL_LOGISTIC_S TEPWISE Coeff / Importanc e PVal / Nrules Coeff / Import ance PVal / Nrules Coeff / Importa nce PVal / Nrules Coeff / Importan ce PVal / Nrules Variable 0.1099 2.000 0.1099 2.000 NUM_MEMBERS OPTOM_PRESC 0.6211 19.000 0.2178 0.000 0.6211 19.000 0.1463 0.000 DOCTOR_VISITS 0.4434 20.000 - 0.0171 0.020 0.4434 20.000 -0.0065 0.428 MEMBER_DURATION 0.7843 41.000 - 0.0066 0.000 0.7843 41.000 -0.0065 0.000 TOTAL_SPEND 0.6864 29.000 - 0.0000 0.003 0.6864 29.000 -0.0000 0.004 NO_CLAIMS 1.0000 19.000 0.7752 0.000 1.0000 19.000 0.7610 0.000 INTERCEPT - 0.5767 0.000 -0.5635 0.001 Note: Importance and coefficients share one column as well as p-values and number of rules.
Logistic Selection Steps Model Name M2_TRN _LOGIST IC_STEP WISE # in mo del P- val ue Step Effect Entered Effect Removed 1 .00 1 no_claims 2 member_duration 2 .00 3 optom_presc 3 .00 4 total_spend 4 .00 5 doctor_visits 5 .02 Dropped Num_members.
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
Some conclusions and comments so far: . Logistic stepwise dropped Num_members that is shown with lowest relative importance in GB. Notice that Logistic Regression does not have agreed-upon scale of importance. We can use odds-ratios, e.g. . NO_CLAIMS is deemed most important single variable for GB, but logistic deems OPTOM_PRESC as the second one (via odds ratios), while GB selected MEMBER_DURATION. . Remaining variables have odds ratios of 1 which seem to indicate similar effect, while GB distinguishes relative importance after first two variables.
Visual Tools for explaining Machine Learning Models
Definite monotonic relationship, higher values of NO_CLAIMS (e.g., bin 5) associated with higher probability. Note differences between LG and BG.
More diffuse relationship.
GB monotonic decrease for OPTOM_PRESC, diffuse for TOTAL_SPEND.
Visual Tools for explaining Machine Learning Models
Mg: Effect: Change in Prob as X changes.
LG does not have measure of importance, as GB does  we use marginal effects plots that indicate change in probability along variable range. Except for MEMBER_DURATION (that declines initially), other effects have positive effect of different intensity and max value declines as per logistic shape. Member duration has pronounced decline for low duration levels,  possibility of fraudulent members who join, commit their fraud and leave. Note sharper increase in prob. for NO_CLAIMS at bins 1 and 8. Optom_presc at 6. GB Importance measures impact of individual inputs on predicting Y, but don’t tell how impact changes along range of inputs and individual variable effects are not in consideration  Use Partial Dependency Plots, also for LG in free ride.
Marginal Effects and PDPs Marginal effects refer to change in probability with one unit change in X, ceteris paribus (if meaningful or at least desirable). PDPs do not indicate change in Y at all; instead, PDP measures probability levels at different values of X1 measuring all other predictors at their means (or modes, medians, etc.).  No Marginality in PDPs, unless we measured ‘change’ in probability as well. Shown later on, called Marginal PDPs.
Visual Tools for explaining Machine Learning Models
Tree representation(s) up to 4 levels Model M2_GB_TRN_TREES Requested Tree Models: Names & Descriptions. Pred Level 1 + Prob. Level 2 + Prob. Level 3 + Prob. Level 4 + Prob. 0.464 no_claims < 2.5 ( 0.185 ) no_claims < 0.5 ( 0.159 ) member_duration < 180.5 ( 0.199 ) total_spend < 5250 ( 0.464 ) total_spend >= 5250 ( 0.186 ) 0.186 member_duration >= 180.5 ( 0.103 ) doctor_visits >= 5.5 ( 0.093 ) 0.093 doctor_visits < 5.5 ( 0.126 ) 0.126 no_claims >= 0.5 ( 0.321 ) optom_presc < 3.5 ( 0.291 ) total_spend >= 6300 ( 0.273 ) 0.273 total_spend < 6300 ( 0.467 ) 0.467 optom_presc >= 3.5 ( 0.59 ) member_duration < 154.5 ( 0.67 ) 0.670 member_duration >= 154.5 ( 0.447 ) 0.447 no_claims >= 2.5 ( 0.633 ) no_claims < 4.5 ( 0.57 ) optom_presc < 3.5 ( 0.54 ) member_duration >= 128.5 ( 0.498 ) 0.498 member_duration < 128.5 ( 0.627 ) 0.627 optom_presc >= 3.5 ( 0.81 ) member_duration >= 137 ( 0.785 ) 0.785 member_duration < 137 ( 0.85 ) 0.850 no_claims >= 4.5 ( 0.761 ) member_duration < 303.5 ( 0.778 ) member_duration >= 148 ( 0.757 ) 0.757 member_duration < 148 ( 0.823 ) 0.823Missing one line.
Tree representation(s) up to 4 levels Model M2_LG_TRN_TREES Requested Tree Models: Names & Descriptions. Pred Level 1 + Prob. Level 2 + Prob. Level 3 + Prob. Level 4 + Prob. 0.195no_claims < 1.5 ( 0.164 ) member_duration < 155.5 ( 0.235 ) optom_presc < 3.5 ( 0.213 ) no_claims < 0.5 ( 0.195 ) no_claims >= 0.5 ( 0.337 ) 0.337 optom_presc >= 3.5 ( 0.49 ) optom_presc < 6.5 ( 0.404 ) 0.404 optom_presc >= 6.5 ( 0.647 ) 0.647 member_duration >= 155.5 ( 0.111 ) optom_presc < 3.5 ( 0.103 ) member_duration >= 246.5 ( 0.065 ) 0.065 member_duration < 246.5 ( 0.122 ) 0.122 optom_presc >= 3.5 ( 0.235 ) no_claims >= 0.5 ( 0.353 ) 0.353 no_claims < 0.5 ( 0.213 ) 0.213 no_claims >= 1.5 ( 0.61 ) no_claims < 2.5 ( 0.451 ) member_duration < 155.5 ( 0.562 ) optom_presc >= 1.5 ( 0.651 ) 0.651 optom_presc < 1.5 ( 0.493 ) 0.493 member_duration >= 155.5 ( 0.353 ) member_duration >= 237 ( 0.204 ) 0.204 member_duration < 237 ( 0.39 ) 0.390 no_claims >= 2.5 ( 0.748 ) no_claims < 4.5 ( 0.675 ) member_duration >= 236.5 ( 0.477 ) 0.477 member_duration < 236.5 ( 0.721 ) 0.721 no_claims >= 4.5 ( 0.899 ) member_duration >= 272 ( 0.741 ) 0.741 Missing one line.
