PLearn 0.1
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Neural network kernel that can be used for Automatic Relevance Determination. More...
#include <NeuralNetworkARDKernel.h>
Public Member Functions | |
NeuralNetworkARDKernel () | |
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; for now, this mostly maps to 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 NeuralNetworkARDKernel * | 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 () |
Static Public Attributes | |
static StaticInitializer | _static_initializer_ |
Protected Member Functions | |
real | derivIspGlobalSigma (int i, int j, int arg, real K) const |
Derivative function with respect to isp_global_sigma. | |
void | computeGramMatrixDerivIspSignalSigma (Mat &KD) const |
void | computeGramMatrixDerivIspInputSigma (Mat &KD, int arg) const |
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. |
Neural network kernel that can be used for Automatic Relevance Determination.
This kernel is designed to be used within a GaussianProcessRegressor. It is similar to the "arcsin" kernel of C.E. Rasmussen's GPML code (see http://www.gaussianprocess.org), but can be used with full Automatic Relevance Determination (ARD). It takes the form:
k(x,y) = sf * asin(2*x*P*y / sqrt((1+2*x*P*x)*(1+2*y*P*y))) * k_kron(x,y)
where sf is softplus(isp_signal_sigma), P is softplus(isp_global_sigma + isp_input_sigma[i])^-2 times the unit matrix, where the x and y vectors on the right-hand-side have an extra bias (1.0) added in front. (Note that if ARD is desired, the number of elements provided for isp_input_sigma must be ONE MORE than the number of inputs, and the first element of the isp_input_sigma vector corresponds to this bias). Also note that in keeping with Rasmussen and Williams, we raise these elements to the -2 power, so these hyperparameters can be interpreted as true length-scales. The last factor 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).
See SquaredExponentialARDKernel for more information about using this kernel within a SummationKernel in order to add IID noise to the examples.
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 80 of file NeuralNetworkARDKernel.h.
typedef ARDBaseKernel PLearn::NeuralNetworkARDKernel::inherited [private] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 82 of file NeuralNetworkARDKernel.h.
PLearn::NeuralNetworkARDKernel::NeuralNetworkARDKernel | ( | ) |
string PLearn::NeuralNetworkARDKernel::_classname_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
OptionList & PLearn::NeuralNetworkARDKernel::_getOptionList_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
RemoteMethodMap & PLearn::NeuralNetworkARDKernel::_getRemoteMethodMap_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
Object * PLearn::NeuralNetworkARDKernel::_new_instance_for_typemap_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
StaticInitializer NeuralNetworkARDKernel::_static_initializer_ & PLearn::NeuralNetworkARDKernel::_static_initialize_ | ( | ) | [static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
void PLearn::NeuralNetworkARDKernel::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 94 of file NeuralNetworkARDKernel.cc.
{ // ### Nothing to add here, simply calls build_ inherited::build(); build_(); }
void PLearn::NeuralNetworkARDKernel::build_ | ( | ) | [private] |
This does the actual building.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 104 of file NeuralNetworkARDKernel.cc.
{ // Ensure that we multiply in Kronecker terms inherited::m_default_value = 1.0; }
string PLearn::NeuralNetworkARDKernel::classname | ( | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
void PLearn::NeuralNetworkARDKernel::computeGramMatrix | ( | Mat | K | ) | const [virtual] |
Compute the Gram Matrix.
Reimplemented from PLearn::KroneckerBaseKernel.
Definition at line 181 of file NeuralNetworkARDKernel.cc.
References DUFF_DOTLOOP, i, j, m, PLearn::TMat< T >::mod(), n, PLASSERT, PLearn::TMat< T >::size(), PLearn::softplus(), and PLearn::sqrt().
{ PLASSERT( !m_isp_input_sigma.size() || dataInputsize()+1 == 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); m_input_sigma.resize(dataInputsize() + 1); 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]); m_input_sigma[i] *= m_input_sigma[i]; m_input_sigma[i] = 2. / 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; int k = n; // Handle the bias for x1 and x2 real sigma = *p_inpsigma++; real dot_x1_x1 = sigma; real dot_x2_x2 = sigma; real dot_x1_x2 = sigma; switch (k % 8) { case 0: do { DUFF_DOTLOOP case 7: DUFF_DOTLOOP case 6: DUFF_DOTLOOP case 5: DUFF_DOTLOOP case 4: DUFF_DOTLOOP case 3: DUFF_DOTLOOP case 2: DUFF_DOTLOOP case 1: DUFF_DOTLOOP } 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 * asin(dot_x1_x2 / sqrt((1 + dot_x1_x1) * (1 + dot_x2_x2))); *Kij++ = Kij_cur; } } if (cache_gram_matrix) { gram_matrix.resize(l,l); gram_matrix << K; gram_matrix_is_cached = true; } }
void PLearn::NeuralNetworkARDKernel::computeGramMatrixDerivative | ( | Mat & | KD, |
const string & | kernel_param, | ||
real | epsilon = 1e-6 |
||
) | const [virtual] |
Directly compute the derivative with respect to hyperparameters; for now, this mostly maps to finite differences.
Reimplemented from PLearn::Kernel.
Definition at line 262 of file NeuralNetworkARDKernel.cc.
