Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Task-driven adaptive statistical compressive sensing of gaussian mixture models

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific sensing protocols specifically and jointly designed for classification and reconstruction. A two-step adaptive sensing paradigm is developed, where online sensing is applied to detect the signal class in the first step, followed by a reconstruction step adapted to the detected class and the observed samples. The approach is based on information theory, here tailored for Gaussian mixture models (GMMs), where an information-theoretic objective relationship between the sensed signals and a representation of the specific task of interest is maximized. Experimental results using synthetic signals, Landsat satellite attributes, and natural images of different sizes and with different noise levels show the improvements achieved using the proposed framework when compared to more standard sensing protocols. The underlying formulation can be applied beyond GMMs, at the price of higher mathematical and computational complexity. © 1991-2012 IEEE.

Later Life Consequences of Subteratogenic Exposure to a Complex PAH Mixture in the Atlantic Killifish (Fundulus heteroclitus)

Subteratogenic and other low-level chronic exposures to toxicant mixtures are an understudied threat to environmental and human health. It is especially important to understand the effects of these exposures for contaminants, such as polycyclic aromatic hydrocarbons (PAHs) a large group of more than 100 individual compounds, which are important environmental (including aquatic) contaminants. Aquatic sediments constitute a major sink for hydrophobic pollutants, and studies show PAHs can persist in sediments over time. Furthermore, estuarine systems (namely breeding grounds) are of particular concern, as they are highly impacted by a wide variety of pollutants, and estuarine fishes are often exposed to some of the highest levels of contaminants of any vertebrate taxon. Acute embryonic exposure to PAHs results in cardiac teratogenesis in fish, and early life exposure to certain individual PAHs and PAH mixtures cause heart alterations with decreased swimming capacity in adult fish. Consequently, the heart and cardiorespiratory system are thought to be targets of PAH mixture exposure. While many studies have investigated acute, teratogenic PAH exposures, few studies have longitudinally examined the impacts of subtle, subteratogenic PAH mixture exposures, which are arguably more broadly applicable to environmental contamination scenarios. The goal of this dissertation was to highlight the later-life consequences of early-life exposure to subteratogenic concentrations of a complex, environmentally relevant PAH mixture.

A unique population of Fundulus heteroclitus (the Atlantic killifish or mummichog, hereafter referred to as killifish), has adapted to creosote-based polycyclic aromatic hydrocarbons (PAHs) found at the Atlantic Wood Industries (AW) Superfund site in the southern branch of the Elizabeth River, VA, USA. This killifish population survives in a site heavily contaminated with a mixture of PAHs from former creosote operations. They have developed resistance to the acute toxicity and teratogenic effects caused by the mixture of PAHs in sediment from the site. The primary goal of this dissertation was to compare and contrast later-life outcomes of early-life, subteratogenic PAH mixture exposure in both the Atlantic Wood killifish (AW) and a naïve reference population of killifish from King’s Creek (KC; a relatively uncontaminated tributary of the Severn River, VA). Killifish from both populations were exposed to subteratogenic concentrations of a complex PAH-sediment extract, Elizabeth River Sediment Extract (ERSE), made by collecting sediment from the AW site. Fish were reared over a 5-month period in the laboratory, during which they were examined for a variety of molecular, physiological and behavioral responses.

The central aims of my dissertation were to determine alterations to embryonic gene expression, larval swimming activity, adult behavior, heart structure, enzyme activity, and swimming/cardiorespiratory performance following subteratogenic exposure to ERSE. I hypothesized that subteratogenic exposure to ERSE would impair cardiac ontogenic processes in a way that would be detectable via gene expression in embryos, and that the misregulation of cardiac genes would help to explain activity changes, behavioral deficits, and later-life swimming deficiencies. I also hypothesized that fish heart structure would be altered. In addition, I hypothesized that the AW killifish population would be resistant to developmental exposures and perform normally in later life challenges. To investigate these hypotheses, a series of experiments were carried out in PAH-adapted killifish from Elizabeth River and in reference killifish. As an ancillary project to the primary aims of the dissertation, I examined the toxicity of weaker aryl hydrocarbon receptor (AHR) agonists in combination with fluoranthene (FL), an inhibitor of cytochrome P4501A1 (CYP1A1). This side project was conducted in both Danio rerio (zebrafish) and the KC and AW killifish.

Embryonic gene expression was measured in both killifish populations over an ERSE dose response with multiple time points (12, 24, 48, and 144 hours post exposure). Genes known to play critical roles in cardiac structure/development, cardiac function, and angiogenesis were elevated, indicating cardiac damage and activation of cardiovascular repair mechanisms. These data helped to inform later-life swimming performance and cardiac histology studies. Behavior was assessed during light and dark cycles in larvae of both populations following developmental exposure to ERSE. While KC killifish showed activity differences following exposure, AW killifish showed no significant changes even at concentrations that would cause overt cardiac toxicity in KC killifish. Juvenile behavior experiments demonstrated hyperactivity following ERSE exposure in KC killifish, but no significant behavioral changes in AW killifish. Adult swimming performance via prolonged critical swimming capacity (Ucrit) demonstrated performance costs in the AW killifish. Furthermore, swimming performance decline was observed in KC killifish following exposure to increasing dilutions of ERSE. Lastly, cardiac histology suggested that early-life exposure to ERSE could result in cardiac structural alteration and extravasation of blood into the pericardial cavity.