Comment on Tree Representations LG starts by splitting on NO_CLAIMS at 2, while GB splits at 3. Predictions for first level across 2 models are similar ( .185 ; .633) for GB vs. (.164, .61) for LG, which indicates that structures identified so far are similar so far (UMI interpr.) While in 2nd level, GB only splits on NO_CLAIMS, LG splits on MEMBER_DURATION for suspected non-fraudsters in the first stage and on NO_CLAIMS for the fraudster suspects (BMI already different). Predictions are similar only for the 4th node in level 2 (.748 and .761) but different otherwise. The careful reader may verify that these two predictions emerge by splitting on NO_CLAIMS albeit at different values, which supports the notion of No_claims being the leading clue in our research.
Visual Tools for explaining Machine Learning Models
bù shì deMaybe?.
Comment on Tree Representations (cont.1) NO_CLAIMS not so heavily used after 2nd level however, and the structures of the models are clearly different. GB does not use it at all, while LG splits at 4.5 to produce the highest prediction level of .899. While GB did split initially on No_claims 2.5 and then on 4.5, it did not reach the same level of prediction as LG that started splitting at 1.5. By going to the marginal effects plot, we can see that No_claims has the largest slope for low values, but member_duration has the highest for highest value of the variable. But no similar plots can be created for GB. Thus, found structures and consequent interpretations differ and there is no isomorphism from one into the other. Perhaps fractal approximation?
Visual Tools for explaining Machine Learning Models
2nd most “important variable”, very different structures.
1st most “important” variable, very different structures.
Visual Tools for explaining Machine Learning Models
Both probs increasing as No_claims increases except for GB between 14 and 17. GB > LG up to NO_CLAIMS = 3, later reverse. Notice increasing difference in prob. after No_CLAIMS = 5.
Different binned residual results by model and by variables. Notice LG better fit except between bins 11 through 17.
Overall declining relation except for area around bin 15. Notice no consistent Higher levels of prob. of either model, contrary to two previous slides.
Both models fit relatively poorly for large values of Member_Duration.
Similar gulf in probabilities and severe divergence between 11 and 13. GB makes more extreme jumps.
Similar behavior as that of Member_Duration.
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
Strict interpretations: different. Obvious similarities: e.g., high values of NO_CLAIMS related to high Probability Values mostly. INTERESTING: curves not fully monotonically increasing or decreasing. Residual plots show that there are patterns not well fitted.
.... Ranking the models by GOF. Strongly summarized area for brevity sake, added just for completion.
GOF ranks GOF measure rank AUR OC Avg Squa re Error Class Rate Cum Lift 3rd bin Cum Resp Rate 3rd Gini Preci sion Rate Rsqu are Cram er Tjur Ran k Ran k Ran k Ran k Ran k Ran k Ran k Ran k Unw . Mea n Unw . Medi an Model Name 1 1 2 1 1 1 1 1 1.13 1 02_M2_TRN_GRAD_BOOST ING 03_M2_TRN_LOGISTIC_ST EPWISE 2 2 1 2 2 2 2 2 1.88 2 GOF ranks GOF measure rank AUR OC Avg Squa re Error Class Rate Cum Lift 3rd bin Cum Resp Rate 3rd Gini Preci sion Rate Rsqu are Cram er Tjur Rank Rank Rank Rank Rank Rank Rank Rank Unw. Mean Unw. Medi an Model Name 1 1 2 1 1 1 1 1 1.13 1 04_M2_VAL_GRAD_BOOS TING 05_M2_VAL_LOGISTIC_S TEPWISE 2 2 1 2 2 2 2 2 1.88 2
.... Profile and Model Interpretation Area. .... Univariate Profile diagnostics for 6 Important Vars.
.... Event Proportions and Posterior Probabilites for 5 Important Vars. by original Model Names. Variables and probabilities binned for ease of visualization. Proportion events same across models (it’s just original data), but probabilities differ across models. Not all cases shown.
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
Etc for the other variables.
Some observations Binned No_claims: While similar in shape, GradBoost seriously underestimates proportion of events throughout, while logistic has the problem for bins 2, 3, 5, 6, 7. Logistic has a positive slope, while GB flattens due to interactive GB model. Up to bin 7, similar behavior for GB and LG, and then LG jumps to higher level of probability. Binned Member_Duration: Probability distributions are similar but not identical. For bins 1, 2, 3 and 16 methods underestimate proportion of events. Slightly declining slope for both models. Binned OPTOM_PRESC: Both methods failed to match proportion of events in the mid range of the bins. Sudden positive upshift in positive slope for GB starting at bin 15, while overall flat but positive slope for Logistic.
.... Rescaled Variables along binned Posterior Probability.
Interpretation: In bin 5, No_claims reaches overall max (100), while for bin 1 max is around 35 and 15 in 0-100 scale for respective models. Same interpretation for Q3, etc.
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
And Conversely ….. (GB = Tree repr. Of Grad_boosting …)
Visual Tools for explaining Machine Learning Models
.... Partial Dependency Plots and variants for Non Ensemble Models. Some variables may be dropped due to computer resources.
Note the narrow range of GB PDPs compared to those of LG due to GB interactive nature  more difficult to interpret.
Visual Tools for explaining Machine Learning Models
Marginal (1) PDP comparative notes (Marginal (1): one var at a time. Could also marginalize two vars at a time, not done in this presentation). BG marginals are rather flat, except for MEMBER_DURATION, of which caveat later on. LG is juicier, NO_CLAIMS increase of probability declines along range, but OPTOM_PRESC increases, which seems to indicate that leading reason would be prescriptions and not overall claims. Corresponding marginals for logistic end up with slowing down of growh due to logistic shape. BG is not constrained in that way.
PDP comparative notes Overall PDP is Model probability when all predictors are at their means. For LG, it’s about .17, while GB is .53. Individual PDPs (by def.) are deviations from Overall when var of interest measured along its range, while others remain at mean values. GB clumps most PDPs around Overall, LG clearly distinct values instead. Highest probability level for GB is around .7 while LG reaches 1, and minima are around .6 and 0 respectively. Note LG monotonicity while GB is mostly monotonic (except for Doctor_visits), possibly product of data set created artificially. In both cases, NO_CLAIMS appears as leading variable, especially in LG but while Member_duration is rather flat in GB, it certainly declines steadily in LG, with a very different interpretation. Longer member duration implies steadier customer and familiarity. No_members had been excluded in LG’s stepwise and should not be confused with MEMBER_DURATION.
.... Now, mix All previous Probability and PDPs Together.
Visual Tools for explaining Machine Learning Models
Member_duration alone brags too much.
Visual Tools for explaining Machine Learning Models
UMI: Univariate Model Interpretation. From preceding pages, we can conclude that: No_claims: positively associated with increased fraud, for both logistic and grad, but far steeper slope in Logistic. Grad_b stays in narrow band of probabilty and more interactive with other predictors  Grad_b requires more BMI and MMI. GB’s PDP overshoots posterior probability  other vars bring down this effect in GB. Member_duration has a U shape relationship, especially in Logistic case, while GB has a more spiky one. Note the high spike at duration minimal and immediate decline which seems to indicate members that committed fraud as soon as they joined and left immediately.
UMI: Univariate Model Interpretation (cont. 1) PDP view: logistic shows positive effects of NO_CLAIMS and OPTOM_PRESC, balanced by negative effects of remaining variables. Comparing posterior probability with No_claims PDP, they are almost the same for Logistic. Similarly for MEMBER_DURATION. Grad_b instead shows more tepid effects of same variables, and almost unchanging effects of remaining predictors. Comparing PDP with probability, other predictors bring down PDP of No_claims. Similar effects for MEMBER_DURATION.
