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NETWORKS, PREDICT EDGES
Can we predict if two nodes in the graph are connected or not?
But let’s make it very practical:
Let’s say you work in a social media company and your boss asks you to create a model to predict who will be friends, so you can feed those recommendations back to the website and serve those to users.
You are tasked to create a model that predicts, once a day for all users, who is likely to connect to whom.
PART 2 my previous post about rectangling network data
BUILD MODEL WITH TIDYMODELS
Loading packages and data
Using {tidymodels} (a package that also loads {broom}, {recipes}, {dials}, {rsample}, {dplyr}, {tibble}, {ggplot2}, {tidyr}, {infer}, {tune}, {workflows}, {modeldata}, {parsnip}, {yardstick}, and {purrr})
also using {themis}, {vip} {readr}, {dplyr}, {ggplot2}, for models using {glmnet}, {ranger}
library(tidymodels) ── Attaching packages ───────────────────────────────────── tidymodels 0.1.2 ── ✓ broom 0.7.2 ✓ recipes 0.1.15 ✓ dials 0.0.9 ✓ rsample 0.0.8 ✓ dplyr 1.0.2 ✓ tibble 3.0.4 ✓ ggplot2 3.3.2 ✓ tidyr 1.1.2 ✓ infer 0.5.3 ✓ tune 0.1.2 ✓ modeldata 0.1.0 ✓ workflows 0.2.1 ✓ parsnip 0.1.4 ✓ yardstick 0.0.7 ✓ purrr 0.3.4 ── Conflicts ──────────────────────────────────────── tidymodels_conflicts() ── x purrr::discard() masks scales::discard() x dplyr::filter() masks stats::filter() x dplyr::lag() masks stats::lag() x recipes::step() masks stats::step()
Load data CONTAINS ALSO FROM ADVANCED THINGY
enriched_trainingset <- readr::read_rds(file="data/enriched_trainingset2.Rds") %>% mutate(target=as.factor(target)) names(enriched_trainingset) [1] "from" "to" "target" [4] "degree" "betweenness" "pg_rank" [7] "eigen" "closeness" "br_score" [10] "coreness" "degree_to" "betweenness_to" [13] "pg_rank_to" "eigen_to" "closeness_to" [16] "br_score_to" "coreness_to" "commonneighbors_1" [19] "commonneighbors_2" "unique_neighbors"
Feature information
IS THERE ENOUGH INFORMATION IN THE DATASET TO PREDICT
MANY MORE NEGATIVE THAN POSITIVE EXAMPLES.
enriched_trainingset %>% count(target) # A tibble: 2 x 2 target n <fct> <int> 1 0 34306 2 1 1606
MAKE SUBSET TO VISUALISE
smpl_trainingset <- enriched_trainingset %>% group_by(target) %>% sample_n(1000) %>% mutate(label = ifelse(target ==1,"link","no-link")) %>% ungroup() smpl_trainingset %>% count(label) # A tibble: 2 x 2 label n <chr> <int> 1 link 1000 2 no-link 1000
OVERVIERW OF ALL VARIABLES THIS IS NOT A BEST PRACTICE, AND I’M NOT EVEN SURE IF THE INFORMATION I’M SHOWING HERE IS TELLING US SOMETHING.
(NODE)-[EDGE]-(NODE)
BOTH SIDES OF EDGE HAVE PROPERTIES. WE DON’T CARE ABOUT DIRECTION AND SO
IS MORE OR LESS EQUIVALIENT. MAYBE THE COMBIANTOIN OF THE TWO IS MORE IMPORTANT?
