A single, stationary topic model such as latent Dirichlet allocation is inappropriate for modeling corpora that span long time periods, as the popularity of topics is likely to change over time. A number of models that incorporate time have been proposed, but in general they either exhibit limited forms of temporal variation, or require computationally expensive inference methods. In this paper we propose non-parametric Topics over Time (npTOT), a model for time-varying topics that allows an unbounded number of topics and flexible distribution over the temporal variations in those topics' popularity. We develop a collapsed Gibbs sampler for the proposed model and compare against existing models on synthetic and real document sets.

Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead we want our model to vary fluidly with some set of covariates. Since the concept of dependent nonparametric processes was formalized by MacEachern, there have been a number of models proposed and used in the statistics and machine learning literatures. Many of these models exhibit underlying similarities, an understanding of which, we hope, will help in selecting an appropriate prior, developing new models, and leveraging inference techniques.

BACKGROUND/OBJECTIVES: Little is currently known about how exercise may influence dietary patterns and/or food preferences. The present study aimed to examine the effect of a 15-week exercise training program on overall dietary patterns among young adults. SUBJECTS/METHODS: This study consisted of 2680 young adults drawn from the Training Intervention and Genetics of Exercise Response (TIGER) study. Subjects underwent 15 weeks of aerobic exercise training, and exercise duration, intensity, and dose were recorded for each session using computerized heart rate monitors. In total, 4355 dietary observations with 102 food items were collected using a self-administered food frequency questionnaire before and after exercise training (n = 2476 at baseline; n = 1859 at 15 weeks). Dietary patterns were identified using a Bayesian sparse latent factor model. Changes in dietary pattern preferences were evaluated based on the pre/post-training differences in dietary pattern scores, accounting for the effects of gender, race/ethnicity, and BMI. RESULTS: Within each of the seven dietary patterns identified, most dietary pattern scores were decreased following exercise training, consistent with increased voluntary regulation of food intake. A longer duration of exercise was associated with decreased preferences for the Western ( β : −0.0793; 95% credible interval: −0.1568, −0.0017) and Snacking ( β : −0.1280; 95% credible interval: −0.1877, −0.0637) patterns, while a higher intensity of exercise was linked to an increased preference for the Prudent pattern ( β : 0.0623; 95% credible interval: 0.0159, 0.1111). Consequently, a higher dose of exercise was related to a decreased preference for the Snacking pattern ( β : −0.0023; 95% credible interval: −0.0042, −0.0004) and an increased preference for the Prudent pattern ( β : 0.0029; 95% credible interval: 0.0009, 0.0048). CONCLUSION: The 15-week exercise training appeared to motivate young adults to pursue healthier dietary preferences and to regulate their food intake.

We present a principled Bayesian framework for modeling partial memberships of data points to clusters. Unlike a standard mixture model which assumes that each data point belongs to one and only one mixture component, or cluster, a partial membership model allows data points to have fractional membership in multiple clusters. Algorithms which assign data points partial memberships to clusters can be useful for tasks such as clustering genes based on microarray data (Gasch & Eisen, 2002). Our Bayesian Partial Membership Model (BPM) uses exponential family distributions to model each cluster, and a product of these distibtutions, with weighted parameters, to model each datapoint. Here the weights correspond to the degree to which the datapoint belongs to each cluster. All parameters in the BPM are continuous, so we can use Hybrid Monte Carlo to perform inference and learning. We discuss relationships between the BPM and Latent Dirichlet Allocation, Mixed Membership models, Exponential Family PCA, and fuzzy clustering. Lastly, we show some experimental results and discuss nonparametric extensions to our model.

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