Learning Graphical Models
Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces
However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo.
Structure Learning with Side Information: Sample Complexity
Graphical models are widely used to compactly model the conditional interdependence among multiple random variables Lauritzen [1996] and Pearl [2009]. The vertices of the graph represent the random variables (RVs), while the edges encode the inter-dependence among the RVs. The complete structure of the graph is analytically captured by the joint probability distribution of the random variables. Graphical models offer effective and tractable solutions to various inferential and decision-making solutions in different domains, e.g., computer vision Won and Derin [1992], genetics Chen et al. [2013], Fang et al. [2016], Dobra et al. [2004], social networks Jacob et al. [2014], and power systems Dvijotham et al. [2017].