Browsing by Subject "Factor models"

Humans are constantly exposed to mixtures of different chemicals arising from environmental contamination. While certain compounds, such as heavy metals and mercury, are well known to be toxic, there are many complex mixtures whose health effects are still unknown. It is of fundamental public health importance to understand how these exposures interact to impact risk of disease and the health effects of cumulative exposure to multiple agents. The goal of this thesis is to build data-driven models to tackle major challenges in modern health applications, with a special interest in estimating statistical interactions among correlated exposures. In Chapter 1, we develop a flexible Gaussian process regression model (MixSelect) that allows to simultaneously estimate a complex nonparametric model and provide interpretability. A key component of this approach is the incorporation of a heredity constraint to only include interactions in the presence of main effects, effectively reducing dimensionality of the model search. Next, we focus our modelling effort on characterizing the joint variability of chemical exposures using factor models. In fact, chemicals usually co-occur in the environment or in synthetic mixtures; as a result, their exposure levels can be highly correlated. In Chapter 3, we build a Factor analysis for INteractions (FIN) framework that jointly provides dimensionality reduction in the chemical measurements and allows to estimate main effects and interactions. Through appropriate modifications of the factor modeling structure, FIN can accommodate higher order interactions and multivariate outcomes. Further, we extend FIN to survival analysis and exponential families in Chapter 4, as medical studies often include collect high-dimensional data and time-to-event outcomes. We address these cases through a joint factor analysis modeling approach in which latent factors underlying the predictors are included in a quadratic proportional hazards regression model, and we provide expressions for the induced coefficients on the covariates. In Chapter 5, we combine factor models and nonparametric regression. We build a copula factor model for the chemical exposures and use Bayesian B-splines for flexible dose-response modeling. Finally, in Chapter 6 we we propose a post-processing algorithm that allows for identification and interpretation of the factor loadings matrix and can be easily applied to the models described in the previous chapters.

This dissertation consists of three essays that shed light on various problems in empirical asset pricing and portfolio management by applying high frequency econometric techniques. Chapter 1, An Efficient Factor from Basis “Anomalies”, examines the challenges brought by the massive asset-pricing “anomalies” and develops a novel method to construct a highly ex-post efficient portfolio that prices asset returns in a one-factor model, Relative Asset Pricing Model (RAP). The one single empirical factor outperforms and drives out 11 of the most acclaimed multi-factors combined. It provides evidence that the massive amount of asset pricing “anomalies” are in fact manifested by non-linear effects of three basic stock characteristics, size, book-to-market and momentum. It also demonstrates that an arbitrary number of trading signals can be engineered to pass existing asset pricing tests as new “unique anomalies”, even though they are purely the projections of the efficient factor beta onto a set of characteristics. Chapter 2, Good Volatility, Bad Volatility and the Cross Section of Stock Returns, documents that relative good-minus-bad jump measure extracted from high frequency intra-day data have strong cross-sectional return predictability. Chapter 3, Factors and Their Economic Value in Volatility Forecast, develops a simple and reliable volatility forecast model in large cross-section that incorporates volatility factor structure and add significant values to investors in portfolio optimization.

A major component of most psychiatric disorders is that they affect the internal mental state of the individual.Modern psychiatric research primarily depends on self-report to measure internal state in humans and on behavior to measure internal state in animals. Both of these can be unreliable measures of internal mental state. In order to facilitate psychiatric research, we need models of mental state that are based on neural activity. Such models have proven challenging to design because they must be able to distill the complexity of neural activity distributed across many brain regions. This dissertation describes models that solve this problem, by representing such neural activity as a sum of contributions from many distinct sub-networks in the brain. We call these sub-network electrical functional connectome (electome) networks. Here, I show that electome networks can be used to distinguish between mental states in mice. One of these electome networks distinguishes mice that show depressive symptoms from those that do not, and can be used as a measure depressive phenotype. Electome networks represent a new class of tools that give brain researchers a new way to measure internal mental state and relate it back to brain activity.

Bayesian nonparametric methods are useful for modeling data without having to define the complexity of the entire model a priori, but rather allowing for this complexity to be determined by the data. Two problems considered in this dissertation are the number of components in a mixture model, and the number of factors in a latent factor model, for which the Dirichlet process and the beta process are the two respective Bayesian nonparametric priors selected for handling these issues.

The flexibility of Bayesian nonparametric priors arises from the prior's definition over an infinite dimensional parameter space. Therefore, there are theoretically an infinite number of latent components and an infinite number of latent factors. Nevertheless, draws from each respective prior will produce only a small number of components or factors that appear in a given data set. As mentioned, the number of these components and factors, and their corresponding parameter values, are left for the data to decide.

This dissertation is split between novel practical applications and novel theoretical results for these priors. For the Dirichlet process, we investigate stick-breaking representations for the finite Dirichlet process and their application to novel sampling techniques, as well as a novel mixture modeling framework that incorporates multiple modalities within a data set. For the beta process, we present a new stick-breaking construction for the infinite-dimensional prior, and consider applications to image interpolation problems and dictionary learning for compressive sensing.