There is still turmoil on the classification of HPV carcinogenicity, particularly for the weakly carcinogenic types. 
The subject has been discussed at the IARC Meeting B on biological carcinogenic agents, and Mark Schiffman is reporting in the current IAC Editorial the scientific approach used for the re-classification.
Not all scientists, neither all IARC participants, fully agree on this subject and Mark is again stressing this concept starting with a clear sentence "We do not agree on everything" his presentation (that will likely become a renowned presentation) at Malmo 25th IPV Conference, 
available at the Conference WebCast:
HPV: natural history of the infection from the epidemiological and clinical perspective
(by M. Schiffman)
The real problem is that not only in HPV-associated carcinogenesis, but in the viral oncology in general, and as matter of fact in the whole field of carcinogenesis it is "relatively" simple to identify strong carcinogens; the complexity is to identify weak carcinogenic exposures, implying either the exposure to weak carcinogens that the exposure to minimal/subminimal doses of potent carcinogens. The complexity is not only related to the possible cumulative effect of low carcinogenic exposures and the need for long-term follow up (> 1 year post-exposure), but also to the uncertainty on the background carcinogenic rate (i.e. in vitro transforming activity of empty vectors and even normal human DNA). Stretching any system (not only epidemiology) to the limits could lead to problems on the carcinogenic definition of most (if not all) physical, chemical and biological agents.
Franco Buonaguro
Dr Buonaguro is the Editor-in-Chief of Infectious Agents and Cancer. He is currently the Director of Molecular Biology and Viral Oncology Unit, in the Department of Experimental Oncology at the Natl Cancer Institute “Fondazione Pascale”, Naples - Italy.
Latest posts by Franco Buonaguro (see all)
- Red de Institutos Nacionales de Cancer de Latinoamérica RINC-ALC - 26th June 2019
- Pioneers in Infectious Agents and Cancer Meeting - 2nd March 2017
- IARC 50th Anniversary Meeting 2016 - 13th June 2016
The HPV’s mechanism of carcinogenesis is not completely understood. The possibility of evolving into direction of malignancy depends on the type of virus, the synergic action with different physical, chemical and biological agents, the genetic constitution of the host and the immune defense mechanism of the host, all of which are able to modify the course of HPV infection.