Planning as satisfiability is known as an efficient approach to deal with many types of planning problems. However, this approach has not been competitive with the state-space based methods in temporal planning. This paper describes ITSAT as an efficient SAT-based (satisfiability based) temporal planner capable of temporally expressive planning. The novelty of ITSAT lies in the way it handles temporal constraints of given problems without getting involved in the difficulties of introducing continuous variables into the corresponding satisfiability problems. We also show how, as in SAT-based classical planning, carefully devised preprocessing and encoding schemata can considerably improve the efficiency of SAT-based temporal planning. We present two preprocessing methods for mutex relation extraction and action compression. We also show that the separation of causal and temporal reasoning enables us to employ compact encodings that are based on the concept of parallel execution semantics. Although such encodings have been shown to be quite effective in classical planning, ITSAT is the first temporal planner utilizing this type of encoding. Our empirical results show that not only does ITSAT outperform the state-of-the-art temporally expressive planners, it is also competitive with the fast temporal planners that cannot handle required concurrency.

To date, there have been massive Semi-Structured Documents (SSDs) during the evolution of the Internet. These SSDs contain both unstructured features (e.g., plain text) and metadata (e.g., tags). Most previous works focused on modeling the unstructured text, and recently, some other methods have been proposed to model the unstructured text with specific tags. To build a general model for SSDs remains an important problem in terms of both model fitness and efficiency. We propose a novel method to model the SSDs by a so-called Tag-Weighted Topic Model (TWTM). TWTM is a framework that leverages both the tags and words information, not only to learn the document-topic and topic-word distributions, but also to infer the tag-topic distributions for text mining tasks. We present an efficient variational inference method with an EM algorithm for estimating the model parameters. Meanwhile, we propose three large-scale solutions for our model under the MapReduce distributed computing platform for modeling large-scale SSDs. The experimental results show the effectiveness, efficiency and the robustness by comparing our model with the state-of-the-art methods in document modeling, tags prediction and text classification. We also show the performance of the three distributed solutions in terms of time and accuracy on document modeling.

Previously, we proposed a physically-inspired method to construct data points into an effective in-tree (IT) structure, in which the underlying cluster structure in the dataset is well revealed. Although there are some edges in the IT structure requiring to be removed, such undesired edges are generally distinguishable from other edges and thus are easy to be determined. For instance, when the IT structures for the 2-dimensional (2D) datasets are graphically presented, those undesired edges can be easily spotted and interactively determined. However, in practice, there are many datasets that do not lie in the 2D Euclidean space, thus their IT structures cannot be graphically presented. But if we can effectively map those IT structures into a visualized space in which the salient features of those undesired edges are preserved, then the undesired edges in the IT structures can still be visually determined in a visualization environment. Previously, this purpose was reached by our method called IT-map. The outstanding advantage of IT-map is that clusters can still be found even with the so-called crowding problem in the embedding. In this paper, we propose another method, called IT-Dendrogram, to achieve the same goal through an effective combination of the IT structure and the single link hierarchical clustering (SLHC) method. Like IT-map, IT-Dendrogram can also effectively represent the IT structures in a visualization environment, whereas using another form, called the Dendrogram. IT-Dendrogram can serve as another visualization method to determine the undesired edges in the IT structures and thus benefit the IT-based clustering analysis. This was demonstrated on several datasets with different shapes, dimensions, and attributes. Unlike IT-map, IT-Dendrogram can always avoid the crowding problem, which could help users make more reliable cluster analysis in certain problems.

Modern conflict-driven clause-learning (CDCL) Boolean SAT solvers provide efficient automatic analysis of real-world feature models (FM) of systems ranging from cars to operating systems. It is well-known that solver-based analysis of real-world FMs scale very well even though SAT instances obtained from such FMs are large, and the corresponding analysis problems are known to be NP-complete. To better understand why SAT solvers are so effective, we systematically studied many syntactic and semantic characteristics of a representative set of large real-world FMs. We discovered that a key reason why large real-world FMs are easy-to-analyze is that the vast majority of the variables in these models are unrestricted, i.e., the models are satisfiable for both true and false assignments to such variables under the current partial assignment. Given this discovery and our understanding of CDCL SAT solvers, we show that solvers can easily find satisfying assignments for such models without too many backtracks relative to the model size, explaining why solvers scale so well. Further analysis showed that the presence of unrestricted variables in these real-world models can be attributed to their high-degree of variability. Additionally, we experimented with a series of well-known non-backtracking simplifications that are particularly effective in solving FMs. The remaining variables/clauses after simplifications, called the core, are so few that they are easily solved even with backtracking, further strengthening our conclusions.

