Supervised Machine Learning for Time-Frequency Analysis of Time Series with Applications to Neuroscience

Abstract

In this thesis, I present supervised machine learning (ML) approaches to time-frequency analysis of time series data. Specifically, I show that supervised learning methods can reliably classify time-frequency representations of spontaneous local field potential (LFP) by their underlying social context. I argue that supervised ML models can be used as effective information detectors for neural data analysis, helping to determine whether specific information is encoded within the neural activity of particular brain regions. Additionally, under certain conditions, I posit that using shallow, matched filter inspired models in place of more powerful deep models can be comparable at time-frequency classification while also being more biologically interpretable. That is, the proposed shallow models provide more direct insights about the basic time-frequency features most important to decoding social context from spontaneous LFP, leading to new hypotheses about \textit{how} social context might be encoded in the brain. I start by presenting a reliable ML framework for detecting the presence of information encoded in neural time series data. I compute spectrograms of time series, which quantify the time-frequency content of a signal in two dimensions, and show that such time-frequency representations provide a reliable feature space for training supervised learning models in cases where raw time-domain classification fails. Using the spectrograms as inputs, I compare a simple two-layer convolutional neural network (CNN) against a support vector machine (SVM) using radial basis function (RBF) kernels. The models are tasked with classifying spectrograms of baseline local field potential (LFP) activity in primate amygdala by the social context under which they were recorded. Both models boast a classification accuracy near 80% across datasets collected from different subjects and nuclei (anatomical regions) of the amygdala, and track each other well in their performance. These results confirm this approach is a reliable methodology for detecting the presence of contextual information encoding in neural signals. The fact that both classifiers can successfully decode context from LFP during spontaneous activity, and that there is no apparent nuclear specificity, suggests the existence of context-related brain-wide states that can persist long before or after stimulus delivery. While these traditional ML methods are quite accurate at detecting subtle differences in the time-frequency features of the data, they remain opaque and thus difficult to interpret in a biological sense. In other words, these models are useful information detectors, but their complexity makes it difficult to determine how that information is encoded. In the second chapter of this thesis, I present two alternative ML models inspired by matched filters, a technique from signal processing. I develop two model architectures: (1) a shallow model which learns from data a set of time-frequency matched filters and (2) a generalized matched filter model which relaxes some of the constraints on the filters imposed in (1) to provide additional network flexibility. I train these shallow models using data from the same neuroscience experiment and show they can attain comparable performance to the classic ML models under certain conditions. Moreover, by design, the feature spaces learned by these models are more biologically interpretable and their size and complexity can be controlled through traditional regularization techniques. These novel supervised learning models provide an alternative to more opaque classical ML methods, offering a balance between classification accuracy and biological interpretability that can be used to improve our understanding of information encoding in the brain.