A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightforward to implement, since the RKHS moves can be integrated out analytically: our proposal distribution in the original space is a normal distribution whose mean and covariance depend on where the current sample lies in the support of the target distribution, and adapts to its local covariance structure. Furthermore, the procedure requires neither gradients nor any other higher order information about the target, making it particularly attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive Metropolis-Hastings outperforms competing fixed and adaptive samplers on multivariate, highly nonlinear target distributions, arising in both real-world and synthetic examples. Code may be downloaded at https://github.com/karlnapf/kameleon-mcmc.

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation and the low-rank matrix recovery problem is solved through minimization of the nuclear norm regularized problem. However, a major limitation of nuclear norm minimization is that all the singular values are simultaneously minimized and the rank may not be well approximated \cite{hu2012fast}. Correspondingly, in this paper, we propose a new multi-stage algorithm, which makes use of the concept of Truncated Nuclear Norm Regularization (TNNR) proposed in \citep{hu2012fast} and Iterative Support Detection (ISD) proposed in \citep{wang2010sparse} to overcome the above limitation. Besides matrix completion problems considered in \citep{hu2012fast}, the proposed method can be also extended to the general low-rank matrix recovery problems. Extensive experiments well validate the superiority of our new algorithms over other state-of-the-art methods.

Many applications, ranging from video games to dynamic robotics, require solving single-agent, deterministic search problems in partially known environments under very tight time constraints. Real-Time Heuristic Search (RTHS) algorithms are specifically designed for those applications. As a subroutine, most of them invoke a standard, but bounded, search algorithm that searches for the goal. In this paper we present FRIT, a simple approach for single-agent deterministic search problems under tight constraints and partially known environments that unlike traditional RTHS does not search for the goal but rather searches for a path that connects the current state with a so-called ideal tree T . When the agent observes that an arc in the tree cannot be traversed in the actual environment, it removes such an arc from T and then carries out a reconnection search whose objective is to find a path between the current state and any node in T . The reconnection search is done using an algorithm that is passed as a parameter to FRIT. If such a parameter is an RTHS algorithm, then the resulting algorithm can be an RTHS algorithm. We show, in addition, that FRIT may be fed with a (bounded) complete blind-search algorithm. We evaluate our approach over grid pathfinding benchmarks including game maps and mazes. Our results show that FRIT, used with RTAA*, a standard RTHS algorithm, outperforms RTAA* significantly; by one order of magnitude under tight time constraints. In addition, FRIT(daRTAA*) substantially outperforms daRTAA*, a state-of-the-art RTHS algorithm, usually obtaining solutions 50% cheaper on average when performing the same search effort. Finally, FRIT(BFS), i.e., FRIT using breadth-first-search, obtains best-quality solutions when time is limited compared to Adaptive A* and Repeated A*. Finally we show that Bug2, a pathfinding-specific navigation algorithm, outperforms FRIT(BFS) when planning time is extremely limited, but when given more time, the situation reverses.

Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied to them scale well. We propose a fast non-iterative approximate inference method that uses a feedforward network to implement efficient exact sampling from the variational posterior. The model and this inference network are trained jointly by maximizing a variational lower bound on the log-likelihood. Although the naive estimator of the inference model gradient is too high-variance to be useful, we make it practical by applying several straightforward model-independent variance reduction techniques. Applying our approach to training sigmoid belief networks and deep autoregressive networks, we show that it outperforms the wake-sleep algorithm on MNIST and achieves state-of-the-art results on the Reuters RCV1 document dataset.

Games have always been a popular test bed for artificial intelligence techniques. Game developers are always in constant search for techniques that can automatically create computer games minimizing the developer's task. In this work we present an evolutionary strategy based solution towards the automatic generation of two player board games. To guide the evolutionary process towards games, which are entertaining, we propose a set of metrics. These metrics are based upon different theories of entertainment in computer games. This work also compares the entertainment value of the evolved games with the existing popular board based games. Further to verify the entertainment value of the evolved games with the entertainment value of the human user a human user survey is conducted. In addition to the user survey we check the learnability of the evolved games using an artificial neural network based controller. The proposed metrics and the evolutionary process can be employed for generating new and entertaining board games, provided an initial search space is given to the evolutionary algorithm.

