PLearn 0.1
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Matern kernel with nu=1/2 that can be used for Automatic Relevance Determination. More...
#include <Matern1ARDKernel.h>
Public Member Functions | |
Matern1ARDKernel () | |
Default constructor. | |
virtual real | evaluate (const Vec &x1, const Vec &x2) const |
Compute K(x1,x2). | |
virtual void | computeGramMatrix (Mat K) const |
Compute the Gram Matrix. | |
virtual void | computeGramMatrixDerivative (Mat &KD, const string &kernel_param, real epsilon=1e-6) const |
Directly compute the derivative with respect to hyperparameters (Faster than finite differences...) | |
virtual void | evaluate_all_i_x (const Vec &x, const Vec &k_xi_x, real squared_norm_of_x=-1, int istart=0) const |
Fill k_xi_x with K(x_i, x), for all i from istart to istart + k_xi_x.length() - 1. | |
virtual string | classname () const |
virtual OptionList & | getOptionList () const |
virtual OptionMap & | getOptionMap () const |
virtual RemoteMethodMap & | getRemoteMethodMap () const |
virtual Matern1ARDKernel * | deepCopy (CopiesMap &copies) const |
virtual void | build () |
Post-constructor. | |
virtual void | makeDeepCopyFromShallowCopy (CopiesMap &copies) |
Transforms a shallow copy into a deep copy. | |
Static Public Member Functions | |
static string | _classname_ () |
static OptionList & | _getOptionList_ () |
static RemoteMethodMap & | _getRemoteMethodMap_ () |
static Object * | _new_instance_for_typemap_ () |
static bool | _isa_ (const Object *o) |
static void | _static_initialize_ () |
static const PPath & | declaringFile () |
Public Attributes | |
real | m_isp_persistence |
Inverse softplus of the O-U persistence parameter. | |
Static Public Attributes | |
static StaticInitializer | _static_initializer_ |
Protected Member Functions | |
real | derivIspSignalSigma (int i, int j, int arg, real K) const |
Derivative function with respect to isp_signal_sigma. | |
real | derivIspGlobalSigma (int i, int j, int arg, real K) const |
Derivative function with respect to isp_global_sigma. | |
void | derivIspPersistence (int i, int j, int arg, real K) const |
Compute derivative w.r.t. isp_persistence. | |
void | computeGramMatrixDerivIspSignalSigma (Mat &KD) const |
Compute derivative w.r.t. isp_signal_sigma for WHOLE MATRIX. | |
void | computeGramMatrixDerivIspInputSigma (Mat &KD, int arg) const |
Compute derivative w.r.t. isp_input_sigma[arg] for WHOLE MATRIX. | |
Static Protected Member Functions | |
static void | declareOptions (OptionList &ol) |
Declares the class options. | |
Private Types | |
typedef ARDBaseKernel | inherited |
Private Member Functions | |
void | build_ () |
This does the actual building. |
Matern kernel with nu=1/2 that can be used for Automatic Relevance Determination.
With nu=1/2, the Matern kernel corresponds to the Ornstein-Uhlenbeck process. This function is specified as:
k(x,y) = (sf / (2*a)) * exp(-a sum_i |x_i - y_i|/w_i) * k_kron(x,y)
where sf = softplus(isp_signal_sigma), a = softplus(isp_persistence), w_i = softplus(isp_global_sigma + isp_input_sigma[i]), and k_kron(x,y) is the result of the KroneckerBaseKernel evaluation, or 1.0 if there are no Kronecker terms. Note that since the Kronecker terms are incorporated multiplicatively, the very presence of the term associated to this kernel can be gated by the value of some input variable(s) (that are incorporated within one or more Kronecker terms).
Note that to make its operations more robust when used with unconstrained optimization of hyperparameters, all hyperparameters of this kernel are specified in the inverse softplus domain. See IIDNoiseKernel for more explanations.
Definition at line 69 of file Matern1ARDKernel.h.
typedef ARDBaseKernel PLearn::Matern1ARDKernel::inherited [private] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 71 of file Matern1ARDKernel.h.
PLearn::Matern1ARDKernel::Matern1ARDKernel | ( | ) |
Default constructor.
Definition at line 69 of file Matern1ARDKernel.cc.
