  Domain generalization aims to develop a model that can perform well on unseen
target domains by learning from multiple source domains. However,
recent-proposed domain generalization models usually rely on domain labels,
which may not be available in many real-world scenarios. To address this
challenge, we propose a Discriminant Risk Minimization (DRM) theory and the
corresponding algorithm to capture the invariant features without domain
labels. In DRM theory, we prove that reducing the discrepancy of prediction
distribution between overall source domain and any subset of it can contribute
to obtaining invariant features. To apply the DRM theory, we develop an
algorithm which is composed of Bayesian inference and a new penalty termed as
Categorical Discriminant Risk (CDR). In Bayesian inference, we transform the
output of the model into a probability distribution to align with our
theoretical assumptions. We adopt sliding update approach to approximate the
overall prediction distribution of the model, which enables us to obtain CDR
penalty. We also indicate the effectiveness of these components in finding
invariant features. We evaluate our algorithm against various domain
generalization methods on multiple real-world datasets, providing empirical
support for our theory.
