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SCFGP

SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.

Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.

Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.

The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)

SCFGP Formulas

SCFGP is implemented in python using Theano by Max W. Y. Lam (maxingaussian@gmail.com).

Installation

SCFGP

To install SCFGP, use pip:

$ pip install SCFGP

Or clone this repo:

$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Dependencies

Theano

Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:

http://deeplearning.net/software/theano/install.html

scikit-learn (only used in the experiments)

To install scikit-learn, see this page:

https://github.com/scikit-learn/scikit-learn

Try SCFGP with Only 3 Lines of Code

fromSCFGPimport*# <>: necessary inputs, {}: optional inputsmodel=SCFGP(rank=<rank_of_frequency_matrix>,
feature_size=<number_of_Fourier_features>,
fftype={feature_type},
msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std=model.predict(X_test, {y_test})

License

Copyright (c) 2016, Max W. Y. Lam All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

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SCFGP: Sparsely Correlated Fourier Features Based Gaussian Process

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covariance-matrixfourier-featuresfrequency-matrixgaussian-processes

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Readme
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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all 
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})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

Skip to content
BranchesTags
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SCFGP
SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.
Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.
Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.
The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)
SCFGP Formulas
SCFGP is implemented in python using Theano by Max W. Y. Lam (maxingaussian@gmail.com).
Installation
SCFGP
To install SCFGP, use pip:
$ pip install SCFGP

Or clone this repo:
$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Dependencies
Theano
Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:
http://deeplearning.net/software/theano/install.html
scikit-learn (only used in the experiments)
To install scikit-learn, see this page:
https://github.com/scikit-learn/scikit-learn
Try SCFGP with Only 3 Lines of Code
fromSCFGPimport*# <>: necessary inputs, {}: optional inputsmodel=SCFGP(rank=<rank_of_frequency_matrix>,
feature_size=<number_of_Fourier_features>,
fftype={feature_type},
msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std=model.predict(X_test, {y_test})
License
Copyright (c) 2016, Max W. Y. Lam
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
About
SCFGP: Sparsely Correlated Fourier Features Based Gaussian Process
Topics
covariance-matrixfourier-featuresfrequency-matrixgaussian-processes
Resources
Readme
BSD-3-Clause license
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1 watching
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0 forks
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
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})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
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SCFGP
SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.
Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.
Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.
The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)
SCFGP Formulas
SCFGP is implemented in python using Theano by Max W. Y. Lam (maxingaussian@gmail.com).
Installation
SCFGP
To install SCFGP, use pip:
$ pip install SCFGP

Or clone this repo:
$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Dependencies
Theano
Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:
http://deeplearning.net/software/theano/install.html
scikit-learn (only used in the experiments)
To install scikit-learn, see this page:
https://github.com/scikit-learn/scikit-learn
Try SCFGP with Only 3 Lines of Code
fromSCFGPimport*# <>: necessary inputs, {}: optional inputsmodel=SCFGP(rank=<rank_of_frequency_matrix>,
feature_size=<number_of_Fourier_features>,
fftype={feature_type},
msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std=model.predict(X_test, {y_test})
License
Copyright (c) 2016, Max W. Y. Lam
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
About
SCFGP: Sparsely Correlated Fourier Features Based Gaussian Process
Topics
covariance-matrixfourier-featuresfrequency-matrixgaussian-processes
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
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SCFGP
SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.
Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.
Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.
The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)
SCFGP Formulas
SCFGP is implemented in python using Theano by Max W. Y. Lam (maxingaussian@gmail.com).
Installation
SCFGP
To install SCFGP, use pip:
$ pip install SCFGP

Or clone this repo:
$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Dependencies
Theano
Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:
http://deeplearning.net/software/theano/install.html
scikit-learn (only used in the experiments)
To install scikit-learn, see this page:
https://github.com/scikit-learn/scikit-learn
Try SCFGP with Only 3 Lines of Code
fromSCFGPimport*# <>: necessary inputs, {}: optional inputsmodel=SCFGP(rank=<rank_of_frequency_matrix>,
feature_size=<number_of_Fourier_features>,
fftype={feature_type},
msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std=model.predict(X_test, {y_test})
License
Copyright (c) 2016, Max W. Y. Lam
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
About
SCFGP: Sparsely Correlated Fourier Features Based Gaussian Process
Topics
covariance-matrixfourier-featuresfrequency-matrixgaussian-processes
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

