  We study the Schatten class membership of semicommutative martingale
paraproducts and use the transference method to describe Schatten class
membership of purely noncommutative martingale paraproducts, especially for CAR
algebras and $\mathop{\otimes}\limits_{k=1}^{\infty}\mathbb{M}_{d}$ in terms of
martingale Besov spaces.
  Using Hyt\"{o}nen's dyadic martingale technique, we also obtain sufficient
conditions on the Schatten class membership and the boundedness of
operator-valued commutators involving general singular integral operators.
  We establish the complex median method, which is applicable to complex-valued
functions. We apply it to get the optimal necessary conditions on the Schatten
class membership of operator-valued commutators associated with non-degenerate
kernels in Hyt\"{o}nen's sense. This resolves the problem on the
characterization of Schatten class membership of operator-valued commutators.
Our results are new even in the scalar case.
  Our new approach is built on Hyt\"{o}nen's dyadic martingale technique and
the complex median method. Compared with all the previous ones, this new one is
more powerful in several aspects: $(a)$ it permits us to deal with more general
singular integral operators with little smoothness; $(b)$ it allows us to deal
with commutators with complex-valued kernels; $(c)$ it goes much further beyond
the scalar case and can be applied to the semicommutative setting.
  By a weak-factorization type decomposition, we get some necessary but not
optimal conditions on the boundedness of operator-valued commutators. In
addition, we give a new proof of the boundedness of commutators still involving
general singular integral operators concerning $BMO$ spaces in the commutative
setting.