.... PDPs for "Pairs of Variables" Note: 3d plots tend to interpolate areas of no data producing false expectations of results. Thus, sometimes 3d charts preferable to plots. Not all Pairs of variables available due to computer resources.
Same for LG. Note correlations (No_claims) with other variables are relative small when compared to the pair Member_duration – Doctor_visits and Member_duration - optom_presc. How will this translate in PDPs for 2 variables at a time?
M_: 'M2_TRN_LOGISTIC_STEPWISE' 'ORIGINAL' PDP Corr '-0.02542' LG High levels of NO_CLAIMS have high probability for lowest level of total_spend which probably denotes one time fraud. Otherwise, even mid levels of NO_CLAIMS associated with high probability for any level of TOTAL_SPEND. It seems that FRAUD is not necessarily linked to TOTAL_SPEND alone.
BINNED ORIGINAL PDP M2_TRN_GRAD_BOOSTING Corr ' 0.05073' NO_CLAIMS DOCTOR_VISITS Combination of No_claims & Doctor_visits shows high probability at NE corner and middle section stable high prob. level. Too many charts to show but necessary for full interpretation.
BINNED ORIGINAL PDP M2_TRN_GRAD_BOOSTING Corr ' 0.02549' NO_CLAIMS MEMBER_DURATION About NO_CLAIMS and MEMBER_DURATION, fraud happens for low level of duration, after which fraudsters leave.
M_: 'M2_TRN_GRAD_BOOSTING' 'ORIGINAL' PDP Corr ' 0.06580' Prob. growth for low NO_CLAIMS and OPTOM_PRESC increase (not at dramatic as in LG), and then slow and steady prob. growth with increases in both vars.
BINNED ORIGINAL PDP M2_TRN_LOGISTIC_STEPWISE Corr ' 0.06580' NO_CLAIMS OPTOM_PRESC Steep prob. growth for low NO_CLAIMS and OPTOM_PRESC increase, similar but not so pronounced growth for small OPTOM_PRESC and increasing NO_CLAIMS.
BINNED ORIGINAL PDP M2_TRN_GRAD_BOOSTING Corr '-0.10759' MEMBER_DURATION OPTOM_PRESC About the pair Optom_presc and Member_duration for which we have contrasting Pair PDPs, with corr = -0.10, interpretation is very different. While GB shows flat probabilities throughout, except in NE empty corner, logistic shows more extreme NE corner, plus declining probabilities from NW top.
BINNED ORIGINAL PDP M2_TRN_LOGISTIC_STEPWISE Corr '-0.10759' MEMBER_DURATION OPTOM_PRESC
M_: 'M2_TRN_GRAD_BOOSTING' 'ORIGINAL' PDP Corr '-0.02542' Rather flat relationship in GB, but steeper in LG (next slide)
M_: 'M2_TRN_LOGISTIC_STEPWISE' 'ORIGINAL' PDP Corr '-0.02542'
Some BMI comments Previous charts suggest that one type of fraud happens once for low levels of duration. Different types of fraud are linked with Prescriptions and Claims. For low levels of claims, increasing prescriptions leads to fraud, as well as a combination of increasing claims and prescriptions combined. So it is possible that there are at least 3 types of Fraud being committed. Other pair combinations were not interesting and rather flat surfaces.
For 2 dimensional visualization, collapse 3d chart by averaging levels of variable 2 into those of variable 1 and compare to original PDP. Original and collapsed PDPs (CPDPs) are derived from posterior model probabilities.
No room for TOTAL_SPEND
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
Comments for BMI. In case of NO_CLAIMS, all cases show overlapping of collapsed and Original, except for OPTOM_PRESC. In GB case, DURATION brings down probability slightly because duration is itself strong predictor. LG shows that presence of OPTOM_PRESC raises posterior probability, not so accentuated in GB. LG model could benefit of NO_CLAIMS and OPTOM_PRESC interaction or possibly overall transformation by way of obtaining information per month and per number of members. (LG chart with TOTAL_SPEND omitted for space brevity). MEMBER_DURATION shows overlap with all second variables, plus declining slope, more evident in LG models.
Comments for BMI (cont). It is possible to obtain 3-way and higher PDPs, and also collapse them, not tried here. Given overlap between Original and CPDP, UMI effects are correct so far, except possibly for triplet NO_CLAIMS, MEMBER_DURATION and OPTOM_PRESC.
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
Visual Tools for explaining Machine Learning Models
Collapsed Triad and Tetrad PDPs. In like manner as 3d PDPs, possible to obtain PDPs for 3 or more variables but not possible to graph (at least, not yet). Collapsed Triads bypasses problems by obtaining PDP of specific three variable set (triads). And Tetrads, for 4 variable sets. While it is possible to collapse two of them and present average PDP compared to univariate PDPs, bivariate and original probability, also possible to collapse Mean PDP but along 4 quartile ranges of the third variable (in TRIAD case) or fourth variable (in TETRAD case) (we bypass the quartile presentation for brevity). In addition to mean PDPs, we also include max and min PDPs as an overlay to provide view of probability variation. Still working on improving these presentations.
Original probability not truly represented well by any combination of PDPs in GB case. GB searches solution over residuals, not fully represented hereby.
Minor differences when compared to previous TRIAD.
Original probability represented very well with 3 variables
Minor differences between triads and tetrad representations.
.... MMI PDPs in Difference form
Same as previous slide but in difference form.
Residual – iterative GB nature shows that just 3 variable do not capture full Interpretation since Posterior probability remains below and above most of data points.
Same as previous slide in difference form.
Comment on Triads and Tetrads For present data set and choice of represented variables, there was not much difference between TRIADS and TETRADS, which means that omission of the fourth variable does not alter our results by much. Still we emphasize that it is quite illusory to merely concentrate on average values. The graphs also contain max and min values of probability that show the high variability except for large values of NO_CLAIMS. This is clear since the event rate was %20 and concentrated on high values of that variable.
Visual Tools for explaining Machine Learning Models
Lowest prob level represented by lowest levels of predictors, except for member duration.
Highest prob levels determined by mid-levels of No_claims and higher total spend than in bin 1..
Conclusions on multivariate distribution of predictors along Prob. bins. Since event rate is %20, good model should clump those observations in higher prob. bins. In lowest bin, predictors bins are typically lowest ones, except for member_duration. Again, this seems to indicate presence of fraudsters with short duration that leave immediately, as evinced in bin 5 of probability slide. In this one, most predictors have observations from higher bins. Other probability bins not listed for brevity sake.
