This paper proposes an online tree-based Bayesian approach for reinforcement learning. For inference, we employ a generalised context tree model. This defines a distribution on multivariate Gaussian piecewise-linear models, which can be updated in closed form. The tree structure itself is constructed using the cover tree method, which remains efficient in high dimensional spaces. We combine the model with Thompson sampling and approximate dynamic programming to obtain effective exploration policies in unknown environments. The flexibility and computational simplicity of the model render it suitable for many reinforcement learning problems in continuous state spaces. We demonstrate this in an experimental comparison with least squares policy iteration.

We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, single-path formulation of the nCRP, allowing a document to more easily express thematic borrowings as a random effect. We derive a stochastic variational inference algorithm for the model, in addition to a greedy subtree selection method for each document, which allows for efficient inference using massive collections of text documents. We demonstrate our algorithm on 1.8 million documents from The New York Times and 3.3 million documents from Wikipedia.

A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are partially exchangeable sequences, a generalization of exchangeable sequences. We prove that a family of tractable EVMs is optimal under zero-one loss for a large class of functions, including parity and threshold functions, and strictly subsumes existing tractable independence-based model families. Extensive experiments show that EVMs outperform state of the art classifiers such as SVMs and probabilistic models which are solely based on independence assumptions.

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models.

One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their shortcomings, which led to development of numerous enrichments. Among the most general ones are the abstract dialectical frameworks, also known as the ADFs. They make use of the so-called acceptance conditions to represent arbitrary relations. This level of abstraction brings not only new challenges, but also requires addressing existing problems in the field. One of the most controversial issues, recognized not only in argumentation, concerns the support cycles. In this paper we introduce a new method to ensure acyclicity of the chosen arguments and present a family of extension-based semantics built on it. We also continue our research on the semantics that permit cycles and fill in the gaps from the previous works. Moreover, we provide ADF versions of the properties known from the Dung setting. Finally, we also introduce a classification of the developed sub-semantics and relate them to the existing labeling-based approaches.

A semantic net can be used to represent a sentence. A sentence in a language contains semantics which are polar in nature, that is, semantics which are positive, neutral and negative. Neutrosophy is a relatively new field of science which can be used to mathematically represent triads of concepts. These triads include truth, indeterminacy and falsehood, and so also positivity, neutrality and negativity. Thus a conventional semantic net has been extended in this paper using neutrosophy into a Polar Fuzzy Neutrosophic Semantic Net. A Polar Fuzzy Neutrosophic Semantic Net has been implemented in MATLAB and has been used to illustrate a polar sentence in English language. The paper demonstrates a method for the representation of polarity in a computers memory. Thus, polar concepts can be applied to imbibe a machine such as a robot, with emotions, making machine emotion representation possible.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions is two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most of existing work which deal with the problem by adding some sparsity penalties on various objectives of PCA, in this paper, we propose a new method SPCArt, whose motivation is to find a rotation matrix and a sparse basis such that the sparse basis approximates the basis of PCA after the rotation. The algorithm of SPCArt consists of three alternating steps: rotate PCA basis, truncate small entries, and update the rotation matrix. Its performance bounds are also given. SPCArt is efficient, with each iteration scaling linearly with the data dimension. It is easy to choose parameters in SPCArt, due to its explicit physical explanations. Besides, we give a unified view to several existing sparse PCA methods and discuss the connection with SPCArt. Some ideas in SPCArt are extended to GPower, a popular sparse PCA algorithm, to overcome its drawback. Experimental results demonstrate that SPCArt achieves the state-of-the-art performance. It also achieves a good tradeoff among various criteria, including sparsity, explained variance, orthogonality, balance of sparsity among loadings, and computational speed.

Given a collection of categorical data, we want to find the parameters of a Dirichlet distribution which maximizes the likelihood of that data. Newton's method is typically used for this purpose but current implementations require reading through the entire dataset on each iteration. In this paper, we propose a modification which requires only a single pass through the dataset and substantially decreases running time. Furthermore we analyze both theoretically and empirically the performance of the proposed algorithm, and provide an open source implementation.

In recent years, the task of automatically linking pieces of text (anchors) mentioned in a document to Wikipedia articles that represent the meaning of these anchors has received extensive research attention. Typically, link-to-Wikipedia systems try to find a set of Wikipedia articles that are candidates to represent the meaning of the anchor and, later, rank these candidates to select the most appropriate one. In this ranking process the systems rely on context information obtained from the document where the anchor is mentioned and/or from Wikipedia. In this paper we center our attention in the use of Wikipedia links as context information. In particular, we offer a review of several candidate ranking approaches in the state-of-the-art that rely on Wikipedia link information. In addition, we provide a comparative empirical evaluation of the different approaches on five different corpora: the TAC 2010 corpus and four corpora built from actual Wikipedia articles and news items.