GPYTORCH: BLACKBOX MATRIX- MATRIX GAUSSIAN PROCESS INFERENCE WITH GPU ACCELERATION
Jacob R. Gardner, Geoff Pleiss, David Bindel, Kilian Q. Weinberger, Andrew Gordon Wilson
GPYTORCH : BLACKBOX MATRIX- MATRIX GAUSSIAN PROCESS INFERENCE WITH - - PowerPoint PPT Presentation
GPYTORCH : BLACKBOX MATRIX- MATRIX GAUSSIAN PROCESS INFERENCE WITH GPU ACCELERATION Jacob R. Gardner, Geoff Pleiss , David Bindel, Kilian Q. Weinberger, Andrew Gordon Wilson DEEP LEARNING & RAPID PROTOTYPING 1. GPU acceleration 2. Modular
Jacob R. Gardner, Geoff Pleiss, David Bindel, Kilian Q. Weinberger, Andrew Gordon Wilson
W X
W X
model.add_module( nn.Linear(64, 128) )
W X
model.add_module( nn.Linear(64, 128) )
log det(K)
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log det(K)
<latexit sha1_base64="fGkQsLQdY9OIe/yBzWzgFWPy0=">AB/HicbVDLSgNBEJz1GeNrNUcvg0GIl7Argh6DXgQvEcwDkhBmJ51kyOzsMtMrhiX+ihcPinj1Q7z5N06SPWhiQUNR1U13VxBLYdDzvp2V1bX1jc3cVn57Z3dv3z04rJso0RxqPJKRbgbMgBQKaihQjPWwMJAQiMYXU/9xgNoIyJ1j+MYOiEbKNEXnKGVum6hLaMBbSM8YtoDnNDS7WnXLXplbwa6TPyMFEmGatf9avcinoSgkEtmTMv3YuykTKPgEib5dmIgZnzEBtCyVLEQTCedHT+hJ1bp0X6kbSmkM/X3RMpCY8ZhYDtDhkOz6E3F/7xWgv3LTipUnCAoPl/UTyTFiE6ToD2hgaMcW8K4FvZWyodM42r7wNwV98eZnUz8q+V/bvzouVqyOHDkix6REfHJBKuSGVEmNcDImz+SVvDlPzovz7nzMW1ecbKZA/sD5/AHXgJQ5</latexit><latexit sha1_base64="fGkQsLQdY9OIe/yBzWzgFWPy0=">AB/HicbVDLSgNBEJz1GeNrNUcvg0GIl7Argh6DXgQvEcwDkhBmJ51kyOzsMtMrhiX+ihcPinj1Q7z5N06SPWhiQUNR1U13VxBLYdDzvp2V1bX1jc3cVn57Z3dv3z04rJso0RxqPJKRbgbMgBQKaihQjPWwMJAQiMYXU/9xgNoIyJ1j+MYOiEbKNEXnKGVum6hLaMBbSM8YtoDnNDS7WnXLXplbwa6TPyMFEmGatf9avcinoSgkEtmTMv3YuykTKPgEib5dmIgZnzEBtCyVLEQTCedHT+hJ1bp0X6kbSmkM/X3RMpCY8ZhYDtDhkOz6E3F/7xWgv3LTipUnCAoPl/UTyTFiE6ToD2hgaMcW8K4FvZWyodM42r7wNwV98eZnUz8q+V/bvzouVqyOHDkix6REfHJBKuSGVEmNcDImz+SVvDlPzovz7nzMW1ecbKZA/sD5/AHXgJQ5</latexit><latexit