RGB-D cameras, which give an RGB image to- gether with depths, are becoming increasingly popular for robotic perception. In this paper, we address the task of detecting commonly found objects in the 3D point cloud of indoor scenes obtained from such cameras. Our method uses a graphical model that captures various features and contextual relations, including the local visual appearance and shape cues, object co-occurence relationships and geometric relationships. With a large number of object classes and relations, the model's parsimony becomes important and we address that by using multiple types of edge potentials. We train the model using a maximum-margin learning approach. In our experiments over a total of 52 3D scenes of homes and offices (composed from about 550 views), we get a performance of 84.06% and 73.38% in labeling office and home scenes respectively for 17 object classes each. We also present a method for a robot to search for an object using the learned model and the contextual information available from the current labelings of the scene. We applied this algorithm successfully on a mobile robot for the task of finding 12 object classes in 10 different offices and achieved a precision of 97.56% with 78.43% recall.

We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes. Due to the inherent conjugacy of the GPs, one can analytically marginalize the GPs and compute the conditional likelihood of the observations given the partition tree. This property allows for efficient inference of the partition itself, for which we employ graph-theoretic techniques. We apply the multiresolution GP to the analysis of Magnetoencephalography (MEG) recordings of brain activity.

Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alpha-mixtures, with a particular form of mixing component relating to each agent's wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts.

The technological applications of hidden Markov models have been extremely diverse and successful, including natural language processing, gesture recognition, gene sequencing, and Kalman filtering of physical measurements. HMMs are highly non-linear statistical models, and just as linear models are amenable to linear algebraic techniques, non-linear models are amenable to commutative algebra and algebraic geometry. This paper closely examines HMMs in which all the hidden random variables are binary. Its main contributions are (1) a birational parametrization for every such HMM, with an explicit inverse for recovering the hidden parameters in terms of observables, (2) a semialgebraic model membership test for every such HMM, and (3) minimal defining equations for the 4-node fully binary model, comprising 21 quadrics and 29 cubics, which were computed using Grobner bases in the cumulant coordinates of Sturmfels and Zwiernik. The new model parameters in (1) are rationally identifiable in the sense of Sullivant, Garcia-Puente, and Spielvogel, and each model's Zariski closure is therefore a rational projective variety of dimension 5. Grobner basis computations for the model and its graph are found to be considerably faster using these parameters. In the case of two hidden states, item (2) supersedes a previous algorithm of Schonhuth which is only generically defined, and the defining equations (3) yield new invariants for HMMs of all lengths $\geq 4$. Such invariants have been used successfully in model selection problems in phylogenetics, and one can hope for similar applications in the case of HMMs.

A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In regular statistical models, the Bayes free energy, which is defined by the minus logarithm of Bayes marginal likelihood, can be asymptotically approximated by the Schwarz Bayes information criterion (BIC), whereas in singular models such approximation does not hold. Recently, it was proved that the Bayes free energy of a singular model is asymptotically given by a generalized formula using a birational invariant, the real log canonical threshold (RLCT), instead of half the number of parameters in BIC. Theoretical values of RLCTs in several statistical models are now being discovered based on algebraic geometrical methodology. However, it has been difficult to estimate the Bayes free energy using only training samples, because an RLCT depends on an unknown true distribution. In the present paper, we define a widely applicable Bayesian information criterion (WBIC) by the average log likelihood function over the posterior distribution with the inverse temperature $1/\log n$, where $n$ is the number of training samples. We mathematically prove that WBIC has the same asymptotic expansion as the Bayes free energy, even if a statistical model is singular for and unrealizable by a statistical model. Since WBIC can be numerically calculated without any information about a true distribution, it is a generalized version of BIC onto singular statistical models.

Bayesian learning is often hampered by large computational expense. As a powerful generalization of popular belief propagation, expectation propagation (EP) efficiently approximates the exact Bayesian computation. Nevertheless, EP can be sensitive to outliers and suffer from divergence for difficult cases. To address this issue, we propose a new approximate inference approach, relaxed expectation propagation (REP). It relaxes the moment matching requirement of expectation propagation by adding a relaxation factor into the KL minimization. We penalize this relaxation with a $l_1$ penalty. As a result, when two distributions in the relaxed KL divergence are similar, the relaxation factor will be penalized to zero and, therefore, we obtain the original moment matching; In the presence of outliers, these two distributions are significantly different and the relaxation factor will be used to reduce the contribution of the outlier. Based on this penalized KL minimization, REP is robust to outliers and can greatly improve the posterior approximation quality over EP. To examine the effectiveness of REP, we apply it to Gaussian process classification, a task known to be suitable to EP. Our classification results on synthetic and UCI benchmark datasets demonstrate significant improvement of REP over EP and Power EP--in terms of algorithmic stability, estimation accuracy and predictive performance.

In literature there are several studies on the performance of Bayesian network structure learning algorithms. The focus of these studies is almost always the heuristics the learning algorithms are based on, i.e. the maximisation algorithms (in score-based algorithms) or the techniques for learning the dependencies of each variable (in constraint-based algorithms). In this paper we investigate how the use of permutation tests instead of parametric ones affects the performance of Bayesian network structure learning from discrete data. Shrinkage tests are also covered to provide a broad overview of the techniques developed in current literature.

We present a multi-task learning approach to jointly estimate the means of multiple independent data sets. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the single-task maximum likelihood estimates. We derive the optimal minimum risk estimator and the minimax estimator, and show that these estimators can be efficiently estimated. Simulations and real data experiments demonstrate that MTA estimators often outperform both single-task and James-Stein estimators.

Bayes Classifiers are widely used currently for recognition, identification and knowledge discovery. The fields of application are, for example, image processing, medicine, chemistry (QSAR). But by mysterious way the Naive Bayes Classifier usually gives a very nice and good presentation of a recognition. It can not be improved considerably by more complex models of Bayes Classifier. We demonstrate here a very nice and simple proof of the Naive Bayes Classifier optimality, that can explain this interesting fact.The derivation in the current paper is based on arXiv:cs/0202020v1

Domain-independent planning is one of the foundational areas in the field of Artificial Intelligence. A description of a planning task consists of an initial world state, a goal, and a set of actions for modifying the world state. The objective is to find a sequence of actions, that is, a plan, that transforms the initial world state into a goal state. In optimal planning, we are interested in finding not just a plan, but one of the cheapest plans. A prominent approach to optimal planning these days is heuristic state-space search, guided by admissible heuristic functions. Numerous admissible heuristics have been developed, each with its own strengths and weaknesses, and it is well known that there is no single "best'' heuristic for optimal planning in general. Thus, which heuristic to choose for a given planning task is a difficult question. This difficulty can be avoided by combining several heuristics, but that requires computing numerous heuristic estimates at each state, and the tradeoff between the time spent doing so and the time saved by the combined advantages of the different heuristics might be high. We present a novel method that reduces the cost of combining admissible heuristics for optimal planning, while maintaining its benefits. Using an idealized search space model, we formulate a decision rule for choosing the best heuristic to compute at each state. We then present an active online learning approach for learning a classifier with that decision rule as the target concept, and employ the learned classifier to decide which heuristic to compute at each state. We evaluate this technique empirically, and show that it substantially outperforms the standard method for combining several heuristics via their pointwise maximum.