  Optimal asset allocation is a key topic in modern finance theory. To realize
the optimal asset allocation on investor's risk aversion, various portfolio
construction methods have been proposed. Recently, the applications of machine
learning are rapidly growing in the area of finance. In this article, we
propose the Student's $t$-process latent variable model (TPLVM) to describe
non-Gaussian fluctuations of financial timeseries by lower dimensional latent
variables. Subsequently, we apply the TPLVM to minimum-variance portfolio as an
alternative of existing nonlinear factor models. To test the performance of the
proposed portfolio, we construct minimum-variance portfolios of global stock
market indices based on the TPLVM or Gaussian process latent variable model. By
comparing these portfolios, we confirm the proposed portfolio outperforms that
of the existing Gaussian process latent variable model.