sha1_base64="fGkQsLQdY9OIe/yBzWzgFWPy0=">AB/HicbVDLSgNBEJz1GeNrNUcvg0GIl7Argh6DXgQvEcwDkhBmJ51kyOzsMtMrhiX+ihcPinj1Q7z5N06SPWhiQUNR1U13VxBLYdDzvp2V1bX1jc3cVn57Z3dv3z04rJso0RxqPJKRbgbMgBQKaihQjPWwMJAQiMYXU/9xgNoIyJ1j+MYOiEbKNEXnKGVum6hLaMBbSM8YtoDnNDS7WnXLXplbwa6TPyMFEmGatf9avcinoSgkEtmTMv3YuykTKPgEib5dmIgZnzEBtCyVLEQTCedHT+hJ1bp0X6kbSmkM/X3RMpCY8ZhYDtDhkOz6E3F/7xWgv3LTipUnCAoPl/UTyTFiE6ToD2hgaMcW8K4FvZWyodM42r7wNwV98eZnUz8q+V/bvzouVqyOHDkix6REfHJBKuSGVEmNcDImz+SVvDlPzovz7nzMW1ecbKZA/sD5/AHXgJQ5</latexit><latexit sha1_base64="fGkQsLQdY9OIe/yBzWzgFWPy0=">AB/HicbVDLSgNBEJz1GeNrNUcvg0GIl7Argh6DXgQvEcwDkhBmJ51kyOzsMtMrhiX+ihcPinj1Q7z5N06SPWhiQUNR1U13VxBLYdDzvp2V1bX1jc3cVn57Z3dv3z04rJso0RxqPJKRbgbMgBQKaihQjPWwMJAQiMYXU/9xgNoIyJ1j+MYOiEbKNEXnKGVum6hLaMBbSM8YtoDnNDS7WnXLXplbwa6TPyMFEmGatf9avcinoSgkEtmTMv3YuykTKPgEib5dmIgZnzEBtCyVLEQTCedHT+hJ1bp0X6kbSmkM/X3RMpCY8ZhYDtDhkOz6E3F/7xWgv3LTipUnCAoPl/UTyTFiE6ToD2hgaMcW8K4FvZWyodM42r7wNwV98eZnUz8q+V/bvzouVqyOHDkix6REfHJBKuSGVEmNcDImz+SVvDlPzovz7nzMW1ecbKZA/sD5/AHXgJQ5</latexit>K−1y
<latexit sha1_base64="jyPGRDI4av08loOa7WKxnwt7irc=">AB73icbVBNS8NAEJ34WetX1aOXxSJ4sSQi6LHoRfBSwX5AG8tmO2mXbjZxdyOU0D/hxYMiXv073vw3btsctPXBwO9GWbmBYng2rjut7O0vLK6tl7YKG5ube/slvb2GzpOFcM6i0WsWgHVKLjEuFGYCtRSKNAYDMYXk/85hMqzWN5b0YJ+hHtSx5yRo2VWrcP2ak3JqNuqexW3CnIvFyUoYctW7pq9OLWRqhNExQrduemxg/o8pwJnBc7KQaE8qGtI9tSyWNUPvZ9N4xObZKj4SxsiUNmaq/JzIaT2KAtsZUTPQ895E/M9rpya89DMuk9SgZLNFYSqIicnkedLjCpkRI0soU9zeStiAKsqMjahoQ/DmX14kjbOK51a8u/Ny9SqPowCHcAQn4MEFVOEGalAHBgKe4RXenEfnxXl3PmatS04+cwB/4Hz+ACpzj2I=</latexit><latexit sha1_base64="jyPGRDI4av08loOa7WKxnwt7irc=">AB73icbVBNS8NAEJ34WetX1aOXxSJ4sSQi6LHoRfBSwX5AG8tmO2mXbjZxdyOU0D/hxYMiXv073vw3btsctPXBwO9GWbmBYng2rjut7O0vLK6tl7YKG5ube/slvb2GzpOFcM6i0WsWgHVKLjEuFGYCtRSKNAYDMYXk/85hMqzWN5b0YJ+hHtSx5yRo2VWrcP2ak3JqNuqexW3CnIvFyUoYctW7pq9OLWRqhNExQrduemxg/o8pwJnBc7KQaE8qGtI9tSyWNUPvZ9N4xObZKj4SxsiUNmaq/JzIaT2KAtsZUTPQ895E/M9rpya89DMuk9SgZLNFYSqIicnkedLjCpkRI0soU9zeStiAKsqMjahoQ/DmX14kjbOK51a8u/Ny9SqPowCHcAQn4MEFVOEGalAHBgKe4RXenEfnxXl3PmatS04+cwB/4Hz+ACpzj2I=</latexit><latexit sha1_base64="jyPGRDI4av08loOa7WKxnwt7irc=">AB73icbVBNS8NAEJ34WetX1aOXxSJ4sSQi6LHoRfBSwX5AG8tmO2mXbjZxdyOU0D/hxYMiXv073vw3btsctPXBwO9GWbmBYng2rjut7O0vLK6tl7YKG5ube/slvb2GzpOFcM6i0WsWgHVKLjEuFGYCtRSKNAYDMYXk/85hMqzWN5b0YJ+hHtSx5yRo2VWrcP2ak3JqNuqexW3CnIvFyUoYctW7pq9OLWRqhNExQrduemxg/o8pwJnBc7KQaE8qGtI9tSyWNUPvZ9N4xObZKj4SxsiUNmaq/JzIaT2KAtsZUTPQ895E/M9rpya89DMuk9SgZLNFYSqIicnkedLjCpkRI0soU9zeStiAKsqMjahoQ/DmX14kjbOK51a8u/Ny9SqPowCHcAQn4MEFVOEGalAHBgKe4RXenEfnxXl3PmatS04+cwB/4Hz+ACpzj2I=</latexit><latexit sha1_base64="jyPGRDI4av08loOa7WKxnwt7irc=">AB73icbVBNS8NAEJ34WetX1aOXxSJ4sSQi6LHoRfBSwX5AG8tmO2mXbjZxdyOU0D/hxYMiXv073vw3btsctPXBwO9GWbmBYng2rjut7O0vLK6tl7YKG5ube/slvb2GzpOFcM6i0WsWgHVKLjEuFGYCtRSKNAYDMYXk/85hMqzWN5b0YJ+hHtSx5yRo2VWrcP2ak3JqNuqexW3CnIvFyUoYctW7pq9OLWRqhNExQrduemxg/o8pwJnBc7KQaE8qGtI9tSyWNUPvZ9N4xObZKj4SxsiUNmaq/JzIaT2KAtsZUTPQ895E/M9rpya89DMuk9SgZLNFYSqIicnkedLjCpkRI0soU9zeStiAKsqMjahoQ/DmX14kjbOK51a8u/Ny9SqPowCHcAQn4MEFVOEGalAHBgKe4RXenEfnxXl3PmatS04+cwB/4Hz+ACpzj2I=</latexit>data covariance matrix
−1
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<latexit sha1_base64="fGkQsLQdY9OIe/yBzWzgFWPy0=">AB/HicbVDLSgNBEJz1GeNrNUcvg0GIl7Argh6DXgQvEcwDkhBmJ51kyOzsMtMrhiX+ihcPinj1Q7z5N06SPWhiQUNR1U13VxBLYdDzvp2V1bX1jc3cVn57Z3dv3z04rJso0RxqPJKRbgbMgBQKaihQjPWwMJAQiMYXU/9xgNoIyJ1j+MYOiEbKNEXnKGVum6hLaMBbSM8YtoDnNDS7WnXLXplbwa6TPyMFEmGatf9avcinoSgkEtmTMv3YuykTKPgEib5dmIgZnzEBtCyVLEQTCedHT+hJ1bp0X6kbSmkM/X3RMpCY8ZhYDtDhkOz6E3F/7xWgv3LTipUnCAoPl/UTyTFiE6ToD2hgaMcW8K4FvZWyodM42r7wNwV98eZnUz8q+V/bvzouVqyOHDkix6REfHJBKuSGVEmNcDImz+SVvDlPzovz7nzMW1ecbKZA/sD5/AHXgJQ5</latexit><latexit