Logical hidden Markov models (LOHMMs) upgrade traditional hidden Markov models to deal with sequences of structured symbols in the form of logical atoms, rather than flat characters. This note formally introduces LOHMMs and presents solutions to the three central inference problems for LOHMMs: evaluation, most likely hidden state sequence and parameter estimation. The resulting representation and algorithms are experimentally evaluated on problems from the domain of bioinformatics.
We define a language for representing context-sensitive probabilistic knowledge. A knowledge base consists of a set of universally quantified probability sentences that include context constraints, which allow inference to be focused on only the relevant portions of the probabilistic knowledge. We provide a declarative semantics for our language. We present a query answering procedure that takes a query Q and a set of evidence E and constructs a Bayesian network to compute P(Q¦E). The posterior probability is then computed using any of a number of Bayesian network inference algorithms. We use the declarative semantics to prove the query procedure sound and complete. We use concepts from logic programming to justify our approach.   We present a probabilistic model for constraint-based grammars and a method for estimating the parameters of such models from incomplete, i.e., unparsed data. Whereas methods exist to estimate the parameters of probabilistic context-free grammars from incomplete data (Baum 1970), so far for probabilistic grammars involving context-dependencies only parameter estimation techniques from complete, i.e., fully parsed data have been presented (Abney 1997). However, complete-data estimation requires labor-intensive, error-prone, and grammar-specific hand-annotating of large language corpora. We present a log-linear probability model for constraint logic programming, and a general algorithm to estimate the parameters of such models from incomplete data by extending the estimation algorithm of Della-Pietra, Della-Pietra, and Lafferty (1997) to incomplete data settings. A large portion of real-world data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with "flat" data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much of the relational structure present in our database. This paper builds on the recent work on probabilistic relational models (PRMs), and describes how to learn them from databases. PRMs allow the properties of an object to depend probabilistically both on other properties of that object and on properties of related objects. Although PRMs are significantly more expressive than standard models, such as Bayesian networks, we show how to extend well-known statistical methods for learning Bayesian networks to learn these models. We describe both parameter estimation and structure learning -- the automatic induction of the dependency structure in a model. Moreover, we show how the learning procedure can exploit standard database retrieval techniques for efficient learning from large datasets. We present experimental results on both real and synthetic relational databases. A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is directly represented by a Bayesian network. By using a powerful way of specifying conditional probability distributions in these networks, the resulting formalism is more expressive than the previous ones. Particularly, it provides for constraints on equalities of events, and it allows to define complex, nested combination functions. Probabilistic inductive logic programming, sometimes also called statistical relational learning, addresses one of the central questions of artificial intelligence: the integration of probabilistic reasoning with first order logic representations and machine learning. A rich variety of different formalisms and learning techniques have been developed. In the present paper, we start from inductive logic programming and sketch how it can be extended with probabilistic methods. More precisely, we outline three classical settings for inductive logic programming, namely learning from entailment, learning from interpretations, and learning from proofs or traces, and show how they can be used to learn different types of probabilistic representations. We propose a logical mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm. Intelligent agents must function in an uncertain world, containing multiple objects and relations that change over time. Unfortunately, no representation is currently available that can handle all these issues, while allowing for principled and efficient inference. This paper addresses this need by introducing dynamic probabilistic relational models (DPRMs). DPRMs are an extension of dynamic Bayesian networks (DBNs) where each time slice (and its dependences on previous slices) is represented by a probabilistic relational model (PRM). Particle filtering, the standard method for inference in DBNs, has severe limitations when applied to DPRMs, but we are able to greatly improve its performance through a form of relational Rao-Blackwellisation. Further gains in efficiency arc obtained through the use of abstraction trees, a novel data structure. We successfully apply DPRMs to execution monitoring and fault diagnosis of an assembly plan, in which a complex product is gradually constructed from subparts. Recently, new representation languages that integrate first order logic with Bayesian networks have been developed. Bayesian logic programs are one of these languages. In this paper, we present results on combining Inductive Logic Programming (ILP) with Bayesian networks to learn both the qualitative and the quantitative components of Bayesian logic programs. More precisely, we show how to combine the ILP setting learning from interpretations with score-based techniques for learning Bayesian networks. Thus, the paper positively answers Koller and Pfeffer's question, whether techniques from ILP could help to learn the logical component of first order probabilistic models.