Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we propose a framework for optimizing orthogonal matrices, that is the parallel of coordinate-descent in Euclidean spaces. It is based on {\em Givens-rotations}, a fast-to-compute operation that affects a small number of entries in the learned matrix, and preserves orthogonality. We show two applications of this approach: an algorithm for tensor decomposition that is used in learning mixture models, and an algorithm for sparse-PCA. We study the parameter regime where a Givens rotation approach converges faster and achieves a superior model on a genome-wide brain-wide mRNA expression dataset.

For almost two decades, monotonic, or ``delete free,'' relaxation has been one of the key auxiliary tools in the practice of domain-independent deterministic planning. In the particular contexts of both satisficing and optimal planning, it underlies most state-of-the-art heuristic functions. While satisficing planning for monotonic tasks is polynomial-time, optimal planning for monotonic tasks is NP-equivalent. Here we establish both negative and positive results on the complexity of some wide fragments of optimal monotonic planning, with the fragments being defined around the causal graph topology. Our results shed some light on the link between the complexity of general optimal planning and the complexity of optimal planning for the respective monotonic relaxations.

VT (Viterbi training), or hard EM, is an efficient way of parameter learning for probabilistic models with hidden variables. Given an observation $y$, it searches for a state of hidden variables $x$ that maximizes $p(x,y \mid \theta)$ by coordinate ascent on parameters $\theta$ and $x$. In this paper we introduce VT to PRISM, a logic-based probabilistic modeling system for generative models. VT improves PRISM in three ways. First VT in PRISM converges faster than EM in PRISM due to the VT's termination condition. Second, parameters learned by VT often show good prediction performance compared to those learned by EM. We conducted two parsing experiments with probabilistic grammars while learning parameters by a variety of inference methods, i.e.\ VT, EM, MAP and VB. The result is that VT achieved the best parsing accuracy among them in both experiments. Also we conducted a similar experiment for classification tasks where a hidden variable is not a prediction target unlike probabilistic grammars. We found that in such a case VT does not necessarily yield superior performance. Third since VT always deals with a single probability of a single explanation, Viterbi explanation, the exclusiveness condition that is imposed on PRISM programs is no more required if we learn parameters by VT. Last but not least we can say that as VT in PRISM is general and applicable to any PRISM program, it largely reduces the need for the user to develop a specific VT algorithm for a specific model. Furthermore since VT in PRISM can be used just by setting a PRISM flag appropriately, it makes VT easily accessible to (probabilistic) logic programmers. To appear in Theory and Practice of Logic Programming (TPLP).

Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we introduce novel statistics based on block sizes for representing sample sets of partitionings and feature allocations. We develop an element-based definition of entropy to quantify segmentation among their elements. Then we propose a simple algorithm called entropy agglomeration (EA) to summarize and visualize this information. Experiments on various infinite mixture posteriors as well as a feature allocation dataset demonstrate that the proposed statistics are useful in practice.

This article presents a probabilistic sub-tree alignment model and its application to tree-to-tree machine translation. Unlike previous work, we do not resort to surface heuristics or expensive annotated data, but instead derive an unsupervised model to infer the syntactic correspondence between two languages. More importantly, the developed model is syntactically-motivated and does not rely on word alignments. As a by-product, our model outputs a sub-tree alignment matrix encoding a large number of diverse alignments between syntactic structures, from which machine translation systems can efficiently extract translation rules that are often filtered out due to the errors in 1-best alignment. Experimental results show that the proposed approach outperforms three state-of-the-art baseline approaches in both alignment accuracy and grammar quality. When applied to machine translation, our approach yields a +1.0 BLEU improvement and a -0.9 TER reduction on the NIST machine translation evaluation corpora. With tree binarization and fuzzy decoding, it even outperforms a state-of-the-art hierarchical phrase-based system.

We present NaturalOWL, a natural language generation system that produces texts describing individuals or classes of OWL ontologies. Unlike simpler OWL verbalizers, which typically express a single axiom at a time in controlled, often not entirely fluent natural language primarily for the benefit of domain experts, we aim to generate fluent and coherent multi-sentence texts for end-users. With a system like NaturalOWL, one can publish information in OWL on the Web, along with automatically produced corresponding texts in multiple languages, making the information accessible not only to computer programs and domain experts, but also end-users. We discuss the processing stages of NaturalOWL, the optional domain-dependent linguistic resources that the system can use at each stage, and why they are useful. We also present trials showing that when the domain-dependent llinguistic resources are available, NaturalOWL produces significantly better texts compared to a simpler verbalizer, and that the resources can be created with relatively light effort.

Symmetric binary matrices representing relations among entities are commonly collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being in inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By using a logistic mapping function from the probability matrix space to the latent relational space, we obtain a flexible and computational tractable formulation. Employing P\`olya-Gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide some theoretical results on flexibility of the model, and illustrate performance via simulation experiments. We also consider an application to co-movements in world financial markets.

Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic composition, including grammatical representations, probabilistic methods, neural networks, symbolic rule-based systems, constraint programming and evolutionary algorithms. This survey aims to be a comprehensive account of research on algorithmic composition, presenting a thorough view of the field for researchers in Artificial Intelligence.

To solve the big topic modeling problem, we need to reduce both time and space complexities of batch latent Dirichlet allocation (LDA) algorithms. Although parallel LDA algorithms on the multi-processor architecture have low time and space complexities, their communication costs among processors often scale linearly with the vocabulary size and the number of topics, leading to a serious scalability problem. To reduce the communication complexity among processors for a better scalability, we propose a novel communication-efficient parallel topic modeling architecture based on power law, which consumes orders of magnitude less communication time when the number of topics is large. We combine the proposed communication-efficient parallel architecture with the online belief propagation (OBP) algorithm referred to as POBP for big topic modeling tasks. Extensive empirical results confirm that POBP has the following advantages to solve the big topic modeling problem: 1) high accuracy, 2) communication-efficient, 3) fast speed, and 4) constant memory usage when compared with recent state-of-the-art parallel LDA algorithms on the multi-processor architecture.

We present a newly developed Replica Exchange algorithm using q -Gaussian Swarm Quantum Particle Optimization (REX@q-GSQPO) method for solving the problem of finding the global optimum. The basis of the algorithm is to run multiple copies of independent swarms at different values of q parameter. Based on an energy criterion, chosen to satisfy the detailed balance, we are swapping the particle coordinates of neighboring swarms at regular iteration intervals. The swarm replicas with high q values are characterized by high diversity of particles allowing escaping local minima faster, while the low q replicas, characterized by low diversity of particles, are used to sample more efficiently the local basins. We compare the new algorithm with the standard Gaussian Swarm Quantum Particle Optimization (GSQPO) and q-Gaussian Swarm Quantum Particle Optimization (q-GSQPO) algorithms, and we found that the new algorithm is more robust in terms of the number of fitness function calls, and more efficient in terms ability convergence to the global minimum. In additional, we also provide a method of optimally allocating the swarm replicas among different q values. Our algorithm is tested for three benchmark functions, which are known to be multimodal problems, at different dimensionalities. In addition, we considered a polyalanine peptide of 12 residues modeled using a G\=o coarse-graining potential energy function.