expNormalize, from Kevin Doherty

gtsam/discrete/DiscreteFactor.cpp

@@ -17,12 +17,59 @@
  * @author Frank Dellaert
  */
 
+#include <gtsam/base/Vector.h>
 #include <gtsam/discrete/DiscreteFactor.h>
 
+#include <cmath>
 #include <sstream>
 
 using namespace std;
 
 namespace gtsam {
 
+/* ************************************************************************* */
+std::vector<double> expNormalize(const std::vector<double>& logProbs) {
+  double maxLogProb = -std::numeric_limits<double>::infinity();
+  for (size_t i = 0; i < logProbs.size(); i++) {
+    double logProb = logProbs[i];
+    if ((logProb != std::numeric_limits<double>::infinity()) &&
+        logProb > maxLogProb) {
+      maxLogProb = logProb;
+    }
+  }
+
+  // After computing the max = "Z" of the log probabilities L_i, we compute
+  // the log of the normalizing constant, log S, where S = sum_j exp(L_j - Z).
+  double total = 0.0;
+  for (size_t i = 0; i < logProbs.size(); i++) {
+    double probPrime = exp(logProbs[i] - maxLogProb);
+    total += probPrime;
+  }
+  double logTotal = log(total);
+
+  // Now we compute the (normalized) probability (for each i):
+  // p_i = exp(L_i - Z - log S)
+  double checkNormalization = 0.0;
+  std::vector<double> probs;
+  for (size_t i = 0; i < logProbs.size(); i++) {
+    double prob = exp(logProbs[i] - maxLogProb - logTotal);
+    probs.push_back(prob);
+    checkNormalization += prob;
+  }
+
+  // Numerical tolerance for floating point comparisons
+  double tol = 1e-9;
+
+  if (!gtsam::fpEqual(checkNormalization, 1.0, tol)) {
+    std::string errMsg =
+        std::string("expNormalize failed to normalize probabilities. ") +
+        std::string("Expected normalization constant = 1.0. Got value: ") +
+        std::to_string(checkNormalization) +
+        std::string(
+            "\n This could have resulted from numerical overflow/underflow.");
+    throw std::logic_error(errMsg);
+  }
+  return probs;
+}
+
 }  // namespace gtsam

gtsam/discrete/DiscreteFactor.h

@@ -122,4 +122,24 @@ public:
 // traits
 template<> struct traits<DiscreteFactor> : public Testable<DiscreteFactor> {};
 
+
+/**
+ * @brief Normalize a set of log probabilities.
+ *
+ * Normalizing a set of log probabilities in a numerically stable way is
+ * tricky. To avoid overflow/underflow issues, we compute the largest
+ * (finite) log probability and subtract it from each log probability before
+ * normalizing. This comes from the observation that if:
+ *    p_i = exp(L_i) / ( sum_j exp(L_j) ),
+ * Then,
+ *    p_i = exp(Z) exp(L_i - Z) / (exp(Z) sum_j exp(L_j - Z)),
+ *        = exp(L_i - Z) / ( sum_j exp(L_j - Z) )
+ *
+ * Setting Z = max_j L_j, we can avoid numerical issues that arise when all
+ * of the (unnormalized) log probabilities are either very large or very
+ * small.
+ */
+std::vector<double> expNormalize(const std::vector<double> &logProbs);
+
+
 }// namespace gtsam