: m_isp_persistence(pl_log(exp(1.0) - 1.)) // inverse-softplus(1.0) { }
string PLearn::Matern1ARDKernel::_classname_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
OptionList & PLearn::Matern1ARDKernel::_getOptionList_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
RemoteMethodMap & PLearn::Matern1ARDKernel::_getRemoteMethodMap_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
Object * PLearn::Matern1ARDKernel::_new_instance_for_typemap_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
StaticInitializer Matern1ARDKernel::_static_initializer_ & PLearn::Matern1ARDKernel::_static_initialize_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
void PLearn::Matern1ARDKernel::build | ( | ) | [virtual] |
Post-constructor.
The normal implementation should call simply inherited::build(), then this class's build_(). This method should be callable again at later times, after modifying some option fields to change the "architecture" of the object.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 92 of file Matern1ARDKernel.cc.
References PLearn::ARDBaseKernel::build(), and build_().
{ // ### Nothing to add here, simply calls build_ inherited::build(); build_(); }
void PLearn::Matern1ARDKernel::build_ | ( | ) | [private] |
This does the actual building.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 102 of file Matern1ARDKernel.cc.
References PLearn::KroneckerBaseKernel::m_default_value.
Referenced by build().
{ // Ensure that we multiply in Kronecker terms inherited::m_default_value = 1.0; }
string PLearn::Matern1ARDKernel::classname | ( | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
void PLearn::Matern1ARDKernel::computeGramMatrix | ( | Mat | K | ) | const [virtual] |
Compute the Gram Matrix.
Reimplemented from PLearn::KroneckerBaseKernel.
Definition at line 156 of file Matern1ARDKernel.cc.
References PLearn::Kernel::cache_gram_matrix, PLearn::KroneckerBaseKernel::computeGramMatrix(), PLearn::TVec< T >::data(), PLearn::Kernel::data, PLearn::Kernel::dataInputsize(), PLearn::diff(), PLearn::exp(), PLearn::TVec< T >::fill(), PLearn::Kernel::gram_matrix, PLearn::Kernel::gram_matrix_is_cached, i, j, PLearn::VMat::length(), m, PLearn::MemoryCachedKernel::m_data_cache, PLearn::ARDBaseKernel::m_input_sigma, PLearn::ARDBaseKernel::m_isp_global_sigma, PLearn::ARDBaseKernel::m_isp_input_sigma, m_isp_persistence, PLearn::ARDBaseKernel::m_isp_signal_sigma, PLearn::TMat< T >::mod(), n, PLASSERT, PLearn::TMat< T >::resize(), PLearn::TVec< T >::resize(), PLearn::TMat< T >::size(), PLearn::TVec< T >::size(), PLearn::softplus(), and PLearn::KroneckerBaseKernel::softplusFloor().
{ PLASSERT( !m_isp_input_sigma.size() || dataInputsize() == m_isp_input_sigma.size() ); PLASSERT( K.size() == 0 || m_data_cache.size() > 0 ); // Ensure data cached OK // Compute Kronecker gram matrix inherited::computeGramMatrix(K); // Precompute some terms. Make sure that the input sigmas don't get too // small real sf = softplus(m_isp_signal_sigma); real persistence = softplus(m_isp_persistence); m_input_sigma.resize(dataInputsize()); softplusFloor(m_isp_global_sigma, 1e-6); m_input_sigma.fill(m_isp_global_sigma); // Still in ISP domain for (int i=0, n=m_input_sigma.size() ; i<n ; ++i) { if (m_isp_input_sigma.size() > 0) { softplusFloor(m_isp_input_sigma[i], 1e-6); m_input_sigma[i] += m_isp_input_sigma[i]; } m_input_sigma[i] = softplus(m_input_sigma[i]); } // Compute Gram Matrix int l = data->length(); int m = K.mod(); int n = dataInputsize(); int cache_mod = m_data_cache.mod(); real *data_start = &m_data_cache(0,0); real *Ki = K[0]; // Start of current row real *Kij; // Current element along row real *input_sigma_data = m_input_sigma.data(); real *xi = data_start; for (int i=0 ; i<l ; ++i, xi += cache_mod, Ki+=m) { Kij = Ki; real *xj = data_start; for (int j=0; j<=i; ++j, xj += cache_mod) { // Kernel evaluation per se real *x1 = xi; real *x2 = xj; real *p_inpsigma = input_sigma_data; real sum_wt = 0.0; int k = n; // Use Duff's device to unroll the following loop: // while (k--) { // real diff = *x1++ - *x2++; // sum_wt += fabs(diff) / *p_inpsigma++; // } real diff; switch (k % 8) { case 0: do { diff = *x1++ - *x2++; sum_wt += fabs(diff) / *p_inpsigma++; case 7: diff = *x1++ - *x2++; sum_wt += fabs(diff) / *p_inpsigma++; case 6: diff = *x1++ - *x2++; sum_wt += fabs(diff) / *p_inpsigma++; case 5: diff = *x1++ - *x2++; sum_wt += fabs(diff) / *p_inpsigma++; case 4: diff = *x1++ - *x2++; sum_wt += fabs(diff) / *p_inpsigma++; case 3: diff = *x1++ - *x2++; sum_wt += fabs(diff) / *p_inpsigma++; case 2: diff = *x1++ - *x2++; sum_wt += fabs(diff) / *p_inpsigma++; case 1: diff = *x1++ - *x2++; sum_wt += fabs(diff) / *p_inpsigma++; } while((k -= 8) > 0); } // Multiplicatively update kernel matrix (already pre-filled with // Kronecker terms, or 1.0 if no Kronecker terms, as per build_). real Kij_cur = *Kij * sf / (2.*persistence) * exp(-persistence * sum_wt); *Kij++ = Kij_cur; } } if (cache_gram_matrix) { gram_matrix.resize(l,l); gram_matrix << K; gram_matrix_is_cached = true; } }
void PLearn::Matern1ARDKernel::computeGramMatrixDerivative | ( | Mat & | KD, |
const string & | kernel_param, | ||
real | epsilon = 1e-6 |
||
) | const [virtual] |
Directly compute the derivative with respect to hyperparameters (Faster than finite differences...)
Reimplemented from PLearn::Kernel.
Definition at line 238 of file Matern1ARDKernel.cc.
References PLearn::Kernel::computeGramMatrixDerivative(), and computeGramMatrixDerivIspSignalSigma().
{ static const string ISS("isp_signal_sigma"); static const string IGS("isp_global_sigma"); static const string IIS("isp_input_sigma["); static const string IPe("isp_persistence"); if (kernel_param == ISS) { computeGramMatrixDerivIspSignalSigma(KD); // computeGramMatrixDerivNV< // Matern1ARDKernel, // &Matern1ARDKernel::derivIspSignalSigma>(KD, this, -1); } /* else if (kernel_param == IGS) { computeGramMatrixDerivNV< Matern1ARDKernel, &Matern1ARDKernel::derivIspGlobalSigma>(KD, this, -1); } else if (string_begins_with(kernel_param, IIS) && kernel_param[kernel_param.size()-1] == ']') { int arg = tolong(kernel_param.substr( IIS.size(), kernel_param.size() - IIS.size() - 1)); PLASSERT( arg < m_isp_input_sigma.size() ); computeGramMatrixDerivIspInputSigma(KD, arg); } */ else inherited::computeGramMatrixDerivative(KD, kernel_param, epsilon); }
void PLearn::Matern1ARDKernel::computeGramMatrixDerivIspInputSigma | ( | Mat & | KD, |
int | arg | ||
) | const [protected] |
Compute derivative w.r.t. isp_input_sigma[arg] for WHOLE MATRIX.
Definition at line 328 of file Matern1ARDKernel.cc.
References PLearn::TMat< T >::data(), PLearn::Kernel::data, PLearn::diff(), PLearn::Kernel::gram_matrix, i, j, PLearn::TMat< T >::length(), PLearn::VMat::length(), PLearn::MemoryCachedKernel::m_data_cache, PLearn::ARDBaseKernel::m_input_sigma, PLearn::ARDBaseKernel::m_isp_global_sigma, PLearn::ARDBaseKernel::m_isp_input_sigma, PLearn::TMat< T >::mod(), PLASSERT_MSG, PLearn::TMat< T >::resize(), PLearn::sigmoid(), and PLearn::TMat< T >::width().
