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Graphs provide a natural way to represent information in structured form. When the entities in a graph are random variables, it gives rise to probabilistic graphical models (PGMs). Traditional methods in PGMs are concerned with the structured data generated with known individual's association. These methods are not applicable in the setting when the data is generated by a large population of individuals with unknown individual's association. First part of the thesis is concerned with inference and learning from aggregate data generated by a large population of individuals each following a certain PGM. The second part of the thesis address the problem of representation learning over signed graphs. We propose spectral signed graph neural network (GNN) designs for learning node embeddings for signed graphs. Furthermore, we introduce signed Magnetic Laplacian for spectral analysis of directed signed graphs and use it to propose new spectral GNN designs applicable to directed signed graphs.