We demonstrate that any physical object, as long as its volume is conserved when coupled with suitable operations, provides a sophisticated decision-making capability. We consider the problem of finding, as accurately and quickly as possible, the most profitable option from a set of options that gives stochastic rewards. These decisions are made as dictated by a physical object, which is moved in a manner similar to the fluctuations of a rigid body in a tug-of-war game. Our analytical calculations validate statistical reasons why our method exhibits higher efficiency than conventional algorithms. The computing principles in modern digital paradigms have been designed to be dissociated from the underlying physics of natural phenomena [1].

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. We consider two different interpretations of the RCC8 algebra, one uses a weak connectedness relation, the other uses a strong connectedness relation. In both interpretations, we show that reasoning with topological and directional information is decidable and remains in NP. Our computational complexity results unveil the significant differences between RA and CDC, and that between weak and strong RCC8 models. Take the combination of basic RCC8 and basic CDC constraints as an example: we show that the consistency problem is in P only when we use the strong RCC8 algebra and explicitly know the corresponding basic RA constraints.

Rating Prediction is a basic problem in Recommender System, and one of the most widely used method is Factorization Machines(FM). However, traditional matrix factorization methods fail to utilize the benefit of implicit feedback, which has been proved to be important in Rating Prediction problem. In this work, we consider a specific situation, movie rating prediction, where we assume that a user's watching history has a big influence on his/her rating behavior on an item. We introduce two models, Latent Dirichlet Allocation(LDA) and word2vec, both of which perform state-of-the-art results in training latent features. Based on that, we propose two feature based models. One is the Topic-based FM Model which provides the implicit feedback to the matrix factorization, the other is the Vector-based FM Model which exploits the order info of a user's watching history resulting in better performance. Empirical results on three datasets demonstrate that our method performs better than the baseline model and confirm that Vector-based FM Model usually works better as it contains the order info.

Multi-agent Pathfinding is a relevant problem in a wide range of domains, for example in robotics and video games research. Formally, the problem considers a graph consisting of vertices and edges, and a set of agents occupying vertices. An agent can only move to an unoccupied, neighbouring vertex, and the problem of finding the minimal sequence of moves to transfer each agent from its start location to its destination is an NP-hard problem. We present Push and Rotate, a new algorithm that is complete for Multi-agent Pathfinding problems in which there are at least two empty vertices. Push and Rotate first divides the graph into subgraphs within which it is possible for agents to reach any position of the subgraph, and then uses the simple push, swap, and rotate operations to find a solution; a post-processing algorithm is also presented that eliminates redundant moves. Push and Rotate can be seen as extending Luna and Bekris's Push and Swap algorithm, which we showed to be incomplete in a previous publication. In our experiments we compare our approach with the Push and Swap, MAPP, and Bibox algorithms. The latter algorithm is restricted to a smaller class of instances as it requires biconnected graphs, but can nevertheless be considered state of the art due to its strong performance. Our experiments show that Push and Swap suffers from incompleteness, MAPP is generally not competitive with Push and Rotate, and Bibox is better than Push and Rotate on randomly generated biconnected instances, while Push and Rotate performs better on grids.

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of answering a wide range of mathematical queries automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39% of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.

We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the multi-label predictor, we instead minimize the tail sum of the singular values of the predictor in multi-label learning. Benefiting from the use of the local Rademacher complexity, our algorithm, therefore, has a sharper generalization error bound and a faster convergence rate. Compared to methods that minimize over all singular values, concentrating on the tail singular values results in better recovery of the low-rank structure of the multi-label predictor, which plays an import role in exploiting label correlations. We propose a new conditional singular value thresholding algorithm to solve the resulting objective function. Empirical studies on real-world datasets validate our theoretical results and demonstrate the effectiveness of the proposed algorithm.

In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the network in order to achieve an overall network performance superior to that of the simple diffusion LMS, albeit at the cost of increased computational overhead. In this paper, we provide analytical as well as experimental results which show that the convex regularization can be selectively applied only to some chosen nodes keeping rest of the nodes sparsity agnostic, while still enjoying the same optimum behavior as can be realized by deploying the convex regularization at all the nodes. Due to the incorporation of unregularized learning at a subset of nodes, less computational cost is needed in the proposed approach. We also provide a guideline for selection of the sparsity aware nodes and a closed form expression for the optimum regularization parameter.

This paper introduces a novel encoding of Model Based Diagnosis (MBD) to Boolean Satisfaction (SAT) focusing on minimal cardinality diagnosis. The encoding is based on a combination of sophisticated MBD preprocessing algorithms and the application of a SAT compiler which optimizes the encoding to provide more succinct CNF representations than obtained with previous works. Experimental evidence indicates that our approach is superior to all published algorithms for minimal cardinality MBD. In particular, we can determine, for the first time, minimal cardinality diagnoses for the entire standard ISCAS-85 and 74XXX benchmarks. Our results open the way to improve the state-of-the-art on a range of similar MBD problems.

It is widely acknowledged that stochastic local search (SLS) algorithms can efficiently find models for satisfiable instances of the satisfiability (SAT) problem, especially for random k-SAT instances. However, compared to random 3-SAT instances where SLS algorithms have shown great success, random k-SAT instances with long clauses remain very difficult. Recently, the notion of second level score, denoted as "score_2", was proposed for improving SLS algorithms on long-clause SAT instances, and was first used in the powerful CCASat solver as a tie breaker. In this paper, we propose three new scoring functions based on score_2. Despite their simplicity, these functions are very effective for solving random k-SAT with long clauses. The first function combines score and score_2, and the second one additionally integrates the diversification property "age". These two functions are used in developing a new SLS algorithm called CScoreSAT. Experimental results on large random 5-SAT and 7-SAT instances near phase transition show that CScoreSAT significantly outperforms previous SLS solvers. However, CScoreSAT cannot rival its competitors on random k-SAT instances at phase transition. We improve CScoreSAT for such instances by another scoring function which combines score_2 with age. The resulting algorithm HScoreSAT exhibits state-of-the-art performance on random k-SAT (k>3) instances at phase transition. We also study the computation of score_2, including its implementation and computational complexity.

We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this setting that provably can improve over passive learning. Unlike other learning settings (such as classification), in regression the passive learning rate of $O(1/\epsilon)$ cannot in general be improved upon. Nonetheless, the so-called `constant' in the rate of convergence, which is characterized by a distribution-dependent risk, can be improved in many cases. For a given distribution, achieving the optimal risk requires prior knowledge of the distribution. Following the stratification technique advocated in Monte-Carlo function integration, our active learner approaches the optimal risk using piecewise constant approximations.