Visual Tools for explaining Machine Learning Models
Similar coeffs among logistic , GB and beta regressions. By Beta Regression, standard interpretation of log odds is possible, with caveats. Vars * Models * Coeffs Model Name M2_TRN_ GRAD_BO OSTING M2_TRN_ GRAD_BO OSTING_ BETA_RE G M2_TRN_ LOGISTIC _STEPWI SE M2_TRN_ LOGISTIC _STEPWI SE_BETA_ REG M2_VAL_ GRAD_BO OSTING M2_VAL_ LOGISTIC _STEPWI SE Coeff / Importan ce Coeff / Importan ce Coeff / Importan ce Coeff / Importan ce Coeff / Importan ce Coeff / Importan ce Variable 0.7318 -0.0051 -0.0057 -0.0057 0.7318 -0.0084 MEMBER_DURATIO N DOCTOR_VISITS 0.3925 -0.0061 0.3925 TOTAL_SPEND 0.6610 -0.0000 -0.0000 -0.0000 0.6610 -0.0000 OPTOM_PRESC 0.5944 0.1713 0.2132 0.2132 0.5944 0.1634 NO_CLAIMS 1.0000 0.7027 0.7921 0.7921 1.0000 0.7351 SCALE 21.8895 2.590291 516E16 INTERCEPT -0.7979 -0.8352 -0.8352 -0.3111
Beta Regression results Results of analyzing posterior probabilities (i.e., original GB and LG posteriors) via BETA regression show very similar coefficients and structures  Beta is reassuring but not providing additional information.
Visual Tools for explaining Machine Learning Models
Possible to say that … 1) Manipulate just NO_CLAIMS and problem solved? 2) Maybe add MEMBER_DURATION and OPTOM_PRESC for parts of NO_CLAIMS range? 3) Maybe add if-then rules from simplified TREE_REPRESENTATION because easier than GB and more interactive than LG? 4) If using Neural Network, and NN derivatives abandon all hope of interpretation? 5)  Interpretation needs definition of INTENDED AUDIENCE (see Tolstoy ut supra).
Possible to say that … (cont. 1) 1) The analyst needs to focus on NO_CLAIMS, MEMBER_DURATION and OPTOM_PRESC as an ‘IMPORTANT’ group. 2) Different model Interpretations should be entertained. 3) Different marginal effects must be explained.
Final thoughts … MI analysis must proceed further for large number of predictors obtaining insights from collapsing 3+ way PDPs for instance. If preferred ‘easier’ linear model explanation, beta regression on posterior probability would provide regression like information. Still, beta regression is not straightforward and model selection is big issue.
Visual Tools for explaining Machine Learning Models
Ch. 1.1-127 2019-06-14 Future steps Focus on MMI 1) Beta regression for ‘linear’ interpretation. More difficult because it requires model search as well. Plus, additional error in modeling posterior probability of original model. 2) Andrews’ curves.
Visual Tools for explaining Machine Learning Models
Lime: Local Interpretable Model-Agnostic Explanations: Uses surrogate interpretable model on black-box model, applied to observations of interest. Tree representation in this presentation similar to this. (https://homes.cs.washington.edu/~marcotcr/blog/lime/) ICE: Clusters or classification variable applied to PDP results. For given predictor, ICE plots draw one line per obs., representing how instance’s prediction changes when predictor changes. Shap Values: Shapley Additive Explanation (Lundberg et al, 2017): Measures +/- feature contribution to prob. Technique used in game theory to determine each player’s contribution to success in a game. Affected by corrs among predictors  focusing just on one predictor to change behavior may change other predictors as well (available in Python). AND OTHERS ….
References Lundberg SM, Lee SI (2017), “Consistent feature attribution for tree ensembles”, presented at the 2017 ICML Workshop on Human Interpretability in Machine Learning (WHI 2017), Sydney, NSW, Australia (https://arxiv.org/abs/1706.06060) Molnar C. (2018): Interpretable Machine Learning, A guide for making black box models explainable, https://christophm.github.io/interpretable-ml-book/ Tolstoy Leo: “The Kingdom of God Is Within You”, (1894)
Visual Tools for explaining Machine Learning Models

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Visual Tools for explaining Machine Learning Models

  • 2. Abstract Statistical and data science models are considered to be, somewhat pejoratively, black-boxes, interpretation of which has not been systematically studied. Molnar’s “Interpretable Machine Learning” is a big effort in finding solutions. Our presentation is humbler. We aim at presenting visual tools for model interpretation based on partial dependency plots and their variants, such as collapsed PDPs created by the presenter, some of which may be polemical and debatable. The audience should be versed in models creation, and at least some insight into partial dependency plots. The presentation will be based on a simple working example with 6 predictors and one binary target variable for ease of exposition. Not possible to detail exhaustively every method described in this presentation. Extensive document in preparation. Presentation requires 3 hours and wide awake audience. Double if not awake. Slides Marked **** can be skipped for easier first reading.
  • 4. Overall comments and introduction. Presentation by way of example focusing on Fraud/Default Data sets and continuing previous chapters. Aim: study interpretation/diagnosis mostly via Partial Dependency Plots of logistic regression, Classification Trees and Regression Boosting. Presentation available at https://www.slideshare.net/LeonardoAuslender/visual- tools-for-interpretation-of-machine-learning-models At present, lots of written opinions and distinctions about topic. No time to discuss them all. See Molnar’s (2018) recent book for an overall view.
  • 5. Overall comments and introduction (cont 1). No discussion about imbalanced data set modeling or other modeling issues. No discussion on literature, all due to time constraints. This presentation introduces novel visual concepts as well as tools derived from Partial Dependency Plots (PDP): -Overall PDP -Collapsed PDP -Marginal PDP and how they assist in model interpretation.
  • 6. Objectives of Interpretation. Why does the model make mistakes (large residuals, outliers, etc.)? Which attributes (alone / group) end up being important? Why is this attribute/s not important? Why is this observation predicted with high probability score? However, immediate aim is NOT explanations at observation level (why predicted sick/churner/innocent…) but
  • 7. Objectives of Interpretation (cont. 1) Why not directly at observation level? Suppose model to predict entertainment type preference for database of families in large cities. Since not possible to obtain updated family preferences consistently, since data is ‘soft’, models necessarily are not created at specific family levels. Contrariwise, disease diagnostic prediction is closer to individual explanation and interpretablity.
  • 9. Model Interpretation categorization. Just as in EDA (but on model results, not on initial data), three types: Univariate Model Interpretation (UMI): One variable at a type. EASIEST to understand and huge source of “makes sense”. E.g., Classical linear models interpretations. E.g., reasons to decline a loan. Bivariate Model Interpretation (BMI): Looking at pairs of variables to interpret model results. Multivariate Model Interpreation (MMI): Overall model interpretation, most difficult. Typically, most work results in UMI and perhaps BMI.
  • 11. Days of Linear Regression Interpretation *** Based on “ceteris paribus” assumption that fails In case of Even relatively small VIFs. At present, rule of thumb VIF >= 10 (R-sq = .90 among predictors)  unstable model. “Ceteris paribus” exercise: Keeping all other predictors Constant, an increase in …. But if R-sq among predictors is Even 10%, not possible to keep all predictors constant while Increasing by 1 the variable of interest. Advantages: EASY to conceptualize because practice Follows notion of bivariate correlation. But notion is generally wrong in multivariate case..
