Kernel Analysis Based on Dirichlet Processes Mixture Models

Kernels play a crucial role in Gaussian process regression. Analyzing kernels from their spectral domain has attracted extensive attention in recent years. Gaussian mixture models (GMM) are used to model the spectrum of kernels. However, the number of components in a GMM is fixed. Thus, this model suffers from overfitting or underfitting. In this paper, we try to combine the spectral domain of kernels with nonparametric Bayesian models. Dirichlet processes mixture models are used to resolve this problem by changing the number of components according to the data size. Multiple experiments have been conducted on this model and it shows competitive performance.

Personalized Monitors for Real-Time Detection of Physiological States

The authors introduce an algorithmic framework to process real-time physiological data using nonparametric Bayesian models under the context of developing and testing personalized wellness monitors. A wearable device aggregates signals from various sensors while periodically transmitting the collected data to a backend server, which builds custom user profiles based on inferred hidden Markov states. They discuss how these user profiles can be used in various contexts as proxies for fluctuating physiological states and leveraged for various longitudinal classification tasks. Using data collected in a two-week study hosted at Jaslok Hospital, the authors show how physiological changes induced by different environments with various levels of stress can be quantified by the authors' platform. To minimize the dependence on continuous connectivity with the backend server, they introduce a heuristic to enable real-time state identification using the modest processing capabilities of the wearable device.

Structure and Flexibility in Bayesian Models of Cognition

Probability theory forms a natural framework for explaining the impressive success of people at solving many difficult inductive problems, such as learning words and categories, inferring the relevant features of objects, and identifying functional relationships. Probabilistic models of cognition use Bayes’s rule to identify probable structures or representations that could have generated a set of observations, whether the observations are sensory input or the output of other psychological processes. In this chapter we address an important question that arises within this framework: How do people infer representations that are complex enough to faithfully encode the world but not so complex that they “overfit” noise in the data? We discuss nonparametric Bayesian models as a potential answer to this question. To do so, first we present the mathematical background necessary to understand nonparametric Bayesian models. We then delve into nonparametric Bayesian models for three types of hidden structure: clusters, features, and functions. Finally, we conclude with a summary and discussion of open questions for future research.

Personalized Monitors for Real-Time Detection of Physiological States

The authors introduce an algorithmic framework to process real-time physiological data using nonparametric Bayesian models under the context of developing and testing personalized wellness monitors. A wearable device aggregates signals from various sensors while periodically transmitting the collected data to a backend server, which builds custom user profiles based on inferred hidden Markov states. They discuss how these user profiles can be used in various contexts as proxies for fluctuating physiological states and leveraged for various longitudinal classification tasks. Using data collected in a two-week study hosted at Jaslok Hospital, the authors show how physiological changes induced by different environments with various levels of stress can be quantified by the authors' platform. To minimize the dependence on continuous connectivity with the backend server, they introduce a heuristic to enable real-time state identification using the modest processing capabilities of the wearable device.