Shandian Zhe: Probabilistic Machine Learning
Research Topics:1. Bayesian Nonparametrics 2. Bayesian Deep Learning3. Probabilistic Graphical Models4. Large-Scale Learning System5. Tensor/Matrix Factorization6. Embedding Learning
Assistant Professor, School of Computing, University of Utah
Applications:• Collaborative Filtering• Online Advertising• Physical Simulation• Brain Imaging Data Analysis
….
Stochastic Nonparametric Event-Tensor Decomposition
Shandian Zhe, Yishuai [email protected], [email protected]
School of Computing, University of Utah
Tensor Data: Widely Used High-Order Data Structures to Represent Interactions of Multiple Objects/Entities
(user, item, online-store) (user, user, location, message-type)
(subject, voxel, electrode)(user, advertisement, page-section)
(patient, gene, condition)
(user, movie, episode)
Tensor Decomposition
user item page purchase
100 25 35 �
23 21 �� �
100 25 �� �
.. .. ..
32 33 �� �
���� �������������
user
item
page
1/0
Traditional methods: Multilinear assumptions������
�
������������
Tensor Decomposition with Time��������� ������������������
user item page purchase time-stamp
100 25 35 � ���������������
23 21 � � ���������������
100 25 �� � ����������������
.. .. .. ..
32 33 � � ����������������
����� �� ��������� ������ ������� ��� ��������������������� �������������
(i1, i2, i3)<latexit sha1_base64="zMPzi3yWFkUyZVRZ+VKsskf2mmc=">AAAB+HicbVDLSsNAFL2pr1ofrbp0M1iEClKSKuiy6MZlBfuANoTJdNIOnUzCzESooV/ixoUibv0Ud/6NkzYLbT1wL4dz7mXuHD/mTGnb/rYKa+sbm1vF7dLO7t5+uXJw2FFRIgltk4hHsudjRTkTtK2Z5rQXS4pDn9OuP7nN/O4jlYpF4kFPY+qGeCRYwAjWRvIq5RrznHPEvEbWLs68StWu23OgVeLkpAo5Wl7lazCMSBJSoQnHSvUdO9ZuiqVmhNNZaZAoGmMywSPaN1TgkCo3nR8+Q6dGGaIgkqaERnP190aKQ6WmoW8mQ6zHatnLxP+8fqKDazdlIk40FWTxUJBwpCOUpYCGTFKi+dQQTCQztyIyxhITbbIqmRCc5S+vkk6j7th15/6y2rzJ4yjCMZxADRy4gibcQQvaQCCBZ3iFN+vJerHerY/FaMHKd47gD6zPH5sRkRg=</latexit><latexit