Latent variable models for neural data analysis

The brain is perhaps the most complex system to have ever been subjected to rigorous scientific investigation. The scale is staggering: over 10^11 neurons, each making an average of 10^3 synapses, with computation occurring on scales ranging from a single dendritic spine, to an entire cortical area. Slowly, we are beginning to acquire experimental tools that can gather the massive amounts of data needed to characterize this system. However, to understand and interpret these data will also require substantial strides in inferential and statistical techniques. This dissertation attempts to meet this need, extending and applying the modern tools of latent variable modeling to problems in neural data analysis.

It is divided into two parts. The first begins with an exposition of the general techniques of latent variable modeling. A new, extremely general, optimization algorithm is proposed - called Relaxation Expectation Maximization (REM) - that may be used to learn the optimal parameter values of arbitrary latent variable models. This algorithm appears to alleviate the common problem of convergence to local, sub-optimal, likelihood maxima. REM leads to a natural framework for model size selection; in combination with standard model selection techniques the quality of fits may be further improved, while the appropriate model size is automatically and efficiently determined. Next, a new latent variable model, the mixture of sparse hidden Markov models, is introduced, and approximate inference and learning algorithms are derived for it. This model is applied in the second part of the thesis.

The second part brings the technology of part I to bear on two important problems in experimental neuroscience. The first is known as spike sorting; this is the problem of separating the spikes from different neurons embedded within an extracellular recording. The dissertation offers the first thorough statistical analysis of this problem, which then yields the first powerful probabilistic solution. The second problem addressed is that of characterizing the distribution of spike trains recorded from the same neuron under identical experimental conditions. A latent variable model is proposed. Inference and learning in this model leads to new principled algorithms for smoothing and clustering of spike data.

Modeling the Effect of Vapor Wall Deposition on the Formation of Secondary Organic Aerosol in Chamber Studies

Laboratory chamber experiments are used to investigate formation of secondary organic aerosol (SOA) from biogenic and anthropogenic precursors under a variety of environmental conditions. Simulations of these experiments test our understanding of the prevailing chemistry of SOA formation as well as the dynamic processes occurring in the chamber itself. One dynamic process occurring in the chamber that was only recently recognized is the deposition of vapor species to the Teflon walls of the chamber. Low-volatility products formed from the oxidation of volatile organic compounds (VOCs) deposit on the walls rather than forming SOA, decreasing the amount of SOA formed (quantified as the SOA yield: mass of SOA formed per mass of VOC reacted). In this work, several modeling studies are presented that address the effect of vapor wall deposition on SOA formation in chambers.

A coupled vapor-particle dynamics model is used to examine the competition among the rates of gas-phase oxidation to low volatility products, wall deposition of these products, and mass transfer to the particle phase. The relative time scales of these rates control the amount of SOA formed by affecting the influence of vapor wall deposition. Simulations show that an effect on SOA yield of changing the vapor-particle mass transfer rate is only observed when SOA formation is kinetically limited. For systems with kinetically limited SOA formation, increasing the rate of vapor-particle mass transfer by increasing the concentration of seed particles is an effective way to minimize the effect of vapor wall deposition.

This coupled vapor-particle dynamics model is then applied to α-pinene ozonolysis SOA experiments. Experiments show that the SOA yield is affected when changing the oxidation rate but not when changing the rate of gas-particle mass transfer by changing the concentration of seed particles. Model simulations show that the absence of an effect of changing the seed particle concentration is consistent with SOA formation being governed by quasi-equilibrium growth, in which gas-particle equilibrium is established much faster than the rate of change of the gas-phase concentration. The observed effect of oxidation rate on SOA yield arises due to the presence of vapor wall deposition: gas-phase oxidation products are produced more quickly and condense preferentially onto seed particles before being lost to the walls. Therefore, for α-pinene ozonolysis, increasing the oxidation rate is the most effective way to mitigate the influence of vapor wall deposition.

Finally, the detailed model GECKO-A (Generator for Explicit Chemistry and Kinetics of Organics in the Atmosphere) is used to simulate α-pinene photooxidation SOA experiments. Unexpectedly, α-pinene OH oxidation experiments show no effect when changing either the oxidation rate or the vapor-particle mass transfer rate, whereas GECKO-A predicts that changing the oxidation rate should drastically affect the SOA yield. Sensitivity studies show that the assumed magnitude of the vapor wall deposition rate can greatly affect conclusions drawn from comparisons between simulations and experiments. If vapor wall loss in the Caltech chamber is of order 10^-5 s^-1, GECKO-A greatly overpredicts SOA during high UV experiments, likely due to an overprediction of second-generation products. However, if instead vapor wall loss in the Caltech chamber is of order 10^-3 s^-1, GECKO-A greatly underpredicts SOA during low UV experiments, possibly due to missing autoxidation pathways in the α-pinene mechanism.