In this paper we show how the combination of Behaviour Tree and Utility Based AI architecture can be used to design more realistic bots for Military Simulators. In this work, we have designed a mathematical model of a simulator system which in turn helps in analyzing the results and finding out the various spaces on which our favorable situation might exist, this is done geometrically. In the mathematical model, we have explained the matrix formation and its significance followed up in dynamic programming approach we explained the possible graph formation which will led improvisation of AI, latter we explained the possible geometrical structure of the matrix operations and its impact on a particular decision, we also explained the conditions under which it tend to fail along with a possible solution in future works.

When solving instances of problem domains that feature a large branching factor, A* may generate a large number of nodes whose cost is greater than the cost of the optimal solution. We designate such nodes as surplus. Generating surplus nodes and adding them to the OPEN list may dominate both time and memory of the search. A recently introduced variant of A* called Partial Expansion A* (PEA*) deals with the memory aspect of this problem. When expanding a node n, PEA* generates all of its children and puts into OPEN only the children with f = f (n). n is re-inserted in the OPEN list with the f -cost of the best discarded child. This guarantees that surplus nodes are not inserted into OPEN. In this paper, we present a novel variant of A* called Enhanced Partial Expansion A* (EPEA*) that advances the idea of PEA* to address the time aspect. Given a priori domain- and heuristic- specific knowledge, EPEA* generates only the nodes with f = f(n). Although EPEA* is not always applicable or practical, we study several variants of EPEA*, which make it applicable to a large number of domains and heuristics. In particular, the ideas of EPEA* are applicable to IDA* and to the domains where pattern databases are traditionally used. Experimental studies show significant improvements in run-time and memory performance for several standard benchmark applications. We provide several theoretical studies to facilitate an understanding of the new algorithm.

Many problems in machine learning and other fields can be (re)for-mulated as linearly constrained separable convex programs. In most of the cases, there are multiple blocks of variables. However, the traditional alternating direction method (ADM) and its linearized version (LADM, obtained by linearizing the quadratic penalty term) are for the two-block case and cannot be naively generalized to solve the multi-block case. So there is great demand on extending the ADM based methods for the multi-block case. In this paper, we propose LADM with parallel splitting and adaptive penalty (LADMPSAP) to solve multi-block separable convex programs efficiently. When all the component objective functions have bounded subgradients, we obtain convergence results that are stronger than those of ADM and LADM, e.g., allowing the penalty parameter to be unbounded and proving the sufficient and necessary conditions} for global convergence. We further propose a simple optimality measure and reveal the convergence rate of LADMPSAP in an ergodic sense. For programs with extra convex set constraints, with refined parameter estimation we devise a practical version of LADMPSAP for faster convergence. Finally, we generalize LADMPSAP to handle programs with more difficult objective functions by linearizing part of the objective function as well. LADMPSAP is particularly suitable for sparse representation and low-rank recovery problems because its subproblems have closed form solutions and the sparsity and low-rankness of the iterates can be preserved during the iteration. It is also highly parallelizable and hence fits for parallel or distributed computing. Numerical experiments testify to the advantages of LADMPSAP in speed and numerical accuracy.

In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear norm regularizes all singular values equally, which is however not flexible enough to fit real scenarios. Weighted nuclear norm minimization (WNNM) is a natural extension and generalization of NNM. By assigning properly different weights to different singular values, WNNM can lead to state-of-the-art results in applications such as image denoising. Nevertheless, so far the global optimal solution of WNNM problem is not completely solved yet due to its non-convexity in general cases. In this article, we study the theoretical properties of WNNM and prove that WNNM can be equivalently transformed into a quadratic programming problem with linear constraints. This implies that WNNM is equivalent to a convex problem and its global optimum can be readily achieved by off-the-shelf convex optimization solvers. We further show that when the weights are non-descending, the globally optimal solution of WNNM can be obtained in closed-form.

We introduce a deep, generative autoencoder capable of learning hierarchies of distributed representations from data. Successive deep stochastic hidden layers are equipped with autoregressive connections, which enable the model to be sampled from quickly and exactly via ancestral sampling. We derive an efficient approximate parameter estimation method based on the minimum description length (MDL) principle, which can be seen as maximising a variational lower bound on the log-likelihood, with a feedforward neural network implementing approximate inference. We demonstrate state-of-the-art generative performance on a number of classic data sets: several UCI data sets, MNIST and Atari 2600 games.