Bayesian Nonparametric Hidden Semi-Markov Models

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markovianity, which has been developed mainly in the parametric frequentist setting, to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicit-duration Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for efficient posterior inference. The methods we introduce also provide new methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs sampling methods can be embedded in samplers for larger hierarchical Bayesian models, adding semi-Markov chain modeling as another tool in the Bayesian inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference methods on both synthetic and real experiments

Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment

Using a combination of resist reflow to form a highly circular etch mask pattern and a low-damage plasma dry etch, high-quality-factor silicon optical microdisk resonators are fabricated out of silicon-on-insulator (SOI) wafers. Quality factors as high as Q = 5×10^6 are measured in these microresonators, corresponding to a propagation loss coefficient as small as α ~ 0.1 dB/cm. The different optical loss mechanisms are identified through a study of the total optical loss, mode coupling, and thermally-induced optical bistability as a function of microdisk radius (5-30 µm). These measurements indicate that optical loss in these high-Q microresonators is limited not by surface roughness, but rather by surface state absorption and bulk free-carrier absorption

Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator

Direct time-domain observations are reported of a low-power, self-induced modulation of the transmitted optical power through a high-Q silicon microdisk resonator. Above a threshold input power of 60 μW the transmission versus wavelength deviates from a simple optical bistability behavior, and the transmission intensity becomes highly oscillatory in nature. The transmission oscillations are seen to consist of a train of sharp transmission dips of width approximately 100 ns and period close to 1 μs. A model of the system is developed incorporating thermal and free-carrier dynamics, and is compared to the observed behavior. Good agreement is found, and the self-induced optical modulation is attributed to a nonlinear interaction between competing free-carrier and phonon populations within the microdisk

Measuring the role of surface chemistry in silicon microphotonics

Utilizing a high quality factor (Q~1.5×10^6) optical microresonator to provide sensitivity down to a fractional surface optical loss of alphas[prime]~10^–7, we show that the optical loss within Si microphotonic components can be dramatically altered by Si surface preparation, with alphas[prime]~1×10^–5 measured for chemical oxide surfaces as compared to alphas[prime]<=1×10^–6 for hydrogen-terminated Si surfaces. These results indicate that the optical properties of Si surfaces can be significantly and reversibly altered by standard microelectronic treatments, and that stable, high optical quality surface passivation layers will be critical in future Si micro- and nanophotonic systems

Accurate measurement of scattering and absorption loss in microphotonic devices

We present a simple measurement and analysis technique to determine the fraction of optical loss due to both radiation (scattering) and linear absorption in microphotonic components. The method is generally applicable to optical materials in which both nonlinear and linear absorption are present and requires only limited knowledge of absolute optical power levels, material parameters, and the structure geometry. The technique is applied to high-quality-factor (Q=1×10^6 to Q=5×10^6) silicon-on-insulator (SOI) microdisk resonators. It is determined that linear absorption can account for more than half of the total optical loss in the high-Q regime of these devices

A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation

Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and propose a nonparametric Bayesian approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a nonparametric Bayesian model. Specifically, to analyze rat hippocampal ensemble spiking activity, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). We demonstrate the effectiveness of our Bayesian approaches on recordings from a freely-behaving rat navigating in an open field environment. We find that MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes