def meanField(self):
N,K,T,S,A,X,t = self.N,self.K,self.T,self.S,self.A,self.X,self.t
Tr,L,D,pS0,pA0 = self.Tr,self.L,self.D,self.pS0,self.pA0
### initialize
qA = pr.func(vars=list(A.values()), val='unif').normalize()
qS = {**{i: pr.func(vars=[S[i]], val='unif').normalize([S[i]]) for i in range(0,t+1)},
**{i: pr.func(vars=[S[i],*[A[j] for j in range(t,i)]],val='unif').normalize([S[i]]) for i in range(t+1,T+1)}}
## repeat:
for iter in range(self.iterations):
if t > 0:
qS[0] = (L[0]*pS0*pr.exp_tr(pr.sum([S[1]],pr.log(Tr[0])*qS[1]))).normalize([S[0]])
for tau in range(1,t):
qS[tau] = (L[tau]*pr.exp_tr(pr.sum([S[tau-1]],pr.log(Tr[tau-1])*qS[tau-1]))
+pr.sum([S[tau+1]],pr.log(Tr[tau])*qS[tau+1])).normalize([S[tau]])
qS[t] = (L[t]*pr.exp_tr(pr.sum([S[t-1]],pr.log(Tr[t-1])*qS[t-1]))
+pr.sum([S[t+1],A[t]],pr.log(Tr[t])*qS[t+1]*pr.sum(qA,[A[t]]))).normalize([S[t]])
else:
qS[0] = (L[0]*pS0*pr.exp_tr(pr.sum([S[1],A[0]],pr.log(Tr[0])*qS[1]*pr.sum(qA,[A[0]])))).normalize([S[0]])
for tau in range(t+1,T):
qS[tau] = (pr.exp_tr(pr.sum([S[tau-1]],pr.log(Tr[tau-1])*qS[tau-1])
+ pr.sum([S[tau+1],A[tau]],pr.log(Tr[tau])*qS[tau+1]*pr.sum(qA,[A[tau]]))
+ pr.sum([X[tau]],pr.log(D[tau])*L[tau])
)).normalize([S[tau]])
qS[T] = (pr.exp_tr(pr.sum([S[T-1]],pr.log(Tr[T-1])*qS[T-1])
+ pr.sum([X[T]],pr.log(D[T])*L[T])
)).normalize([S[T]])
G = 0
for tau in range(t+1,T+1):
G = G + ( pr.sum([S[tau-1],S[tau]],pr.log(Tr[tau-1])*qS[tau]*qS[tau-1])
- pr.sum([S[tau]],pr.log(qS[tau])*qS[tau])
+ pr.sum([X[tau],S[tau]],pr.log(D[tau])) )
qA = (pA0*pr.exp_tr(self.alpha*G)).normalize()
return pr.sum(qA,[A[t]]).val
def meanField(self):
precision=1e-4
N,K,T,S,A,X,t = self.N,self.K,self.T,self.S,self.A,self.X,self.t
Tr,L,D,pS0,pA0 = self.Tr,self.L,self.D,self.pS0,self.pA0
### initialize
qA = pr.func(vars=list(A.values()), val='unif').normalize()
qS = {**{i: pr.func(vars=[S[i],*[A[j] for j in range(t,T)]], val='unif').normalize([S[i]]) for i in range(0,t+1)},
**{i: pr.func(vars=[S[i],*[A[j] for j in range(t,T)]],val='unif').normalize([S[i]]) for i in range(t+1,T+1)}}
## repeat:
q0 = 0
for iter in range(self.iterations):
qS[0] = (L[0]*pS0*pr.exp_tr(pr.sum([S[1]],pr.log(Tr[0])*qS[1]))).normalize([S[0]])
if t > 0:
for tau in range(1,t):
qS[tau] = (L[tau]*pr.exp_tr(pr.sum([S[tau-1]],pr.log(Tr[tau-1])*qS[tau-1]))
+pr.sum([S[tau+1]],pr.log(Tr[tau])*qS[tau+1])).normalize([S[tau]])
qS[t] = (L[t]*pr.exp_tr(pr.sum([S[t-1]],pr.log(Tr[t-1])*qS[t-1]))
+pr.sum([S[t+1]],pr.log(Tr[t])*qS[t+1])).normalize([S[t]])
for tau in range(t+1,T):
qS[tau] = (pr.exp_tr(pr.sum([S[tau-1]],pr.log(Tr[tau-1])*qS[tau-1])
+ pr.sum([S[tau+1]],pr.log(Tr[tau])*qS[tau+1]))).normalize([S[tau]])
qS[T] = pr.exp_tr(pr.sum([S[T-1]],pr.log(Tr[T-1])*qS[T-1])).normalize([S[T]])
G = 0
for tau in range(t+1,T+1):
G = G + ( pr.sum([S[tau-1],S[tau]],pr.log(Tr[tau-1])*qS[tau]*qS[tau-1])
- pr.sum([S[tau]],pr.log(qS[tau])*qS[tau])
+ pr.sum([X[tau],S[tau]],(pr.log(L[tau])+pr.log(D[tau]))*L[tau]*qS[tau])
- pr.sum([X[tau],S[tau]],pr.log(pr.sum([S[tau]],L[tau]*qS[tau]))*L[tau]*qS[tau]))
G = G + ( pr.sum([S[0]],pr.log(pS0)*qS[0])
- pr.sum([S[0]],pr.log(qS[0])*qS[0])
