Hinge-Loss Markov Random Fields and Probabilistic Soft Logic (1505.04406v3)

Abstract: A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large scale, from social and biological networks, to knowledge graphs and the Web, to images, video, and natural language. In this paper, we introduce two new formalisms for modeling structured data, and show that they can both capture rich structure and scale to big data. The first, hinge-loss Markov random fields (HL-MRFs), is a new kind of probabilistic graphical model that generalizes different approaches to convex inference. We unite three approaches from the randomized algorithms, probabilistic graphical models, and fuzzy logic communities, showing that all three lead to the same inference objective. We then define HL-MRFs by generalizing this unified objective. The second new formalism, probabilistic soft logic (PSL), is a probabilistic programming language that makes HL-MRFs easy to define using a syntax based on first-order logic. We introduce an algorithm for inferring most-probable variable assignments (MAP inference) that is much more scalable than general-purpose convex optimization methods, because it uses message passing to take advantage of sparse dependency structures. We then show how to learn the parameters of HL-MRFs. The learned HL-MRFs are as accurate as analogous discrete models, but much more scalable. Together, these algorithms enable HL-MRFs and PSL to model rich, structured data at scales not previously possible.

• The paper introduces HL-MRFs and PSL as unified frameworks that combine hinge-loss functions with first-order logic for efficient convex inference on large structured datasets.
• The paper presents an ADMM-based MAP inference algorithm that exploits sparse dependency structures to enhance scalability in complex applications like social networks and natural language processing.
• The paper demonstrates that HL-MRFs achieve competitive accuracy and efficiency compared to traditional discrete models, validating their effectiveness in tasks such as node and link labeling.

Hinge-Loss Markov Random Fields and Probabilistic Soft Logic

The paper introduces Hinge-Loss Markov Random Fields (HL-MRFs) and Probabilistic Soft Logic (PSL) as new methodologies for scalable structured modeling. This work addresses the prevalent challenge in machine learning of balancing model complexity against scalability, particularly in domains such as social networks, knowledge graphs, and natural language processing, where data is both large-scale and richly structured.

HL-MRFs are a variant of probabilistic graphical models that generalize discrete Markov Random Fields to continuous spaces by using a [0,1] unit interval to model variables. They employ hinge-loss functions to capture dependencies, which are instrumental in retaining convexity and enabling efficient inference through convex optimization. This framework unifies approaches from multiple disciplines, showing that inference objectives from randomized algorithms, probabilistic graphical models, and fuzzy logic converge to a unified convex programming task.

PSL extends HL-MRFs by providing a probabilistic programming language that defines HL-MRF models using a syntax derived from first-order logic. PSL allows users to describe interdependencies in their data easily and supports the modeling of complex structured data through both probabilistic and deterministic rules. Through PSL, HL-MRFs can be applied effortlessly to large datasets, benefiting from the reusable and flexible nature of its relational descriptions, which ground the dependencies in the data into a coherent HL-MRF.

The paper also introduces an ADMM-based (Alternating Direction Method of Multipliers) algorithm for performing MAP (maximum a posteriori) inference in HL-MRFs. The algorithm is designed to be scalable, exploiting the sparse dependency structure of many real-world problems, an area where traditional convex optimization techniques falter due to scalability issues. This approach is comprehensively evaluated and shown to be effective in handling large-scale data through experimental validation on social network datasets.

In terms of learning, the paper presents structured perceptron, maximum pseudolikelihood estimation, and large-margin estimation for learning the weights of HL-MRFs. These methods are adapted to leverage the HL-MRF structure, facilitating the learning of parameters that offer competitive accuracy and prediction quality on various tasks such as node labeling, link labeling, and preference prediction.

The results showcased indicate that HL-MRFs, when compared to traditional discrete models like MLNs (Markov Logic Networks), offer significant advantages in scalability without sacrificing predictive performance. Tasks are addressed with greater efficiency and retain high levels of accuracy, emphasizing the practical applicability of HL-MRFs to real-world problems where both scalability and model performance are critical.

The introduction of HL-MRFs and PSL is significant for the advancement of machine learning within large-scale and richly structured domains. Future steps could involve further expansion of PSL's expressivity to handle broader classes of constraints and dependencies, along with the continued exploration of distributed and parallel implementations to enhance scalability. Additionally, examining the application of these models on a more diverse set of domains could further establish the versatility and robustness of HL-MRFs and PSL, ensuring their place within the toolkit of modern machine learning practitioners and researchers.