We present a novel algorithm and a new understanding of reasoning about a sequence of deterministic actions with a probabilistic prior. When the initial state of a dynamic system is unknown, a probability distribution can be still specified over the initial states. Estimating the posterior distribution over states filtering after some deterministic actions occurred is a problem relevant to AI planning, natural language processing (NLP), and robotics among others. Current approaches to filtering deterministic actions are not tractable even if the distribution over the initial system state is represented compactly. The reason is that state variables become correlated after a few steps. The main innovation in this paper is a method for sidestepping this problem by redefining state variables dynamically at each time step such that the posterior for time t is represented in a factored form. This update is done using a progression algorithm as a subroutine, and our algorithm's tractability follows when that subroutine is tractable. Our results are for general deterministic actions and in particular, our algorithm is tractable for one-to-one and STRIPS actions. We apply our reasoning algorithm about deterministic actions to reasoning about sequences of probabilistic actions and improve the efficiency of the current probabilistic reasoning approaches. We demonstrate the efficiency of the new algorithm empirically over AI-Planning data sets.

It seems to be a common view that in order to interpret probabilistic first-order sentences, either a statistical approach that counts (tuples of) individuals has to be used, or the knowledge base has to be grounded to make a possible worlds semantics applicable, for a subjective interpretation of probabilities. In this paper, we propose novel semantical perspectives on first-order (or relational) probabilistic conditionals that are motivated by considering them as subjective, but population-based statements. We propose two different semantics for relational probabilistic conditionals, and a set of postulates for suitable inference operators in this framework. Finally, we present two inference operators by applying the maximum entropy principle to the respective model theories. Both operators are shown to yield reasonable inferences according to the postulates.

In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing which vertex to query in order to learn as much as possible about the attributes of the other vertices. We assume the network is generated by a stochastic block model, but we make no assumptions about its assortativity or disassortativity. We choose which vertex to query using two methods: 1) maximizing the mutual information between its attributes and those of the others (a well-known approach in active learning) and 2) maximizing the average agreement between two independent samples of the conditional Gibbs distribution. Experimental results show that both these methods do much better than simple heuristics. They also consistently identify certain vertices as important by querying them early on.

Luhmann (1984) defined society as a communication system which is structurally coupled to, but not an aggregate of, human action systems. The communication system is then considered as self-organizing ("autopoietic"), as are human actors. Communication systems can be studied by using Shannon's (1948) mathematical theory of communication. The update of a network by action at one of the local nodes is then a well-known problem in artificial intelligence (Pearl 1988). By combining these various theories, a general algorithm for probabilistic structure/action contingency can be derived. The consequences of this contingency for each system, its consequences for their further histories, and the stabilization on each side by counterbalancing mechanisms are discussed, in both mathematical and theoretical terms. An empirical example is elaborated.

One of the objectives of designing feature selection learning algorithms is to obtain classifiers that depend on a small number of attributes and have verifiable future performance guarantees. There are few, if any, approaches that successfully address the two goals simultaneously. Performance guarantees become crucial for tasks such as microarray data analysis due to very small sample sizes resulting in limited empirical evaluation. To the best of our knowledge, such algorithms that give theoretical bounds on the future performance have not been proposed so far in the context of the classification of gene expression data. In this work, we investigate the premise of learning a conjunction (or disjunction) of decision stumps in Occam's Razor, Sample Compression, and PAC-Bayes learning settings for identifying a small subset of attributes that can be used to perform reliable classification tasks. We apply the proposed approaches for gene identification from DNA microarray data and compare our results to those of well known successful approaches proposed for the task. We show that our algorithm not only finds hypotheses with much smaller number of genes while giving competitive classification accuracy but also have tight risk guarantees on future performance unlike other approaches. The proposed approaches are general and extensible in terms of both designing novel algorithms and application to other domains.

