Visualizing and understanding Sum-Product Networks

Vergari, Antonio; Mauro, Nicola Di; Esposito, Floriana

doi:10.1007/s10994-018-5760-y

Cited by 19 publications

(17 citation statements)

References 17 publications

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“…Vergari et al [90] also evaluated SPNs for representation learning [91]. Their SPNs encode a hierarchy of part-based representations which can be ordered by scope length.…”

Section: Other Applicationsmentioning

confidence: 99%

Sum-product networks: A survey

Sánchez-Cauce¹,

Paris²,

Vegas³

2021

IEEE Trans. Pattern Anal. Mach. Intell.

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A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent probability distributions and non-terminal nodes represent convex sums (weighted averages) and products of probability distributions. They are closely related to probabilistic graphical models, in particular to Bayesian networks with multiple context-specific independencies. Their main advantage is the possibility of building tractable models from data, i.e., models that can perform several inference tasks in time proportional to the number of edges in the graph. They are somewhat similar to neural networks and can address the same kinds of problems, such as image processing and natural language understanding. This paper offers a survey of SPNs, including their definition, the main algorithms for inference and learning from data, several applications, a brief review of software libraries, and a comparison with related models.

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“…Vergari et al [90] also evaluated SPNs for representation learning [91]. Their SPNs encode a hierarchy of part-based representations which can be ordered by scope length.…”

Section: Other Applicationsmentioning

confidence: 99%

Sum-product networks: A survey

Sánchez-Cauce¹,

Paris²,

Vegas³

2021

IEEE Trans. Pattern Anal. Mach. Intell.

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show abstract

“…These techniques, however, have not been extended to hybrid domains. On the other hand, MSPNs (Molina et al 2018;) are state-of-the-art density estimators that extend Sum-Product Networks (Poon and Domingos 2011;Darwiche 2009;Vergari, Di Mauro, and Esposito 2019) by introducing continuous variables and polynomial densities at the leaves. Like DETs, MSPNs allow efficient inference so long as the query formula is axis-aligned, and are learned using a greedy scheme.…”

Section: Related Workmentioning

confidence: 99%

Learning Weighted Model Integration Distributions

Morettin

Kolb

Teso

et al. 2020

AAAI

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Weighted model integration (WMI) is a framework for probabilistic inference over distributions with discrete and continuous variables and structured supports. Despite the growing popularity of WMI, existing density estimators ignore the problem of learning a structured support, and thus fail to handle unfeasible configurations and piecewise-linear relations between continuous variables. We propose lariat, a novel method to tackle this challenging problem. In a first step, our approach induces an SMT(ℒℛA) formula representing the support of the structured distribution. Next, it combines the latter with a density learned using a state-of-the-art estimation method. The overall model automatically accounts for the discontinuous nature of the underlying structured distribution. Our experimental results with synthetic and real-world data highlight the promise of the approach.

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“…Please note that in such a way we are encompassing highly expressive and complex joint distributions that might have generated the data (while retaining control over their statistical dependencies, types and likelihood models. Indeed, SPNs have been demonstrated to capture linear [22] and highly non-linear correlations [23,35] in the data, being also able to model constrained random vectors, as ones drawn from the simplex (see. [23]).…”

Section: Synthetic Data Experimentsmentioning

confidence: 99%

Automatic Bayesian Density Analysis

Vergari

Molina

Peharz

et al. 2019

AAAI

Self Cite

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Making sense of a dataset in an automatic and unsupervised fashion is a challenging problem in statistics and AI. Classical approaches for exploratory data analysis are usually not flexible enough to deal with the uncertainty inherent to real-world data: they are often restricted to fixed latent interaction models and homogeneous likelihoods; they are sensitive to missing, corrupt and anomalous data; moreover, their expressiveness generally comes at the price of intractable inference. As a result, supervision from statisticians is usually needed to find the right model for the data. However, since domain experts are not necessarily also experts in statistics, we propose Automatic Bayesian Density Analysis (ABDA) to make exploratory data analysis accessible at large. Specifically, ABDA allows for automatic and efficient missing value estimation, statistical data type and likelihood discovery, anomaly detection and dependency structure mining, on top of providing accurate density estimation. Extensive empirical evidence shows that ABDA is a suitable tool for automatic exploratory analysis of mixed continuous and discrete tabular data. arXiv:1807.09306v3 [stat.ML]

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Visualizing and understanding Sum-Product Networks

Cited by 19 publications

References 17 publications

Sum-product networks: A survey

Sum-product networks: A survey

Learning Weighted Model Integration Distributions

Automatic Bayesian Density Analysis

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