Maximum likelihood is the most widely used statistical estimation technique. Recent work by Jiao, Venkat, Han, and Weissman [1] introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements - both in theory and in practice - over the maximum likelihood estimator (MLE), particularly in high dimensional scenarios involving parameter dimension comparable to or larger than the number of samples. This approach to estimation, building on results from approximation theory, is shown to yield minimax rate-optimal estimators for a wide class of functionals, implementable with modest computational requirements. In a nutshell, a message of this recent work is that, for a wide class of functionals, the performance of these essentially optimal estimators with n samples is comparable to that of the MLE with nlnn samples. In the present paper, we highlight the applicability of the aforementioned methodology to statistical problems beyond functional estimation, and show that it can yield substantial gains. For example, we demonstrate that for learning tree-structured graphical models, our approach achieves a significant reduction of the required data size compared with the classical Chow-Liu algorithm, which is an implementation of the MLE, to achieve the same accuracy. The key step in improving the Chow-Liu algorithm is to replace the empirical mutual information with the estimator for mutual information proposed in [1]. Further, applying the same replacement approach to classical Bayesian network classification, the resulting classifiers uniformly outperform the previous classifiers on 26 widely used datasets.

Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging problem lacking an analytical solution. We derive a new expectation maximization (EM) type algorithm that produce maximum likelihood estimates of the model parameters. Our development hinges upon recent progress in combining particle filters with Markov chain Monte Carlo methods in solving the nonlinear state smoothing problem inherent in the EM formulation. Key to our development is that we exploit a conditionally linear Gaussian substructure in the model, allowing for an efficient algorithm.

A difficult task in modeling with Bayesian networks is the elicitation of numerical parameters of Bayesian networks. A large number of parameters is needed to specify a conditional probability table (CPT) that has a larger parent set. In this paper we show that, most CPTs from real applications of Bayesian networks can actually be very well approximated by tables that require substantially less parameters. This observation has practical consequence not only for model elicitation but also for efficient probabilistic reasoning with these networks.

Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example of Expectation Propagation, before establishing the connection with the other approximation methods. Corrections by expansion about the expectation propagation are then explained. Finally some advanced inference topics and applications are explored in the final sections.

Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each depending on two specific labels. Intuitively, the more pairwise terms are used, the better the expected accuracy. However, there is currently no theoretical account of this intuition. This paper takes a significant step in this direction. We formulate the problem as classifying the vertices of a known graph $G=(V,E)$, where the vertices and edges of the graph are labelled and correlate semi-randomly with the ground truth. We show that the prospects for achieving low expected Hamming error depend on the structure of the graph $G$ in interesting ways. For example, if $G$ is a very poor expander, like a path, then large expected Hamming error is inevitable. Our main positive result shows that, for a wide class of graphs including 2D grid graphs common in machine vision applications, there is a polynomial-time algorithm with small and information-theoretically near-optimal expected error. Our results provide a first step toward a theoretical justification for the empirical success of the efficient approximate inference algorithms that are used for structured prediction in models where exact inference is intractable.

Gibbs sampling is a workhorse for Bayesian inference but has several limitations when used for parameter estimation, and is often much slower than non-sampling inference methods. SAME (State Augmentation for Marginal Estimation) \cite{Doucet99,Doucet02} is an approach to MAP parameter estimation which gives improved parameter estimates over direct Gibbs sampling. SAME can be viewed as cooling the posterior parameter distribution and allows annealed search for the MAP parameters, often yielding very high quality (lower loss) estimates. But it does so at the expense of additional samples per iteration and generally slower performance. On the other hand, SAME dramatically increases the parallelism in the sampling schedule, and is an excellent match for modern (SIMD) hardware. In this paper we explore the application of SAME to graphical model inference on modern hardware. We show that combining SAME with factored sample representation (or approximation) gives throughput competitive with the fastest symbolic methods, but with potentially better quality. We describe experiments on Latent Dirichlet Allocation, achieving speeds similar to the fastest reported methods (online Variational Bayes) and lower cross-validated loss than other LDA implementations. The method is simple to implement and should be applicable to many other models.

In this study, we enrich the framework of nonparametric kernel Bayesian inference via the flexible incorporation of certain probabilistic models, such as additive Gaussian noise models. Nonparametric inference expressed in terms of kernel means, which is called kernel Bayesian inference, has been studied using basic rules such as the kernel sum rule (KSR), kernel chain rule, kernel product rule, and kernel Bayes' rule (KBR). However, the current framework used for kernel Bayesian inference deals only with nonparametric inference and it cannot allow inference when combined with probabilistic models. In this study, we introduce a novel KSR, called model-based KSR (Mb-KSR), which exploits the knowledge obtained from some probabilistic models of conditional distributions. The incorporation of Mb-KSR into nonparametric kernel Bayesian inference facilitates more flexible kernel Bayesian inference than nonparametric inference. We focus on combinations of Mb-KSR, Non-KSR, and KBR, and we propose a filtering algorithm for state space models, which combines nonparametric learning of the observation process using kernel means and additive Gaussian noise models of the transition dynamics. The idea of the Mb-KSR for additive Gaussian noise models can be extended to more general noise model cases, including a conjugate pair with a positive-definite kernel and a probabilistic model.

The Infinite Relational Model (IRM) is a probabilistic model for relational data clustering that partitions objects into clusters based on observed relationships. This paper presents Averaged CVB (ACVB) solutions for IRM, convergence-guaranteed and practically useful fast Collapsed Variational Bayes (CVB) inferences. We first derive ordinary CVB and CVB0 for IRM based on the lower bound maximization. CVB solutions yield deterministic iterative procedures for inferring IRM given the truncated number of clusters. Our proposal includes CVB0 updates of hyperparameters including the concentration parameter of the Dirichlet Process, which has not been studied in the literature. To make the CVB more practically useful, we further study the CVB inference in two aspects. First, we study the convergence issues and develop a convergence-guaranteed algorithm for any CVB-based inferences called ACVB, which enables automatic convergence detection and frees non-expert practitioners from difficult and costly manual monitoring of inference processes. Second, we present a few techniques for speeding up IRM inferences. In particular, we describe the linear time inference of CVB0, allowing the IRM for larger relational data uses. The ACVB solutions of IRM showed comparable or better performance compared to existing inference methods in experiments, and provide deterministic, faster, and easier convergence detection.

Knowledge-based or Artificial Intelligence techniques are used increasingly as alternatives to more classical techniques to model ENVIRONMENTAL SYSTEMS. Use of Artificial Intelligence (AI) in environmental modelling has increased with recognition of its potential. In this paper we examine the DIFFERENT TECHNIQUES of Artificial intelligence with profound examples of human perception, learning and reasoning to solve complex problems. However with the increase of complexity better methods are required. Keeping in view of the above some researchers introduced the idea of hybrid mechanism in which two or more methods can be combined which seems to be a positive effort for creating a more complex; advanced and intelligent system which has the capability to in- cooperate human decisions thus driving the landscape changes.

Agent programming is mostly a symbolic discipline and, as such, draws little benefits from probabilistic areas as machine learning and graphical models. However, the greatest objective of agent research is the achievement of autonomy in dynamical and complex environments --- a goal that implies embracing uncertainty and therefore the entailed representations, algorithms and techniques. This paper proposes an innovative and conflict free two layer approach to agent programming that uses already established methods and tools from both symbolic and probabilistic artificial intelligence. Moreover, this framework is illustrated by means of a widely used agent programming example, GoldMiners.