**Co-occurrence Rate Networks: Towards separate training for undirected graphical models**

by Zhemin Zhu

Dependence is a universal phenomenon which can be observed everywhere. In machine learning, probabilistic graphical models (PGMs) represent dependence relations with graphs. PGMs find wide applications in natural language processing (NLP), speech processing, computer vision, biomedicine, information retrieval, etc. Many traditional models, such as hidden Markov models (HMMs), Kalman filters, can be put under the umbrella of PGMs. The central idea of PGMs is to decompose (factorize) a joint probability into a product of local factors. Learning, inference and storage can be conducted efficiently over the factorization representation.

Two major types of PGMs can be distinguished: (i) Bayesian networks (directed graphs), and (ii) Markov networks (undirected graphs). Bayesian networks represent *directed dependence* with *directed edges*. Local factors of Bayesian networks are *conditional probabilities*. Directed dependence, directed edges and conditional probabilities are all *asymmetric* notions. In contrast, Markov networks represent *mutual dependence* with *undirected edges*. Both of mutual dependence and undirected edges are *symmetric* notions. For general Markov networks, based on the Hammersley–Clifford theorem, local factors are *positive functions* over maximum cliques. These local factors are explained using intuitive notions like ‘compatibility’ or ‘affinity’. Specially, if a graph forms a clique tree, the joint probability can be reparameterized into a junction tree factorization.

In this thesis, we propose a novel framework motivated by the Minimum Shared Information Principle (MSIP): *We try to find a factorization in which the information shared between factors is minimum. In other words, we try to make factors as independent as possible.*

The benefit of doing this is that we can train factors separately without paying a lot of efforts to guarantee consistency between them. To achieve this goal, we develop a theoretical framework called co-occurrence rate networks (CRNs) to obtain such a factorization. Briefly, given a joint probability, the CRN factorization is obtained as follows. We first strip off singleton probabilities from the joint probability. The quantity left is called co-occurrence rate (CR). CR is a symmetric quantity which measures mutual dependence among variables involved. Then we further decompose the joint CR into smaller and indepen dent CRs. Finally, we obtain a CRN factorization whose factors consist of all singleton probabilities and CR factors. There exist two kinds of independencies between these factors: (i) a singleton probability is independent (Here independent means two factors do not share information.) of other singleton probabilities; (ii) a CR factor is independent of other CR factors conditioned by singleton probabilities. Based on a CRN factorization, we propose an efficient two-step separate training method: (i) in the first step, we train a separate model for each singleton probability; (ii) given singleton probabilities, we train a separate model for each CR factor. Experimental results on three important natural language processing tasks show that our separate training method is two orders of magnitude faster than conditional random fields, while achieving competitive quality (often better on the overall quality metric F1).

The second contribution of this thesis is applying PGMs to a real-world NLP application: open relation extraction (ORE). In open relation extraction, two entities in a sentence are given, and the goal is to automatically extract their relation expression. ORE is a core technique, especially in the age of big data, for transforming unstructured information into structured data. We propose our model SimpleIE for this task. The basic idea is to decompose an extraction pattern into a sequence of simplification operations (components). The benefit by doing this is that these components can be re-combined in a new way to generate new extraction patterns. Hence SimpleIE can represent and capture diverse extraction patterns. This model is essentially a sequence labeling model. Experimental results on three benchmark data sets show that SimpleIE boosts recall and F1 by at least 15% comparing with seven ORE systems.

As tangible outputs of this thesis, we contribute open source implementations of our research results as well as an annotated data set.

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