void BinomialFactor::mkFactor(matrix_t &m) const{
boost::math::binomial binom(N_, prob_);
//Return vector with probabilities over x
for(int j = 0; j < m.size2(); ++j){
if( j+minv_ > N_)
m(0,j) = 0;
else
m(0,j) = pdf( binom, j+minv_);
}
}
void normalizeRM(matrix_t & Q, StateMap const & staMap, float subs)
{
vector_t equiFreq = deriveEquiFreqForReversibleRM(Q);
HammingDistance hammingDistance(staMap);
number_t normConst = 0;
for (unsigned i = 0; i < Q.size1(); ++ i)
for (unsigned j = 0; j < Q.size2(); ++ j)
normConst += equiFreq(i) * Q(i,j) * hammingDistance(i,j);
Q = Q * (subs / normConst);
}
void output_matrix(ostream& out, matrix_t& M, unsigned n) {
out << "matrix_t M[" << n << "] = {\n";
for (unsigned i=0; i<M.size1(); ++i) {
out << "\t{ ";
out << M(i,0);
for (unsigned j=1; j<M.size2() ; ++j)
out << ',' << M(i,j);
out << " },\n";
}
out << "}\n";
}
// LU factorization of a general matrix A.
// Computes an LU factorization of a general M-by-N matrix A using
// partial pivoting with row interchanges. Factorization has the form
// A = P*L*U.
// a (IN/OUT - matrix(M,N)) On entry, the coefficient matrix A to be factored. On exit, the factors L and U from the factorization A = P*L*U.
// ipivot (OUT - vector(min(M,N))) Integer vector. The row i of A was interchanged with row IPIV(i).
// info (OUT - int)
// 0 : successful exit
// < 0 : If INFO = -i, then the i-th argument had an illegal value.
// > 0 : If INFO = i, then U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.
int getrf (matrix_t& a, pivot_t& ipivot)
{
matrix_t::value_type* _a = a.data().begin();
int _m = int(a.size1());
int _n = int(a.size2());
int _lda = _m; // minor size
int _info;
rawLAPACK::getrf (_m, _n, _a, _lda, ipivot.data().begin(), _info);
return _info;
}
// QR Factorization of a MxN General Matrix A.
// a (IN/OUT - matrix(M,N)) On entry, the coefficient matrix A. On exit , the upper triangle and diagonal is the min(M,N) by N upper triangular matrix R. The lower triangle, together with the tau vector, is the orthogonal matrix Q as a product of min(M,N) elementary reflectors.
// tau (OUT - vector (min(M,N))) Vector of the same numerical type as A. The scalar factors of the elementary reflectors.
// info (OUT - int)
// 0 : function completed normally
// < 0 : The ith argument, where i = abs(return value) had an illegal value.
int geqrf (matrix_t& a, vector_t& tau)
{
int _m = int(a.size1());
int _n = int(a.size2());
int _lda = int(a.size1());
int _info;
// make_sure tau's size is greater than or equal to min(m,n)
if (int(tau.size()) < (_n<_m ? _n : _m) )
return -104;
int ldwork = _n*_n;
vector_t dwork(ldwork);
rawLAPACK::geqrf (_m, _n, a.data().begin(), _lda, tau.data().begin(), dwork.data().begin(), ldwork, _info);
return _info;
}
// Solution to a system using LU factorization
// Solves a system of linear equations A*X = B with a general NxN
// matrix A using the LU factorization computed by GETRF.
// transa (IN - char) 'T' for the transpose of A, 'N' otherwise.
// a (IN - matrix(M,N)) The factors L and U from the factorization A = P*L*U as computed by GETRF.
// ipivot (IN - vector(min(M,N))) Integer vector. The pivot indices from GETRF; row i of A was interchanged with row IPIV(i).
// b (IN/OUT - matrix(ldb,NRHS)) Matrix of same numerical type as A. On entry, the right hand side matrix B. On exit, the solution matrix X.