sha1_base64="zMPzi3yWFkUyZVRZ+VKsskf2mmc=">AAAB+HicbVDLSsNAFL2pr1ofrbp0M1iEClKSKuiy6MZlBfuANoTJdNIOnUzCzESooV/ixoUibv0Ud/6NkzYLbT1wL4dz7mXuHD/mTGnb/rYKa+sbm1vF7dLO7t5+uXJw2FFRIgltk4hHsudjRTkTtK2Z5rQXS4pDn9OuP7nN/O4jlYpF4kFPY+qGeCRYwAjWRvIq5RrznHPEvEbWLs68StWu23OgVeLkpAo5Wl7lazCMSBJSoQnHSvUdO9ZuiqVmhNNZaZAoGmMywSPaN1TgkCo3nR8+Q6dGGaIgkqaERnP190aKQ6WmoW8mQ6zHatnLxP+8fqKDazdlIk40FWTxUJBwpCOUpYCGTFKi+dQQTCQztyIyxhITbbIqmRCc5S+vkk6j7th15/6y2rzJ4yjCMZxADRy4gibcQQvaQCCBZ3iFN+vJerHerY/FaMHKd47gD6zPH5sRkRg=</latexit><latexit sha1_base64="zMPzi3yWFkUyZVRZ+VKsskf2mmc=">AAAB+HicbVDLSsNAFL2pr1ofrbp0M1iEClKSKuiy6MZlBfuANoTJdNIOnUzCzESooV/ixoUibv0Ud/6NkzYLbT1wL4dz7mXuHD/mTGnb/rYKa+sbm1vF7dLO7t5+uXJw2FFRIgltk4hHsudjRTkTtK2Z5rQXS4pDn9OuP7nN/O4jlYpF4kFPY+qGeCRYwAjWRvIq5RrznHPEvEbWLs68StWu23OgVeLkpAo5Wl7lazCMSBJSoQnHSvUdO9ZuiqVmhNNZaZAoGmMywSPaN1TgkCo3nR8+Q6dGGaIgkqaERnP190aKQ6WmoW8mQ6zHatnLxP+8fqKDazdlIk40FWTxUJBwpCOUpYCGTFKi+dQQTCQztyIyxhITbbIqmRCc5S+vkk6j7th15/6y2rzJ4yjCMZxADRy4gibcQQvaQCCBZ3iFN+vJerHerY/FaMHKd47gD6zPH5sRkRg=</latexit><latexit sha1_base64="zMPzi3yWFkUyZVRZ+VKsskf2mmc=">AAAB+HicbVDLSsNAFL2pr1ofrbp0M1iEClKSKuiy6MZlBfuANoTJdNIOnUzCzESooV/ixoUibv0Ud/6NkzYLbT1wL4dz7mXuHD/mTGnb/rYKa+sbm1vF7dLO7t5+uXJw2FFRIgltk4hHsudjRTkTtK2Z5rQXS4pDn9OuP7nN/O4jlYpF4kFPY+qGeCRYwAjWRvIq5RrznHPEvEbWLs68StWu23OgVeLkpAo5Wl7lazCMSBJSoQnHSvUdO9ZuiqVmhNNZaZAoGmMywSPaN1TgkCo3nR8+Q6dGGaIgkqaERnP190aKQ6WmoW8mQ6zHatnLxP+8fqKDazdlIk40FWTxUJBwpCOUpYCGTFKi+dQQTCQztyIyxhITbbIqmRCc5S+vkk6j7th15/6y2rzJ4yjCMZxADRy4gibcQQvaQCCBZ3iFN+vJerHerY/FaMHKd47gD6zPH5sRkRg=</latexit>
=<latexit sha1_base64="NXXyo5YwHjQEa14yJBBpMTmsH6Q=">AAACHnicbVDLSsNAFJ34rPEVdelmsARakJJURTdC0Y0boYJ9QFvCZDpph04mYWYilNAvceOvuHGhiOBK/8ZJm4W2HpjhcM693HuPHzMqleN8G0vLK6tr64UNc3Nre2fX2ttvyigRmDRwxCLR9pEkjHLSUFQx0o4FQaHPSMsfXWd+64EISSN+r8Yx6YVowGlAMVJa8qwzu0Q99xhSr5p9J2XT7oZIDTFi6e1kwQtKpl02Lz2r6FScKeAicXNSBDnqnvXZ7Uc4CQlXmCEpO64Tq16KhKKYkYnZTSSJER6hAeloylFIZC+dnjeBtlb6MIiEflzBqfq7I0WhlOPQ15XZ6nLey8T/vE6igoteSnmcKMLxbFCQMKgimGUF+1QQrNhYE4QF1btCPEQCYaUTNXUI7vzJi6RZrbhOxb07Ldau8jgK4BAcgRJwwTmogRtQBw2AwSN4Bq/gzXgyXox342NWumTkPQfgD4yvH7CenJY=</latexit><latexit