{ // Precompute some terms real input_sigma_arg = m_input_sigma[arg]; real input_sigma_sq = input_sigma_arg * input_sigma_arg; real input_sigmoid = sigmoid(m_isp_global_sigma + m_isp_input_sigma[arg]); // Compute Gram Matrix derivative w.r.t. isp_input_sigma[arg] int l = data->length(); PLASSERT_MSG( gram_matrix.width() == l && gram_matrix.length() == l, "To compute the derivative with respect to 'isp_input_sigma[i]', the\n" "Gram matrix must be precomputed and cached in Matern1ARDKernel."); // Variables that walk over the data matrix int cache_mod = m_data_cache.mod(); real *data_start = &m_data_cache(0,0); real *xi = data_start+arg; // Iterator on data rows // Variables that walk over the gram cache int gram_cache_mod = gram_matrix.mod(); real *gram_cache_row = gram_matrix.data(); real *gram_cache_cur; // Variables that walk over the kernel derivative matrix (KD) KD.resize(l,l); real* KDi = KD.data(); // Start of row i real* KDij; // Current element on row i int KD_mod = KD.mod(); // Iterate on rows of derivative matrix for (int i=0 ; i<l ; ++i, xi += cache_mod, KDi += KD_mod, gram_cache_row += gram_cache_mod) { KDij = KDi; real *xj = data_start+arg; // Inner iterator on data rows gram_cache_cur = gram_cache_row; // Iterate on columns of derivative matrix for (int j=0 ; j <= i ; ++j, xj += cache_mod, ++gram_cache_cur) { real diff = *xi - *xj; real sq_diff = diff * diff; real KD_cur = 0.5 * *gram_cache_cur * input_sigmoid * sq_diff / input_sigma_sq; // Set into derivative matrix *KDij++ = KD_cur; } } }
void PLearn::Matern1ARDKernel::computeGramMatrixDerivIspSignalSigma | ( | Mat & | KD | ) | const [protected] |
Compute derivative w.r.t. isp_signal_sigma for WHOLE MATRIX.
Definition at line 312 of file Matern1ARDKernel.cc.
References PLearn::Kernel::data, PLearn::Kernel::gram_matrix, PLearn::TMat< T >::length(), PLearn::VMat::length(), PLearn::ARDBaseKernel::m_isp_signal_sigma, PLASSERT_MSG, PLearn::TMat< T >::resize(), PLearn::sigmoid(), PLearn::softplus(), and PLearn::TMat< T >::width().
Referenced by computeGramMatrixDerivative().
{ int l = data->length(); KD.resize(l,l); PLASSERT_MSG( gram_matrix.width() == l && gram_matrix.length() == l, "To compute the derivative with respect to 'isp_signal_sigma', the\n" "Gram matrix must be precomputed and cached in Matern1ARDKernel."); KD << gram_matrix; KD *= sigmoid(m_isp_signal_sigma)/softplus(m_isp_signal_sigma); }
void PLearn::Matern1ARDKernel::declareOptions | ( | OptionList & | ol | ) | [static, protected] |
Declares the class options.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file Matern1ARDKernel.cc.
References PLearn::OptionBase::buildoption, PLearn::declareOption(), PLearn::ARDBaseKernel::declareOptions(), and m_isp_persistence.
{ declareOption( ol, "isp_persistence", &Matern1ARDKernel::m_isp_persistence, OptionBase::buildoption, "Inverse softplus of the O-U persistence parameter. Default value =\n" "isp(1.0)."); // Now call the parent class' declareOptions inherited::declareOptions(ol); }
static const PPath& PLearn::Matern1ARDKernel::declaringFile | ( | ) | [inline, static] |
Matern1ARDKernel * PLearn::Matern1ARDKernel::deepCopy | ( | CopiesMap & | copies | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
real PLearn::Matern1ARDKernel::derivIspGlobalSigma | ( | int | i, |
int | j, | ||
int | arg, | ||
real | K | ||
) | const [protected] |
Derivative function with respect to isp_global_sigma.
Definition at line 295 of file Matern1ARDKernel.cc.
References PLearn::fast_is_equal(), PLearn::ARDBaseKernel::m_isp_global_sigma, PLearn::ARDBaseKernel::m_isp_signal_sigma, pl_log, PLearn::sigmoid(), and PLearn::softplus().
