Linguistic large-scale group decision making (LGDM) problems are more and more common nowadays. In such problems a large group of decision makers are involved in the decision process and elicit linguistic information that are usually assessed in different linguistic scales with diverse granularity because of decision makers' distinct knowledge and background. To keep maximum information in initial stages of the linguistic LGDM problems, the use of multi-granular linguistic distribution assessments seems a suitable choice, however to manage such multigranular linguistic distribution assessments, it is necessary the development of a new linguistic computational approach. In this paper it is proposed a novel computational model based on the use of extended linguistic hierarchies, which not only can be used to operate with multi-granular linguistic distribution assessments, but also can provide interpretable linguistic results to decision makers. Based on this new linguistic computational model, an approach to linguistic large-scale multi-attribute group decision making is proposed and applied to a talent selection process in universities.

In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the $\ell^1$ norm of the time varying sub-linear coefficients, (2) a Lipschitz assumption on the predictors and (3) moment conditions on the noise appearing in the linear representation. Two kinds of aggregations are considered giving rise to different moment conditions on the noise and more or less sharp oracle inequalities. We apply this approach for deriving an adaptive predictor for locally stationary time varying autoregressive (TVAR) processes. It is obtained by aggregating a finite number of well chosen predictors, each of them enjoying an optimal minimax convergence rate under specific smoothness conditions on the TVAR coefficients. We show that the obtained aggregated predictor achieves a minimax rate while adapting to the unknown smoothness. To prove this result, a lower bound is established for the minimax rate of the prediction risk for the TVAR process. Numerical experiments complete this study. An important feature of this approach is that the aggregated predictor can be computed recursively and is thus applicable in an online prediction context.

This book-length article combines several peer reviewed papers and new material to analyze the issues of ethical artificial intelligence (AI). The behavior of future AI systems can be described by mathematical equations, which are adapted to analyze possible unintended AI behaviors and ways that AI designs can avoid them. This article makes the case for utility-maximizing agents and for avoiding infinite sets in agent definitions. It shows how to avoid agent self-delusion using model-based utility functions and how to avoid agents that corrupt their reward generators (sometimes called "perverse instantiation") using utility functions that evaluate outcomes at one point in time from the perspective of humans at a different point in time. It argues that agents can avoid unintended instrumental actions (sometimes called "basic AI drives" or "instrumental goals") by accurately learning human values. This article defines a self-modeling agent framework and shows how it can avoid problems of resource limits, being predicted by other agents, and inconsistency between the agent's utility function and its definition (one version of this problem is sometimes called "motivated value selection"). This article also discusses how future AI will differ from current AI, the politics of AI, and the ultimate use of AI to help understand the nature of the universe and our place in it.

Normalized random measures (NRMs) provide a broad class of discrete random measures that are often used as priors for Bayesian nonparametric models. Dirichlet process is a well-known example of NRMs. Most of posterior inference methods for NRM mixture models rely on MCMC methods since they are easy to implement and their convergence is well studied. However, MCMC often suffers from slow convergence when the acceptance rate is low. Tree-based inference is an alternative deterministic posterior inference method, where Bayesian hierarchical clustering (BHC) or incremental Bayesian hierarchical clustering (IBHC) have been developed for DP or NRM mixture (NRMM) models, respectively. Although IBHC is a promising method for posterior inference for NRMM models due to its efficiency and applicability to online inference, its convergence is not guaranteed since it uses heuristics that simply selects the best solution after multiple trials are made. In this paper, we present a hybrid inference algorithm for NRMM models, which combines the merits of both MCMC and IBHC. Trees built by IBHC outlines partitions of data, which guides Metropolis-Hastings procedure to employ appropriate proposals. Inheriting the nature of MCMC, our tree-guided MCMC (tgMCMC) is guaranteed to converge, and enjoys the fast convergence thanks to the effective proposals guided by trees. Experiments on both synthetic and real-world datasets demonstrate the benefit of our method.

Stéphan Clémençon LTCI, CNRS, Télécom ParisTech Université Paris-Saclay 75013 Paris, France first.last@telecom-paristech.fr Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of U-statistics, relying on more expensive averaging over pairs of observations, is a less investigated area. Yet, such data functionals are essential to describe global properties of a statistical population, with important examples including Area Under the Curve, empirical variance, Gini mean difference and within-cluster point scatter. This paper proposes new synchronous and asynchronous randomized gossip algorithms which simultaneously propagate data across the network and maintain local estimates of the U-statistic of interest. We establish convergence rate bounds of O(1/t) and O(log t/t) for the synchronous and asynchronous cases respectively, where t is the number of iterations, with explicit data and network dependent terms. Beyond favorable comparisons in terms of rate analysis, numerical experiments provide empirical evidence the proposed algorithms surpasses the previously introduced approach.

