diff --git a/python/tempo/ml.py b/python/tempo/ml.py
index 1c9f14ac..3db858af 100644
--- a/python/tempo/ml.py
+++ b/python/tempo/ml.py
@@ -12,32 +12,35 @@
 TMP_SPLIT_COL = "__tmp_split_col"
 TMP_GAP_COL = "__tmp_gap_row"
 
+
 class TimeSeriesCrossValidator(CrossValidator):
     # some additional parameters
     timeSeriesCol: Param[str] = Param(
         Params._dummy(),
         "timeSeriesCol",
         "The name of the time series column",
-        typeConverter=TypeConverters.toString
+        typeConverter=TypeConverters.toString,
     )
     seriesIdCols: Param[List[str]] = Param(
         Params._dummy(),
         "seriesIdCols",
         "The name of the series id columns",
-        typeConverter=TypeConverters.toListString
+        typeConverter=TypeConverters.toListString,
     )
     gap: Param[int] = Param(
         Params._dummy(),
         "gap",
         "The gap between training and test set",
-        typeConverter=TypeConverters.toInt
+        typeConverter=TypeConverters.toInt,
     )
 
-    def __init__(self,
-                 timeSeriesCol: str = "event_ts",
-                 seriesIdCols: List[str] = [],
-                 gap: int = 0,
-                 **other_kwargs) -> None:
+    def __init__(
+        self,
+        timeSeriesCol: str = "event_ts",
+        seriesIdCols: List[str] = [],
+        gap: int = 0,
+        **other_kwargs
+    ) -> None:
         super(TimeSeriesCrossValidator, self).__init__(**other_kwargs)
         self._setDefault(timeSeriesCol="event_ts", seriesIdCols=[], gap=0)
         self._set(timeSeriesCol=timeSeriesCol, seriesIdCols=seriesIdCols, gap=gap)
@@ -72,19 +75,24 @@ def _get_split_win(self, desc: bool = False) -> WindowSpec:
 
     def _kFold(self, dataset: DataFrame) -> List[Tuple[DataFrame, DataFrame]]:
         nFolds = self.getOrDefault(self.numFolds)
-        nSplits = nFolds+1
+        nSplits = nFolds + 1
 
         # split the data into nSplits subsets by timeseries order
-        split_df = dataset.withColumn(TMP_SPLIT_COL,
-                                      sfn.ntile(nSplits).over(self._get_split_win()))
-        all_splits = [split_df.filter(sfn.col(TMP_SPLIT_COL) == i).drop(TMP_SPLIT_COL)
-                      for i in range(1, nSplits+1)]
+        split_df = dataset.withColumn(
+            TMP_SPLIT_COL, sfn.ntile(nSplits).over(self._get_split_win())
+        )
+        all_splits = [
+            split_df.filter(sfn.col(TMP_SPLIT_COL) == i).drop(TMP_SPLIT_COL)
+            for i in range(1, nSplits + 1)
+        ]
         assert len(all_splits) == nSplits
 
         # compose the k folds by including all previous splits in the training set,
         # and the next split in the test set
-        kFolds = [(reduce(lambda a, b: a.union(b), all_splits[:i+1]), all_splits[i+1])
-                  for i in range(nFolds)]
+        kFolds = [
+            (reduce(lambda a, b: a.union(b), all_splits[: i + 1]), all_splits[i + 1])
+            for i in range(nFolds)
+        ]
         assert len(kFolds) == nFolds
         for tv in kFolds:
             assert len(tv) == 2
@@ -94,13 +102,21 @@ def _kFold(self, dataset: DataFrame) -> List[Tuple[DataFrame, DataFrame]]:
         if gap > 0:
             order_cols = self.getSeriesIdCols() + [self.getTimeSeriesCol()]
             # trim each training dataset by the specified gap
-            kFolds = [((train_df.withColumn(TMP_GAP_COL,
-                                            sfn.row_number().over(self._get_split_win(desc=True)))
+            kFolds = [
+                (
+                    (
+                        train_df.withColumn(
+                            TMP_GAP_COL,
+                            sfn.row_number().over(self._get_split_win(desc=True)),
+                        )
                         .where(sfn.col(TMP_GAP_COL) > gap)
                         .drop(TMP_GAP_COL)
-                        .orderBy(*order_cols)),
-                       test_df)
-                      for (train_df, test_df) in kFolds]
+                        .orderBy(*order_cols)
+                    ),
+                    test_df,
+                )
+                for (train_df, test_df) in kFolds
+            ]
 
         # return the k folds (training, test) datasets
         return kFolds