Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path through a graph or a grammatical derivation, and are given a real-valued score (often interpreted as a probability) that depends on the real weights of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the PRODUCT transformation, which can merge two weighted logic programs into a new one. The resulting program optimizes a product of proof scores from the original programs, constituting a scoring function known in machine learning as a ``product of experts.'' Through the addition of intuitive constraining side conditions, we show that several important dynamic programming algorithms can be derived by applying PRODUCT to weighted logic programs corresponding to simpler weighted logic programs. In addition, we show how the computation of Kullback-Leibler divergence, an information-theoretic measure, can be interpreted using PRODUCT.

Markov decision processes (MDPs) are widely used for modeling decision-making problems in robotics, automated control, and economics. Traditional MDPs assume that the decision maker (DM) knows all states and actions. However, this may not be true in many situations of interest. We define a new framework, MDPs with unawareness (MDPUs) to deal with the possibilities that a DM may not be aware of all possible actions. We provide a complete characterization of when a DM can learn to play near-optimally in an MDPU, and give an algorithm that learns to play near-optimally when it is possible to do so, as efficiently as possible. In particular, we characterize when a near-optimal solution can be found in polynomial time.

Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of $n$ objects scales factorially in $n$. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called \emph{riffled independence}, encompassing a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the \emph{riffle shuffle}, common in card games, to combine the two permutations to form a single permutation. Within the context of ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. In this paper, we provide a formal introduction to riffled independence and present algorithms for using riffled independence within Fourier-theoretic frameworks which have been explored by a number of recent papers. Additionally, we propose an automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled independence.

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

Pac-Bayes bounds are among the most accurate generalization bounds for classifiers learned from independently and identically distributed (IID) data, and it is particularly so for margin classifiers: there have been recent contributions showing how practical these bounds can be either to perform model selection (Ambroladze et al., 2007) or even to directly guide the learning of linear classifiers (Germain et al., 2009). However, there are many practical situations where the training data show some dependencies and where the traditional IID assumption does not hold. Stating generalization bounds for such frameworks is therefore of the utmost interest, both from theoretical and practical standpoints. In this work, we propose the first - to the best of our knowledge - Pac-Bayes generalization bounds for classifiers trained on data exhibiting interdependencies. The approach undertaken to establish our results is based on the decomposition of a so-called dependency graph that encodes the dependencies within the data, in sets of independent data, thanks to graph fractional covers. Our bounds are very general, since being able to find an upper bound on the fractional chromatic number of the dependency graph is sufficient to get new Pac-Bayes bounds for specific settings. We show how our results can be used to derive bounds for ranking statistics (such as Auc) and classifiers trained on data distributed according to a stationary {\ss}-mixing process. In the way, we show how our approach seemlessly allows us to deal with U-processes. As a side note, we also provide a Pac-Bayes generalization bound for classifiers learned on data from stationary $\varphi$-mixing distributions.

We introduce a framework for representing a variety of interesting problems as inference over the execution of probabilistic model programs. We represent a "solution" to such a problem as a guide program which runs alongside the model program and influences the model program's random choices, leading the model program to sample from a different distribution than from its priors. Ideally the guide program influences the model program to sample from the posteriors given the evidence. We show how the KL- divergence between the true posterior distribution and the distribution induced by the guided model program can be efficiently estimated (up to an additive constant) by sampling multiple executions of the guided model program. In addition, we show how to use the guide program as a proposal distribution in importance sampling to statistically prove lower bounds on the probability of the evidence and on the probability of a hypothesis and the evidence. We can use the quotient of these two bounds as an estimate of the conditional probability of the hypothesis given the evidence. We thus turn the inference problem into a heuristic search for better guide programs.

We propose automatically learning probabilistic Hierarchical Task Networks (pH-TNs) in order to capture a user's preferences on plans, by observing only the user's behavior. HTNs are a common choice of representation for a variety of purposes in planning, including work on learning in planning. Our contributions are (a) learning structure and (b) representing preferences. In contrast, prior work employing HTNs considers learning method preconditions (instead of structure) and representing domain physics or search control knowledge (rather than preferences). Initially we will assume that the observed distribution of plans is an accurate representation of user preference, and then generalize to the situation where feasibility constraints frequently prevent the execution of preferred plans. In order to learn a distribution on plans we adapt an Expectation-Maximization (EM) technique from the discipline of (probabilistic) grammar induction, taking the perspective of task reductions as productions in a context-free grammar over primitive actions. To account for the difference between the distributions of possible and preferred plans we subsequently modify this core EM technique, in short, by rescaling its input.

Rapid identification of object from radar cross section (RCS) signals is important for many space and military applications. This identification is a problem in pattern recognition which either neural networks or support vector machines should prove to be high-speed. Bayesian networks would also provide value but require significant preprocessing of the signals. In this paper, we describe the use of a support vector machine for object identification from synthesized RCS data. Our best results are from data fusion of X-band and S-band signals, where we obtained 99.4%, 95.3%, 100% and 95.6% correct identification for cylinders, frusta, spheres, and polygons, respectively. We also compare our results with a Bayesian approach and show that the SVM is three orders of magnitude faster, as measured by the number of floating point operations.

Collaborative tagging systems, such as Delicious, CiteULike, and others, allow users to annotate resources, e.g., Web pages or scientific papers, with descriptive labels called tags. The social annotations contributed by thousands of users, can potentially be used to infer categorical knowledge, classify documents or recommend new relevant information. Traditional text inference methods do not make best use of social annotation, since they do not take into account variations in individual users' perspectives and vocabulary. In a previous work, we introduced a simple probabilistic model that takes interests of individual annotators into account in order to find hidden topics of annotated resources. Unfortunately, that approach had one major shortcoming: the number of topics and interests must be specified a priori. To address this drawback, we extend the model to a fully Bayesian framework, which offers a way to automatically estimate these numbers. In particular, the model allows the number of interests and topics to change as suggested by the structure of the data. We evaluate the proposed model in detail on the synthetic and real-world data by comparing its performance to Latent Dirichlet Allocation on the topic extraction task. For the latter evaluation, we apply the model to infer topics of Web resources from social annotations obtained from Delicious in order to discover new resources similar to a specified one. Our empirical results demonstrate that the proposed model is a promising method for exploiting social knowledge contained in user-generated annotations.

In this paper, a new learning algorithm for adaptive network intrusion detection using naive Bayesian classifier and decision tree is presented, which performs balance detections and keeps false positives at acceptable level for different types of network attacks, and eliminates redundant attributes as well as contradictory examples from training data that make the detection model complex. The proposed algorithm also addresses some difficulties of data mining such as handling continuous attribute, dealing with missing attribute values, and reducing noise in training data. Due to the large volumes of security audit data as well as the complex and dynamic properties of intrusion behaviours, several data miningbased intrusion detection techniques have been applied to network-based traffic data and host-based data in the last decades. However, there remain various issues needed to be examined towards current intrusion detection systems (IDS). We tested the performance of our proposed algorithm with existing learning algorithms by employing on the KDD99 benchmark intrusion detection dataset. The experimental results prove that the proposed algorithm achieved high detection rates (DR) and significant reduce false positives (FP) for different types of network intrusions using limited computational resources.