The emergence of advanced computational techniques and artificial intelligence has strongly impacted the materials discovery and optimization. This study focuses on applying computational methods to extract information from complex spectral systems. Three distinct tiers of information extraction from hyperspectral data are explored: integrating light data treatment with computational modeling, employing convolutional neural networks for signal reconstruction, and advancing quantification using probabilistic machine learning. In the first tier, utilizing electron energy loss spectroscopy (EELS) in conjunction with boundary element method modeling, we uncovered the broadband plasmonic properties in wrinkled gold structures and their origin. We demonstrated the link between broadband plasmonic characteristics and surface nano-features, offering insights into property tunability. To benefit the broader microscopy community, in the second tier, we developed EELSpecNet, a Python script based on convolutional neural networks. EELSpecNet reconstructs signals to retrieve details that were obscured by various signal artifacts. EELSpecNet was benchmarked for near-zero-loss EELS, a challenging signal that contains crucial phononic and plasmonic information. The results clearly show that this neural network approach surpasses conventional Bayesian methods in deconvolution, particularly in terms of information retrieval, signal fidelity, and noise reduction. The final tier of this research introduces an innovative approach to spectral analysis and quantification using probabilistic machine learning methods. By employing the Markov Chain Monte Carlo sampling and Gaussian Process Regression models, this tool facilitates spectral quantifications, provides comprehensive uncertainty analysis, reduces human biases in the decision-making and model selection processes. This tool is particularly useful for in-operando X-ray diffraction data analysis, a key technique for examining battery materials. This method effectively disentangles overlapping peaks, quantifies each peak, and tracks their evolution. Tested on both synthetic and real experimental data, the tool demonstrated its efficacy and versatility. Given its broad adaptability, this method is suitable for a variety of spectroscopy techniques. / Thesis / Doctor of Science (PhD)