Add SHAP interaction effects, fix minor bug, and add cox loss (#3043)

* Add interaction effects and cox loss

* Minimize whitespace changes

* Cox loss now no longer needs a pre-sorted dataset.

* Address code review comments

* Remove mem check, rename to pred_interactions, include bias

* Make lint happy

* More lint fixes

* Fix cox loss indexing

* Fix main effects and tests

* Fix lint

* Use half interaction values on the off-diagonals

* Fix lint again

src/metric/rank_metric.cc

@@ -304,6 +304,52 @@ struct EvalMAP : public EvalRankList {
   }
 };
 
+/*! \brief Cox: Partial likelihood of the Cox proportional hazards model */
+struct EvalCox : public Metric {
+ public:
+  EvalCox() {}
+  bst_float Eval(const std::vector<bst_float> &preds,
+                 const MetaInfo &info,
+                 bool distributed) const override {
+    CHECK(!distributed) << "Cox metric does not support distributed evaluation";
+    using namespace std;  // NOLINT(*)
+
+    const bst_omp_uint ndata = static_cast<bst_omp_uint>(info.labels.size());
+    const std::vector<size_t> &label_order = info.LabelAbsSort();
+
+    // pre-compute a sum for the denominator
+    double exp_p_sum = 0;  // we use double because we might need the precision with large datasets
+    for (omp_ulong i = 0; i < ndata; ++i) {
+      exp_p_sum += preds[i];
+    }
+
+    double out = 0;
+    double accumulated_sum = 0;
+    bst_omp_uint num_events = 0;
+    for (bst_omp_uint i = 0; i < ndata; ++i) {
+      const size_t ind = label_order[i];
+      const auto label = info.labels[ind];
+      if (label > 0) {
+        out -= log(preds[ind]) - log(exp_p_sum);
+        ++num_events;
+      }
+
+      // only update the denominator after we move forward in time (labels are sorted)
+      accumulated_sum += preds[ind];
+      if (i == ndata - 1 || std::abs(label) < std::abs(info.labels[label_order[i + 1]])) {
+        exp_p_sum -= accumulated_sum;
+        accumulated_sum = 0;
+      }
+    }
+
+    return out/num_events;  // normalize by the number of events
+  }
+
+  const char* Name() const override {
+    return "cox-nloglik";
+  }
+};
+
 XGBOOST_REGISTER_METRIC(AMS, "ams")
 .describe("AMS metric for higgs.")
 .set_body([](const char* param) { return new EvalAMS(param); });
@@ -323,5 +369,9 @@ XGBOOST_REGISTER_METRIC(NDCG, "ndcg")
 XGBOOST_REGISTER_METRIC(MAP, "map")
 .describe("map@k for rank.")
 .set_body([](const char* param) { return new EvalMAP(param); });
+
+XGBOOST_REGISTER_METRIC(Cox, "cox-nloglik")
+.describe("Negative log partial likelihood of Cox proportioanl hazards model.")
+.set_body([](const char* param) { return new EvalCox(); });
 }  // namespace metric
 }  // namespace xgboost