sha1_base64="NXXyo5YwHjQEa14yJBBpMTmsH6Q=">AAACHnicbVDLSsNAFJ34rPEVdelmsARakJJURTdC0Y0boYJ9QFvCZDpph04mYWYilNAvceOvuHGhiOBK/8ZJm4W2HpjhcM693HuPHzMqleN8G0vLK6tr64UNc3Nre2fX2ttvyigRmDRwxCLR9pEkjHLSUFQx0o4FQaHPSMsfXWd+64EISSN+r8Yx6YVowGlAMVJa8qwzu0Q99xhSr5p9J2XT7oZIDTFi6e1kwQtKpl02Lz2r6FScKeAicXNSBDnqnvXZ7Uc4CQlXmCEpO64Tq16KhKKYkYnZTSSJER6hAeloylFIZC+dnjeBtlb6MIiEflzBqfq7I0WhlOPQ15XZ6nLey8T/vE6igoteSnmcKMLxbFCQMKgimGUF+1QQrNhYE4QF1btCPEQCYaUTNXUI7vzJi6RZrbhOxb07Ldau8jgK4BAcgRJwwTmogRtQBw2AwSN4Bq/gzXgyXox342NWumTkPQfgD4yvH7CenJY=</latexit><latexit sha1_base64="NXXyo5YwHjQEa14yJBBpMTmsH6Q=">AAACHnicbVDLSsNAFJ34rPEVdelmsARakJJURTdC0Y0boYJ9QFvCZDpph04mYWYilNAvceOvuHGhiOBK/8ZJm4W2HpjhcM693HuPHzMqleN8G0vLK6tr64UNc3Nre2fX2ttvyigRmDRwxCLR9pEkjHLSUFQx0o4FQaHPSMsfXWd+64EISSN+r8Yx6YVowGlAMVJa8qwzu0Q99xhSr5p9J2XT7oZIDTFi6e1kwQtKpl02Lz2r6FScKeAicXNSBDnqnvXZ7Uc4CQlXmCEpO64Tq16KhKKYkYnZTSSJER6hAeloylFIZC+dnjeBtlb6MIiEflzBqfq7I0WhlOPQ15XZ6nLey8T/vE6igoteSnmcKMLxbFCQMKgimGUF+1QQrNhYE4QF1btCPEQCYaUTNXUI7vzJi6RZrbhOxb07Ldau8jgK4BAcgRJwwTmogRtQBw2AwSN4Bq/gzXgyXox342NWumTkPQfgD4yvH7CenJY=</latexit><latexit sha1_base64="NXXyo5YwHjQEa14yJBBpMTmsH6Q=">AAACHnicbVDLSsNAFJ34rPEVdelmsARakJJURTdC0Y0boYJ9QFvCZDpph04mYWYilNAvceOvuHGhiOBK/8ZJm4W2HpjhcM693HuPHzMqleN8G0vLK6tr64UNc3Nre2fX2ttvyigRmDRwxCLR9pEkjHLSUFQx0o4FQaHPSMsfXWd+64EISSN+r8Yx6YVowGlAMVJa8qwzu0Q99xhSr5p9J2XT7oZIDTFi6e1kwQtKpl02Lz2r6FScKeAicXNSBDnqnvXZ7Uc4CQlXmCEpO64Tq16KhKKYkYnZTSSJER6hAeloylFIZC+dnjeBtlb6MIiEflzBqfq7I0WhlOPQ15XZ6nLey8T/vE6igoteSnmcKMLxbFCQMKgimGUF+1QQrNhYE4QF1btCPEQCYaUTNXUI7vzJi6RZrbhOxb07Ldau8jgK4BAcgRJwwTmogRtQBw2AwSN4Bq/gzXgyXox342NWumTkPQfgD4yvH7CenJY=</latexit>f(<latexit