In this paper, computational aspects of the panel aggregation problem are addressed. Motivated primarily by applications of risk assessment, an algorithm is developed for aggregating large corpora of internally incoherent probability assessments. The algorithm is characterized by a provable performance guarantee, and is demonstrated to be orders of magnitude faster than existing tools when tested on several real-world data-sets. In addition, unexpected connections between research in risk assessment and wireless sensor networks are exposed, as several key ideas are illustrated to be useful in both fields.
@cite_20 consider a Bayesian approach to reconciling probability forecasts, whereby noisy" observations @math are assumed to arise from a coherent set @math . CAP can be viewed as a special-case of their model, since as discussed above, the solution to ) admits a Bayesian interpretation as the maximum-likelihood coherent forecasts given additive white noise corrupted observations @math . However, note that @cite_20 sought to eliminate incoherence from a single judge, whereas CAP was introduced to address the panel aggregation problem. Moreover, Osherson and Vardi were motivated by non-statistical interpretations of CAP and as here, addressed the computational issue of implementing CAP.
@cite_20
1509045286
In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by @math , which is just about the frequency of natural light. This paper rigorously establishes that this super-resolution problem can be solved via linear programming in a stable manner. We prove that the quality of the reconstruction crucially depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within a square of side length about @math . The theoretical performance guarantee is complemented with a converse result showing that our simple convex program convex is nearly optimal. Finally, numerical experiments illustrate our methods. This paper studies problems of inferring order given noisy information. In these problems there is an unknown order (permutation) @math on @math elements denoted by @math . We assume that information is generated in a way correlated with @math . The goal is to find a maximum likelihood @math given the information observed. We will consider two different types of observations: noisy comparisons and noisy orders. The data in Noisy orders are permutations given from an exponential distribution correlated with (this is also called the Mallow's model). The data in Noisy Comparisons is a signal given for each pair of elements which is correlated with their true ordering. In this paper we present polynomial time algorithms for solving both problems with high probability. As part of our proof we show that for both models the maximum likelihood solution @math is close to the original permutation @math . Our results are of interest in applications to ranking, such as ranking in sports, or ranking of search items based on comparisons by experts. The co-existence of cellular and wired networks has been exploited almost exclusively in the direction of OffLoading traffic from the former onto the latter. In this paper we claim that there exist cases that call for the exact opposite, i.e, use the cellular network to assist a fixed wired network. In particular, we show that by "OnLoading'' traffic from the wired broadband network onto the cellular network we can usefully speedup wired connections, on the downlink or the uplink. We consider the technological challenges pertaining to this idea and implement a prototype 3G OnLoading service that we call 3GOL, that can be deployed by an operator providing both the wired and cellular network services. By strategically OnLoading a fraction of the data transfers to the 3G network, one can significantly enhance the performance of particular applications. In particular we demonstrate non-trivial performance benefits of 3GOL to two widely used applications: video-on-demand and multimedia upload. We also consider the case when the operator that provides wired and cellular services is different, adding the analysis on economic constraints and volume cap on cellular data plans that need to be respected. Simulating 3GOL over a DSLAM trace we show that 3GOL can reduce video pre-buffering time by at least 20 for 50 of the users while respecting data caps and we design a simple estimator to compute the daily allowance that can be used towards 3GOL while respecting caps. Our prototype is currently being piloted in 30 households in a large European city by a large network provider. Real-world tasks in computer vision often touch upon open set recognition: multi-class recognition with incomplete knowledge of the world and many unknown inputs. Recent work on this problem has proposed a model incorporating an open space risk term to account for the space beyond the reasonable support of known classes. This paper extends the general idea of open space risk limiting classification to accommodate non-linear classifiers in a multiclass setting. We introduce a new open set recognition model called compact abating probability (CAP), where the probability of class membership decreases in value (abates) as points move from known data toward open space. We show that CAP models improve open set recognition for multiple algorithms. Leveraging the CAP formulation, we