SFI Seminar: A Hidden Markov
Tuesday, Dec, 6 • 12:15 p.m. • Medium Conference Room • 1399 Hyde Park, Santa Fe
Abstract: A Hidden Markov
Model (HMM) is a Markov process observed through a noisy channel. HMMs are used extensively for modeling sequential data and have various applications in natural language processing, bioinformatics, mathematical economics, and so on.
One of the main problems underlying HMMs is inferring the hidden state sequence based on noise-corrupted observations, which is usually solved via the maximum a posteriori (MAP) method.
Here I present a statistical physics analysis of MAP estimation for a simple binary HMM, by reducing it to an appropriately defined Ising model.
It is shown that for sufficiently low noise levels, the MAP solution is uniquely related to the observed sequence.
Above a critical noise level, however, there are exponentially many solutions to the estimation problem, which means that one cannot uniquely reconstruct the hidden state sequence based on observations.
I will also discuss how one can mitigate this undesirable feature by active inference, i.e., by adaptively acquiring information about the (true) hidden states.
Note: We are unable to accommodate members of the public for SFI’s limited lunch service; you’re welcome to bring your own.
SFI Host: Cris Moore
The Santa Fe Institute http://www.santafe.edu/ is a nonprofit research center located in Santa Fe, New Mexico. Its scientists collaborate across disciplines to understand the complex systems that underlie critical questions for science and humanity. The Institute is supported by philanthropic individuals and foundations, forward-thinking partner companies, and government science agencies.