sha1_base64="HtlbdolTZQFq43eOq2hXhuNOZ0I=">AAACGHicbVDLSsNAFL2prxpfUZduBkuhgtSkCrosunEjVLAPaEuYTCft0MmDmYlQQj/Djb/ixoUibrvzb5y0WWj1wAyHc+7l3nu8mDOpbPvLKKysrq1vFDfNre2d3T1r/6Alo0QQ2iQRj0THw5JyFtKmYorTTiwoDjxO2974JvPbj1RIFoUPahLTfoCHIfMZwUpLrnVWrjDXOUXMrWXf+YlZ7gVYjQjm6d102fMrrlWyq/Yc6C9xclKCHA3XmvUGEUkCGirCsZRdx45VP8VCMcLp1OwlksaYjPGQdjUNcUBlP50fNkVlrQyQHwn9QoXm6s+OFAdSTgJPV2ZLy2UvE//zuonyr/opC+NE0ZAsBvkJRypCWUpowAQlik80wUQwvSsiIywwUTpLU4fgLJ/8l7RqVceuOvcXpfp1HkcRjuAYKuDAJdThFhrQBAJP8AJv8G48G6/Gh/G5KC0Yec8h/IIx+wZXMpuW</latexit><latexit sha1_base64="HtlbdolTZQFq43eOq2hXhuNOZ0I=">AAACGHicbVDLSsNAFL2prxpfUZduBkuhgtSkCrosunEjVLAPaEuYTCft0MmDmYlQQj/Djb/ixoUibrvzb5y0WWj1wAyHc+7l3nu8mDOpbPvLKKysrq1vFDfNre2d3T1r/6Alo0QQ2iQRj0THw5JyFtKmYorTTiwoDjxO2974JvPbj1RIFoUPahLTfoCHIfMZwUpLrnVWrjDXOUXMrWXf+YlZ7gVYjQjm6d102fMrrlWyq/Yc6C9xclKCHA3XmvUGEUkCGirCsZRdx45VP8VCMcLp1OwlksaYjPGQdjUNcUBlP50fNkVlrQyQHwn9QoXm6s+OFAdSTgJPV2ZLy2UvE//zuonyr/opC+NE0ZAsBvkJRypCWUpowAQlik80wUQwvSsiIywwUTpLU4fgLJ/8l7RqVceuOvcXpfp1HkcRjuAYKuDAJdThFhrQBAJP8AJv8G48G6/Gh/G5KC0Yec8h/IIx+wZXMpuW</latexit><latexit sha1_base64="HtlbdolTZQFq43eOq2hXhuNOZ0I=">AAACGHicbVDLSsNAFL2prxpfUZduBkuhgtSkCrosunEjVLAPaEuYTCft0MmDmYlQQj/Djb/ixoUibrvzb5y0WWj1wAyHc+7l3nu8mDOpbPvLKKysrq1vFDfNre2d3T1r/6Alo0QQ2iQRj0THw5JyFtKmYorTTiwoDjxO2974JvPbj1RIFoUPahLTfoCHIfMZwUpLrnVWrjDXOUXMrWXf+YlZ7gVYjQjm6d102fMrrlWyq/Yc6C9xclKCHA3XmvUGEUkCGirCsZRdx45VP8VCMcLp1OwlksaYjPGQdjUNcUBlP50fNkVlrQyQHwn9QoXm6s+OFAdSTgJPV2ZLy2UvE//zuonyr/opC+NE0ZAsBvkJRypCWUpowAQlik80wUQwvSsiIywwUTpLU4fgLJ/8l7RqVceuOvcXpfp1HkcRjuAYKuDAJdThFhrQBAJP8AJv8G48G6/Gh/G5KC0Yec8h/IIx+wZXMpuW</latexit><latexit sha1_base64="HtlbdolTZQFq43eOq2hXhuNOZ0I=">AAACGHicbVDLSsNAFL2prxpfUZduBkuhgtSkCrosunEjVLAPaEuYTCft0MmDmYlQQj/Djb/ixoUibrvzb5y0WWj1wAyHc+7l3nu8mDOpbPvLKKysrq1vFDfNre2d3T1r/6Alo0QQ2iQRj0THw5JyFtKmYorTTiwoDjxO2974JvPbj1RIFoUPahLTfoCHIfMZwUpLrnVWrjDXOUXMrWXf+YlZ7gVYjQjm6d102fMrrlWyq/Yc6C9xclKCHA3XmvUGEUkCGirCsZRdx45VP8VCMcLp1OwlksaYjPGQdjUNcUBlP50fNkVlrQyQHwn9QoXm6s+OFAdSTgJPV2ZLy2UvE//zuonyr/opC+NE0ZAsBvkJRypCWUpowAQlik80wUQwvSsiIywwUTpLU4fgLJ/8l7RqVceuOvcXpfp1HkcRjuAYKuDAJdThFhrQBAJP8AJv8G48G6/Gh/G5KC0Yec8h/IIx+wZXMpuW</latexit>