  • 12. Corr (X,Y) = if SD(Y) = SD(X). E.g., if both Standardized, otherwise same sign at least, and interpretation from correlation holds in simple regression case. Notice that regression of X on Y is NOT inverse of regression of Y on X because of SD(X) and SD(Y). / Confusion on signs of coefficients and interpretation. ( ) ˆ { ( ) } ˆ( ) ( )yi xy xy xi xy Y X sY Y r r sX X sg r sg                2 1 2 2
  • 13. 13 2019-06-14 In multiple linear regression, previous relationship does not hold because predictors can be correlated (rxz) weighted by ryz, hinting at co-linearity and/or relationships of supression/enhancement  . . . 2 2 But in multivariate, e.g.: , estimated equation (emphasizing "partial") and for example: ˆ ˆ ˆ , ˆ 1 ˆ( ) ( ) ( ) ( ) and 1 YX Z YZ X Y YX YZ XZ YX Z X XZ YX YX YZ XZ XZ Y X Z Y a X Z s r r r s r sg sg r abs r abs r r r                        
  • 14. Comment on Linear Model Interpretation Even in traditional UMI land, we find that multivariate relations given by Partial- and semi- partial correlations must be part of the interpretation. Note that while correlation is a bivariate relationship, partial and semipartial corrs can be extended to multivariate setting. However, even BMI and certainly MMI not so often performed.
  • 16. Searching for Important variables en route to answering modeling question. Case study: minimum components to make a car go along highway. 1) Engine 2) Tires 3) Steering wheel 4) Transmission 5) Gas 6) ….. Other MMI aspects and interrelations. Take just one of them out, and the car won’t drive. There is no SINGLE most important variable but a minimum irreducible set of them. In Data Science case with n  ∞, possibly many subsets of ‘important’ variables. But “suspect VARS” good starting point of research.
  • 19. Model Name Item Information M2 TRN DATA set train . TRN num obs 3595 VAL DATA set validata . VAL num obs 2365 TST DATA set . TST num obs 0 Dep. Var fraud TRN % Events 20.389 VAL % Events 19.281 TST % Events
  • 20. Original Vars + Labels Model Name M2 Variable Label ** DOCTOR_VISITS Total visits to a doctor MEMBER_DURATION Membership duration ** NO_CLAIMS No of claims made recently ** NUM_MEMBERS Number of members covered ** OPTOM_PRESC Number of opticals claimed ** TOTAL_SPEND Total spent on opticals **
  • 21. Requested Models: Names & Descriptions. Full Model Name Model Description Overall Models M2 20 pct prior M2_BY_DEPVAR Inference 01_M2_GB_TRN_TREES Tree Repr. for Gradient Boosting 02_M2_TRN_GRAD_BOOSTING Gradient Boosting 03_M2_TRN_LOGISTIC_STEPWISE Logistic TRN STEPWISE 04_M2_VAL_GRAD_BOOSTING Gradient Boosting 05_M2_VAL_LOGISTIC_STEPWISE Logistic VAL STEPWISE
  • 22. — 22 — Data set: Definition by way of Example • Health insurance company: Ophtamologic Insurance Claims • Is claim valid or fraudulent? Binary target. • No transformations created to have simple data set. • Full description and analysis of this data set in https://www.slideshare.net/LeonardoAuslender (lectures at Principal Analytics Prep).
  • 23. Ch. 1.1-23 Alphabetic List of Variables and Attributes # Variable Type Len Format Informa t Label 3 DOCTOR_VISITS Num 8 BEST12 . F12. Total visits to a doctor 1 FRAUD Num 8 BEST12 . F12. Fraudulent Activity yes/no 5 MEMBER_DURAT ION Num 8 Membership duration 4 NO_CLAIMS Num 8 BEST12 . F12. No of claims made recently 7 NUM_MEMBERS Num 8 Number of members covered 6 OPTOM_PRESC Num 8 BEST12 . F12. Number of opticals claimed 2 TOTAL_SPEND Num 8 BEST12 . F12. Total spent on opticals Note: No nominal predictors. No transformations to keep presentation simple but not simpler than necessary
  • 24. .... Reporting area for all Model.s coefficients Importance, etc. and Selected Variables.
  • 25. Vars * Models * Coeffs Model Name M2_TRN_GRAD_BO OSTING M2_TRN_LOGIS TIC_STEPWISE M2_VAL_GRAD_BO OSTING M2_VAL_LOGISTIC_S TEPWISE Coeff / Importanc e PVal / Nrules Coeff / Import ance PVal / Nrules Coeff / Importa nce PVal / Nrules Coeff / Importan ce PVal / Nrules Variable 0.1099 2.000 0.1099 2.000 NUM_MEMBERS OPTOM_PRESC 0.6211 19.000 0.2178 0.000 0.6211 19.000 0.1463 0.000 DOCTOR_VISITS 0.4434 20.000 - 0.0171 0.020 0.4434 20.000 -0.0065 0.428 MEMBER_DURATION 0.7843 41.000 - 0.0066 0.000 0.7843 41.000 -0.0065 0.000 TOTAL_SPEND 0.6864 29.000 - 0.0000 0.003 0.6864 29.000 -0.0000 0.004 NO_CLAIMS 1.0000 19.000 0.7752 0.000 1.0000 19.000 0.7610 0.000 INTERCEPT - 0.5767 0.000 -0.5635 0.001 Note: Importance and coefficients share one column as well as p-values and number of rules.
  • 26. Logistic Selection Steps Model Name M2_TRN _LOGIST IC_STEP WISE # in mo del P- val ue Step Effect Entered Effect Removed 1 .00 1 no_claims 2 member_duration 2 .00 3 optom_presc 3 .00 4 total_spend 4 .00 5 doctor_visits 5 .02 Dropped Num_members.
  • 29. Some conclusions and comments so far: . Logistic stepwise dropped Num_members that is shown with lowest relative importance in GB. Notice that Logistic Regression does not have agreed-upon scale of importance. We can use odds-ratios, e.g. . NO_CLAIMS is deemed most important single variable for GB, but logistic deems OPTOM_PRESC as the second one (via odds ratios), while GB selected MEMBER_DURATION. . Remaining variables have odds ratios of 1 which seem to indicate similar effect, while GB distinguishes relative importance after first two variables.
  • 31. Definite monotonic relationship, higher values of NO_CLAIMS (e.g., bin 5) associated with higher probability. Note differences between LG and BG.
  • 33. GB monotonic decrease for OPTOM_PRESC, diffuse for TOTAL_SPEND.
  • 35. Mg: Effect: Change in Prob as X changes.
  • 36. LG does not have measure of importance, as GB does  we use marginal effects plots that indicate change in probability along variable range. Except for MEMBER_DURATION (that declines initially), other effects have positive effect of different intensity and max value declines as per logistic shape. Member duration has pronounced decline for low duration levels,  possibility of fraudulent members who join, commit their fraud and leave. Note sharper increase in prob. for NO_CLAIMS at bins 1 and 8. Optom_presc at 6. GB Importance measures impact of individual inputs on predicting Y, but don’t tell how impact changes along range of inputs and individual variable effects are not in consideration  Use Partial Dependency Plots, also for LG in free ride.
  • 37. Marginal Effects and PDPs Marginal effects refer to change in probability with one unit change in X, ceteris paribus (if meaningful or at least desirable). PDPs do not indicate change in Y at all; instead, PDP measures probability levels at different values of X1 measuring all other predictors at their means (or modes, medians, etc.).  No Marginality in PDPs, unless we measured ‘change’ in probability as well. Shown later on, called Marginal PDPs.
