{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T12:09:33Z","timestamp":1772885373913,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,8,30]],"date-time":"2018-08-30T00:00:00Z","timestamp":1535587200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s10994-018-5760-y","type":"journal-article","created":{"date-parts":[[2018,8,30]],"date-time":"2018-08-30T16:55:12Z","timestamp":1535648112000},"page":"551-573","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Visualizing and understanding Sum-Product Networks"],"prefix":"10.1007","volume":"108","author":[{"given":"Antonio","family":"Vergari","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5858-1931","authenticated-orcid":false,"given":"Nicola","family":"Di Mauro","sequence":"additional","affiliation":[]},{"given":"Floriana","family":"Esposito","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,8,30]]},"reference":[{"issue":"11","key":"5760_CR1","doi-asserted-by":"publisher","first-page":"1475","DOI":"10.1109\/TPAMI.2004.108","volume":"26","author":"S Agarwal","year":"2004","unstructured":"Agarwal, S., Awan, A., & Roth, D. (2004). Learning to detect objects in images via a sparse, part-based representation. IEEE TPAMI, 26(11), 1475\u20131490.","journal-title":"IEEE TPAMI"},{"issue":"4","key":"5760_CR2","doi-asserted-by":"publisher","first-page":"800","DOI":"10.1109\/TPAMI.2015.2465955","volume":"38","author":"MR Amer","year":"2015","unstructured":"Amer, M. R., & Todorovic, S. (2015). Sum Product Networks for activity recognition. IEEE TPAMI, 38(4), 800\u2013813.","journal-title":"IEEE TPAMI"},{"issue":"8","key":"5760_CR3","doi-asserted-by":"publisher","first-page":"1798","DOI":"10.1109\/TPAMI.2013.50","volume":"35","author":"Y Bengio","year":"2013","unstructured":"Bengio, Y., Courville, A., & Vincent, P. (2013). Representation learning: A review and new perspectives. IEEE TPAMI, 35(8), 1798\u20131828.","journal-title":"IEEE TPAMI"},{"key":"5760_CR4","doi-asserted-by":"crossref","unstructured":"Cheng, W., Kok, S., Pham, H.V., Chieu, H. L., & Chai, K. M. A. (2014). Language modeling with Sum-Product Networks. In ISCA (pp. 2098\u20132102).","DOI":"10.21437\/Interspeech.2014-476"},{"key":"5760_CR5","unstructured":"Choi, A., & Darwiche, A. (2017). On relaxing determinism in arithmetic circuits. In ICML (pp. 825\u2013833)."},{"key":"5760_CR6","unstructured":"Coates, A., Lee, H., & Ng, A. Y. (2011). An analysis of single layer networks in unsupervised feature learning. In AISTATS (pp. 215\u2013223)."},{"key":"5760_CR7","unstructured":"Conaty, D., de\u00a0Campos, C. P., & Mau\u00e1, D. D. (2017). Approximation complexity of maximum a posteriori inference in Sum-Product Networks. In UAI."},{"issue":"3","key":"5760_CR8","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1145\/765568.765570","volume":"50","author":"A Darwiche","year":"2003","unstructured":"Darwiche, A. (2003). A differential approach to inference in Bayesian networks. JACM, 50(3), 280\u2013305.","journal-title":"JACM"},{"key":"5760_CR9","unstructured":"Delalleau, O., & Bengio, Y. (2011). Shallow vs. deep Sum-Product Networks. In NIPS (pp. 666\u2013674)."},{"key":"5760_CR10","unstructured":"Dennis, A. W., & Ventura, D. (2015). Greedy Structure Search for Sum-Product Networks. In IJCAI (pp. 932\u2013938)."},{"key":"5760_CR11","unstructured":"Erhan, D., Bengio, Y., Courville, A., & Vincent, P. (2009). Visualizing higher-layer features of a deep network. Technical report, University of Montreal."