go on to describe the novel Weibull-calibrated SVM (W-SVM) algorithm, which combines the useful properties of statistical extreme value theory for score calibration with one-class and binary support vector machines. Our experiments show that the W-SVM is significantly better for open set object detection and OCR problems when compared to the state-of-the-art for the same tasks. Power consumption of extreme-scale supercomputers has become a key performance bottleneck. Yet current practices do not leverage power management opportunities, instead running at "maximum power". This is not sustainable. Future systems will need to manage power as a critical resource, directing it to where it has greatest benefit. Power capping is one mechanism for managing power budgets, however its behavior is not well understood. This paper presents an empirical evaluation of several key HPC workloads running under a power cap on a Cray XC40 system, and provides a comparison of this technique with p-state control, demonstrating the performance differences of each. These results show: 1.) Maximum performance requires ensuring the cap is not reached; 2.) Performance slowdown under a cap can be attributed to cascading delays which result in unsynchronized performance variability across nodes; and, 3.) Due to lag in reaction time, considerable time is spent operating above the set cap. This work provides a timely and much needed comparison of HPC application performance under a power cap and attempts to enable users and system administrators to understand how to best optimize application performance on power-constrained HPC systems. Extracting useful information from high-dimensional data is an important focus of today's statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L 1 -penalized squared error minimization method Lasso has been popular in regression models and beyond. In this paper, we combine different norms including L 1 to form an intelligent penalty in order to add side information to the fitting of a regression or classification model to obtain reasonable estimates. Specifically, we introduce the Composite Absolute Penalties (CAP) family, which allows given grouping and hierarchical relationships between the predictors to be expressed. CAP penalties are built by defining groups and combining the properties of norm penalties at the across-group and within-group levels. Grouped selection occurs for nonoverlapping groups. Hierarchical variable selection is reached by defining groups with particular overlapping patterns. We propose using the BLASSO and cross-validation to compute CAP estimates in general. For a subfamily of CAP estimates involving only the L 1 and L ∞ norms, we introduce the iCAP algorithm to trace the entire regularization path for the grouped selection problem. Within this subfamily, unbiased estimates of the degrees of freedom (df) are derived so that the regularization parameter is selected without cross-validation. CAP is shown to improve on the predictive performance of the LASSO in a series of simulated experiments, including cases with p » n and possibly mis-specified groupings. When the complexity of a model is properly calculated, iCAP is seen to be parsimonious in the experiments. In this paper we study noisy sorting without re-sampling. In this problem there is an unknown order @math for all pairs @math , where @math is a constant and @math for all @math and @math . It is assumed that the errors are independent. Given the status of the queries the goal is to find the maximum likelihood order. In other words, the goal is find a permutation @math that minimizes the number of pairs @math where @math . The problem so defined is the feedback arc set problem on distributions of inputs, each of which is a tournament obtained as a noisy perturbations of a linear order. Note that when @math and @math is large, it is impossible to recover the original order @math . It is known that the weighted feedback are set problem on tournaments is NP-hard in general. Here we present an algorithm of running time @math and sampling complexity @math that with high probability solves the noisy sorting without re-sampling problem. We also show that if @math is an optimal solution of the problem then it is close'' to the original order. More formally, with high probability it holds that @math and @math . Our results are of interest in applications to ranking, such as ranking in sports, or ranking of search items based on comparisons by experts. Millimeter-wave wireless systems are emerging as a promising technology for meeting the exploding capacity requirements of wireless communication networks. Besides large bandwidths, small wavelengths at mm-wave lead to a high-dimensional spatial signal space, that can be exploited for significant capacity gains through high-dimensional multiple-input multiple-output (MIMO) techniques. In conventional MIMO approaches, optimal performance requires prohibitively high transceiver complexity. By combining the concept of beamspace MIMO communication with a hybrid analog-digital transceiver, continuous aperture phased (CAP) MIMO achieves near-optimal performance with dramatically lower complexity. This paper presents a framework for physically-accurate computational modeling and analysis of CAP-MIMO, and reports measurement