)<latexit sha1_base64="lqIbaNKhk/UYMmUKExWnsmvmU4s=">AAACG3icbVDLSsNAFL2prxpfUZduBkuhBSlJFXRZdONGqGBroS1hMp20QycPZiZCCf0PN/6KGxeKuBJc+DdO2iy09cAMh3Pu5d57vJgzqWz72yisrK6tbxQ3za3tnd09a/+gLaNEENoiEY9Ex8OSchbSlmKK004sKA48Tu+98VXm3z9QIVkU3qlJTPsBHobMZwQrLblWvVxhrnOCmFvPvtOqWe4FWI0I5unNdMnzK2bVtUp2zZ4BLRMnJyXI0XStz94gIklAQ0U4lrLr2LHqp1goRjidmr1E0hiTMR7SrqYhDqjsp7PbpqislQHyI6FfqNBM/d2R4kDKSeDpymxvuehl4n9eN1H+RT9lYZwoGpL5ID/hSEUoCwoNmKBE8YkmmAimd0VkhAUmSsdp6hCcxZOXSbtec+yac3tWalzmcRThCI6hAg6cQwOuoQktIPAIz/AKb8aT8WK8Gx/z0oKR9xzCHxhfP3QTnAw=</latexit><latexit sha1_base64="lqIbaNKhk/UYMmUKExWnsmvmU4s=">AAACG3icbVDLSsNAFL2prxpfUZduBkuhBSlJFXRZdONGqGBroS1hMp20QycPZiZCCf0PN/6KGxeKuBJc+DdO2iy09cAMh3Pu5d57vJgzqWz72yisrK6tbxQ3za3tnd09a/+gLaNEENoiEY9Ex8OSchbSlmKK004sKA48Tu+98VXm3z9QIVkU3qlJTPsBHobMZwQrLblWvVxhrnOCmFvPvtOqWe4FWI0I5unNdMnzK2bVtUp2zZ4BLRMnJyXI0XStz94gIklAQ0U4lrLr2LHqp1goRjidmr1E0hiTMR7SrqYhDqjsp7PbpqislQHyI6FfqNBM/d2R4kDKSeDpymxvuehl4n9eN1H+RT9lYZwoGpL5ID/hSEUoCwoNmKBE8YkmmAimd0VkhAUmSsdp6hCcxZOXSbtec+yac3tWalzmcRThCI6hAg6cQwOuoQktIPAIz/AKb8aT8WK8Gx/z0oKR9xzCHxhfP3QTnAw=</latexit><latexit sha1_base64="lqIbaNKhk/UYMmUKExWnsmvmU4s=">AAACG3icbVDLSsNAFL2prxpfUZduBkuhBSlJFXRZdONGqGBroS1hMp20QycPZiZCCf0PN/6KGxeKuBJc+DdO2iy09cAMh3Pu5d57vJgzqWz72yisrK6tbxQ3za3tnd09a/+gLaNEENoiEY9Ex8OSchbSlmKK004sKA48Tu+98VXm3z9QIVkU3qlJTPsBHobMZwQrLblWvVxhrnOCmFvPvtOqWe4FWI0I5unNdMnzK2bVtUp2zZ4BLRMnJyXI0XStz94gIklAQ0U4lrLr2LHqp1goRjidmr1E0hiTMR7SrqYhDqjsp7PbpqislQHyI6FfqNBM/d2R4kDKSeDpymxvuehl4n9eN1H+RT9lYZwoGpL5ID/hSEUoCwoNmKBE8YkmmAimd0VkhAUmSsdp6hCcxZOXSbtec+yac3tWalzmcRThCI6hAg6cQwOuoQktIPAIz/AKb8aT8WK8Gx/z0oKR9xzCHxhfP3QTnAw=</latexit><latexit