function y_hat = approx_yhat(X,x,alpha,b)
% X is a cell array

global Tgram

nx = length(x); % for how many x's are we evaluating?
y_hat = zeros(nx,1);
if (nx>1), PROGstart(nx); end
for n=1:nx
  x_n = x{n};
  %s = 0;
  s = b;
  for i=1:length(alpha)
    x_i = X{i};
    s = s + alpha(i) * UK_appr(x_n,x_i,Tgram);
  end
  y_hat(n) = sign(s);
  if (nx>1), PROGupdate(n); end
end
if (nx>1), PROGend; end
return