  We propose a method to infer lead-lag networks of traders from the
observation of their trade record as well as to reconstruct their state of
supply and demand when they do not trade. The method relies on the Kinetic
Ising model to describe how information propagates among traders, assigning a
positive or negative "opinion" to all agents about whether the traded asset
price will go up or down. This opinion is reflected by their trading behavior,
but whenever the trader is not active in a given time window, a missing value
will arise. Using a recently developed inference algorithm, we are able to
reconstruct a lead-lag network and to estimate the unobserved opinions, giving
a clearer picture about the state of supply and demand in the market at all
times.
  We apply our method to a dataset of clients of a major dealer in the Foreign
Exchange market at the 5 minutes time scale. We identify leading players in the
market and define a herding measure based on the observed and inferred
opinions. We show the causal link between herding and liquidity in the
inter-dealer market used by dealers to rebalance their inventories.