//
// info (OUT - int)
// 0 : function completed normally
// < 0 : The ith argument, where i = abs(return value) had an illegal value.
// > 0 : if INFO = i, U(i,i) is exactly zero; the matrix is singular and its inverse could not be computed.
int getrs (char transa, matrix_t& a,
pivot_t& ipivot, matrix_t& b)
{
matrix_t::value_type* _a = a.data().begin();
int a_n = int(a.size1());
int _lda = a_n;
int p_n = int(ipivot.size());
matrix_t::value_type* _b = b.data().begin();
int b_n = int(b.size1());
int _ldb = b_n;
int _nrhs = int(b.size2()); /* B's size2 is the # of vectors on rhs */
if (a_n != b_n) /*Test to see if AX=B has correct dimensions */
return -101;
if (p_n < a_n) /*Check to see if ipivot is big enough */
return -102;
int _info;
rawLAPACK::getrs (transa, a_n, _nrhs, _a, _lda, ipivot.data().begin(),
_b, _ldb, _info);
return _info;
}
HMM::posterior_t HMM::posterior_gradient(const Data::Set &dataset,
const Training::Task &task,
bitmask_t present,
matrix_t &transition_g,
matrix_t &emission_g) const {
// Training::Task task(task_);
if (verbosity >= Verbosity::verbose)
cout << "Posterior gradient calculation (Feature)." << endl;
SubHMM subhmm(*this, complementary_states_mask(present));
// cout << subhmm << endl;
if (verbosity >= Verbosity::debug) {
cout << "Transition targets are";
for (auto x : task.targets.transition)
cout << " " << x;
cout << endl;
cout << "Emission targets are";
for (auto x : task.targets.emission)
cout << " " << x;
cout << endl;
}
if (not task.targets.transition.empty())
transition_g = zero_matrix(n_states, n_states);
if (not task.targets.emission.empty())
emission_g = zero_matrix(n_states, n_emissions);
double posterior = 0;
vector<matrix_t> t_g, e_g;
Training::Targets reduced_targets = subhmm.map_down(task.targets);
if (verbosity >= Verbosity::debug) {
cout << "targets emission = ";
for (auto &x : task.targets.emission)
cout << " " << x;
cout << endl;
cout << "targets transition = ";
for (auto &x : task.targets.transition)
cout << " " << x;
cout << endl;
cout << "reduced targets emission = ";
for (auto &x : reduced_targets.emission)
cout << " " << x;
cout << endl;
cout << "reduced targets transition = ";
for (auto &x : reduced_targets.transition)
cout << " " << x;
cout << endl;
}
double l = 0;
#pragma omp parallel shared(emission_g, transition_g) if (DO_PARALLEL)
{
#pragma omp single
// Initalize storage for thread intermediate results
{
size_t n_threads = omp_get_num_threads();
// cout << "B Num threads = " << n_threads << endl;
if (not task.targets.transition.empty())
t_g = vector<matrix_t>(
n_threads, zero_matrix(transition_g.size1(), transition_g.size2()));
if (not task.targets.emission.empty())
e_g = vector<matrix_t>(
n_threads, zero_matrix(emission_g.size1(), emission_g.size2()));
}
#pragma omp for reduction(+ : posterior, l)
// Compute gradient for each sequence
for (size_t i = 0; i < dataset.sequences.size(); i++) {
int thread_idx = omp_get_thread_num();
if (verbosity >= Verbosity::debug)
cout << "Thread " << thread_idx << " Data sample " << i << endl
<< seq2string(dataset.sequences[i].isequence) << endl;
// Compute expected statistics, for the full and reduced models
matrix_t T, Tr, E, Er;
double logp
= BaumWelchIteration_single(T, E, dataset.sequences[i], task.targets);
double logpr = subhmm.BaumWelchIteration_single(
Tr, Er, dataset.sequences[i], reduced_targets);
Tr = subhmm.lift_transition(Tr);
Er = subhmm.lift_emission(Er);
if (verbosity >= Verbosity::debug)
cout << "Full logp = " << logp << endl << "Reduced logp = " << logpr
<< endl << "Expected transitions full = " << T << endl
<< "Expected emissions full = " << E << endl
<< "Expected transitions constitutive_range = " << Tr << endl
<< "Expected emissions constitutive_range = " << Er << endl;
if (not task.targets.transition.empty()) {
// Compute log likelihood gradients for the full model w.r.t. transition
// probability
matrix_t t = transition_gradient(T, task.targets.transition);
// Compute log likelihood gradients for the reduced model w.r.t.
