Our initial investigation identifies which distributions accurately characterize the feature space, subsequently leveraging this priori to guide the alignment of the weakly supervised embeddings. Specifically, we analyze the superiority of the mixture of von Mises-Fisher distributions (moVMF) among several common distribution candidates.

In addition, we examine two common computation frameworks for this problem, i.e., population-based training (PBT) and iterative learning

Numerical experiments are conducted tosupport our theoretical results.

Specifically,we prove that, forasimple data distribution with sparsesignal amidst high-variance noise, a simple convolutional neural network trained using stochastic gradient descent simultaneously learnstothreshold outthenoiseandfindthesignal.

A classical problem that fits in the framework of (1) is the best subset selection problem in linear regression [6,20].

The problem of (point) forecastingunivariate time series is considered.