smpl_trainingset %>% mutate( degree2 = degree*degree_to, eigen2 = eigen* eigen_to, pg_rank2 = pg_rank* pg_rank_to, betweenness2 = betweenness* betweenness_to, br_score2 = br_score* br_score_to, coreness2 = coreness * coreness_to, closeness2 = closeness * closeness_to ) %>% select(label, degree2:closeness2) %>% group_by(label) %>% summarise(across(.fns = c(mean=mean,sd=sd))) %>% pivot_longer(-label) %>% tidyr::separate(name, into = c("metric","summary"),sep="2_") %>% pivot_wider(names_from = summary, values_from = value) %>% ggplot(aes(label, color=label))+ geom_point(aes(label, y=mean),shape=22, fill="grey50")+ geom_point(aes(label, y=mean+sd), shape=2)+ geom_point(aes(label, y=mean-sd), shape=6)+ geom_linerange(aes(label, ymin=mean-sd, ymax=mean+sd))+ facet_wrap(~metric, scales="free")+ labs( title="Small differences in features for link vs no-link", subtitle="mean (+/-) 1 sd", x=NULL, y="feature" ) `summarise()` ungrouping output (override with `.groups` argument)
VISUALIZE
BETWEENNESS
smpl_trainingset %>% select(betweenness, betweenness_to, label) %>% pivot_longer(-label) %>% ggplot(aes(value,color = label))+ geom_density() + facet_wrap(~name)+ scale_x_continuous(trans=scales::log1p_trans())
DEGREE
smpl_trainingset %>% ggplot(aes(degree, degree_to, color = label))+ geom_point()+ scale_x_continuous(trans=scales::log1p_trans())+ scale_y_continuous(trans=scales::log1p_trans())
PAGE RANK
smpl_trainingset %>% ggplot(aes(pg_rank, pg_rank_to, color = label))+ geom_point(alpha = 1/2)
EIGEN DOESN’T REALLY SEEM TO BE DIFFERENT
smpl_trainingset %>% ggplot(aes(eigen, eigen_to, color = label))+ geom_point(alpha = 1/2)
ETCETEA
ADVANCED
smpl_trainingset %>% ggplot(aes(commonneighbors_1, commonneighbors_2, color=label))+ geom_point(alpha=1/2)+ labs( title="Neighbors in common between two nodes", x="Neighbors at distance 1", y= "Neighbors at distance 2" )
SO YEAH THERE IS SOME INFOMRATION IN THERE, IS SEE SOME CLUSTERING BUT THE BOUNDARIES ARE QUITE VAGUE.
Actual feature engineering (recipe)
I decided to create some interactions between page rank of two nodes, and the degree of the nodes, drop the identifiers to and from and make the target a factor. Furthermore I drop correlated features and normalize and center all features (there are no nominal variables in this dataset).
This recipe is only a plan of action, nothing has happened yet.
# make it very simple first. ntwrk_recipe <- recipe(enriched_trainingset,formula = target~.) %>% recipes::update_role(to, new_role = "other") %>% recipes::update_role(from, new_role = "other") %>% step_interact(terms = ~ pg_rank:pg_rank_to) %>% step_interact(terms = ~ degree:degree_to) %>% step_interact(terms = ~ eigen:eigen_to) %>% step_interact(terms = ~ betweenness:betweenness_to) %>% step_interact(terms = ~ closeness:closeness_to) %>% step_interact(terms = ~ coreness:coreness_to) %>% step_interact(terms = ~ br_score:br_score_to) %>% step_corr(all_numeric()) %>% step_nzv(all_predictors()) %>% step_normalize(all_predictors(), -all_nominal()) %>% step_mutate(target = as.factor(target))
Model
simple model to start with generalized linear model
So what are we going to do with the model? I’m using a logistic regression from {glmnet} and capture the steps of data preparation and modeling into 1 workflow-object.
ntwrk_spec <- logistic_reg(penalty = tune(), mixture = 1) %>% # pure lasso set_engine("glmnet") ntwrk_workflow <- workflow() %>% add_recipe(ntwrk_recipe) %>% add_model(ntwrk_spec)
Train and test sets
I split the data into a test and train set, but making sure the proportion of targets is the same in test and train data.
### split into training and test set set.seed(2345) tr_te_split <- initial_split(enriched_trainingset,strata = target) val_set <- validation_split(training(tr_te_split),strata = target, prop = .8)
Model tuning
I don’t know what the best penalty is for this model and data, so we have to test different versions and choose the best one.