Skip to content
BranchesTags
Repository files navigation
SCFGP
SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.
Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.
Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.
The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)
SCFGP Formulas
SCFGP is implemented in python using Theano by Max W. Y. Lam (maxingaussian@gmail.com).
Installation
SCFGP
To install SCFGP, use pip:
$ pip install SCFGP

Or clone this repo:
$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Dependencies
Theano
Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:
http://deeplearning.net/software/theano/install.html
scikit-learn (only used in the experiments)
To install scikit-learn, see this page:
https://github.com/scikit-learn/scikit-learn
Try SCFGP with Only 3 Lines of Code
fromSCFGPimport*# <>: necessary inputs, {}: optional inputsmodel=SCFGP(rank=<rank_of_frequency_matrix>,
feature_size=<number_of_Fourier_features>,
fftype={feature_type},
msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std=model.predict(X_test, {y_test})
License
Copyright (c) 2016, Max W. Y. Lam
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
About
SCFGP: Sparsely Correlated Fourier Features Based Gaussian Process
Topics
covariance-matrixfourier-featuresfrequency-matrixgaussian-processes
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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SCFGP
SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.
Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.
Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.
The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)
SCFGP Formulas
SCFGP is implemented in python using Theano by Max W. Y. Lam (maxingaussian@gmail.com).
Installation
SCFGP
To install SCFGP, use pip:
$ pip install SCFGP

Or clone this repo:
$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Dependencies
Theano
Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:
http://deeplearning.net/software/theano/install.html
scikit-learn (only used in the experiments)
To install scikit-learn, see this page:
https://github.com/scikit-learn/scikit-learn
Try SCFGP with Only 3 Lines of Code
fromSCFGPimport*# <>: necessary inputs, {}: optional inputsmodel=SCFGP(rank=<rank_of_frequency_matrix>,
feature_size=<number_of_Fourier_features>,
fftype={feature_type},
msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std=model.predict(X_test, {y_test})
License
Copyright (c) 2016, Max W. Y. Lam
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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SCFGP
SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.
Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.
Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.
The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)
SCFGP Formulas
SCFGP is implemented in python using Theano by Max W. Y. Lam (maxingaussian@gmail.com).
Installation
SCFGP
To install SCFGP, use pip:
$ pip install SCFGP

Or clone this repo:
$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Dependencies
Theano
Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:
http://deeplearning.net/software/theano/install.html
scikit-learn (only used in the experiments)
To install scikit-learn, see this page:
https://github.com/scikit-learn/scikit-learn
Try SCFGP with Only 3 Lines of Code
fromSCFGPimport*# <>: necessary inputs, {}: optional inputsmodel=SCFGP(rank=<rank_of_frequency_matrix>,
feature_size=<number_of_Fourier_features>,
fftype={feature_type},
msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std=model.predict(X_test, {y_test})
License
Copyright (c) 2016, Max W. Y. Lam
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
About
SCFGP: Sparsely Correlated Fourier Features Based Gaussian Process
Topics
covariance-matrixfourier-featuresfrequency-matrixgaussian-processes
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
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0 forks
Report repository
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

Skip to content
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SCFGP
SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.
Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.
Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.
The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)
SCFGP Formulas
SCFGP is implemented in python using Theano by Max W. Y. Lam (maxingaussian@gmail.com).
Installation
SCFGP
To install SCFGP, use pip:
$ pip install SCFGP

Or clone this repo:
$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Dependencies
Theano
Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:
http://deeplearning.net/software/theano/install.html
scikit-learn (only used in the experiments)
To install scikit-learn, see this page:
https://github.com/scikit-learn/scikit-learn
Try SCFGP with Only 3 Lines of Code
fromSCFGPimport*# <>: necessary inputs, {}: optional inputsmodel=SCFGP(rank=<rank_of_frequency_matrix>,
feature_size=<number_of_Fourier_features>,
fftype={feature_type},
msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std=model.predict(X_test, {y_test})
License
Copyright (c) 2016, Max W. Y. Lam
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
About
SCFGP: Sparsely Correlated Fourier Features Based Gaussian Process
Topics
covariance-matrixfourier-featuresfrequency-matrixgaussian-processes
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
Releases
Packages
Used by
Contributors
Languages