Paragraph Vectors has been recently proposed as an unsupervised method for learning distributed representations for pieces of texts. In their work, the authors showed that the method can learn an embedding of movie review texts which can be leveraged for sentiment analysis. That proof of concept, while encouraging, was rather narrow. Here we consider tasks other than sentiment analysis, provide a more thorough comparison of Paragraph Vectors to other document modelling algorithms such as Latent Dirichlet Allocation, and evaluate performance of the method as we vary the dimensionality of the learned representation. We benchmarked the models on two document similarity data sets, one from Wikipedia, one from arXiv. We observe that the Paragraph Vector method performs significantly better than other methods, and propose a simple improvement to enhance embedding quality. Somewhat surprisingly, we also show that much like word embeddings, vector operations on Paragraph Vectors can perform useful semantic results.

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing randomized matrix algorithms in large-scale parallel and distributed environments. Randomized algorithms for matrix problems have received a great deal of attention in recent years, thus far typically either in theory or in machine learning applications or with implementations on a single machine. Our main focus is on the underlying theory and practical implementation of random projection and random sampling algorithms for very large very overdetermined (i.e., overconstrained) $\ell_1$ and $\ell_2$ regression problems. Randomization can be used in one of two related ways: either to construct sub-sampled problems that can be solved, exactly or approximately, with traditional numerical methods; or to construct preconditioned versions of the original full problem that are easier to solve with traditional iterative algorithms. Theoretical results demonstrate that in near input-sparsity time and with only a few passes through the data one can obtain very strong relative-error approximate solutions, with high probability. Empirical results highlight the importance of various trade-offs (e.g., between the time to construct an embedding and the conditioning quality of the embedding, between the relative importance of computation versus communication, etc.) and demonstrate that $\ell_1$ and $\ell_2$ regression problems can be solved to low, medium, or high precision in existing distributed systems on up to terabyte-sized data.

Temporally extended actions have proven useful for reinforcement learning, but their duration also makes them valuable for efficient planning. The options framework provides a concrete way to implement and reason about temporally extended actions. Existing literature has demonstrated the value of planning with options empirically, but there is a lack of theoretical analysis formalizing when planning with options is more efficient than planning with primitive actions. We provide a general analysis of the convergence rate of a popular Approximate Value Iteration (AVI) algorithm called Fitted Value Iteration (FVI) with options. Our analysis reveals that longer duration options and a pessimistic estimate of the value function both lead to faster convergence. Furthermore, options can improve convergence even when they are suboptimal and sparsely distributed throughout the state-space. Next we consider the problem of generating useful options for planning based on a subset of landmark states. This suggests a new algorithm, Landmark-based AVI (LAVI), that represents the value function only at the landmark states. We analyze both FVI and LAVI using the proposed landmark-based options and compare the two algorithms. Our experimental results in three different domains demonstrate the key properties from the analysis. Our theoretical and experimental results demonstrate that options can play an important role in AVI by decreasing approximation error and inducing fast convergence.

Random forests are a type of ensemble method which makes predictions by combining the results of several independent trees. However, the theory of random forests has long been outpaced by their application. In this paper, we propose a novel random forests algorithm based on cooperative game theory. Banzhaf power index is employed to evaluate the power of each feature by traversing possible feature coalitions. Unlike the previously used information gain rate of information theory, which simply chooses the most informative feature, the Banzhaf power index can be considered as a metric of the importance of each feature on the dependency among a group of features. More importantly, we have proved the consistency of the proposed algorithm, named Banzhaf random forests (BRF). This theoretical analysis takes a step towards narrowing the gap between the theory and practice of random forests for classification problems. Experiments on several UCI benchmark data sets show that BRF is competitive with state-of-the-art classifiers and dramatically outperforms previous consistent random forests. Particularly, it is much more efficient than previous consistent random forests.

Mixture models are powerful statistical models used in many applications ranging from density estimation to clustering and classification. When dealing with mixture models, there are many issues that the experimenter should be aware of and needs to solve. The MixEst toolbox is a powerful and user-friendly package for MATLAB that implements several state-of-the-art approaches to address these problems. Additionally, MixEst gives the possibility of using manifold optimization for fitting the density model, a feature specific to this toolbox. MixEst simplifies using and integration of mixture models in statistical models and applications. For developing mixture models of new densities, the user just needs to provide a few functions for that statistical distribution and the toolbox takes care of all the issues regarding mixture models. MixEst is available at visionlab.ut.ac.ir/mixest and is fully documented and is licensed under GPL.

Variable selection plays an important role in the high-dimensional data analysis. However the high-dimensional data often induces the strongly correlated variables problem. In this paper, we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate. By a simulation study, we show that the strongly correlated variables problem can be better handled by the Elastic Net procedure than Lasso, ALasso and Ridge. Based on an empirical analysis, we can get that the Elastic Net procedure is particularly useful when the number of predictors $p$ is much bigger than the sample size $n$.