## Setting up tune grid manually, because it is just one column lr_reg_grid <- tibble(penalty = 10^seq(-5, -1, length.out = 30)) ntwrk_res <- ntwrk_workflow %>% tune_grid(val_set, grid = lr_reg_grid, control = control_grid(save_pred = TRUE), metrics = metric_set(roc_auc)) Attaching package: 'rlang' The following objects are masked from 'package:purrr': %@%, as_function, flatten, flatten_chr, flatten_dbl, flatten_int, flatten_lgl, flatten_raw, invoke, list_along, modify, prepend, splice Attaching package: 'vctrs' The following object is masked from 'package:tibble': data_frame The following object is masked from 'package:dplyr': data_frame Loading required package: Matrix Attaching package: 'Matrix' The following objects are masked from 'package:tidyr': expand, pack, unpack Loaded glmnet 4.0-2
Visualise results (I DID SOME DEEPER DIVE ANY SMALL PENALTY LESS THAN 10E-05 LEADS TO THE SAME VALUES ~ 0.0000240 as pentlay is boundary)
ntwrk_res %>% collect_metrics() %>% ggplot(aes(x = penalty, y = mean)) + geom_point() + geom_line() + labs( subtitle="Ideal penalty is larger then 1.610e-05, but certainly less than 0.04", title = "Penalty values", y= "Area under the ROC Curve", x="Penalty values for this GLM" ) + scale_x_log10(labels = scales::label_number())+ geom_vline(xintercept = 0.0386, color="tomato3")+ geom_vline(xintercept=1.610e-05, color='tomato3')+ theme_minimal()
What are the best models?
## show best models top_models <- ntwrk_res %>% show_best("roc_auc", n = 5) %>% arrange(penalty) lr_best <- ntwrk_res %>% collect_metrics() %>% arrange(penalty) %>% slice(5) pred_auc <- ntwrk_res %>% collect_predictions(parameters = lr_best) %>% roc_curve(target, .pred_0) %>% mutate(model = "Logistic Regression") autoplot(pred_auc)+ ggtitle("ROC curve of GLM")
Let’s use the best performing model and modify the current workflow, by replacing the penalty value in the model with one of the best values.
(this model is still untrained, we used the crossvalidation to find the best parameter values)
best_penalty <- top_models %>% pull(penalty) %>% .[[3]] ntwrk_spec_1 <- logistic_reg(penalty = best_penalty, mixture = 1) %>% set_engine("glmnet") ## change model updated_workflow <- ntwrk_workflow %>% update_model(ntwrk_spec_1)
Last fit is a special function from tune that fits data on the training set and predicts on the testset.
ntwrk_fit <- updated_workflow %>% last_fit(tr_te_split) ntwrk_fit %>% pull(.metrics) [[1]] # A tibble: 2 x 4 .metric .estimator .estimate .config <chr> <chr> <dbl> <chr> 1 accuracy binary 0.957 Preprocessor1_Model1 2 roc_auc binary 0.821 Preprocessor1_Model1
Performs really well!
Unpacking predictions. We never predicted a link when there was one! So the score looks good, but the results are not that useful.
ntwrk_fit$.predictions[[1]] %>% group_by(target, .pred_class) %>% summarize( count = n(), avg_prob1 = mean(.pred_1) ) `summarise()` regrouping output by 'target' (override with `.groups` argument) # A tibble: 3 x 4 # Groups: target [2] target .pred_class count avg_prob1 <fct> <fct> <int> <dbl> 1 0 0 8591 0.0417 2 0 1 4 0.690 3 1 0 383 0.129 library(vip) Attaching package: 'vip' The following object is masked from 'package:utils': vi prediction_model_glm <- fit( ntwrk_fit$.workflow[[1]], enriched_trainingset ) prediction_model_glm %>% pull_workflow_fit() %>% vip(geom="point")+ ggtitle("Variable importance of Generalized Linear Model", subtitle = "Top 10")
Undersampling for better performance.
PROBABLY SHOULD GIVE SOME REASON FOR THIS. GLM DOESN’T REALLY CARE
using undersampling.
using only mixture doesn’t really help using undersampling doesn’t really help either.
ntwrk_recipe_undersample <- ntwrk_recipe %>% themis::step_downsample(target,under_ratio = 1.5) Registered S3 methods overwritten by 'themis': method from bake.step_downsample recipes bake.step_upsample recipes prep.step_downsample recipes prep.step_upsample recipes tidy.step_downsample recipes tidy.step_upsample recipes tunable.step_downsample recipes tunable.step_upsample recipes # ntwrk_spec2 <- # logistic_reg(penalty = tune(), mixture = tune()) %>% # set_engine("glmnet") ntwrk_workflow2 <- ntwrk_workflow %>% update_recipe(ntwrk_recipe_undersample) crossvalidation_sets <- vfold_cv(training(tr_te_split),v = 3, strata = target) all_cores <- parallel::detectCores(logical = TRUE)-1 library(doParallel) Loading required package: foreach Attaching package: 'foreach' The following objects are masked from 'package:purrr': accumulate, when Loading required package: iterators Loading required package: parallel cl <- makePSOCKcluster(all_cores) registerDoParallel(cl)
HEAVIY COMPUTATION HERE
ntwrk_res2 <- ntwrk_workflow2 %>% tune_grid(crossvalidation_sets, grid = lr_reg_grid, control = control_grid(save_pred = TRUE, allow_par = TRUE), metrics = metric_set(roc_auc)) ntwrk_res2 %>% collect_metrics() %>% select(mean, penalty) %>% pivot_longer(penalty, values_to = "value", names_to = "parameter" ) %>% ggplot(aes(value, mean, color = parameter)) + geom_point(alpha = 0.8, show.legend = FALSE) + facet_wrap(~parameter, scales = "free_x") + geom_hline(yintercept = 0.8206, color="tomato3")+ labs(x = NULL, y = "AUC")
Performance equivalent to earlier. (logically, because glm takes care of it?)
