Structure Learning for Relational Logistic Regression: An Ensemble Approach (original) (raw)

Towards structural logistic regression: Combining relational and statistical learning

2002

Abstract Inductive logic programming (ILP) techniques are useful for analyzing data in multi-table relational databases. Learned rules can potentially discover relationships that are not obvious in" flattened" data. Statistical learners, on the other hand, are generally not constructed to search relational data; they expect to be presented with a single table containing a set of feature candidates.

Gradient-based boosting for statistical relational learning: The relational dependency network case

Machine Learning, 2012

Dependency networks approximate a joint probability distribution over multiple random variables as a product of conditional distributions. Relational Dependency Networks (RDNs) are graphical models that extend dependency networks to relational domains. This higher expressivity, however, comes at the expense of a more complex modelselection problem: an unbounded number of relational abstraction levels might need to be explored. Whereas current learning approaches for RDNs learn a single probability tree per random variable, we propose to turn the problem into a series of relational function-approximation problems using gradient-based boosting. In doing so, one can easily induce highly complex features over several iterations and in turn estimate quickly a very expressive model. Our experimental results in several different data sets show that this boosting method results in efficient learning of RDNs when compared to state-of-the-art statistical relational learning approaches.

A taxonomy of weight learning methods for statistical relational learning

Machine Learning

Statistical relational learning (SRL) frameworks are effective at defining probabilistic models over complex relational data. They often use weighted first-order logical rules where the weights of the rules govern probabilistic interactions and are usually learned from data. Existing weight learning approaches typically attempt to learn a set of weights that maximizes some function of data likelihood; however, this does not always translate to optimal performance on a desired domain metric, such as accuracy or F1 score. In this paper, we introduce a taxonomy of search-based weight learning approaches for SRL frameworks that directly optimize weights on a chosen domain performance metric. To effectively apply these search-based approaches, we introduce a novel projection, referred to as scaled space (SS), that is an accurate representation of the true weight space. We show that SS removes redundancies in the weight space and captures the semantic distance between the possible weight ...

Relational Logistic Regression

2014

Logistic regression is a commonly used representation for aggregators in Bayesian belief networks when a child has multiple parents. In this paper we consider extending logistic regression to relational models, where we want to model varying populations and interactions among parents. In this paper, we first examine the representational problems caused by population variation. We show how these problems arise even in simple cases with a single parametrized parent, and propose a linear relational logistic regression which we show can represent arbitrary linear (in population size) decision thresholds, whereas the traditional logistic regression cannot. Then we examine representing interactions among the parents of a child node, and representing non-linear dependency on population size. We propose a multi-parent relational logistic regression which can represent interactions among parents and arbitrary polynomial decision thresholds. Finally, we show how other well-known aggregators c...

Ensemble Relational Learning based on Selective Propositionalization

Dealing with structured data needs the use of expressive representation formalisms that, however, puts the problem to deal with the computational complexity of the machine learning process. Furthermore, real world domains require tools able to manage their typical uncertainty. Many statistical relational learning approaches try to deal with these problems by combining the construction of relevant relational features with a probabilistic tool. When the combination is static (static propositionalization), the constructed features are considered as boolean features and used offline as input to a statistical learner; while, when the combination is dynamic (dynamic propositionalization), the feature construction and probabilistic tool are combined into a single process. In this paper we propose a selective propositionalization method that search the optimal set of relational features to be used by a probabilistic learner in order to minimize a loss function. The new propositionalization approach has been combined with the random subspace ensemble method. Experiments on real-world datasets shows the validity of the proposed method.

Scalable Structure Learning for Probabilistic Soft Logic

ArXiv, 2018

Statistical relational frameworks such as Markov logic networks and probabilistic soft logic (PSL) encode model structure with weighted first-order logical clauses. Learning these clauses from data is referred to as structure learning. Structure learning alleviates the manual cost of specifying models. However, this benefit comes with high computational costs; structure learning typically requires an expensive search over the space of clauses which involves repeated optimization of clause weights. In this paper, we propose the first two approaches to structure learning for PSL. We introduce a greedy search-based algorithm and a novel optimization method that trade-off scalability and approximations to the structure learning problem in varying ways. The highly scalable optimization method combines data-driven generation of clauses with a piecewise pseudolikelihood (PPLL) objective that learns model structure by optimizing clause weights only once. We compare both methods across five ...

BOWL: Bayesian Optimization for Weight Learning in Probabilistic Soft Logic

Proceedings of the AAAI Conference on Artificial Intelligence, 2020

Probabilistic soft logic (PSL) is a statistical relational learning framework that represents complex relational models with weighted first-order logical rules. The weights of the rules in PSL indicate their importance in the model and influence the effectiveness of the model on a given task. Existing weight learning approaches often attempt to learn a set of weights that maximizes some function of data likelihood. However, this does not always translate to optimal performance on a desired domain metric, such as accuracy or F1 score. In this paper, we introduce a new weight learning approach called Bayesian optimization for weight learning (BOWL) based on Gaussian process regression that directly optimizes weights on a chosen domain performance metric. The key to the success of our approach is a novel projection that captures the semantic distance between the possible weight configurations. Our experimental results show that our proposed approach outperforms likelihood-based approac...

Learning Parameters for Relational Probabilistic Models with Noisy-Or Combining Rule

2009

Languages that combine predicate logic with probabilities are needed to succinctly represent knowledge in many real-world domains. We consider a formalism based on universally quantified conditional influence statements that capture local interactions between object attributes. The effects of different conditional influence statements can be combined using rules such as Noisy-OR. To combine multiple instantiations of the same rule we need other combining rules at a lower level. In this paper we derive and implement algorithms based on gradient-descent and EM for learning the parameters of these multi-level combining rules. We compare our approaches to learning in Markov Logic Networks and show superior performance in multiple domains.

Max-Margin Weight Learning for Markov Logic Networks

Lecture Notes in Computer Science, 2009

Markov logic networks (MLNs) are an expressive representation for statistical relational learning that generalizes both first-order logic and graphical models. Existing discriminative weight learning methods for MLNs all try to learn weights that optimize the Conditional Log Likelihood (CLL) of the training examples. In this work, we present a new discriminative weight learning method for MLNs based on a maxmargin framework. This results in a new model, Max-Margin Markov Logic Networks (M3LNs), that combines the expressiveness of MLNs with the predictive accuracy of structural Support Vector Machines (SVMs). To train the proposed model, we design a new approximation algorithm for loss-augmented inference in MLNs based on Linear Programming (LP). The experimental result shows that the proposed approach generally achieves higher F 1 scores than the current best discriminative weight learner for MLNs.

Statistical relational learning: Four claims and a survey

2003

Statistical relational learning (SRL) research has made significant progress over the last 5 years. We have successfully demonstrated the feasibility of a number of probabilistic models for relational data, including probabilistic relational models, Bayesian logic programs, and relational probability trees, and the interest in SRL is growing. However, in order to sustain and nurture the growth of SRL as a subfield we need to refocus our efforts on the science of machine learning—moving from demonstrations to comparative and ablation studies.