Are random quantum phenomena happening without a cause? In everyday life, most of us assumes every event and object has a cause in some sense. I am wondering if the same is true for quantum physics. 
Does the random nature of quantum phenomena mean they have no cause or does the theory say that causes of quantum randomness are unknown?
The word "random" is used here in its ontological sense.
 A: Seems to me there is a misunderstanding here:

Does the random nature of quantum phenomena mean they have no cause or does the theory say that causes of quantum randomness are unknown?

Quantum phenomena are not random. They have been found to obey strict dynamical equations which are different than classical mechanics etc equations,  but still the phenomena are constrained by the bounds given by the solutions to these equations. 
We would not exist if it were not for the beautiful atomic energy levels. Nothing random about them.
Maybe you are confused by the probabilistic nature of quantum mechanics, probabilities do not mean randomness. There are dynamical systems behind the functions giving the probability distributions in space or energy etc. and a causal direction. 
Edit after discussions in comments:
Randomness in individual measurements at levels commensurate to $\hbar$ are bounded by  the Heisenberg Uncertainty principle so dynamical equations do not enter explicitly. Randomness in the energy levels  for individual particles are bounded by the width of the energy level given by dynamical equations. In general though, the solutions of quantum dynamical equations are deterministic for the ensemble of measurements from many individual particles/setups. The distribution for the ensemble is predictable from the dynamics, and causal. For example: if one measures a  lifetime from an ensemble plot of the order of $10^{-8}$ seconds one knows it cannot be an electromagnetic interaction, it is the weak interaction that is responsible for the decay.
A: Per request, made to an answer from a comment:
It was John Stuart Bell in 1964who proved by simple arithmetics that there are no hidden local variables behind the statistical nature of quantum processes, and behind the spooky non-locality displayed by entangled particles. Consequently, the paradox presented in the 1935 Einstein-Podolsky-Rosen paper upon which they claimed that quantum physics cannot be complete ("since it relies on statistical laws, it cannot give the ultimate full description of nature") is inherently wrong.
We understand causality as a relation that links post-events (effect) to prior-events (cause) (note that this does not necessarily mean similar chronological sequence, see here). In this sense, observable phenomena are dependent on deeper, possibly hidden variables, that nevertheless can be usually uncovered, at least at the macroscopic level. However, as Bell has proven, there are no hidden variables responsible for lowest-level quantum processes e.g. the random decay of radioactive elements. Therefore I would say that there exist no lower-level, ultimate cause for these processes.
A: Currently, we don't even know why the laws of quantum physics exist or what they are dependent upon, we only observe their properties, their results.
The "random" decay of an atom is not without cause, it's machinations are simply unpredictable, too complex to predict accurately and therefore we call them "random" but then prove they are not random through statistical evidence of billions of such events.