},{"issue":"9","key":"5760_CR12","doi-asserted-by":"publisher","first-page":"1627","DOI":"10.1109\/TPAMI.2009.167","volume":"32","author":"PF Felzenszwalb","year":"2010","unstructured":"Felzenszwalb, P. F., Girshick, R. B., McAllester, D., & Ramanan, D. (2010). Object detection with discriminatively trained part-based models. IEEE TPAMI, 32(9), 1627\u20131645.","journal-title":"IEEE TPAMI"},{"key":"5760_CR13","unstructured":"Gens, R., & Domingos, P. (2012). Discriminative learning of Sum-Product Networks. In NIPS (pp. 3239\u20133247)."},{"key":"5760_CR14","unstructured":"Gens, R., & Domingos, P. (2013). Learning the structure of Sum-Product Networks. In ICML (pp. 873\u2013880)."},{"key":"5760_CR15","unstructured":"Germain, M., Gregor, K., Murray, I., & Larochelle, H. (2015). MADE: Masked autoencoder for distribution estimation. In ICML (pp. 881\u2013889)."},{"issue":"5786","key":"5760_CR16","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1126\/science.1127647","volume":"313","author":"GE Hinton","year":"2006","unstructured":"Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. Science, 313(5786), 504\u2013507.","journal-title":"Science"},{"key":"5760_CR17","unstructured":"Hsu, W., Kalra, A., & Poupart, P. (2017). Online structure learning for Sum-Product Networks with Gaussian leaves. CoRR abs\/1701.05265."},{"key":"5760_CR18","unstructured":"Karpathy, A., Johnson, J., & Li, F. (2015). Visualizing and understanding recurrent networks. CoRR abs\/1506.02078."},{"key":"5760_CR19","unstructured":"Kingma, D. P., & Welling, M. (2013). Auto-encoding variational Bayes. In ICLR, 2014."},{"key":"5760_CR20","volume-title":"Probabilistic graphical models: Principles and techniques","author":"D Koller","year":"2009","unstructured":"Koller, D., & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques. Cambridge, MA: MIT Press."},{"key":"5760_CR21","doi-asserted-by":"crossref","unstructured":"Larochelle, H., & Bengio, Y. (2008). Classification using discriminative restricted Boltzmann machines. In ICML (pp. 536\u2013543).","DOI":"10.1145\/1390156.1390224"},{"key":"5760_CR22","doi-asserted-by":"crossref","unstructured":"Larochelle, H., Erhan, D., Courville, A., Bergstra, J., & Bengio, Y. (2007). An empirical evaluation of deep architectures on problems with many factors of variation. In ICML (pp. 473\u2013480).","DOI":"10.1145\/1273496.1273556"},{"key":"5760_CR23","unstructured":"Larochelle, H., & Murray, I. (2011). The neural autoregressive distribution estimator. In AISTATS (pp. 29\u201337)."},{"key":"5760_CR24","unstructured":"Marlin, B. M., Swersky, K., Chen, B., & Freitas, N. D. (2010). Inductive principles for restricted Boltzmann machine learning. In AISTATS (pp. 509\u2013516)."},{"key":"5760_CR25","unstructured":"Martens, J., & Medabalimi, V. (2014). On the expressive efficiency of Sum Product Networks. CoRR abs\/1411.7717."},{"key":"5760_CR26","doi-asserted-by":"crossref","unstructured":"Molina, A., Natarajan, S., & Kersting, K. (2017). Poisson Sum-Product Networks: A deep architecture for tractable multivariate Poisson distributions. In AAAI (pp. 2357\u20132363).","DOI":"10.1609\/aaai.v31i1.10844"},{"key":"5760_CR27","doi-asserted-by":"crossref","unstructured":"Peharz, R., Geiger, B., & Pernkopf, F. (2013). Greedy part-wise learning of Sum-Product Networks. In ECML\/PKDD (pp. 612\u2013627).","DOI":"10.1007\/978-3-642-40991-2_39"},{"key":"5760_CR28","unstructured":"Peharz, R., Gens, R., Pernkopf, F., & Domingos, P. M. (2016). On the latent variable interpretation in Sum-Product Networks. CoRR abs\/1601.06180."},{"key":"5760_CR29","doi-asserted-by":"crossref","unstructured":"Peharz, R., Kapeller, G., Mowlaee, P., & Pernkopf, F. (2014). Modeling speech with Sum-Product Networks: Application to bandwidth extension. In IEEE ICASSP (pp. 3699\u20133703).","DOI":"10.1109\/ICASSP.2014.6854292"},{"key":"5760_CR30","unstructured":"Peharz, R., Tschiatschek, S., Pernkopf, F., & Domingos, P. (2015). On theoretical properties of Sum-Product Networks. In AISTATS."