diff --git a/src/dialect/models/interaction.py b/src/dialect/models/interaction.py
index 03fb6ce..b5d02f2 100644
--- a/src/dialect/models/interaction.py
+++ b/src/dialect/models/interaction.py
@@ -47,10 +47,14 @@ def __str__(self):
         )
 
         pi_a = (
-            f"{self.gene_a.pi:.3e}" if self.gene_a.pi is not None else "Not estimated"
+            f"{self.gene_a.pi:.3e}"
+            if self.gene_a.pi is not None
+            else "Not estimated"
         )
         pi_b = (
-            f"{self.gene_b.pi:.3e}" if self.gene_b.pi is not None else "Not estimated"
+            f"{self.gene_b.pi:.3e}"
+            if self.gene_b.pi is not None
+            else "Not estimated"
         )
 
         cm = self.compute_contingency_table()
@@ -146,7 +150,9 @@ def verify_taus_are_valid(self, taus, tol=1e-6):
         :param tol: (float) Tolerance for the sum of tau parameters (default: 1e-1).
         :raises ValueError: If any or all tau parameters are invalid.
         """
-        if not all(0 <= t <= 1 for t in taus) or not np.isclose(sum(taus), 1, atol=tol):
+        if not all(0 <= t <= 1 for t in taus) or not np.isclose(
+            sum(taus), 1, atol=tol
+        ):
             logging.info(f"Invalid tau parameters: {taus}")
             raise ValueError(
                 "Invalid tau parameters. Ensure 0 <= tau_i <= 1 and sum(tau) == 1."
@@ -173,7 +179,9 @@ def verify_pi_values(self, pi_a, pi_b):
             logging.warning(
                 f"Driver probabilities (pi) are not defined for genes in interaction {self.name}."
             )
-            raise ValueError("Driver probabilities are not defined for both genes.")
+            raise ValueError(
+                "Driver probabilities are not defined for both genes."
+            )
 
     # ---------------------------------------------------------------------------- #
     #                        Likelihood & Metric Evaluation                        #
@@ -294,7 +302,8 @@ def compute_likelihood_ratio(self, taus):
         driver_b_marginal = tau_01 + tau_11
 
         tau_null = (
-            (1 - driver_a_marginal) * (1 - driver_b_marginal),  #  both genes passengers
+            (1 - driver_a_marginal)
+            * (1 - driver_b_marginal),  #  both genes passengers
             (1 - driver_a_marginal)
             * driver_b_marginal,  # gene a passenger, gene b driver
             driver_a_marginal
@@ -370,7 +379,9 @@ def compute_wald_statistic(self, taus):
         self.verify_taus_are_valid(taus)
         log_odds_ratio = self.compute_log_odds_ratio(taus)
         if log_odds_ratio is None:
-            logging.warning(f"Log odds ratio is None for interaction {self.name}.")
+            logging.warning(
+                f"Log odds ratio is None for interaction {self.name}."
+            )
             return None
 
         try:
@@ -522,7 +533,9 @@ def estimate_tau_with_em_from_scratch(
         **Returns**:
         :return: (tuple) The estimated values of \( (\\tau_{00}, \\tau_{01}, \\tau_{10}, \\tau_{11}) \).
         """
-        logging.info("Estimating tau parameters using EM algorithm from scratch.")
+        logging.info(
+            "Estimating tau parameters using EM algorithm from scratch."
+        )
 
         self.verify_bmr_pmf_and_counts_exist()
 
@@ -532,10 +545,22 @@ def estimate_tau_with_em_from_scratch(
             total_probabilities = self.compute_total_probability(
                 tau_00, tau_01, tau_10, tau_11
             )  # denominator in E-Step equation
-            z_i_00 = self.compute_joint_probability(tau_00, 0, 0) / total_probabilities
-            z_i_01 = self.compute_joint_probability(tau_01, 0, 1) / total_probabilities
-            z_i_10 = self.compute_joint_probability(tau_10, 1, 0) / total_probabilities
-            z_i_11 = self.compute_joint_probability(tau_11, 1, 1) / total_probabilities
+            z_i_00 = (
+                self.compute_joint_probability(tau_00, 0, 0)
+                / total_probabilities
+            )
+            z_i_01 = (
+                self.compute_joint_probability(tau_01, 0, 1)
+                / total_probabilities
+            )
+            z_i_10 = (
+                self.compute_joint_probability(tau_10, 1, 0)
+                / total_probabilities
+            )
+            z_i_11 = (
+                self.compute_joint_probability(tau_11, 1, 1)
+                / total_probabilities
+            )
 
             # M-Step: Update tau parameters
             curr_tau_00 = np.mean(z_i_00)
@@ -566,7 +591,9 @@ def estimate_tau_with_em_from_scratch(
             tau_10,
             tau_11,
         )
-        logging.info(" EM algorithm converged after {} iterations.".format(it + 1))
+        logging.info(
+            " EM algorithm converged after {} iterations.".format(it + 1)
+        )
         logging.info(
             f"Estimated tau parameters for interaction {self.name}: tau_00={self.tau_00}, tau_01={self.tau_01}, tau_10={self.tau_10}, tau_11={self.tau_11}"
         )