  We revisit widely used preferential Gaussian processes by Chu et al.(2005)
and challenge their modelling assumption that imposes rankability of data items
via latent utility function values. We propose a generalisation of pgp which
can capture more expressive latent preferential structures in the data and thus
be used to model inconsistent preferences, i.e. where transitivity is violated,
or to discover clusters of comparable items via spectral decomposition of the
learned preference functions. We also consider the properties of associated
covariance kernel functions and its reproducing kernel Hilbert Space (RKHS),
giving a simple construction that satisfies universality in the space of
preference functions. Finally, we provide an extensive set of numerical
experiments on simulated and real-world datasets showcasing the competitiveness
of our proposed method with state-of-the-art. Our experimental findings support
the conjecture that violations of rankability are ubiquitous in real-world
preferential data.