We propose combinatorial cascading bandits, a class of partial monitoring problems where at each step a learning agent chooses a tuple of ground items subject to constraints and receives a reward if and only if the weights of all chosen items are one. The weights of the items are binary, stochastic, and drawn independently of each other. The agent observes the index of the first chosen item whose weight is zero. This observation model arises in network routing, for instance, where the learning agent may only observe the first link in the routing path which is down, and blocks the path. We propose a UCB-like algorithm for solving our problems, CombCascade; and prove gap-dependent and gap-free upper bounds on its $n$-step regret. Our proofs build on recent work in stochastic combinatorial semi-bandits but also address two novel challenges of our setting, a non-linear reward function and partial observability. We evaluate CombCascade on two real-world problems and show that it performs well even when our modeling assumptions are violated. We also demonstrate that our setting requires a new learning algorithm.

We consider the problem of recovering a complete (i.e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb R^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse. This recovery problem is central to the theoretical understanding of dictionary learning, which seeks a sparse representation for a collection of input signals, and finds numerous applications in modern signal processing and machine learning. We give the first efficient algorithm that provably recovers $\mathbf A_0$ when $\mathbf X_0$ has $O(n)$ nonzeros per column, under suitable probability model for $\mathbf X_0$. In contrast, prior results based on efficient algorithms provide recovery guarantees when $\mathbf X_0$ has only $O(n^{1-\delta})$ nonzeros per column for any constant $\delta \in (0, 1)$. Our algorithmic pipeline centers around solving a certain nonconvex optimization problem with a spherical constraint, and hence is naturally phrased in the language of manifold optimization. To show this apparently hard problem is tractable, we first provide a geometric characterization of the high-dimensional objective landscape, which shows that with high probability there are no "spurious" local minima. This particular geometric structure allows us to design a Riemannian trust region algorithm over the sphere that provably converges to one local minimizer with an arbitrary initialization, despite the presence of saddle points. The geometric approach we develop here may also shed light on other problems arising from nonconvex recovery of structured signals.

Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a "nomination list" such that, with high probability, vertices from the interesting block are concentrated near the list's beginning. We propose several vertex nomination schemes. Our basic--but principled--setting and development yields a best nomination scheme (which is a Bayes-Optimal analogue), and also a likelihood maximization nomination scheme that is practical to implement when there are a thousand vertices, and which is empirically near-optimal when the number of vertices is small enough to allow comparison to the best nomination scheme. We then illustrate the robustness of the likelihood maximization nomination scheme to the modeling challenges inherent in real data, using examples which include a social network involving human trafficking, the Enron Graph, a worm brain connectome and a political blog network. In a stochastic block model, the vertices of the graph are partitioned into blocks, and the existence/nonexistence of an edge between any pair of vertices is an independent Bernoulli trial, with the Bernoulli parameter being a function of the block memberships of the pair of vertices. We are concerned here with a graph realized from a stochastic block model such that many or all of the vertices' block labels are hidden (i.e., unobserved). Received August 2014; revised February 2015. Supported in part by Johns Hopkins University Human Language Technology Center of Excellence (JHU HLT COE) and the XDATA program of the Defense Advanced Research Projects Agency (DARPA) administered through Air Force Research Laboratory contract FA8750-12-2-0303.

Pseudo-marginal Metropolis-Hastings (pmMH) is a powerful method for Bayesian inference in models where the posterior distribution is analytical intractable or computationally costly to evaluate directly. It operates by introducing additional auxiliary variables into the model and form an extended target distribution, which then can be evaluated point-wise. In many cases, the standard Metropolis-Hastings is then applied to sample from the extended target and the sought posterior can be obtained by marginalisation. However, in some implementations this approach suffers from poor mixing as the auxiliary variables are sampled from an independent proposal. We propose a modification to the pmMH algorithm in which a Crank-Nicolson (CN) proposal is used instead. This results in that we introduce a positive correlation in the auxiliary variables. We investigate how to tune the CN proposal and its impact on the mixing of the resulting pmMH sampler. The conclusion is that the proposed modification can have a beneficial effect on both the mixing of the Markov chain and the computational cost for each iteration of the pmMH algorithm.

Convolutional neural networks (CNN) have achieved state of the art performance on both classification and segmentation tasks. Applying CNNs to microscopy images is challenging due to the lack of datasets labeled at the single cell level. We extend the application of CNNs to microscopy image classification and segmentation using multiple instance learning (MIL). We present the adaptive Noisy-AND MIL pooling function, a new MIL operator that is robust to outliers. Combining CNNs with MIL enables training CNNs using full resolution microscopy images with global labels. We base our approach on the similarity between the aggregation function used in MIL and pooling layers used in CNNs. We show that training MIL CNNs end-to-end outperforms several previous methods on both mammalian and yeast microscopy images without requiring any segmentation steps.