{ if (fast_is_equal(K,0.)) return 0.; // The norm term inside the exponential may be accessed as Log(K/sf) real inner = pl_log(K / softplus(m_isp_signal_sigma)); return - K * inner * sigmoid(m_isp_global_sigma) / softplus(m_isp_global_sigma); // Note: in the above expression for 'inner' there is the implicit // assumption that the input_sigma[i] are zero, which allows the // sigmoid/softplus term to be factored out of the norm summation. }
void PLearn::Matern1ARDKernel::derivIspPersistence | ( | int | i, |
int | j, | ||
int | arg, | ||
real | K | ||
) | const [protected] |
Compute derivative w.r.t. isp_persistence.
real PLearn::Matern1ARDKernel::derivIspSignalSigma | ( | int | i, |
int | j, | ||
int | arg, | ||
real | K | ||
) | const [protected] |
Derivative function with respect to isp_signal_sigma.
Definition at line 286 of file Matern1ARDKernel.cc.
References PLearn::ARDBaseKernel::m_isp_signal_sigma, PLearn::sigmoid(), and PLearn::softplus().
{ // (No longer used; see computeGramMatrixDerivIspInputSigma below) return K*sigmoid(m_isp_signal_sigma)/softplus(m_isp_signal_sigma); }
Compute K(x1,x2).
Reimplemented from PLearn::KroneckerBaseKernel.
Definition at line 111 of file Matern1ARDKernel.cc.
References PLearn::TVec< T >::data(), PLearn::diff(), PLearn::KroneckerBaseKernel::evaluate(), PLearn::exp(), PLearn::fast_is_equal(), i, PLearn::ARDBaseKernel::m_isp_global_sigma, PLearn::ARDBaseKernel::m_isp_input_sigma, m_isp_persistence, PLearn::ARDBaseKernel::m_isp_signal_sigma, n, PLASSERT, PLearn::TVec< T >::size(), and PLearn::softplus().
{ PLASSERT( x1.size() == x2.size() ); PLASSERT( !m_isp_input_sigma.size() || x1.size() == m_isp_input_sigma.size() ); real gating_term = inherited::evaluate(x1,x2); if (fast_is_equal(gating_term, 0.0)) return 0.0; if (x1.size() == 0) return softplus(m_isp_signal_sigma) / (2*softplus(m_isp_persistence)) * gating_term; const real* px1 = x1.data(); const real* px2 = x2.data(); real sf = softplus(m_isp_signal_sigma); real persistence= softplus(m_isp_persistence); real expval = 0.0; // Case where we have real ARD if (m_isp_input_sigma.size() > 0) { const real* pinpsig = m_isp_input_sigma.data(); for (int i=0, n=x1.size() ; i<n ; ++i) { real diff = *px1++ - *px2++; real absdiff = fabs(diff); expval += absdiff / softplus(m_isp_global_sigma + *pinpsig++); } } // No ARD else { real global_sigma = softplus(m_isp_global_sigma); for (int i=0, n=x1.size() ; i<n ; ++i) { real diff = *px1++ - *px2++; real absdiff = fabs(diff); expval += absdiff / global_sigma; } } // Gate by Kronecker term return sf / (2. * persistence) * exp(-persistence * expval) * gating_term; }
void PLearn::Matern1ARDKernel::evaluate_all_i_x | ( | const Vec & | x, |
const Vec & | k_xi_x, | ||
real | squared_norm_of_x = -1 , |
||
int | istart = 0 |
||
) | const [virtual] |
Fill k_xi_x with K(x_i, x), for all i from istart to istart + k_xi_x.length() - 1.
Reimplemented from PLearn::Kernel.
Definition at line 277 of file Matern1ARDKernel.cc.
References PLearn::Kernel::k_xi_x, and x.
OptionList & PLearn::Matern1ARDKernel::getOptionList | ( | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
OptionMap & PLearn::Matern1ARDKernel::getOptionMap | ( | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
RemoteMethodMap & PLearn::Matern1ARDKernel::getRemoteMethodMap | ( | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 66 of file Matern1ARDKernel.cc.
void PLearn::Matern1ARDKernel::makeDeepCopyFromShallowCopy | ( | CopiesMap & | copies | ) | [virtual] |
Transforms a shallow copy into a deep copy.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 385 of file Matern1ARDKernel.cc.
References PLearn::ARDBaseKernel::makeDeepCopyFromShallowCopy().
{ inherited::makeDeepCopyFromShallowCopy(copies); }
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 108 of file Matern1ARDKernel.h.
Inverse softplus of the O-U persistence parameter.
Default value = isp(1.0).
Definition at line 78 of file Matern1ARDKernel.h.
Referenced by computeGramMatrix(), declareOptions(), and evaluate().