OVERLAY ON PREVIOUS DATA?
Let’s try with random forest.
rf_recipe <- ntwrk_recipe rf_spec <- rand_forest(mtry = tune(), min_n = tune(), trees = 1000) %>% set_mode("classification") %>% set_engine("ranger",importance="impurity") rf_workflow <- workflow() %>% add_recipe(rf_recipe) %>% add_model(rf_spec) set.seed(88708) rf_grid <- grid_max_entropy( mtry(range = c(3,15)), min_n(), size = 15) rf_tune <- tune_grid(rf_workflow, resamples = crossvalidation_sets, grid = rf_grid, control = control_grid(save_pred = TRUE,allow_par = TRUE), metrics = metric_set(roc_auc))
So what is the best parameter set?
rf_tune %>% collect_metrics() %>% select(mean, mtry:min_n) %>% pivot_longer(mtry:min_n, values_to = "value", names_to = "parameter" ) %>% ggplot(aes(value, mean, color = parameter)) + geom_point(alpha = 0.8, show.legend = FALSE) + geom_hline(yintercept = 0.8206, color="tomato3")+ facet_wrap(~parameter, scales = "free_x") + labs( x = NULL, y = "AUC", title="Random Forest approach is way better", subtitle="Quite some variation, but always better than glm (red line)" )
top_models_rf <- rf_tune %>% show_best("roc_auc", n = 5) rf_best <- rf_tune %>% collect_metrics() %>% arrange(mtry) %>% slice(5) pred_auc_rf <- rf_tune %>% collect_predictions(parameters = rf_best) %>% roc_curve(target, .pred_0) %>% mutate(model = "Random Forest")
overlay both models
bind_rows( pred_auc_rf, pred_auc ) %>% ggplot( aes( x = 1 - specificity, y = sensitivity, color = model) )+ geom_line()+ geom_abline( lty = 2, alpha = 0.5, color = "gray50", size = 1.2 )+ theme_minimal()+ labs(title="Overall better performance in the Random Forest model")
best_auc_rf <- select_best(rf_tune, "roc_auc") final_workflow_rf <- finalize_workflow( rf_workflow, best_auc_rf ) final_res_rf <- last_fit(final_workflow_rf, tr_te_split) collect_metrics(final_res_rf) # A tibble: 2 x 4 .metric .estimator .estimate .config <chr> <chr> <dbl> <chr> 1 accuracy binary 0.969 Preprocessor1_Model1 2 roc_auc binary 0.926 Preprocessor1_Model1
Compare this area under the ROC curve (0.91) with the previous value 0.8206.
Investigate feature importance.
library(vip) prediction_model2 <- fit( final_res_rf$.workflow[[1]], enriched_trainingset ) prediction_model2 %>% pull_workflow_fit() %>% vip(geom="point")+ ggtitle("Variable importance of Random Forest model", subtitle = "Top 10")
Conclusion
So the random forest model was better in predicting links than a GLM model. But you should always wonder, what good enough is. Maybe a score of over .80 is enough? In that case why bother using a more complicated model that takes longer to run? GLM’s are usually easier explained and run faster. Provided that we are predicting both classes.
I started this project with the question:
Can we predict if two nodes in the graph are connected or not?
And the practical task was actually:
your boss asks you to create a model to predict who will be friends, so you can feed those recommendations back to the website and serve those to users.
You are tasked to create a model that predicts, once a day for all users, who is likely to connect to whom.
The stakes in this case are not that high. False positives (I predict a link but there is none) is preferable to false negatives (predict no link , but there is).
