Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Neuroinformatics wikipedia , lookup
Artificial neural network wikipedia , lookup
Development of the nervous system wikipedia , lookup
Metastability in the brain wikipedia , lookup
Mathematical model wikipedia , lookup
Nervous system network models wikipedia , lookup
Types of artificial neural networks wikipedia , lookup
Department of Statistics STATISTICS COLLOQUIUM PETER LATHAM Gatsby Computational Neuroscience Unit University College London Zipf’s Law Arises Naturally from Hidden Structure MONDAY, February 9, 2015, at 4:00 PM Eckhart 133, 5734 S. University Avenue Refreshments following the seminar in Eckhart 110 ABSTRACT Both natural and artificial systems often exhibit a surprising degree of statistical regularity. One such regularity is Zipf's law. Originally formulated for word frequency, Zipf's law has since been observed in a broad range of phenomena, including city size, firm size, mutual fund size, amino acid sequences, and neural activity. Partly because it is so unexpected, a great deal of effort has gone into explaining it. So far, almost all explanations are either domain specific or require fine-tuning. For instance, in biology, one explanation for observations of Zipf’s law is that biological systems sit at a special thermodynamic state, the critical point. Here we propose an alternative explanation, which exploits the fact that most real-world datasets can be understood as being generated from a latent variable model. We show that data generated from a such a model exhibits Zipf's law under very mild conditions. We provide the theoretical underpinnings of this result, illustrate it on words and neural data, and point out examples of Zipf's law in the literature for which we can identify a latent variable model. Finally, we show how our results can be used to inform models of neural data. _______________________________ For further information and about building access for persons with disabilities, please contact Kirsten Wellman at 773.702.8333 or send email ([email protected]). If you wish to subscribe to our email list, please visit the following website: https://lists.uchicago.edu/web/arc/statseminars.