However, it has been shown that the antecedents of individual rules Decision rules, which can provide good interpretability may contain irrelevant conditions. C4.5rules (Quinlan, 1993) and flexibility for data mining tasks, uses an optimization procedure to simplify conditions. The have received very little attention in the stream optimization is done in two phases. First, each rule is generalized mining community so far. In this work we introduce by deleting conditions that do not seem to be helpful a new algorithm to learn rule sets, designed in discriminating the classes. A greedy search method is for open-ended data streams.

Topic models have a wide range of applications, including modeling of text documents, images, user preferences, product rankings, and many others. However, learning optimal models may be difficult, especially for large problems. The reason is that inference techniques such as Gibbs sampling often converge to suboptimal models due to the abundance of local minima in large datasets. In this paper, we propose a general method of improving the performance of topic models. The method, called 'grouping transform', works by introducing auxiliary variables which represent assignments of the original model tokens to groups. Using these auxiliary variables, it becomes possible to resample an entire group of tokens at a time. This allows the sampler to make larger state space moves. As a result, better models are learned and performance is improved. The proposed ideas are illustrated on several topic models and several text and image datasets. We show that the grouping transform significantly improves performance over standard models.

Lifted message passing algorithms exploit repeated structure within a given graphical model to answer queries efficiently. Given evidence, they construct a lifted network of supernodes and superpotentials corresponding to sets of nodes and potentials that are indistinguishable given the evidence. Recently, efficient algorithms were presented for updating the structure of an existing lifted network with incremental changes to the evidence. In the inference stage, however, current algorithms need to construct a separate lifted network for each evidence case and run a modified message passing algorithm on each lifted network separately. Consequently, symmetries across the inference tasks are not exploited. In this paper, we present a novel lifted message passing technique that exploits symmetries across multiple evidence cases. The benefits of this multi-evidence lifted inference are shown for several important AI tasks such as computing personalized PageRanks and Kalman filters via multi-evidence lifted Gaussian belief propagation.

In this work we propose an approach for generalization in continuous domain Reinforcement Learning that, instead of using a single function approximator, tries many different function approximators in parallel, each one defined in a different region of the domain. Associated with each approximator is a relevance function that locally quantifies the quality of its approximation, so that, at each input point, the approximator with highest relevance can be selected. The relevance function is defined using parametric estimations of the variance of the q-values and the density of samples in the input space, which are used to quantify the accuracy and the confidence in the approximation, respectively. These parametric estimations are obtained from a probability density distribution represented as a Gaussian Mixture Model embedded in the input-output space of each approximator. In our experiments, the proposed approach required a lesser number of experiences for learning and produced more stable convergence profiles than when using a single function approximator.

Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth degrees. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we develop existing propositional logics of fuzzy probability into a full-blown description logic, and we show decidability of several variants of this logic under Lukasiewicz semantics. We obtain these results in a novel generic framework of fuzzy coalgebraic logic; this enables us to extend our results to logics that combine crisp ingredients including standard crisp roles and crisp numerical probabilities with fuzzy roles and fuzzy probabilities.

Many applications of causal inference, such as finding the relationship between stock prices and news reports, involve both discrete and continuous variables observed over time. Inference with these complex sets of temporal data, though, has remained difficult and required a number of simplifications. We show that recent approaches for inferring temporal relationships (represented as logical formulas) can be adapted for inference with continuous valued effects. Building on advances in logic, PCTLc (an extension of PCTL with numerical constraints) is introduced here to allow representation and inference of relationships with a mixture of discrete and continuous components. Then, finding significant relationships in the continuous case can be done using the conditional expectation of an effect, rather than its conditional probability. We evaluate this approach on both synthetically generated and actual financial market data, demonstrating that it can allow us to answer different questions than the discrete approach can.

Probabilistic logics which is followed by the development of the main methods that support reasoning with probability distributions, used in generalising probabilistic Boolean interaction, and, such as ProbLog, use an implicit definition finally, default logic is briefly discussed. We will use probabilistic of an interaction rule to combine probabilistic evidence Boolean interaction as a sound and generic, algebraic about atoms. In this paper, we show that way to combine uncertain evidence, whereas default this interaction rule is an example of a more general logic will be used as our language to implement the interaction class of interactions that can be described by nonmonotonic operators, again reflecting this double perspective on the logics. We furthermore show that such probabilistic logic. The new probabilistic logical framework local interactions about the probability of an atom is described in Section 3 and compared to other approaches can be described by convolution. The resulting extended in Section 4. The achievements of this research are reflected probabilistic logic supports nonmonotonic upon in Section 5. reasoning with probabilistic information.

Uncertainty is unavoidable when modeling most application domains. In medicine, for example, symptoms (such as pain, dizziness, or nausea) are always subjective, and hence imprecise and incomparable. Additionally, concepts and their relationships may be inexpressible in a crisp, clear-cut manner. We extend the description logic ALC with multi-valued semantics based on lattices that can handle uncertainty on concepts as well as on the axioms of the ontology. We introduce reasoning methods for this logic w.r.t. general concept inclusions and show that the complexity of reasoning is not increased by this new semantics.

Computing the market maker price of a security in a combinatorial prediction market is #P-hard. We devise a fully polynomial randomized approximation scheme (FPRAS) that computes the price of any security in disjunctive normal form (DNF) within an ε multiplicative error factor in time polynomial in 1ε and the size of the input, with high probability and under reasonable assumptions. Our algorithm is a Monte-Carlo technique based on importance sampling. The algorithm can also approximately price securities represented in conjunctive normal form (CNF) with additive error bounds. To illustrate the applicability of our algorithm, we show that many securities in Yahoo!'s popular combinatorial prediction market game called Predictalot can be represented by DNF formulas of polynomial size.

In many of the possible applications as well as the theoretical models of computational social choice,the agents’ preferences are represented as partialorders. In this paper, we extend the maximum likelihood approach for defining “optimal” voting rules to this setting. We consider distributions in which the pairwise comparisons / incomparabilities between alternatives are drawn i.i.d. We call suchmodels pairwise-independentmodels and show that they correspond to a class of voting rules that we call pairwise scoring rules. This generalizes rulessuch as Kemeny and Borda. Moreover, we show that Borda is the only pairwise scoring rule that satisfies neutrality, when the outcome space is the set of all alternatives. We then study which voting rules defined for linear orders can be extended to partial orders via our MLE model. We show that any weakly neutral outcome scoring rule (includingany ranking/candidate scoring rule) based onthe weighted majority graph can be represented as the MLE of a weakly neutral pairwise-independent model. Therefore, all such rules admit natural extensionsto profiles of partial orders. Finally, we propose a specific MLE model π k for generating a set of k winning alternatives, and study the computational complexity of winner determination for the MLE of π k .