sha1_base64="fGkQsLQdY9OIe/yBzWzgFWPy0=">AB/HicbVDLSgNBEJz1GeNrNUcvg0GIl7Argh6DXgQvEcwDkhBmJ51kyOzsMtMrhiX+ihcPinj1Q7z5N06SPWhiQUNR1U13VxBLYdDzvp2V1bX1jc3cVn57Z3dv3z04rJso0RxqPJKRbgbMgBQKaihQjPWwMJAQiMYXU/9xgNoIyJ1j+MYOiEbKNEXnKGVum6hLaMBbSM8YtoDnNDS7WnXLXplbwa6TPyMFEmGatf9avcinoSgkEtmTMv3YuykTKPgEib5dmIgZnzEBtCyVLEQTCedHT+hJ1bp0X6kbSmkM/X3RMpCY8ZhYDtDhkOz6E3F/7xWgv3LTipUnCAoPl/UTyTFiE6ToD2hgaMcW8K4FvZWyodM42r7wNwV98eZnUz8q+V/bvzouVqyOHDkix6REfHJBKuSGVEmNcDImz+SVvDlPzovz7nzMW1ecbKZA/sD5/AHXgJQ5</latexit><latexit sha1_base64="fGkQsLQdY9OIe/yBzWzgFWPy0=">AB/HicbVDLSgNBEJz1GeNrNUcvg0GIl7Argh6DXgQvEcwDkhBmJ51kyOzsMtMrhiX+ihcPinj1Q7z5N06SPWhiQUNR1U13VxBLYdDzvp2V1bX1jc3cVn57Z3dv3z04rJso0RxqPJKRbgbMgBQKaihQjPWwMJAQiMYXU/9xgNoIyJ1j+MYOiEbKNEXnKGVum6hLaMBbSM8YtoDnNDS7WnXLXplbwa6TPyMFEmGatf9avcinoSgkEtmTMv3YuykTKPgEib5dmIgZnzEBtCyVLEQTCedHT+hJ1bp0X6kbSmkM/X3RMpCY8ZhYDtDhkOz6E3F/7xWgv3LTipUnCAoPl/UTyTFiE6ToD2hgaMcW8K4FvZWyodM42r7wNwV98eZnUz8q+V/bvzouVqyOHDkix6REfHJBKuSGVEmNcDImz+SVvDlPzovz7nzMW1ecbKZA/sD5/AHXgJQ5</latexit><latexit sha1_base64="fGkQsLQdY9OIe/yBzWzgFWPy0=">AB/HicbVDLSgNBEJz1GeNrNUcvg0GIl7Argh6DXgQvEcwDkhBmJ51kyOzsMtMrhiX+ihcPinj1Q7z5N06SPWhiQUNR1U13VxBLYdDzvp2V1bX1jc3cVn57Z3dv3z04rJso0RxqPJKRbgbMgBQKaihQjPWwMJAQiMYXU/9xgNoIyJ1j+MYOiEbKNEXnKGVum6hLaMBbSM8YtoDnNDS7WnXLXplbwa6TPyMFEmGatf9avcinoSgkEtmTMv3YuykTKPgEib5dmIgZnzEBtCyVLEQTCedHT+hJ1bp0X6kbSmkM/X3RMpCY8ZhYDtDhkOz6E3F/7xWgv3LTipUnCAoPl/UTyTFiE6ToD2hgaMcW8K4FvZWyodM42r7wNwV98eZnUz8q+V/bvzouVqyOHDkix6REfHJBKuSGVEmNcDImz+SVvDlPzovz7nzMW1ecbKZA/sD5/AHXgJQ5</latexit>K−1y
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K ·
data covariance matrix
log det(K)
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K · Matrix-matrix multiplication w/ K
log det(K)
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K ·
K ·
·
·
⊗
Matrix-matrix multiplication w/ K
Scalable GP Multi-output GP K K
O(n3) O(n2)
GPyTorch
GPyTorch
GPyTorch
1. GPU acceleration 2. Modular design 3. Open source
Poster #13 http://gpytorch.ai