Thong Pham

selected publications

1. Causal Additive Models with Unobserved Causal Paths and Backdoor Paths

   Pham, Thong, Maeda, Takashi Nicholas, and Shimizu, Shohei

   ArXiv e-prints, Oct 2025

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   Causal additive models provide a tractable yet expressive framework for causal discovery in the presence of hidden variables. However, when unobserved backdoor or causal paths exist between two variables, their causal relationship is often unidentifiable under existing theories. We establish sufficient conditions under which causal directions can be identified in many such cases. In particular, we derive conditions that enable identification of the parent-child relationship in a bow, an adjacent pair of observed variables sharing a hidden common parent. This represents a notoriously difficult case in causal discovery, and, to our knowledge, no prior work has established such identifiability in any causal model without imposing assumptions on the hidden variables. Our conditions rely on new characterizations of regression sets and a hybrid approach that combines independence among regression residuals with conditional independencies among observed variables. We further provide a sound and complete algorithm that incorporates these insights, and empirical evaluations demonstrate competitive performance with state-of-the-art methods.

   @article{pham_2025,
     author = {Pham, Thong and Maeda, Takashi Nicholas and Shimizu, Shohei},
     title = {Causal Additive Models with Unobserved Causal Paths and Backdoor Paths},
     year = {2025},
     month = oct,
     journal = {ArXiv e-prints}
   }

2. Non-parametric Estimation of the Preferential Attachment Function from One Network Snapshot

   Pham, Thong, Sheridan, Paul, and Shimodaira, Hidetoshi

   Journal of Complex Networks, Sep 2021

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   Preferential attachment is commonly invoked to explain the emergence of those heavy-tailed degree distributions characteristic of growing network representations of diverse real-world phenomena. Experimentally confirming this hypothesis in real-world growing networks is an important frontier in network science research. Conventional preferential attachment estimation methods require that a growing network be observed across at least two snapshots in time. Numerous publicly available growing network datasets are, however, only available as single snapshots, leaving the applied network scientist with no means of measuring preferential attachment in these cases. We propose a nonparametric method, called PAFit-oneshot, for estimating preferential attachment in a growing network from one snapshot. PAFit-oneshot corrects for a previously unnoticed bias that arises when estimating preferential attachment values only for degrees observed in the single snapshot. Our work provides a means of measuring preferential attachment in a large number of publicly available one-snapshot networks. As a demonstration, we estimated preferential attachment in three such networks, and found sublinear preferential attachment in all cases. PAFit-oneshot is implemented in the R package PAFit.

   @article{pham_2021,
     author = {Pham, Thong and Sheridan, Paul and Shimodaira, Hidetoshi},
     title = {Non-parametric Estimation of the Preferential Attachment Function from One Network Snapshot},
     journal = {Journal of Complex Networks},
     volume = {9},
     number = {5},
     year = {2021},
     month = sep,
     issn = {2051-1329},
     doi = {10.1093/comnet/cnab024},
     url = {https://doi.org/10.1093/comnet/cnab024},
     note = {cnab024},
     eprint = {https://academic.oup.com/comnet/article-pdf/9/5/cnab024/40830667/cnab024.pdf}
   }

3. PAFit: An R Package for the Non-Parametric Estimation of Preferential Attachment and Node Fitness in Temporal Complex Networks

   Pham, Thong, Sheridan, Paul, and Shimodaira, Hidetoshi

   Journal of Statistical Software, Feb 2020

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   Many real-world systems are profitably described as complex networks that grow over time. Preferential attachment and node fitness are two simple growth mechanisms that not only explain certain structural properties commonly observed in real-world systems, but are also tied to a number of applications in modeling and inference. While there are statistical packages for estimating various parametric forms of the preferential attachment function, there is no such package implementing non-parametric estimation procedures. The non-parametric approach to the estimation of the preferential attachment function allows for comparatively finer-grained investigations of the "rich-get-richer" phenomenon that could lead to novel insights in the search to explain certain nonstandard structural properties observed in real-world networks. This paper introduces the R package PAFit, which implements non-parametric procedures for estimating the preferential attachment function and node fitnesses in a growing network, as well as a number of functions for generating complex networks from these two mechanisms. The main computational part of the package is implemented in C++ with OpenMP to ensure scalability to large-scale networks. In this paper, we first introduce the main functionalities of PAFit through simulated examples, and then use the package to analyze a collaboration network between scientists in the field of complex networks. The results indicate the joint presence of "richget-richer" and "fit-get-richer" phenomena in the collaboration network. The estimated attachment function is observed to be near-linear, which we interpret as meaning that the chance an author gets a new collaborator is proportional to their current number of collaborators. Furthermore, the estimated author fitnesses reveal a host of familiar faces from the complex networks community among the field’s topmost fittest network scientists.

   @article{pham_2020,
     author = {Pham, Thong and Sheridan, Paul and Shimodaira, Hidetoshi},
     title = {{PAFit}: An {R} Package for the Non-Parametric Estimation of Preferential Attachment and Node Fitness in Temporal Complex Networks},
     journal = {Journal of Statistical Software},
     volume = {92},
     number = {3},
     year = {2020},
     month = feb,
     keywords = {temporal networks; dynamic networks; preferential attachment; fitness; rich-get-richer; fit-get-richer; R; C++; Rcpp; OpenMP},
     issn = {1548-7660},
     pages = {1--30},
     doi = {10.18637/jss.v092.i03},
     url = {https://www.jstatsoft.org/v092/i03}
   }