Responses to AHR agonists resulted in a ranking of relative potency for agonists, and determined which agonists, when combined with FL, caused cardiac teratogenesis. These experiments showed interesting species differences for zebrafish and killifish. To probe mechanisms responsible for cardiotoxicity, a CYP1A-morpholino and a AHR2-morpholino were used to mimic FL effects or attempt to rescue cardiac deformities respectively. Findings suggested that the cardiac toxicity elicited by weak agonist + FL exposure was likely driven by AHR-independent mechanisms. These studies stand in contrast to previous research from our lab showing that moderate AHR agonist + FL caused cardiac toxicity that can be partially rescued by AHR-morpholino knockdown.

My findings will form better characterization of mechanisms of PAH toxicity, and advance our understanding of how subteratogenic mixtures of PAHs exert their toxic action in naïve killifish. Furthermore, these studies will provide a framework for investigating how subteratogenic exposures to PAH mixtures can impact aquatic organismal health and performance. Most importantly, these experiments have the potential to help inform risk assessment in fish, mammals, and potentially humans. Ultimately, this research will help protect populations exposed to subtle PAH-contamination.

Developmental exposure to a complex PAH mixture causes persistent behavioral effects in naive Fundulus heteroclitus (killifish) but not in a population of PAH-adapted killifish.

Acute exposures to some individual polycyclic aromatic hydrocarbons (PAHs) and complex PAH mixtures are known to cause cardiac malformations and edema in the developing fish embryo. However, the heart is not the only organ impacted by developmental PAH exposure. The developing brain is also affected, resulting in lasting behavioral dysfunction. While acute exposures to some PAHs are teratogenically lethal in fish, little is known about the later life consequences of early life, lower dose subteratogenic PAH exposures. We sought to determine and characterize the long-term behavioral consequences of subteratogenic developmental PAH mixture exposure in both naive killifish and PAH-adapted killifish using sediment pore water derived from the Atlantic Wood Industries Superfund Site. Killifish offspring were embryonically treated with two low-level PAH mixture dilutions of Elizabeth River sediment extract (ERSE) (TPAH 5.04 μg/L and 50.4 μg/L) at 24h post fertilization. Following exposure, killifish were raised to larval, juvenile, and adult life stages and subjected to a series of behavioral tests including: a locomotor activity test (4 days post-hatch), a sensorimotor response tap/habituation test (3 months post hatch), and a novel tank diving and exploration test (3months post hatch). Killifish were also monitored for survival at 1, 2, and 5 months over 5-month rearing period. Developmental PAH exposure caused short-term as well as persistent behavioral impairments in naive killifish. In contrast, the PAH-adapted killifish did not show behavioral alterations following PAH exposure. PAH mixture exposure caused increased mortality in reference killifish over time; yet, the PAH-adapted killifish, while demonstrating long-term rearing mortality, had no significant changes in mortality associated with ERSE exposure. This study demonstrated that early embryonic exposure to PAH-contaminated sediment pore water caused long-term locomotor and behavioral alterations in killifish, and that locomotor alterations could be observed in early larval stages. Additionally, our study highlights the resistance to behavioral alterations caused by low-level PAH mixture exposure in the adapted killifish population. Furthermore, this is the first longitudinal behavioral study to use killifish, an environmentally important estuarine teleost fish, and this testing framework can be used for future contaminant assessment.

Algorithms for Geometric Matching, Clustering, and Covering

With the popularization of GPS-enabled devices such as mobile phones, location data are becoming available at an unprecedented scale. The locations may be collected from many different sources such as vehicles moving around a city, user check-ins in social networks, and geo-tagged micro-blogging photos or messages. Besides the longitude and latitude, each location record may also have a timestamp and additional information such as the name of the location. Time-ordered sequences of these locations form trajectories, which together contain useful high-level information about people's movement patterns.

The first part of this thesis focuses on a few geometric problems motivated by the matching and clustering of trajectories. We first give a new algorithm for computing a matching between a pair of curves under existing models such as dynamic time warping (DTW). The algorithm is more efficient than standard dynamic programming algorithms both theoretically and practically. We then propose a new matching model for trajectories that avoids the drawbacks of existing models. For trajectory clustering, we present an algorithm that computes clusters of subtrajectories, which correspond to common movement patterns. We also consider trajectories of check-ins, and propose a statistical generative model, which identifies check-in clusters as well as the transition patterns between the clusters.

The second part of the thesis considers the problem of covering shortest paths in a road network, motivated by an EV charging station placement problem. More specifically, a subset of vertices in the road network are selected to place charging stations so that every shortest path contains enough charging stations and can be traveled by an EV without draining the battery. We first introduce a general technique for the geometric set cover problem. This technique leads to near-linear-time approximation algorithms, which are the state-of-the-art algorithms for this problem in either running time or approximation ratio. We then use this technique to develop a near-linear-time algorithm for this

shortest-path cover problem.