sha1_base64="lqIbaNKhk/UYMmUKExWnsmvmU4s=">AAACG3icbVDLSsNAFL2prxpfUZduBkuhBSlJFXRZdONGqGBroS1hMp20QycPZiZCCf0PN/6KGxeKuBJc+DdO2iy09cAMh3Pu5d57vJgzqWz72yisrK6tbxQ3za3tnd09a/+gLaNEENoiEY9Ex8OSchbSlmKK004sKA48Tu+98VXm3z9QIVkU3qlJTPsBHobMZwQrLblWvVxhrnOCmFvPvtOqWe4FWI0I5unNdMnzK2bVtUp2zZ4BLRMnJyXI0XStz94gIklAQ0U4lrLr2LHqp1goRjidmr1E0hiTMR7SrqYhDqjsp7PbpqislQHyI6FfqNBM/d2R4kDKSeDpymxvuehl4n9eN1H+RT9lYZwoGpL5ID/hSEUoCwoNmKBE8YkmmAimd0VkhAUmSsdp6hCcxZOXSbtec+yac3tWalzmcRThCI6hAg6cQwOuoQktIPAIz/AKb8aT8WK8Gx/z0oKR9xzCHxhfP3QTnAw=</latexit>
�����
������
…
������ ������ ������
���������������
user
item
page
(user, item, page, week)
����������
Stochastic Nonparametric Event-Tensor Decomposition
user item page time-stamp
100 25 35 �������� ����
23 21 � ��������������
100 25 � �������������
.. .. ..
32 33 � ������������
index time-stamps(100,25,35) {s1, s2...sn}
<latexit sha1_base64="QrucCBJJT+6UOj+9PBvbDcskOwQ=">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</latexit><latexit sha1_base64="QrucCBJJT+6UOj+9PBvbDcskOwQ=">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</latexit><latexit sha1_base64="QrucCBJJT+6UOj+9PBvbDcskOwQ=">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</latexit><latexit sha1_base64="QrucCBJJT+6UOj+9PBvbDcskOwQ=">AAAC33icjVHLSsNAFD3GV62vqjvdBFvBhYSkG10W3bisYFVopSRx1GCahGQilFJw507c+gNu9W/EP9C/8MwYwQeiEzJz5tx7zsyd6yVhkEnbfh4xRsfGJyZLU+Xpmdm5+crC4kEW56kvWn4cxumR52YiDCLRkoEMxVGSCrfnheLQu9hR8cNLkWZBHO3LfiKOe+5ZFJwGvitJdSvLtVpnYGZdx9zgXDcty+IadYa1WrdStS1bD/MncApQRTGaceUJHZwgho8cPQhEkMQhXGT82nBgIyF3jAG5lCjQcYEhytTmzBLMcMlecD7jrl2wEffKM9Nqn6eE/FMqTaxREzMvJVanmTqea2fF/uY90J7qbn2uXuHVIytxTvYv3Ufmf3WqFolTbOkaAtaUaEZV5xcuuX4VdXPzU1WSDgk5hU8YT4l9rfx4Z1NrMl27eltXx190pmLV3i9yc7yqW7LBzvd2/gQHdcsh3qtXG9tFq0tYwSrW2c9NNLCLJlr0vsI9HvBouMa1cWPcvqcaI4VmCV+GcfcGNOuXCw==</latexit>
��������������������������� ����
��������!�����"�� ���� ������������ ��� �������������������������������
���� �� �����!������ ������ �� ���� ����
!�!�������������� ����!��� ���
��!��� �#��!
���� ��������"������ �!����!������
!���������!���������������!��� ��� �