  Leggett-Garg inequalities place bounds on the temporal correlations of a
system based on the principles of macroscopic realism $\textit{per se}$ and
noninvasive measurability. Their conventional formulation relies on the
ensemble-averaged products of observables measured at different instants of
time. However, a complete description that enables a precise understanding and
captures all physically relevant features requires the study of probability
distributions associated with noncommuting observables. In this article, we
propose a scheme to describe the dynamics of generic $N$-level quantum systems
("qudits") via a probability vector representation of the Schr\"odinger
equation and define a precise notion of no-signaling in time (NSIT) for the
probability distributions of noncommuting observables. This provides a
systematic way of identifying the interferences responsible for nonclassical
behavior. In addition, we introduce an interference witness measure to quantify
violations of NSIT for arbitrary general probabilistic states. For single-qubit
systems, we pinpoint the pivotal relation that establishes a connection between
the disturbance of observables incurred during a measurement and the resulting
NSIT violation. For large-$N$ systems where a manual determination is
infeasible, the classification of states as either NSIT-conforming or
NSIT-violating may be performed by a machine learning algorithm. We present a
proof-of-principle implementation of such an algorithm in which the classifier
function is prepared via supervised learning using pseudorandomly generated
training data sets composed of states whose corresponding classifications are
known $\textit{a priori}$.