results on a DLA-based prototype for multimode line-of-sight communication. The model, based on a critically sampled system representation, is used to demonstrate the performance gains of CAP-MIMO over state-of-the-art designs at mm-wave. For example, a CAP-MIMO system can achieve a spectral efficiency of 10-20 bits s Hz with a 17-31 dB power advantage over state-of-the-art, corresponding to a data rate of 10-200 Gbps with 1-10 GHz system bandwidth. The model is refined to analyze critical sources of power loss in an actual multimode system. The prototype-based measurement results closely follow the theoretical predictions, validating CAP-MIMO theory, and illustrating the utility of the model. We consider the scenario where the executions of different business processes are traced into a log, where each trace describes a process instance as a sequence of low-level events representing basic kinds of operations. In this context, we address a novel problem: given a description of the processes' behaviors in terms of high-level activities instead of low-level events, and in the presence of uncertainty in the mapping between events and activities, find all the interpretations of each trace @math . Specifically, an interpretation is a pair @math that provides a two-level "explanation" for @math : @math is a sequence of activities that may have triggered the events in @math , and W is a process whose model admits @math . To solve this problem, we propose a probabilistic framework representing "consistent" @math 's interpretations, where each interpretation is associated with a probability score. We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random variable whose mean is a sparse linear superposition of known patterns. Unlike many conventional problems observations here are not identically distributed since they are associated with different sensing modalities. We analyze the performance of a maximum likelihood (ML) decoder, which for our Poisson setting involves a non-linear optimization but yet is computationally tractable. We derive fundamental sample complexity bounds for sparse recovery when the measurements are contaminated with Poisson noise. In contrast to the least-squares linear regression setting with Gaussian noise, we observe that in addition to sparsity, the scale of the parameters also fundamentally impacts @math error in the Poisson setting. We show that our upper bounds are tight under suitable regularity conditions. Specifically, we derive a minimax matching lower bound on the mean-squared error and show that our constrained ML decoder is minimax optimal for this regime. We introduce the framework of blind regression motivated by matrix completion for recommendation systems: given @math users, @math movies, and a subset of user-movie ratings, the goal is to predict the unobserved user-movie ratings given the data, i.e., to complete the partially observed matrix. Following the framework of non-parametric statistics, we posit that user @math and movie @math have features @math and @math respectively, and their corresponding rating @math is a noisy measurement of @math for some unknown function @math . In contrast with classical regression, the features @math are not observed, making it challenging to apply standard regression methods to predict the unobserved ratings. Inspired by the classical Taylor's expansion for differentiable functions, we provide a prediction algorithm that is consistent for all Lipschitz functions. In fact, the analysis through our framework naturally leads to a variant of collaborative filtering, shedding insight into the widespread success of collaborative filtering in practice. Assuming each entry is sampled independently with probability at least @math with @math , we prove that the expected fraction of our estimates with error greater than @math is less than @math plus a polynomially decaying term, where @math is the variance of the additive entry-wise noise term. Experiments with the MovieLens and Netflix datasets suggest that our algorithm provides principled improvements over basic collaborative filtering and is competitive with matrix factorization methods. A hierarchical Bayesian model is considered for decomposing a matrix into low-rank and sparse components, assuming the observed matrix is a superposition of the two. The matrix is assumed noisy, with unknown and possibly non-stationary noise statistics. The Bayesian framework infers an approximate representation for the noise statistics while simultaneously inferring the low-rank and sparse-outlier contributions; the model is robust to a broad range of noise levels, without having to change model hyperparameter settings. In addition, the Bayesian framework allows exploitation of additional structure in the matrix. For example, in video applications each row (or column) corresponds to a video frame, and we introduce a Markov dependency between consecutive rows in the matrix (corresponding to consecutive frames in the video). The properties of this Markov process are also inferred based on the observed matrix, while simultaneously denoising and recovering the low-rank and sparse components. We compare the Bayesian model to a state-of-the-art optimization-based implementation of robust PCA; considering several examples, we demonstrate competitive