Bringing it to production
- use renv to capture the dependencies
- set up pipeline of data from system to dataset
- see if you can minimize the number of features necessary
- checks on data quality and features
- predict all no connections and check if flow from model to website works
- predict actual data
- keep track of metrics
- retrain when problematic
State of the machine
< details> < summary> At the moment of creation (when I knitted this document ) this was the state of my machine: **click here to expand**sessioninfo::session_info() ─ Session info ────────────────────────────────────────────────────────────── setting value version R version 4.0.2 (2020-06-22) os macOS Catalina 10.15.7 system x86_64, darwin17.0 ui RStudio language (EN) collate en_US.UTF-8 ctype en_US.UTF-8 tz Europe/Amsterdam date 2020-11-25 ─ Packages ────────────────────────────────────────────────────────────────── package * version date lib source assertthat 0.2.1 2019-03-21 [1] CRAN (R 4.0.2) backports 1.2.0 2020-11-02 [1] CRAN (R 4.0.2) BBmisc 1.11 2017-03-10 [1] CRAN (R 4.0.2) blogdown 0.21 2020-10-11 [1] CRAN (R 4.0.2) bookdown 0.21 2020-10-13 [1] CRAN (R 4.0.2) broom * 0.7.2 2020-10-20 [1] CRAN (R 4.0.2) checkmate 2.0.0 2020-02-06 [1] CRAN (R 4.0.2) class 7.3-17 2020-04-26 [1] CRAN (R 4.0.2) cli 2.2.0 2020-11-20 [1] CRAN (R 4.0.2) codetools 0.2-18 2020-11-04 [1] CRAN (R 4.0.2) colorspace 2.0-0 2020-11-11 [1] CRAN (R 4.0.2) crayon 1.3.4 2017-09-16 [1] CRAN (R 4.0.2) data.table 1.13.2 2020-10-19 [1] CRAN (R 4.0.2) dials * 0.0.9 2020-09-16 [1] CRAN (R 4.0.2) DiceDesign 1.8-1 2019-07-31 [1] CRAN (R 4.0.2) digest 0.6.27 2020-10-24 [1] CRAN (R 4.0.2) doParallel * 1.0.16 2020-10-16 [1] CRAN (R 4.0.2) dplyr * 1.0.2 2020-08-18 [1] CRAN (R 4.0.2) ellipsis 0.3.1 2020-05-15 [1] CRAN (R 4.0.2) evaluate 0.14 2019-05-28 [1] CRAN (R 4.0.1) fansi 0.4.1 2020-01-08 [1] CRAN (R 4.0.2) farver 2.0.3 2020-01-16 [1] CRAN (R 4.0.2) fastmatch 1.1-0 2017-01-28 [1] CRAN (R 4.0.2) FNN 1.1.3 2019-02-15 [1] CRAN (R 4.0.2) foreach * 1.5.1 2020-10-15 [1] CRAN (R 4.0.2) furrr 0.2.1 2020-10-21 [1] CRAN (R 4.0.2) future 1.20.1 2020-11-03 [1] CRAN (R 4.0.2) generics 0.1.0 2020-10-31 [1] CRAN (R 4.0.2) ggplot2 * 3.3.2 2020-06-19 [1] CRAN (R 4.0.2) glmnet * 4.0-2 2020-06-16 [1] CRAN (R 4.0.2) globals 0.14.0 2020-11-22 [1] CRAN (R 4.0.2) glue 1.4.2 2020-08-27 [1] CRAN (R 4.0.2) gower 0.2.2 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utf8 1.1.4 2018-05-24 [1] CRAN (R 4.0.2) vctrs * 0.3.5 2020-11-17 [1] CRAN (R 4.0.2) vip * 0.2.2 2020-04-06 [1] CRAN (R 4.0.2) withr 2.3.0 2020-09-22 [1] CRAN (R 4.0.2) workflows * 0.2.1 2020-10-08 [1] CRAN (R 4.0.2) xfun 0.19 2020-10-30 [1] CRAN (R 4.0.2) yaml 2.2.1 2020-02-01 [1] CRAN (R 4.0.2) yardstick * 0.0.7 2020-07-13 [1] CRAN (R 4.0.2) [1] /Library/Frameworks/R.framework/Versions/4.0/Resources/library
Notes
- used this example from Julia Silge as template https://juliasilge.com/blog/xgboost-tune-volleyball/
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