},{"key":"5760_CR31","doi-asserted-by":"crossref","unstructured":"Poon, H., & Domingos, P. (2011). Sum-Product Networks: A new deep architecture. In UAI (pp. 337\u2013346).","DOI":"10.1109\/ICCVW.2011.6130310"},{"key":"5760_CR32","unstructured":"Rahman, T., & Gogate, V. (2016). Merging strategies for Sum-Product Networks: From trees to graphs. In UAI."},{"key":"5760_CR33","unstructured":"Rashwan, A., Zhao, H., & Poupart, P. (2016). Online and distributed Bayesian moment matching for parameter learning in Sum-Product Networks. In AISTATS."},{"key":"5760_CR34","unstructured":"Rooshenas, A., & Lowd, D. (2014). Learning Sum-Product Networks with direct and indirect variable interactions. In ICML (pp. 710\u2013718)."},{"key":"5760_CR35","unstructured":"Salakhutdinov, R., & Hinton, G. (2009). Deep Boltzmann machines. In AISTATS (pp. 448\u2013455)."},{"key":"5760_CR36","unstructured":"Simonyan, K., Vedaldi, A., & Zisserman, A. (2013). Deep inside convolutional networks: Visualising image classification models and saliency maps. CoRR abs\/1312.6034."},{"key":"5760_CR37","unstructured":"Smolensky, P. (1986). Information processing in dynamical systems: Foundations of harmony theory. Technical report, DTIC Document."},{"key":"5760_CR38","doi-asserted-by":"crossref","unstructured":"Vergari, A., Di Mauro, N., & Esposito, F. (2015). Simplifying, regularizing and strengthening Sum-Product Network structure learning. In ECML\/PKDD (pp. 343\u2013358).","DOI":"10.1007\/978-3-319-23525-7_21"},{"key":"5760_CR39","first-page":"3371","volume":"11","author":"P Vincent","year":"2010","unstructured":"Vincent, P., Larochelle, H., Lajoie, I., Bengio, Y., & Manzagol, P. A. (2010). Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. JMLR, 11, 3371\u20133408.","journal-title":"JMLR"},{"key":"5760_CR40","unstructured":"Yosinski, J., Clune, J., Nguyen, A. M., Fuchs, T., & Lipson, H. (2015). Understanding neural networks through deep visualization. CoRR abs\/1506.06579."},{"key":"5760_CR41","doi-asserted-by":"crossref","unstructured":"Zeiler, M. D., & Fergus, R. (2014). Visualizing and understanding convolutional networks. In ECCV (pp. 818\u2013833).","DOI":"10.1007\/978-3-319-10590-1_53"},{"key":"5760_CR42","unstructured":"Zhao, H., Adel, T., Gordon, G., & Amos, B. (2016). Collapsed variational inference for Sum-Product Networks. In ICML (pp. 1310\u20131318)."},{"key":"5760_CR43","unstructured":"Zhao, H., Melibari, M., & Poupart, P. (2015). On the relationship between Sum-Product Networks and Bayesian networks. In ICML (pp. 116\u2013124)."},{"key":"5760_CR44","unstructured":"Zhou, D., Bousquet, O., Lal, T. N., Weston, J., & Sch\u00f6lkopf, B. (2004). Learning with local and global consistency. In NIPS (pp. 321\u2013328)."}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-018-5760-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10994-018-5760-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-018-5760-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T23:20:02Z","timestamp":1661901602000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10994-018-5760-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,30]]},"references-count":44,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["5760"],"URL":"https:\/\/doi.org\/10.1007\/s10994-018-5760-y","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,30]]},"assertion":[{"value":"29 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 August 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 August 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}