fix(stats): keep hidden Markov fitting alive on a single observation

Assisted-by: Qwen 3.8 Flash

CHANGELOG.md

@@ -20,6 +20,12 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
   longer exhausts its passes on a matrix it should have declared
   converged.
 
+**Statistics.**
+
+- `FitHiddenMarkovModel` fits a single-observation sequence instead of
+  crashing the process: a transition row with no evidence keeps its
+  previous estimate rather than dividing by zero.
+
 ## [1.0.0] - 2026-09-03
 
 The initial release of Tensor, a scientific computing library in pure

stats/hmm.go

@@ -524,6 +524,15 @@ func hmmReestimate(model *HiddenMarkovModel, observations []int, gamma, xi [][]f
 		for j := range states {
 			den += transition[k*states+j]
 		}
+		if den == 0 {
+			// No transition evidence reached this row, the single-
+			// observation sequence being the case in point: dividing the
+			// zero fills the row with NaN the constructor refuses, and
+			// the sweep after it crashed on the nil model that refusal
+			// left. The row keeps its previous estimate instead.
+			copy(transition[k*states:(k+1)*states], model.Transition[k*states:(k+1)*states])
+			continue
+		}
 		for j := range states {
 			transition[k*states+j] = math.Max(transition[k*states+j]/den, hmmFloor)
 		}

stats/hmm_test.go

@@ -343,3 +343,35 @@ func TestHiddenMarkovZeroProbabilitySequence(t *testing.T) {
 		t.Fatalf("the certain sequence answered (%g, %v), want (0, [1])", ll, filtered[0])
 	}
 }
+
+func TestHiddenMarkovFitSingleObservation(t *testing.T) {
+	// One observation carries emission and initial evidence but no
+	// transition evidence: the re-estimation divided the zero count into
+	// NaN rows, the constructor refused them, and the sweep then called
+	// a method on the nil model and crashed the process. The fit must
+	// answer with a valid model whose transitions keep their starting
+	// estimate.
+	g := core.NewGenerator(11)
+	res, err := FitHiddenMarkovModel(g, []int{0}, 2, 2)
+	if err != nil {
+		t.Fatalf("FitHiddenMarkovModel on one observation: %v", err)
+	}
+	if res.Model == nil {
+		t.Fatal("FitHiddenMarkovModel on one observation returned no model")
+	}
+	if math.IsNaN(res.LogLikelihood) || math.IsInf(res.LogLikelihood, 0) {
+		t.Fatalf("log likelihood = %g, want a finite value", res.LogLikelihood)
+	}
+	for k := range 2 {
+		sum := 0.0
+		for _, v := range res.Model.Transition[k*2 : k*2+2] {
+			if math.IsNaN(v) || v < 0 {
+				t.Fatalf("transition row %d holds %g, want probabilities", k, v)
+			}
+			sum += v
+		}
+		if math.Abs(sum-1) > 1e-9 {
+			t.Fatalf("transition row %d sums to %g, want 1", k, sum)
+		}
+	}
+}