// transition probability
matrix_t tr = transition_gradient(Tr, task.targets.transition);
// Compute posterior probability gradients for the reduced model w.r.t.
// transition probability and accumulate
t_g[thread_idx] += exp(logpr - logp) * (t - tr);
}
if (not task.targets.emission.empty()) {
// Compute log likelihood gradients for the full model w.r.t. emission
// probability
matrix_t e = emission_gradient(E, task.targets.emission);
// Compute log likelihood gradients for the reduced model w.r.t.
// emission probability
matrix_t er = emission_gradient(Er, task.targets.emission);
// Compute posterior probability gradients for the reduced model w.r.t.
// emission probability and accumulate
e_g[thread_idx] += exp(logpr - logp) * (e - er);
}
posterior += 1 - exp(logpr - logp);
l += logp;
}
#pragma omp single
// Collect results of threads
{
if (not task.targets.transition.empty())
for (auto &x : t_g)
transition_g += x;
if (not task.targets.emission.empty())
for (auto &x : e_g)
emission_g += x;
}
}
if (verbosity >= Verbosity::verbose)
cout << "The posterior coming from the gradient calculus: " << posterior
<< endl;
posterior_t result = {l, posterior};
return result;
}
double HMM::log_likelihood_gradient(const Data::Seqs &seqs,
const Training::Targets &targets,
matrix_t &transition_g,
matrix_t &emission_g) const {
transition_g = zero_matrix(n_states, n_states);
emission_g = zero_matrix(n_states, n_emissions);
double lp = 0;
vector<matrix_t> t_g, e_g;
#pragma omp parallel shared(emission_g, transition_g) if (DO_PARALLEL)
{
#pragma omp single
// Initalize storage for thread intermediate results
{
size_t n_threads = omp_get_num_threads();
// cout << "B Num threads = " << n_threads << endl;
if (not targets.transition.empty())
t_g = vector<matrix_t>(
n_threads, zero_matrix(transition_g.size1(), transition_g.size2()));
if (not targets.emission.empty())
e_g = vector<matrix_t>(
n_threads, zero_matrix(emission_g.size1(), emission_g.size2()));
}
#pragma omp for reduction(+ : lp)
// Compute likelihood for each sequence
for (size_t i = 0; i < seqs.size(); i++) {
int thread_idx = omp_get_thread_num();
vector_t scale;
matrix_t f = compute_forward_scaled(seqs[i], scale);
matrix_t b = compute_backward_prescaled(seqs[i], scale);
// Compute expected statistics
matrix_t T, E;
double logp = BaumWelchIteration_single(T, E, seqs[i], targets);
if (not targets.transition.empty())
// Compute log likelihood gradients w.r.t. transition probability
t_g[thread_idx] += transition_gradient(T, targets.transition);
if (not targets.emission.empty())
// Compute log likelihood gradients w.r.t. emission probability
e_g[thread_idx] += emission_gradient(E, targets.emission);
lp += logp;
}
#pragma omp single
// Collect results of threads
{
if (not targets.transition.empty())
for (auto &x : t_g)
transition_g += x;
if (not targets.emission.empty())
for (auto &x : e_g)
emission_g += x;
}
}
return lp;
}