Seems your model is badly conditioned, with almost as many rows as columns, and few columns with many 0s. Would you be able to run a linear regression using eg scipy?
Also, you should change your prior (Uniform priors are usually bad idea), change the sampler (Metropolis failed saliently sometimes), change the initialization (using MAP as starting value is a bad idea). 
In another word, try with the default:
with model:
trace = sample(1000, tune=1000)