Computing a good policy in stochastic uncertain environments with unknown dynamics and reward model parameters is a challenging task. In a number of domains, ranging from space robotics to epilepsy management, it may be possible to have an initial training period when suboptimal performance is permitted. For such problems it is important to be able to identify when this training period is complete, and the computed policy can be used with high confidence in its future performance. A simple principled criteria for identifying when training has completed is when the error bounds on the value estimates of the current policy are sufficiently small that the optimal policy is fixed, with high probability. We present an upper bound on the amount of training data required to identify the optimal policy as a function of the unknown separation gap between the optimal and the next-best policy values. We illustrate with several small problems that by estimating this gap in an online manner, the number of training samples to provably reach optimality can be significantly lower than predicted offline using a Probably Approximately Correct framework that requires an input epsilon parameter.

Decentralized POMDPs are powerful theoretical models for coordinating agents’ decisions in uncertain environments, but the generally-intractable complexity of optimal joint policy construction presents a significant obstacle in applying Dec-POMDPs to problems where many agents face many policy choices. Here, we argue that when most agent choices are independent of other agents’ choices, much of this complexity can be avoided: instead of coordinating full policies, agents need only coordinate policy abstractions that explicitly convey the essential interaction influences. To this end, we develop a novel framework for influence-based policy abstraction for weakly-coupled transition-dependent Dec-POMDP problems that subsumes several existing approaches. In addition to formally characterizing the space of transition-dependent influences, we provide a method for computing optimal and approximately-optimal joint policies. We present an initial empirical analysis, over problems with commonly-studied flavors of transition-dependent influences, that demonstrates the potential computational benefits of influence-based abstraction over state-of-the-art optimal policy search methods.

An interesting class of planning domains, including planning for daily activities of Mars rovers, involves achievement of goals with time constraints and concurrent actions with probabilistic durations. Current probabilistic approaches, which rely on a discrete time model, introduce a blow up in the search state-space when the two factors of action concurrency and action duration uncertainty are combined. Simulation-based and sampling probabilistic planning approaches would cope with this state explosion by avoiding storing all the explored states in memory, but they remain approximate solution approaches. In this paper, we present an alternative approach relying on a continuous time model which avoids the state explosion caused by time stamping in the presence of action concurrency and action duration uncertainty. Time is represented as a continuous random variable. The dependency between state time variables is conveyed by a Bayesian network, which is dynamically generated by a state-based forward-chaining search based on the action descriptions. A generated plan is characterized by a probability of satisfying a goal. The evaluation of this probability is done by making a query the Bayesian network.

We consider the problem of jointly training structured models for extraction from sources whose instances enjoy partial overlap. This has important applications like user-driven ad-hoc information extraction on the web. Such applications present new challenges in terms of the number of sources and their arbitrary pattern of overlap not seen by earlier collective training schemes applied on two sources. We present an agreement-based learning framework and alternatives within it to trade-off tractability, robustness to noise, and extent of agreement. We provide a principled scheme to discover low-noise agreement sets in unlabeled data across the sources. Through extensive experiments over 58 real datasets, we establish that our method of additively rewarding agreement over maximal segments of text provides the best trade-offs, and also scores over alternatives such as collective inference, staged training, and multi-view learning.

Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d. training set $(X_{1},Y_{1}),... (X_{n},Y_{n})$ where $X_{i}$ represents a feature and $Y_{i}\in \{0,1\}$ is a label attached to that feature. The underlying joint distribution of $(X,Y)$ is unknown, but we can learn about it from the training set and we aim at devising low error classifiers $f:X\to Y$ used to predict the label of new incoming features. Here we solve a quantum analogue of this problem, namely the classification of two arbitrary unknown qubit states. Given a number of `training' copies from each of the states, we would like to `learn' about them by performing a measurement on the training set. The outcome is then used to design mesurements for the classification of future systems with unknown labels. We find the asymptotically optimal classification strategy and show that typically, it performs strictly better than a plug-in strategy based on state estimation. The figure of merit is the excess risk which is the difference between the probability of error and the probability of error of the optimal measurement when the states are known, that is the Helstrom measurement. We show that the excess risk has rate $n^{-1}$ and compute the exact constant of the rate.