  • 39. Tree representation(s) up to 4 levels Model M2_GB_TRN_TREES Requested Tree Models: Names & Descriptions. Pred Level 1 + Prob. Level 2 + Prob. Level 3 + Prob. Level 4 + Prob. 0.464 no_claims < 2.5 ( 0.185 ) no_claims < 0.5 ( 0.159 ) member_duration < 180.5 ( 0.199 ) total_spend < 5250 ( 0.464 ) total_spend >= 5250 ( 0.186 ) 0.186 member_duration >= 180.5 ( 0.103 ) doctor_visits >= 5.5 ( 0.093 ) 0.093 doctor_visits < 5.5 ( 0.126 ) 0.126 no_claims >= 0.5 ( 0.321 ) optom_presc < 3.5 ( 0.291 ) total_spend >= 6300 ( 0.273 ) 0.273 total_spend < 6300 ( 0.467 ) 0.467 optom_presc >= 3.5 ( 0.59 ) member_duration < 154.5 ( 0.67 ) 0.670 member_duration >= 154.5 ( 0.447 ) 0.447 no_claims >= 2.5 ( 0.633 ) no_claims < 4.5 ( 0.57 ) optom_presc < 3.5 ( 0.54 ) member_duration >= 128.5 ( 0.498 ) 0.498 member_duration < 128.5 ( 0.627 ) 0.627 optom_presc >= 3.5 ( 0.81 ) member_duration >= 137 ( 0.785 ) 0.785 member_duration < 137 ( 0.85 ) 0.850 no_claims >= 4.5 ( 0.761 ) member_duration < 303.5 ( 0.778 ) member_duration >= 148 ( 0.757 ) 0.757 member_duration < 148 ( 0.823 ) 0.823Missing one line.
  • 40. Tree representation(s) up to 4 levels Model M2_LG_TRN_TREES Requested Tree Models: Names & Descriptions. Pred Level 1 + Prob. Level 2 + Prob. Level 3 + Prob. Level 4 + Prob. 0.195no_claims < 1.5 ( 0.164 ) member_duration < 155.5 ( 0.235 ) optom_presc < 3.5 ( 0.213 ) no_claims < 0.5 ( 0.195 ) no_claims >= 0.5 ( 0.337 ) 0.337 optom_presc >= 3.5 ( 0.49 ) optom_presc < 6.5 ( 0.404 ) 0.404 optom_presc >= 6.5 ( 0.647 ) 0.647 member_duration >= 155.5 ( 0.111 ) optom_presc < 3.5 ( 0.103 ) member_duration >= 246.5 ( 0.065 ) 0.065 member_duration < 246.5 ( 0.122 ) 0.122 optom_presc >= 3.5 ( 0.235 ) no_claims >= 0.5 ( 0.353 ) 0.353 no_claims < 0.5 ( 0.213 ) 0.213 no_claims >= 1.5 ( 0.61 ) no_claims < 2.5 ( 0.451 ) member_duration < 155.5 ( 0.562 ) optom_presc >= 1.5 ( 0.651 ) 0.651 optom_presc < 1.5 ( 0.493 ) 0.493 member_duration >= 155.5 ( 0.353 ) member_duration >= 237 ( 0.204 ) 0.204 member_duration < 237 ( 0.39 ) 0.390 no_claims >= 2.5 ( 0.748 ) no_claims < 4.5 ( 0.675 ) member_duration >= 236.5 ( 0.477 ) 0.477 member_duration < 236.5 ( 0.721 ) 0.721 no_claims >= 4.5 ( 0.899 ) member_duration >= 272 ( 0.741 ) 0.741 Missing one line.
  • 41. Comment on Tree Representations LG starts by splitting on NO_CLAIMS at 2, while GB splits at 3. Predictions for first level across 2 models are similar ( .185 ; .633) for GB vs. (.164, .61) for LG, which indicates that structures identified so far are similar so far (UMI interpr.) While in 2nd level, GB only splits on NO_CLAIMS, LG splits on MEMBER_DURATION for suspected non-fraudsters in the first stage and on NO_CLAIMS for the fraudster suspects (BMI already different). Predictions are similar only for the 4th node in level 2 (.748 and .761) but different otherwise. The careful reader may verify that these two predictions emerge by splitting on NO_CLAIMS albeit at different values, which supports the notion of No_claims being the leading clue in our research.
  • 44. Comment on Tree Representations (cont.1) NO_CLAIMS not so heavily used after 2nd level however, and the structures of the models are clearly different. GB does not use it at all, while LG splits at 4.5 to produce the highest prediction level of .899. While GB did split initially on No_claims 2.5 and then on 4.5, it did not reach the same level of prediction as LG that started splitting at 1.5. By going to the marginal effects plot, we can see that No_claims has the largest slope for low values, but member_duration has the highest for highest value of the variable. But no similar plots can be created for GB. Thus, found structures and consequent interpretations differ and there is no isomorphism from one into the other. Perhaps fractal approximation?
  • 46. 2nd most “important variable”, very different structures.
  • 47. 1st most “important” variable, very different structures.
  • 49. Both probs increasing as No_claims increases except for GB between 14 and 17. GB > LG up to NO_CLAIMS = 3, later reverse. Notice increasing difference in prob. after No_CLAIMS = 5.
  • 50. Different binned residual results by model and by variables. Notice LG better fit except between bins 11 through 17.
  • 51. Overall declining relation except for area around bin 15. Notice no consistent Higher levels of prob. of either model, contrary to two previous slides.
  • 52. Both models fit relatively poorly for large values of Member_Duration.
  • 53. Similar gulf in probabilities and severe divergence between 11 and 13. GB makes more extreme jumps.
  • 54. Similar behavior as that of Member_Duration.
  • 57. Strict interpretations: different. Obvious similarities: e.g., high values of NO_CLAIMS related to high Probability Values mostly. INTERESTING: curves not fully monotonically increasing or decreasing. Residual plots show that there are patterns not well fitted.
  • 58. .... Ranking the models by GOF. Strongly summarized area for brevity sake, added just for completion.
  • 59. GOF ranks GOF measure rank AUR OC Avg Squa re Error Class Rate Cum Lift 3rd bin Cum Resp Rate 3rd Gini Preci sion Rate Rsqu are Cram er Tjur Ran k Ran k Ran k Ran k Ran k Ran k Ran k Ran k Unw . Mea n Unw . Medi an Model Name 1 1 2 1 1 1 1 1 1.13 1 02_M2_TRN_GRAD_BOOST ING 03_M2_TRN_LOGISTIC_ST EPWISE 2 2 1 2 2 2 2 2 1.88 2 GOF ranks GOF measure rank AUR OC Avg Squa re Error Class Rate Cum Lift 3rd bin Cum Resp Rate 3rd Gini Preci sion Rate Rsqu are Cram er Tjur Rank Rank Rank Rank Rank Rank Rank Rank Unw. Mean Unw. Medi an Model Name 1 1 2 1 1 1 1 1 1.13 1 04_M2_VAL_GRAD_BOOS TING 05_M2_VAL_LOGISTIC_S TEPWISE 2 2 1 2 2 2 2 2 1.88 2
  • 60. .... Profile and Model Interpretation Area. .... Univariate Profile diagnostics for 6 Important Vars.
