The traditional way of obtaining models from data, inductive learning, has proved itself both in theory and in many practical applications. However, in domains where data is difficult or expensive to obtain, e.g., medicine, deep transfer learning is a more promising technique. It circumvents the model acquisition difficulties caused by scarce data in a target domain by carrying over structural properties of a model learned in a source domain where training data is ample. Nonetheless, the lack of a principled view of transfer learning so far has limited its adoption. In this paper, we address this issue by regarding transfer learning as a process that biases learning in a target domain in favor of patterns useful in a source domain. Specifically, we consider a first-order logic model of the data as an instantiation of a set of second-order templates. Hence, the usefulness of a model is partly determined by the learner's prior distribution over these template sets. The main insight of our work is that transferring knowledge amounts to acquiring a posterior over the second-order template sets by learning in the source domain and using this posterior when learning in the target setting. Our experimental evaluation demonstrates our approach to outperform the existing transfer learning techniques in terms of accuracy and runtime.

We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst-case running time of our algorithm is double exponential, we present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.

Innovative methods have been developed for diagnosis, activity monitoring, and state estimation that achieve high accuracy through the use of stochastic models involving hybrid discrete and continuous behaviors. A key bottleneck is the automated acquisition of these hybrid models, and recent methods have focused predominantly on Jump Markov processes and piecewise autoregressive models. In this paper, we present a novel algorithm capable of performing unsupervised learning of guarded Probabilistic Hybrid Automata (PHA) models, which extends prior work by allowing stochastic discrete mode transitions in a hybrid system to have a functional dependence on its continuous state. Our experiments indicate that guarded PHA models can yield significant performance improvements when used by hybrid state estimators, particularly when diagnosing the true discrete mode of the system, without any noticeable impact on their real-time performance.

We present a probabilistic extension of logic programs under the stable model semantics, inspired by the concept of Markov Logic Networks. The proposed language takes advantage of both formalisms in a single framework, allowing us to represent commonsense reasoning problems that require both logical and probabilistic reasoning in an intuitive and elaboration tolerant way.

Documents from the same domain usually discuss similar topics in a similar order. However, the number of topics and the exact topics discussed in each individual document can vary. In this paper we present a simple topic model that uses generalised Mallows models and incomplete topic orderings to incorporate this ordering regularity into the probabilistic generative process of the new model. We show how to reparameterise the new model so that a point-wise sampling algorithm from the Bayesian word segmentation literature can be used for inference. This algorithm jointly samples not only the topic orders and the topic assignments but also topic segmentations of documents. Experimental results show that our model performs significantly better than the other ordering-based topic models on nearly all the corpora that we used, and competitively with other state-of-the-art topic segmentation models on corpora that have a strong ordering regularity.

Markov decision processes (MDPs) with large number of states are of high practical interest. However, conventional algorithms to solve MDP are computationally infeasible in this scenario. Approximate dynamic programming (ADP) methods tackle this issue by computing approximate solutions. A widely applied ADP method is approximate linear program (ALP) which makes use of linear function approximation and offers theoretical performance guarantees. Nevertheless, the ALP is difficult to solve due to the presence of a large number of constraints and in practice, a reduced linear program (RLP) is solved instead. The RLP has a tractable number of constraints sampled from the original constraints of the ALP. Though the RLP is known to perform well in experiments, theoretical guarantees are available only for a specific RLP obtained under idealized assumptions. In this paper, we generalize the RLP to define a generalized reduced linear program (GRLP) which has a tractable number of constraints that are obtained as positive linear combinations of the original constraints of the ALP. The main contribution of this paper is the novel theoretical framework developed to obtain error bounds for any given GRLP. Central to our framework are two max-norm contraction operators. Our result theoretically justifies linear approximation of constraints. We discuss the implication of our results in the contexts of ADP and reinforcement learning. We also demonstrate via an example in the domain of controlled queues that the experiments conform to the theory.

Sum-product networks (SPNs) are a recently-proposed deep architecture that guarantees tractable inference, even on certain high-treewidth models. SPNs are a propositional architecture, treating the instances as independent and identically distributed. In this paper, we introduce Relational Sum-Product Networks (RSPNs), a new tractable first-order probabilistic architecture. RSPNs generalize SPNs by modeling a set of instances jointly, allowing them to influence each other's probability distributions, as well as modeling probabilities of relations between objects. We also present LearnRSPN, the first algorithm for learning high-treewidth tractable statistical relational models. LearnRSPN is a recursive top-down structure learning algorithm for RSPNs, based on Gens and Domingos' LearnSPN algorithm for propositional SPN learning. We evaluate the algorithm on three datasets; the RSPN learning algorithm outperforms Markov Logic Networks in both running time and predictive accuracy.

Faced with the problem of characterizing systematic changes in multivariate time series in an unsupervised manner, we derive and test two methods of regularizing hidden Markov models for this task. Regularization on state transitions provides smooth transitioning among states, such that the sequences are split into broad, contiguous segments. Our methods are compared with a recent hierarchical Dirichlet process hidden Markov model (HDP-HMM) and a baseline standard hidden Markov model, of which the former suffers from poor performance on moderate-dimensional data and sensitivity to parameter settings, while the latter suffers from rapid state transitioning, over-segmentation and poor performance on a segmentation task involving human activity accelerometer data from the UCI Repository. The regularized methods developed here are able to perfectly characterize change of behavior in the human activity data for roughly half of the real-data test cases, with accuracy of 94% and low variation of information. In contrast to the HDP-HMM, our methods provide simple, drop-in replacements for standard hidden Markov model update rules, allowing standard expectation maximization (EM) algorithms to be used for learning.

We study the problem of learning sparse structure changes between two Markov networks P and Q. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes directly via estimating the ratio between two Markov network models.  Such a direct approach was demonstrated to perform excellently in experiments, although its theoretical properties remained unexplored.  In this paper, we give sufficient conditions for successful change detection with respect to the sample size np, nq, the dimension of data m, and the number of changed edges d.

While probabilistic planning models have been extensively used by AI and Decision Theoretic communities for planning under uncertainty, the objective to minimize the expected cumulative cost is inappropriate for high-stake planning problems. With this motivation in mind, we revisit the Risk-Sensitive criterion (RS-criterion), where the objective is to find a policy that maximizes the probability that the cumulative cost is within some user-defined cost threshold. The overall scope of this research is to develop efficient and scalable algorithms to optimize the RS-criterion in probabilistic planning problems. In our recent paper (Hou, Yeoh, and Varakantham 2014), we formally defined Risk-Sensitive MDPs (RS-MDPs) and introduced new algorithms for RS-MDPs with non-negative costs. Next, my plan is to develop algorithm for RS-MDPs with negative cost cycles and for Risk-Sensitive POMDPs (RS-POMDPs).