We offer a novel view of AdaBoost in a statistical setting. We propose a Bayesian model for binary classification in which label noise is modeled hierarchically. Using variational inference to optimize a dynamic evidence lower bound, we derive a new boosting-like algorithm called VIBoost. We show its close connections to AdaBoost and give experimental results from four datasets.

In this article, we address the question of how non-knowledge about future events that influence economic agents' decisions in choice settings has been formally represented in economic theory up to date. To position our discussion within the ongoing debate on uncertainty, we provide a brief review of historical developments in economic theory and decision theory on the description of economic agents' choice behaviour under conditions of uncertainty, understood as either (i) ambiguity, or (ii) unawareness. Accordingly, we identify and discuss two approaches to the formalisation of non-knowledge: one based on decision-making in the context of a state space representing the exogenous world, as in Savage's axiomatisation and some successor concepts (ambiguity as situations with unknown probabilities), and one based on decision-making over a set of menus of potential future opportunities, providing the possibility of derivation of agents' subjective state spaces (unawareness as situation with imperfect subjective knowledge of all future events possible). We also discuss impeding challenges of the formalisation of non-knowledge.

The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and the core semantics defined by Dung can be characterized by specific sub-blocks of the matrix. Furthermore, the elementary permutations of a matrix are employed by which an efficient matrix approach for finding out all extensions under a given semantics is obtained. Different from several established approaches, such as the graph labelling algorithm, Constraint Satisfaction Problem algorithm, the matrix approach not only put the mathematic idea into the investigation for finding out various extensions, but also completely achieve the goal to compute all the extensions needed.

We propose parametric constructive Kripke-semantics for multi-agent KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions of two basic functional building blocks, namely bias (or viewpoint) and visibility, functioning also as the parameters of the doxastic and epistemic accessibility relation. The doxastic accessibility relates two possible worlds whenever the application of the composition of bias with visibility to the first world is equal to the application of visibility to the second world. The epistemic accessibility is the transitive closure of the union of our doxastic accessibility and its converse. Therefrom, accessibility relations for common and distributed belief and knowledge can be constructed in a standard way. As a result, we obtain a general definition of knowledge in terms of belief that enables us to view S5-knowledge as accurate (unbiased and thus true) KD45-belief, negation-complete belief and knowledge as exact KD45-belief and S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and accurate) KD45-belief, and all this generically for arbitrary functions of bias and visibility. Our results can be seen as a semantic complement to previous foundational results by Halpern et al. about the (un)definability and (non-)reducibility of knowledge in terms of and to belief, respectively.

Cumulative resource constraints can model scarce resources in scheduling problems or a dimension in packing and cutting problems. In order to efficiently solve such problems with a constraint programming solver, it is important to have strong and fast propagators for cumulative resource constraints. One such propagator is the recently developed time-table-edge-finding propagator, which considers the current resource profile during the edge-finding propagation. Recently, lazy clause generation solvers, i.e. constraint programming solvers incorporating nogood learning, have proved to be excellent at solving scheduling and cutting problems. For such solvers, concise and accurate explanations of the reasons for propagation are essential for strong nogood learning. In this paper, we develop the first explaining version of time-table-edge-finding propagation and show preliminary results on resource-constrained project scheduling problems from various standard benchmark suites. On the standard benchmark suite PSPLib, we were able to close one open instance and to improve the lower bound of about 60% of the remaining open instances. Moreover, 6 of those instances were closed.

Functional neuroimaging data are currently routinely used to better understand cognitive processes. They rely heavily on previous findings to formulate hypotheses and narrow the search space to regions of interest (ROIs), most often reported as coordinates of activation peaks [1], or from coordinate databases such as BrainMap [2]. However, understanding the literature is increasingly difficult, so that there is a need for more systematic methods, which use the images themselves to characterize the functional specificity of brain regions [3]. Transfer learning is a method that trains a classifier to learn a discriminant model on a source task, and then generalizes on a target task without further training. It can yield insights on some brain mechanisms if the tasks share specific common effects in some brain regions [4]. The goal of this work is to investigate the power of transfer learning procedures applied to pairs of cognitive contrasts, where the discrimination ability of the classifier quantifies the information shared between brain maps, and thus characterizes at which spatial scale functional contrasts can be jointly classified. We show that in many cases, transfer learning gives poor results in terms of spatial selectivity. To address this limitation, we introduce selection transfer, i.e. classification of brain states on the target task following the canonical procedure [5], but using regions defined on the source task.

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markov modeling, which has been developed mainly in the parametric non-Bayesian setting, to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicit-duration Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for efficient posterior inference. The methods we introduce also provide new methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs sampling methods can be embedded in samplers for larger hierarchical Bayesian models, adding semi-Markov chain modeling as another tool in the Bayesian inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference methods on both synthetic and real experiments.

We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-parametric model similar to kernel density estimators. We show that under mild conditions, the resulting model uses only the sufficient statistics if the density is within the chosen exponential family, and asymptotically, it approximates densities outside of the chosen exponential family. Using the proposed approach, we modify the exponential random graph model, commonly used for modeling small-size graph distributions, to address the well-known issue of model degeneracy.

In this paper, we study the problem of controlling a group of indistinguishable agents with non-negligible sizes to take arbitrary desired formations. The agents, confined to an arbitrary connected graph, are capable of moving from one vertex to an adjacent vertex in one time step. The control policy must ensure that no collisions occur, which may happen when two agents attempt to move to the same vertex or move along the same edge. Counting each edge as having unit distance, we show that a (centralized) policy/schedule exists that moves the agents to the desired formation along paths having shortest total distance. The control policy also guarantees that a convergence time (the time when the formation is complete) of no more than n l 1, in which n is the number of agents,lis the maximum (shortest) distance between any two initial and goal vertices.

We study optimal solutions to an abstract optimization problem for measures, which is a generalization of classical variational problems in information theory and statistical physics. In the classical problems, information and relative entropy are defined using the Kullback-Leibler divergence, and for this reason optimal measures belong to a one-parameter exponential family. Measures within such a family have the property of mutual absolute continuity. Here we show that this property characterizes other families of optimal positive measures if a functional representing information has a strictly convex dual. Mutual absolute continuity of optimal probability measures allows us to strictly separate deterministic and non-deterministic Markov transition kernels, which play an important role in theories of decisions, estimation, control, communication and computation. We show that deterministic transitions are strictly sub-optimal, unless information resource with a strictly convex dual is unconstrained. For illustration, we construct an example where, unlike non-deterministic, any deterministic kernel either has negatively infinite expected utility (unbounded expected error) or communicates infinite information.