  We propose an iterative proposal to estimate critical points for statistical
models based on configurations by combing machine-learning tools. Firstly,
phase scenarios and preliminary boundaries of phases are obtained by
dimensionality-reduction techniques. Besides, this step not only provides
labelled samples for the subsequent step but also is necessary for its
application to novel statistical models. Secondly, making use of these samples
as training set, neural networks are employed to assign labels to those samples
between the phase boundaries in an iterative manner. Newly labelled samples
would be put in the training set used in subsequent training and the phase
boundaries would be updated as well. The average of the phase boundaries is
expected to converge to the critical temperature in this proposal. In concrete
examples, we implement this proposal to estimate the critical temperatures for
two q-state Potts models with continuous and first order phase transitions.
Linear and manifold dimensionality-reduction techniques are employed in the
first step. Both a convolutional neural network and a bidirectional recurrent
neural network with long short-term memory units perform well for two Potts
models in the second step. The convergent behaviors of the estimations reflect
the types of phase transitions. And the results indicate that our proposal may
be used to explore phase transitions for new general statistical models.
