We study the estimation of $\beta$ for the nonlinear model $y = f(X\sp{\top}\beta) + \epsilon$ when $f$ is a nonlinear transformation that is known, $\beta$ has sparse nonzero coordinates, and the number of observations can be much smaller than that of parameters ($n\ll p$). We show that in order to bound the $L_2$ error of the $L_0$ regularized estimator $\hat\beta$, i.e., $\|\hat\beta - \beta\|_2$, it is sufficient to establish two conditions. Based on this, we obtain bounds of the $L_2$ error for (1) $L_0$ regularized maximum likelihood estimation (MLE) for exponential linear models and (2) $L_0$ regularized least square (LS) regression for the more general case where $f$ is analytic. For the analytic case, we rely on power series expansion of $f$, which requires taking into account the singularities of $f$.

This paper proposes the application of particle swarm optimization (PSO) to the problem of finite element model (FEM) selection. This problem arises when a choice of the best model for a system has to be made from set of competing models, each developed a priori from engineering judgment. PSO is a population-based stochastic search algorithm inspired by the behaviour of biological entities in nature when they are foraging for resources. Each potentially correct model is represented as a particle that exhibits both individualistic and group behaviour. Each particle moves within the model search space looking for the best solution by updating the parameters values that define it. The most important step in the particle swarm algorithm is the method of representing models which should take into account the number, location and variables of parameters to be updated. One example structural system is used to show the applicability of PSO in finding an optimal FEM. An optimal model is defined as the model that has the least number of updated parameters and has the smallest parameter variable variation from the mean material properties. Two different objective functions are used to compare performance of the PSO algorithm.

In this paper the behavior of three combinational rules for temporal/sequential attribute data fusion for target type estimation are analyzed. The comparative analysis is based on: Dempster's fusion rule proposed in Dempster-Shafer Theory; Proportional Conflict Redistribution rule no. 5 (PCR5), proposed in Dezert-Smarandache Theory and one alternative class fusion rule, connecting the combination rules for information fusion with particular fuzzy operators, focusing on the t-norm based Conjunctive rule as an analog of the ordinary conjunctive rule and t-conorm based Disjunctive rule as an analog of the ordinary disjunctive rule. The way how different t-conorms and t-norms functions within TCN fusion rule influence over target type estimation performance is studied and estimated.

Classification is the problem of categorising data in one of two or more possible classes. In the classical supervised learning framework, examples of each class have already been obtained and the task of the decision maker is to accurately categorise new observations, whose class is unknown. The accuracy is either measured in terms of the rate of misclassification, or in terms of the average cost, for problems where different types of errors carry different costs. In that setting, the problem has three phases: (a) the collection of training data, (b) the estimation of a decision rule based on the training data and (c) the application 1 of the decision rule to new data. Typically, the decision rule remains fixed after the second step.

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corresponding to Gaussian approximations minimizing relative entropy). It is shown how this can be used to build a heuristic approximation to the maximum relationship over a finite set of Gaussian variables, allowing approximate inference by Expectation Propagation on such quantities.

We describe a method for inferring linear causal relations among multi-dimensional variables. The idea is to use an asymmetry between the distributions of cause and effect that occurs if both the covariance matrix of the cause and the structure matrix mapping cause to the effect are independently chosen. The method works for both stochastic and deterministic causal relations, provided that the dimensionality is sufficiently high (in some experiments, 5 was enough). It is applicable to Gaussian as well as non-Gaussian data.

The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result is completely general. No independence, ergodicity, stationarity, identifiability, or other assumption on the model class need to be made. More formally, we show that for any countable class of models, the distributions selected by MDL (or MAP) asymptotically predict (merge with) the true measure in the class in total variation distance. Implications for non-i.i.d. domains like time-series forecasting, discriminative learning, and reinforcement learning are discussed.

Recent research in robot exploration and mapping has focused on sampling environmental hotspot fields. This exploration task is formalized by Low, Dolan, and Khosla (2008) in a sequential decision-theoretic planning under uncertainty framework called MASP. The time complexity of solving MASP approximately depends on the map resolution, which limits its use in large-scale, high-resolution exploration and mapping. To alleviate this computational difficulty, this paper presents an information-theoretic approach to MASP (iMASP) for efficient adaptive path planning; by reformulating the cost-minimizing iMASP as a reward-maximizing problem, its time complexity becomes independent of map resolution and is less sensitive to increasing robot team size as demonstrated both theoretically and empirically. Using the reward-maximizing dual, we derive a novel adaptive variant of maximum entropy sampling, thus improving the induced exploration policy performance. It also allows us to establish theoretical bounds quantifying the performance advantage of optimal adaptive over non-adaptive policies and the performance quality of approximately optimal vs. optimal adaptive policies. We show analytically and empirically the superior performance of iMASP-based policies for sampling the log-Gaussian process to that of policies for the widely-used Gaussian process in mapping the hotspot field. Lastly, we provide sufficient conditions that, when met, guarantee adaptivity has no benefit under an assumed environment model.

Grid environment is a service oriented infrastructure in which many heterogeneous resources participate to provide the high performance computation. One of the bug issues in the grid environment is the vagueness and uncertainty between advertised resources and requested resources. Furthermore, in an environment such as grid dynamicity is considered as a crucial issue which must be dealt with. Classical rough set have been used to deal with the uncertainty and vagueness. But it can just be used on the static systems and can not support dynamicity in a system. In this work we propose a solution, called Dynamic Rough Set Resource Discovery (DRSRD), for dealing with cases of vagueness and uncertainty problems based on Dynamic rough set theory which considers dynamic features in this environment. In this way, requested resource properties have a weight as priority according to which resource matchmaking and ranking process is done. We also report the result of the solution obtained from the simulation in GridSim simulator. The comparison has been made between DRSRD, classical rough set theory based algorithm, and UDDI and OWL S combined algorithm. DRSRD shows much better precision for the cases with vagueness and uncertainty in a dynamic system such as the grid rather than the classical rough set theory based algorithm, and UDDI and OWL S combined algorithm.

This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations from a sensor array. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization procedure based on recent tools of finite random matrix theory, in conjunction with the maximum entropy principle, is used to compute the hypothesis selection criterion. Quite remarkably, explicit expressions for the Bayesian detector are derived which enable to decide on the presence of signal sources in a noisy wireless environment. The proposed Bayesian detector is shown to outperform the classical power detector when the noise power is known and provides very good performance for limited knowledge on the noise power. Simulations corroborate the theoretical results and quantify the gain achieved using the proposed Bayesian framework.