{ static const string ISS("isp_signal_sigma"); static const string IGS("isp_global_sigma"); static const string IIS("isp_input_sigma["); if (kernel_param == ISS) { computeGramMatrixDerivIspSignalSigma(KD); } // else if (kernel_param == IGS) { // computeGramMatrixDerivNV< // NeuralNetworkARDKernel, // &NeuralNetworkARDKernel::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::NeuralNetworkARDKernel::computeGramMatrixDerivIspInputSigma | ( | Mat & | KD, |
int | arg | ||
) | const [protected] |
Definition at line 336 of file NeuralNetworkARDKernel.cc.
References PLearn::TMat< T >::data(), PLearn::diff(), i, j, PLearn::TMat< T >::mod(), PLASSERT_MSG, PLearn::TMat< T >::resize(), and PLearn::sigmoid().
{ // 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 NeuralNetworkARDKernel."); // 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::NeuralNetworkARDKernel::computeGramMatrixDerivIspSignalSigma | ( | Mat & | KD | ) | const [protected] |
Definition at line 320 of file NeuralNetworkARDKernel.cc.
References PLASSERT_MSG, PLearn::TMat< T >::resize(), PLearn::sigmoid(), and PLearn::softplus().
{ 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 NeuralNetworkARDKernel."); KD << gram_matrix; KD *= sigmoid(m_isp_signal_sigma)/softplus(m_isp_signal_sigma); }
void PLearn::NeuralNetworkARDKernel::declareOptions | ( | OptionList & | ol | ) | [static, protected] |
Declares the class options.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 85 of file NeuralNetworkARDKernel.cc.
{ // Now call the parent class' declareOptions inherited::declareOptions(ol); }
static const PPath& PLearn::NeuralNetworkARDKernel::declaringFile | ( | ) | [inline, static] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 117 of file NeuralNetworkARDKernel.h.
:
NeuralNetworkARDKernel * PLearn::NeuralNetworkARDKernel::deepCopy | ( | CopiesMap & | copies | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
real PLearn::NeuralNetworkARDKernel::derivIspGlobalSigma | ( | int | i, |
int | j, | ||
int | arg, | ||
real | K | ||
) | const [protected] |
Derivative function with respect to isp_global_sigma.
Definition at line 303 of file NeuralNetworkARDKernel.cc.
References PLearn::fast_is_equal(), 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. }
Compute K(x1,x2).
Reimplemented from PLearn::KroneckerBaseKernel.
Definition at line 113 of file NeuralNetworkARDKernel.cc.
References PLearn::TVec< T >::data(), PLearn::fast_is_equal(), i, n, PLASSERT, PLearn::TVec< T >::size(), PLearn::softplus(), and PLearn::sqrt().
{ PLASSERT( x1.size() == x2.size() ); PLASSERT( !m_isp_input_sigma.size() || x1.size()+1 == m_isp_input_sigma.size() ); real gating_term = inherited::evaluate(x1,x2); if (fast_is_equal(gating_term, 0.0) || x1.size() == 0) return 0.0; const real* px1 = x1.data(); const real* px2 = x2.data(); real sf = softplus(m_isp_signal_sigma); real dot_x1_x1; real dot_x2_x2; real dot_x1_x2; if (m_isp_input_sigma.size() > 0) { const real* pinpsig = m_isp_input_sigma.data(); real sigma = softplus(*pinpsig++); sigma *= sigma; sigma = 2. / sigma; // Handle bias dot_x1_x1 = dot_x2_x2 = dot_x1_x2 = sigma; for (int i=0, n=x1.size() ; i<n ; ++i, ++px1, ++px2) { sigma = softplus(*pinpsig++); sigma *= sigma; sigma = 2. / sigma; dot_x1_x2 += *px1 * *px2 * sigma; dot_x1_x1 += *px1 * *px1 * sigma; dot_x2_x2 += *px2 * *px2 * sigma; } } else { real global_sigma = softplus(m_isp_global_sigma); global_sigma *= global_sigma; global_sigma = 2. / global_sigma; // Handle bias for x1 and x2 dot_x1_x1 = dot_x2_x2 = dot_x1_x2 = 1; for (int i=0, n=x1.size() ; i<n ; ++i, ++px1, ++px2) { dot_x1_x2 += *px1 * *px2; dot_x1_x1 += *px1 * *px1; dot_x2_x2 += *px2 * *px2; } dot_x1_x2 *= global_sigma; dot_x1_x1 *= global_sigma; dot_x2_x2 *= global_sigma; } // Gate by Kronecker term return sf * asin(dot_x1_x2 / sqrt((1 + dot_x1_x1) * (1 + dot_x2_x2))) * gating_term; }
void PLearn::NeuralNetworkARDKernel::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 294 of file NeuralNetworkARDKernel.cc.
References x.
OptionList & PLearn::NeuralNetworkARDKernel::getOptionList | ( | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
OptionMap & PLearn::NeuralNetworkARDKernel::getOptionMap | ( | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
RemoteMethodMap & PLearn::NeuralNetworkARDKernel::getRemoteMethodMap | ( | ) | const [virtual] |
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 76 of file NeuralNetworkARDKernel.cc.
void PLearn::NeuralNetworkARDKernel::makeDeepCopyFromShallowCopy | ( | CopiesMap & | copies | ) | [virtual] |
Transforms a shallow copy into a deep copy.
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 393 of file NeuralNetworkARDKernel.cc.
{ inherited::makeDeepCopyFromShallowCopy(copies); }
Reimplemented from PLearn::ARDBaseKernel.
Definition at line 117 of file NeuralNetworkARDKernel.h.