Latent Variable Models for Neural Data

iv v Acknowledgements Many thanks are due to my advisors, Richard Andersen and John Hoppeld. Richard has been tremendously supportive throughout, providing valuable advice and encouragement, even when my work has taken me outside the domains typically trodden by members of his group. Furthermore he has assembled an exceptional group of people in whose company I have worked for the last ve years. John graciously provided an intellectual home away from home; as well as invaluable advice and mentoring on a number of thorny research and professional issues. The work on spike sorting that is presented in chapter 5 is a component of a larger multiunit recording project within Richard Andersen's laboratory on which John Pezaris and I have collaborated for the past ve years. This has been a tremendously fruitful and rewarding collaboration. I could not have wished for a more able or more generous colleague. The analysis of chapter 6 was also a collaborative eeort, in this case with Jennifer Linden. This too was an extremely rewarding eeort; in both the intellectual and personal domains my debt to Jennifer is immeasurable. A number of critical conversations have helped to shape the work that appears here. In the rst place, the fact that I chose to study neuroscience at all is largely due to the encouragement of Roweis introduced me to the EM algorithm which forms the core thread running throughout this thesis. Bill Bialek steered me towards the simple greedy approach to spike detection that appears in section 5.13. Tali Tishby brought earlier work on deterministic annealing to my attention, from which the REM algorithm of chapter 3 grew. Sanjoy Mahajan convinced me to take a closer look at the possibility of modeling bursting with hidden Markov models (section 5.10.2). Alan Barr provided a piece of inspirational advice at a critical juncture (see the Preface). Ken Miller and his group at UCSF have been working on the problem of spike sorting over the last few years as well, and we have enjoyed very many useful exchanges of ideas. Besides these speciic points, innumerable conversations with my peers at Caltech have contributed to my understanding involved. Special thanks are due to Sam Roweis and Flip Sabes, who provided crucial support as I made my initial faltering steps into the realm of machine learning and statistics. Members of the Hoppeld group, particularly Sam Roweis, Carlos Brody, Erik Winfree and Sanjoy …