def LQLEP( theta = Th.dvector() , M = Th.dmatrix() ,
STA = Th.dvector() , STC = Th.dmatrix() ,
N_spike = Th.dscalar() , Cm1 = Th.dmatrix() , **other):
'''
The actual Linear-Quadratic-Exponential-Poisson log-likelihood,
as a function of theta and M, without any barriers or priors.
'''
# ImM = Th.identity_like(M)-(M+M.T)/2
ImM = Cm1-(M+M.T)/2
ldet = logdet(ImM)
LQLEP = -0.5 * N_spike *( ldet - logdet(Cm1) \
- Th.sum(Th.dot(matrix_inverse(ImM),theta) * theta) \
+ 2. * Th.sum( theta * STA ) \
+ Th.sum( M * (STC + Th.outer(STA,STA)) ))
other.update(locals())
return named( **other )
def LNLEP( theta = Th.dvector('theta'), M = Th.dmatrix('M') ,
STA = Th.dvector('STA') , STC = Th.dmatrix('STC'),
N_spike = Th.dscalar('N_spike'), **other):
'''
The actual quadratic-Poisson model, as a function of theta and M,
without any barriers or priors.
'''
ImM = Th.identity_like(M)-(M+M.T)/2
ldet = logdet(ImM) # Th.log( det( ImM) ) # logdet(ImM)
return -0.5 * N_spike *(
ldet \
- Th.sum(Th.dot(matrix_inverse(ImM),theta) * theta) \
+ 2. * Th.sum( theta * STA ) \
+ Th.sum( M * (STC + Th.outer(STA,STA)) ))
def quadratic_Poisson( theta = Th.dvector('theta'), M = Th.dmatrix('M') ,
STA = Th.dvector('STA') , STC = Th.dmatrix('STC'),
N_spike = Th.dscalar('N_spike'), logprior = 0 ,
**other):
'''
The actual quadratic-Poisson model, as a function of theta and M,
with a barrier on the log-det term and a prior.
'''
ImM = Th.identity_like(M)-(M+M.T)/2
ldet = logdet(ImM) # Th.log( det( ImM) ) # logdet(ImM)
return -0.5 * N_spike *(
ldet + logprior \
- 1./(ldet+250.)**2. \
- Th.sum(Th.dot(matrix_inverse(ImM),theta) * theta) \
+ 2. * Th.sum( theta * STA ) \
+ Th.sum( M * (STC + Th.outer(STA,STA)) ))
def logdetIM( M = Th.dmatrix('M') , **result):
return logdet( Th.identity_like(M)-(M+M.T)/2 )