Stochastic Modeling and Machine Learning Methods for Analyzing Neural Spike Trains

Neural oscillations and precise spike timing are thought to play a central role in how the lateral hypothalamus (LH) organizes innate behaviours, yet many analysis pipelines still treat spike trains as if they were continuous signals. In this thesis, I develop and apply a point-process–based analysis of LH spike trains recorded in freely behaving mice, using the same dataset originally analysed by Chen–Altafi and colleagues. In contrast to that work, which focused on firing-rate trajectories and their clustering, I concentrate on the spike-timing structure of single units and how it can be described with mathematically consistent point-process methods and unsupervised learning. In the first part, I revisit power spectral density (PSD) estimation for spike trains by directly comparing FFT/Welch spectra of 100-ms binned spike counts with event-periodogram spectra computed from the original spike times. Binned-count spectra collapse to similar low-frequency profiles across neurons and fail to reproduce even the basic refractory dip visible in autocorrelograms. In contrast, point-process PSDs remain well behaved and reveal heterogeneous narrowband peaks in the beta–gamma range for a subset of LH neurons while staying relatively flat for others, demonstrating that spike trains in this dataset must be treated as stochastic point processes rather than as continuous time series. In the second part, I move from single neurons to populations. For 942 units, I compute autocorrelograms (0–100 ms), assemble them into a feature matrix, and reduce dimensionality with principal component analysis, retaining 78 components that explain about 90% of the variance. On this compact representation, I build a cosine k-nearest-neighbour graph and apply spectral clustering; bootstrap stability analysis identifies a highly reproducible two-cluster solution, with 838 neurons consistently assigned to one of two groups. Finally, I characterise these clusters in terms of ACG shape, simple ACG-derived features, and point-process spectra: one cluster shows strong, compact short-lag peaks, low late autocorrelation, and more beta–gamma power, consistent with bursty or rhythmically modulated firing, whereas the other exhibits broader ACGs, higher late baselines, and flatter spectra, indicative of more tonic, irregular activity. Overall, the thesis shows that principled point-process methods combined with graph-based clustering can reveal a small number of robust spike-timing motifs in the Chen–Altafi LH dataset, providing a quantitative starting point for future work linking these motifs to local field potentials and behaviour.