  • 61. .... Event Proportions and Posterior Probabilites for 5 Important Vars. by original Model Names. Variables and probabilities binned for ease of visualization. Proportion events same across models (it’s just original data), but probabilities differ across models. Not all cases shown.
  • 64. Etc for the other variables.
  • 65. Some observations Binned No_claims: While similar in shape, GradBoost seriously underestimates proportion of events throughout, while logistic has the problem for bins 2, 3, 5, 6, 7. Logistic has a positive slope, while GB flattens due to interactive GB model. Up to bin 7, similar behavior for GB and LG, and then LG jumps to higher level of probability. Binned Member_Duration: Probability distributions are similar but not identical. For bins 1, 2, 3 and 16 methods underestimate proportion of events. Slightly declining slope for both models. Binned OPTOM_PRESC: Both methods failed to match proportion of events in the mid range of the bins. Sudden positive upshift in positive slope for GB starting at bin 15, while overall flat but positive slope for Logistic.
  • 67. Interpretation: In bin 5, No_claims reaches overall max (100), while for bin 1 max is around 35 and 15 in 0-100 scale for respective models. Same interpretation for Q3, etc.
  • 71. And Conversely ….. (GB = Tree repr. Of Grad_boosting …)
  • 73. .... Partial Dependency Plots and variants for Non Ensemble Models. Some variables may be dropped due to computer resources.
  • 74. Note the narrow range of GB PDPs compared to those of LG due to GB interactive nature  more difficult to interpret.
  • 76. Marginal (1) PDP comparative notes (Marginal (1): one var at a time. Could also marginalize two vars at a time, not done in this presentation). BG marginals are rather flat, except for MEMBER_DURATION, of which caveat later on. LG is juicier, NO_CLAIMS increase of probability declines along range, but OPTOM_PRESC increases, which seems to indicate that leading reason would be prescriptions and not overall claims. Corresponding marginals for logistic end up with slowing down of growh due to logistic shape. BG is not constrained in that way.
  • 77. PDP comparative notes Overall PDP is Model probability when all predictors are at their means. For LG, it’s about .17, while GB is .53. Individual PDPs (by def.) are deviations from Overall when var of interest measured along its range, while others remain at mean values. GB clumps most PDPs around Overall, LG clearly distinct values instead. Highest probability level for GB is around .7 while LG reaches 1, and minima are around .6 and 0 respectively. Note LG monotonicity while GB is mostly monotonic (except for Doctor_visits), possibly product of data set created artificially. In both cases, NO_CLAIMS appears as leading variable, especially in LG but while Member_duration is rather flat in GB, it certainly declines steadily in LG, with a very different interpretation. Longer member duration implies steadier customer and familiarity. No_members had been excluded in LG’s stepwise and should not be confused with MEMBER_DURATION.
  • 82. UMI: Univariate Model Interpretation. From preceding pages, we can conclude that: No_claims: positively associated with increased fraud, for both logistic and grad, but far steeper slope in Logistic. Grad_b stays in narrow band of probabilty and more interactive with other predictors  Grad_b requires more BMI and MMI. GB’s PDP overshoots posterior probability  other vars bring down this effect in GB. Member_duration has a U shape relationship, especially in Logistic case, while GB has a more spiky one. Note the high spike at duration minimal and immediate decline which seems to indicate members that committed fraud as soon as they joined and left immediately.
  • 83. UMI: Univariate Model Interpretation (cont. 1) PDP view: logistic shows positive effects of NO_CLAIMS and OPTOM_PRESC, balanced by negative effects of remaining variables. Comparing posterior probability with No_claims PDP, they are almost the same for Logistic. Similarly for MEMBER_DURATION. Grad_b instead shows more tepid effects of same variables, and almost unchanging effects of remaining predictors. Comparing PDP with probability, other predictors bring down PDP of No_claims. Similar effects for MEMBER_DURATION.
  • 84. .... PDPs for "Pairs of Variables" Note: 3d plots tend to interpolate areas of no data producing false expectations of results. Thus, sometimes 3d charts preferable to plots. Not all Pairs of variables available due to computer resources.
  • 85. Same for LG. Note correlations (No_claims) with other variables are relative small when compared to the pair Member_duration – Doctor_visits and Member_duration - optom_presc. How will this translate in PDPs for 2 variables at a time?
  • 86. M_: 'M2_TRN_LOGISTIC_STEPWISE' 'ORIGINAL' PDP Corr '-0.02542' LG High levels of NO_CLAIMS have high probability for lowest level of total_spend which probably denotes one time fraud. Otherwise, even mid levels of NO_CLAIMS associated with high probability for any level of TOTAL_SPEND. It seems that FRAUD is not necessarily linked to TOTAL_SPEND alone.
  • 87. BINNED ORIGINAL PDP M2_TRN_GRAD_BOOSTING Corr ' 0.05073' NO_CLAIMS DOCTOR_VISITS Combination of No_claims & Doctor_visits shows high probability at NE corner and middle section stable high prob. level. Too many charts to show but necessary for full interpretation.
  • 88. BINNED ORIGINAL PDP M2_TRN_GRAD_BOOSTING Corr ' 0.02549' NO_CLAIMS MEMBER_DURATION About NO_CLAIMS and MEMBER_DURATION, fraud happens for low level of duration, after which fraudsters leave.
  • 89. M_: 'M2_TRN_GRAD_BOOSTING' 'ORIGINAL' PDP Corr ' 0.06580' Prob. growth for low NO_CLAIMS and OPTOM_PRESC increase (not at dramatic as in LG), and then slow and steady prob. growth with increases in both vars.
  • 90. BINNED ORIGINAL PDP M2_TRN_LOGISTIC_STEPWISE Corr ' 0.06580' NO_CLAIMS OPTOM_PRESC Steep prob. growth for low NO_CLAIMS and OPTOM_PRESC increase, similar but not so pronounced growth for small OPTOM_PRESC and increasing NO_CLAIMS.
  • 91. BINNED ORIGINAL PDP M2_TRN_GRAD_BOOSTING Corr '-0.10759' MEMBER_DURATION OPTOM_PRESC About the pair Optom_presc and Member_duration for which we have contrasting Pair PDPs, with corr = -0.10, interpretation is very different. While GB shows flat probabilities throughout, except in NE empty corner, logistic shows more extreme NE corner, plus declining probabilities from NW top.
  • 92. BINNED ORIGINAL PDP M2_TRN_LOGISTIC_STEPWISE Corr '-0.10759' MEMBER_DURATION OPTOM_PRESC
  • 93. M_: 'M2_TRN_GRAD_BOOSTING' 'ORIGINAL' PDP Corr '-0.02542' Rather flat relationship in GB, but steeper in LG (next slide)
  • 95. Some BMI comments Previous charts suggest that one type of fraud happens once for low levels of duration. Different types of fraud are linked with Prescriptions and Claims. For low levels of claims, increasing prescriptions leads to fraud, as well as a combination of increasing claims and prescriptions combined. So it is possible that there are at least 3 types of Fraud being committed. Other pair combinations were not interesting and rather flat surfaces.
