We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent approximate posterior distributions, and that acts as a stochastic encoder of the data. We develop stochastic back-propagation -- rules for back-propagation through stochastic variables -- and use this to develop an algorithm that allows for joint optimisation of the parameters of both the generative and recognition model. We demonstrate on several real-world data sets that the model generates realistic samples, provides accurate imputations of missing data and is a useful tool for high-dimensional data visualisation.

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.

Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is the case in many real world problems where these latent forces exhibit periodic behaviour. Given this, we develop a new sparse representation of LFMs which considerably improves their computational efficiency, as well as broadening their applicability, in a principled way, to domains with periodic or near periodic latent forces. Our approach uses a linear basis model to approximate one generative model for each periodic force. We assume that the latent forces are generated from Gaussian process priors and develop a linear basis model which fully expresses these priors. We apply our approach to model the thermal dynamics of domestic buildings and show that it is effective at predicting day-ahead temperatures within the homes. We also apply our approach within queueing theory in which quasi-periodic arrival rates are modelled as latent forces. In both cases, we demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs. Further, we show that state estimates obtained using periodic latent force models can reduce the root mean squared error to 17% of that from non-periodic models and 27% of the nearest rival approach which is the resonator model.

In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a physical system. We augment the linear PDE with a functional that accounts for the uncertainty in the mathematical model and is modeled as a {\em Gaussian process}. This gives rise to a stochastic PDE which is characterized by the Gaussian functional. We develop a {\em functional Gaussian process regression} method to determine the posterior mean and covariance of the Gaussian functional, thereby solving the stochastic PDE to obtain the posterior distribution for our prediction of the physical state. Our method has the following features which distinguish itself from other regression methods. First, it incorporates both the mathematical model and the observations into the regression procedure. Second, it can handle the observations given in the form of linear functionals of the field variable. Third, the method is non-parametric in the sense that it provides a systematic way to optimally determine the prior covariance operator of the Gaussian functional based on the observations. Fourth, it provides the posterior distribution quantifying the magnitude of uncertainty in our prediction of the physical state. We present numerical results to illustrate these features of the method and compare its performance to that of the standard Gaussian process regression.

In order to improve children speech therapy, we develop a Fuzzy Expert System based on a speech therapy guide. This guide, write in natural language, was formalized using fuzzy logic paradigm. In this manner we obtain a knowledge base with over 150 rules and 19 linguistic variables. All these researches, including expert system validation, are part of TERAPERS project.

We study the computational complexity of controlling the result of an election by breaking ties strategically. This problem is equivalent to the problem of deciding the winner of an election under parallel universes tie-breaking. When the chair of the election is only asked to break ties to choose between one of the co-winners, the problem is trivially easy. However, in multi-round elections, we prove that it can be NP-hard for the chair to compute how to break ties to ensure a given result. Additionally, we show that the form of the tie-breaking function can increase the opportunities for control. Indeed, we prove that it can be NP-hard to control an election by breaking ties even with a two-stage voting rule.

In this paper we present architecture of a fuzzy expert system used for therapy of dyslalic children. With fuzzy approach we can create a better model for speech therapist decisions. A software interface was developed for validation of the system. The main objectives of this task are: personalized therapy (the therapy must be in according with child's problems level, context and possibilities), speech therapist assistant (the expert system offer some suggestion regarding what exercises are better for a specific moment and from a specific child), (self) teaching (when system's conclusion is different that speech therapist's conclusion the last one must have the knowledge base change possibility).

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.

We present a system that demonstrates how the compositional structure of events, in concert with the compositional structure of language, can interplay with the underlying focusing mechanisms in video action recognition, thereby providing a medium, not only for top-down and bottom-up integration, but also for multi-modal integration between vision and language. We show how the roles played by participants (nouns), their characteristics (adjectives), the actions performed (verbs), the manner of such actions (adverbs), and changing spatial relations between participants (prepositions) in the form of whole sentential descriptions mediated by a grammar, guides the activity-recognition process. Further, the utility and expressiveness of our framework is demonstrated by performing three separate tasks in the domain of multi-activity videos: sentence-guided focus of attention, generation of sentential descriptions of video, and query-based video search, simply by leveraging the framework in different manners.