2013/10/16 by Stefan Webb, Webb, Stefan Douglas
Computer Science · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.1310.4456
openalex publication_date 2013/10/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The cumulative distribution network (CDN) is a recently developed class of\nprobabilistic graphical models (PGMs) permitting a copula factorization, in\nwhich the CDF, rather than the density, is factored. Despite there being much\nrecent interest within the machine learning community about copula\nrepresentations, there has been scarce research into the CDN, its amalgamation\nwith copula theory, and no evaluation of its performance. Algorithms for\ninference, sampling, and learning in these models are underdeveloped compared\nthose of other PGMs, hindering widerspread use.\n One advantage of the CDN is that it allows the factors to be parameterized as\ncopulae, combining the benefits of graphical models with those of copula\ntheory. In brief, the use of a copula parameterization enables greater\nmodelling flexibility by separating representation of the marginals from the\ndependence structure, permitting more efficient and robust learning. Another\nadvantage is that the CDN permits the representation of implicit latent\nvariables, whose parameterization and connectivity are not required to be\nspecified. Unfortunately, that the model can encode only latent relationships\nbetween variables severely limits its utility.\n In this thesis, we present inference, learning, and sampling for CDNs, and\nfurther the state-of-the-art. First, we explain the basics of copula theory and\nthe representation of copula CDNs. Then, we discuss inference in the models,\nand develop the first sampling algorithm. We explain standard learning methods,\npropose an algorithm for learning from data missing completely at random\n(MCAR), and develop a novel algorithm for learning models of arbitrary\ntreewidth and size. Properties of the models and algorithms are investigated\nthrough Monte Carlo simulations. We conclude with further discussion of the\nadvantages and limitations of CDNs, and suggest future work.\n