COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |
University of Cambridge > Talks.cam > Machine Learning Reading Group @ CUED > "Symmetry and sufficiency"
"Symmetry and sufficiency"Add to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact Konstantina Palla. Suppose we represent observational data as a sequence of random variables. If the distribution of this sequence does not depend on the order of the variables, the sequence is conditionally independent given a random probability measure. This result is de Finetti’s theorem, which forms the formal basis of Bayesian statistics and also plays a pivotal role in applied probability. Various generalizations exist, both to other types of invariances than exchangeability, and to other random structures than sequences. A beautiful theorem of Lauritzen provides a common framework for these results and directly links them to statistics, by formalizing invariance by means of a sufficient statistic. I will discuss the relation between symmetry and sufficiency, sketch the general theorem, and discuss how it can be used to determine the fundamental independence structure of Bayesian models when the data is not an exchangeable sequence, but rather some other exchangeable random structure—the examples I will consider in the talk are random partitions and random graphs. The theorem can also be used to derive parametric exponential family models as a special case. With this talk, I will stand in for a cancelled RCC on short notice, and I will use a talk I recently gave in the Statistical Laboratory; this talk has evolved from an RCC titled “Exchangeability” which I gave last spring. The talks differ quite a bit and there is plenty of new material, but if you attended my talk last year and thought it was boring, this one is bound to be worse. This talk is part of the Machine Learning Reading Group @ CUED series. This talk is included in these lists:
Note that ex-directory lists are not shown. |
Other listsOpen Research Cambridge Cambridge Neurological Society Cambridge Language Sciences Annual SymposiumOther talksStereodivergent Catalysis, Strategies and Tactics Towards Secondary Metabolites as enabling tools for the Study of Natural Products Biology A unifying theory of branching morphogenesis Arriva Trains Wales by Tom Joyner Current-Induced Stresses in Ceramic Lithium-Ion Conductors The Exposome in Epidemiological Practice Breast cancer - demographics, presentation, diagnosis and patient pathway Cambridge-Lausanne Workshop 2018 - Day 2 Cyclic Peptides: Building Blocks for Supramolecular Designs Immigration and Freedom The frequency of ‘America’ in America |