  • 96. For 2 dimensional visualization, collapse 3d chart by averaging levels of variable 2 into those of variable 1 and compare to original PDP. Original and collapsed PDPs (CPDPs) are derived from posterior model probabilities.
  • 97. No room for TOTAL_SPEND
  • 100. Comments for BMI. In case of NO_CLAIMS, all cases show overlapping of collapsed and Original, except for OPTOM_PRESC. In GB case, DURATION brings down probability slightly because duration is itself strong predictor. LG shows that presence of OPTOM_PRESC raises posterior probability, not so accentuated in GB. LG model could benefit of NO_CLAIMS and OPTOM_PRESC interaction or possibly overall transformation by way of obtaining information per month and per number of members. (LG chart with TOTAL_SPEND omitted for space brevity). MEMBER_DURATION shows overlap with all second variables, plus declining slope, more evident in LG models.
  • 101. Comments for BMI (cont). It is possible to obtain 3-way and higher PDPs, and also collapse them, not tried here. Given overlap between Original and CPDP, UMI effects are correct so far, except possibly for triplet NO_CLAIMS, MEMBER_DURATION and OPTOM_PRESC.
  • 105. Collapsed Triad and Tetrad PDPs. In like manner as 3d PDPs, possible to obtain PDPs for 3 or more variables but not possible to graph (at least, not yet). Collapsed Triads bypasses problems by obtaining PDP of specific three variable set (triads). And Tetrads, for 4 variable sets. While it is possible to collapse two of them and present average PDP compared to univariate PDPs, bivariate and original probability, also possible to collapse Mean PDP but along 4 quartile ranges of the third variable (in TRIAD case) or fourth variable (in TETRAD case) (we bypass the quartile presentation for brevity). In addition to mean PDPs, we also include max and min PDPs as an overlay to provide view of probability variation. Still working on improving these presentations.
  • 106. Original probability not truly represented well by any combination of PDPs in GB case. GB searches solution over residuals, not fully represented hereby.
  • 107. Minor differences when compared to previous TRIAD.
  • 108. Original probability represented very well with 3 variables
  • 109. Minor differences between triads and tetrad representations.
  • 111. Same as previous slide but in difference form.
  • 112. Residual – iterative GB nature shows that just 3 variable do not capture full Interpretation since Posterior probability remains below and above most of data points.
  • 113. Same as previous slide in difference form.
  • 114. Comment on Triads and Tetrads For present data set and choice of represented variables, there was not much difference between TRIADS and TETRADS, which means that omission of the fourth variable does not alter our results by much. Still we emphasize that it is quite illusory to merely concentrate on average values. The graphs also contain max and min values of probability that show the high variability except for large values of NO_CLAIMS. This is clear since the event rate was %20 and concentrated on high values of that variable.
  • 116. Lowest prob level represented by lowest levels of predictors, except for member duration.
  • 117. Highest prob levels determined by mid-levels of No_claims and higher total spend than in bin 1..
  • 118. Conclusions on multivariate distribution of predictors along Prob. bins. Since event rate is %20, good model should clump those observations in higher prob. bins. In lowest bin, predictors bins are typically lowest ones, except for member_duration. Again, this seems to indicate presence of fraudsters with short duration that leave immediately, as evinced in bin 5 of probability slide. In this one, most predictors have observations from higher bins. Other probability bins not listed for brevity sake.
  • 120. Similar coeffs among logistic , GB and beta regressions. By Beta Regression, standard interpretation of log odds is possible, with caveats. Vars * Models * Coeffs Model Name M2_TRN_ GRAD_BO OSTING M2_TRN_ GRAD_BO OSTING_ BETA_RE G M2_TRN_ LOGISTIC _STEPWI SE M2_TRN_ LOGISTIC _STEPWI SE_BETA_ REG M2_VAL_ GRAD_BO OSTING M2_VAL_ LOGISTIC _STEPWI SE Coeff / Importan ce Coeff / Importan ce Coeff / Importan ce Coeff / Importan ce Coeff / Importan ce Coeff / Importan ce Variable 0.7318 -0.0051 -0.0057 -0.0057 0.7318 -0.0084 MEMBER_DURATIO N DOCTOR_VISITS 0.3925 -0.0061 0.3925 TOTAL_SPEND 0.6610 -0.0000 -0.0000 -0.0000 0.6610 -0.0000 OPTOM_PRESC 0.5944 0.1713 0.2132 0.2132 0.5944 0.1634 NO_CLAIMS 1.0000 0.7027 0.7921 0.7921 1.0000 0.7351 SCALE 21.8895 2.590291 516E16 INTERCEPT -0.7979 -0.8352 -0.8352 -0.3111
  • 121. Beta Regression results Results of analyzing posterior probabilities (i.e., original GB and LG posteriors) via BETA regression show very similar coefficients and structures  Beta is reassuring but not providing additional information.
  • 123. Possible to say that … 1) Manipulate just NO_CLAIMS and problem solved? 2) Maybe add MEMBER_DURATION and OPTOM_PRESC for parts of NO_CLAIMS range? 3) Maybe add if-then rules from simplified TREE_REPRESENTATION because easier than GB and more interactive than LG? 4) If using Neural Network, and NN derivatives abandon all hope of interpretation? 5)  Interpretation needs definition of INTENDED AUDIENCE (see Tolstoy ut supra).
  • 124. Possible to say that … (cont. 1) 1) The analyst needs to focus on NO_CLAIMS, MEMBER_DURATION and OPTOM_PRESC as an ‘IMPORTANT’ group. 2) Different model Interpretations should be entertained. 3) Different marginal effects must be explained.
  • 125. Final thoughts … MI analysis must proceed further for large number of predictors obtaining insights from collapsing 3+ way PDPs for instance. If preferred ‘easier’ linear model explanation, beta regression on posterior probability would provide regression like information. Still, beta regression is not straightforward and model selection is big issue.
  • 127. Ch. 1.1-127 2019-06-14 Future steps Focus on MMI 1) Beta regression for ‘linear’ interpretation. More difficult because it requires model search as well. Plus, additional error in modeling posterior probability of original model. 2) Andrews’ curves.
  • 129. Lime: Local Interpretable Model-Agnostic Explanations: Uses surrogate interpretable model on black-box model, applied to observations of interest. Tree representation in this presentation similar to this. (https://homes.cs.washington.edu/~marcotcr/blog/lime/) ICE: Clusters or classification variable applied to PDP results. For given predictor, ICE plots draw one line per obs., representing how instance’s prediction changes when predictor changes. Shap Values: Shapley Additive Explanation (Lundberg et al, 2017): Measures +/- feature contribution to prob. Technique used in game theory to determine each player’s contribution to success in a game. Affected by corrs among predictors  focusing just on one predictor to change behavior may change other predictors as well (available in Python). AND OTHERS ….
  • 130. References Lundberg SM, Lee SI (2017), “Consistent feature attribution for tree ensembles”, presented at the 2017 ICML Workshop on Human Interpretability in Machine Learning (WHI 2017), Sydney, NSW, Australia (https://arxiv.org/abs/1706.06060) Molnar C. (2018): Interpretable Machine Learning, A guide for making black box models explainable, https://christophm.github.io/interpretable-ml-book/ Tolstoy Leo: “The Kingdom of God Is Within You”, (1894)