+ pr.sum([S[0]],pr.log(L[0])*qS[0]))
for tau in range(1,t+1):
G = G + ( pr.sum([S[tau-1],S[tau]],pr.log(Tr[tau-1])*qS[tau]*qS[tau-1])
- pr.sum([S[tau]],pr.log(qS[tau])*qS[tau])
+ pr.sum([S[tau]],pr.log(L[tau])*qS[tau]) )
qA = (pA0*pr.exp_tr(self.alpha*G)).normalize()
qAmarg = pr.sum(qA,[A[t]]).val
if np.linalg.norm(qAmarg-q0) < precision:
break
q0 = qAmarg
return qAmarg
def meanField(self):
precision=1e-3
N,K,T,S,A,X,t = self.N,self.K,self.T,self.S,self.A,self.X,self.t
Tr,L,D,pS0,pA0 = self.Tr,self.L,self.D,self.pS0,self.pA0
### initialize
qA = pr.func(vars=list(A.values()), val='unif').normalize()
qS = {**{i: pr.func(vars=[S[i]], val='unif').normalize([S[i]]) for i in range(0,t+1)},
**{i: pr.func(vars=[S[i],*[A[j] for j in range(t,i)]],val='unif').normalize([S[i]]) for i in range(t+1,T+1)}}
## repeat:
q0 = 0
for iter in range(self.iterations):
# PAST AND CURRENT STATES
if t > 0:
qS[0] = (L[0]*pS0*pr.exp_tr(pr.sum([S[1]],pr.log(Tr[0])*qS[1]))).normalize([S[0]])
for tau in range(1,t):
qS[tau] = (L[tau]*pr.exp_tr(pr.sum([S[tau-1]],pr.log(Tr[tau-1])*qS[tau-1]))
+pr.sum([S[tau+1]],pr.log(Tr[tau])*qS[tau+1])).normalize([S[tau]])
qS[t] = (L[t]*pr.exp_tr(pr.sum([S[t-1]],pr.log(Tr[t-1])*qS[t-1]))
+pr.sum([S[t+1],A[t]],pr.log(Tr[t])*qS[t+1]*pr.sum(qA,[A[t]]))).normalize([S[t]])
else:
qS[0] = (L[0]*pS0*pr.exp_tr(pr.sum([S[1],A[0]],pr.log(Tr[0])*qS[1]*pr.sum(qA,[A[0]])))).normalize([S[0]])
# FUTURE STATES --- replaced by gradient descent ---------
for tau in range(t+1,T):
qp = qS[tau+1].val
qm = qS[tau-1].val
qS[tau].val = get_qS_GD(t,tau,T,N,K,self.pTrans,self.likelihood,self.pDesired,qm,qp,qA.val)
qS[T].val = get_qS_GD(t,T,T,N,K,self.pTrans,self.likelihood,self.pDesired,qS[T-1].val,[],qA.val)
#----------------------------------------------------------
# ACTION
G = 0
for tau in range(t+1,T+1):
G = G + ( pr.sum([S[tau-1],S[tau]],pr.log(Tr[tau-1])*qS[tau]*qS[tau-1])
- pr.sum([S[tau]],pr.log(qS[tau])*qS[tau])
+ pr.sum([X[tau],S[tau]],(pr.log(L[tau])+pr.log(D[tau]))*L[tau]*qS[tau])
- pr.sum([X[tau],S[tau]],pr.log(pr.sum([S[tau]],L[tau]*qS[tau]))*L[tau]*qS[tau]))
qA = (pA0*pr.exp_tr(self.alpha*G)).normalize()
qAmarg = pr.sum(qA,[A[t]]).val
if np.linalg.norm(qAmarg-q0) < precision:
break
q0 = qAmarg
return qAmarg
def _set_fixed(self):
"""
for current time step t,
put fixed quantities (likelihood, transition,...)
in pr_func instances
"""
S,A,X = self.S,self.A,self.X
self.pS0 = pr.func(vars=['S0'],val='unif').normalize() # unbiased belief of starting state
self.pA0 = pr.func(vars=list(A.values()),val='unif').normalize() # and action, i.e. these priors have no influence
self.Tr = {**{i : pr.func(vars=[S[i],S[i+1]],val=self.pTrans[:,self.a[i],:]) for i in range(0,self.t)}, # p0(S'|S,a)
**{i : pr.func(vars=[S[i],A[i],S[i+1]],val=self.pTrans) for i in range(self.t,self.T)}} # p0(S'|S,A)
self.L = {**{i : pr.func(vars=[S[i]],val=self.likelihood[:,self.x[i]]) for i in range(0,self.t+1)}, # p0(x|S)
**{i : pr.func(vars=[S[i],X[i]],val=self.likelihood) for i in range(self.t+1,self.T+1)}} # p0(X|S)
self.D = {i : pr.func(vars=[X[i]],val=self.pDesired) for i in range(self.t+1,self.T+1)} # pdes(X)