performance of the proposed model. In this paper, we study a classification problem in which sample labels are randomly corrupted. In this scenario, there is an unobservable sample with noise-free labels. However, before being observed, the true labels are independently flipped with a probability @math , and the random label noise can be class-conditional. Here, we address two fundamental problems raised by this scenario. The first is how to best use the abundant surrogate loss functions designed for the traditional classification problem when there is label noise. We prove that any surrogate loss function can be used for classification with noisy labels by using importance reweighting, with consistency assurance that the label noise does not ultimately hinder the search for the optimal classifier of the noise-free sample. The other is the open problem of how to obtain the noise rate @math . We show that the rate is upper bounded by the conditional probability @math of the noisy sample. Consequently, the rate can be estimated, because the upper bound can be easily reached in classification problems. Experimental results on synthetic and real datasets confirm the efficiency of our methods. In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension @math and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal components @math has at most @math non-zero entries. We are particularly interested in the high dimensional regime wherein @math is comparable to, or even much larger than @math . In an influential paper, johnstone2004sparse introduced a simple algorithm that estimates the support of the principal vectors @math by the largest entries in the diagonal of the empirical covariance. This method can be shown to identify the correct support with high probability if @math , and to fail with high probability if @math for two constants @math . Despite a considerable amount of work over the last ten years, no practical algorithm exists with provably better support recovery guarantees. Here we analyze a covariance thresholding algorithm that was recently proposed by KrauthgamerSPCA . On the basis of numerical simulations (for the rank-one case), these authors conjectured that covariance thresholding correctly recover the support with high probability for @math (assuming @math of the same order as @math ). We prove this conjecture, and in fact establish a more general guarantee including higher-rank as well as @math much smaller than @math . Recent lower bounds berthet2013computational, ma2015sum suggest that no polynomial time algorithm can do significantly better. The key technical component of our analysis develops new bounds on the norm of kernel random matrices, in regimes that were not considered before. We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V,E), and a capacity cap(v) ∈ N for each node v ∈ V , the CapMDS problem asks for a subset S ⊆ V of minimal cardinality, such that every network node not in S is covered by at least one neighbor in S, and every node v ∈ S covers at most cap(v) of its neighbors. We prove that in general graphs and even with uniform capacities, the problem is inherently non-local, i.e., every distributed algorithm achieving a non-trivial approximation ratio must have a time complexity that essentially grows linearly with the network diameter. On the other hand, if for some parameter e > 0, capacities can be violated by a factor of 1 + e, CapMDS becomes much more local. Particularly, based on a novel distributed randomized rounding technique, we present a distributed bi-criteria algorithm that achieves an O(log Δ)-approximation in time O(log3n + log(n) e), where n and Δ denote the number of nodes and the maximal degree in G, respectively. Finally, we prove that in geometric network graphs typically arising in wireless settings, the uniform problem can be approximated within a constant factor in logarithmic time, whereas the non-uniform problem remains entirely non-local. Hoeffding's U-statistics model combinatorial-type matrix parameters (appearing in CS theory) in a natural way. This paper proposes using these statistics for analyzing random compressed sensing matrices, in the non-asymptotic regime (relevant to practice). The aim is to address certain pessimisms of worst-case restricted isometry analyses, as observed by both Blanchard and Dossal, We show how U-statistics can obtain average-case analyses, by relating to statistical restricted isometry property (StRIP) type recovery guarantees. However unlike standard StRIP, random signal models are not required; the analysis used here holds in the almost sure (probabilistic) sense. For Gaussian bounded entry matrices, we show that both @math -minimization and LASSO essentially require on the order of @math measurements to respectively recover at least @math fraction, and @math fraction, of the signals. Noisy conditions are considered. Empirical evidence suggests our analysis to compare well to Donoho and Tanner's recent large deviation bounds for @math -equivalence, in the regime of block lengths @math with high undersampling ( @math measurements); similar system sizes are found in recent CS implementation. In this work, it is assumed throughout that matrix columns are independently sampled. We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G=(V,E), and a capacity cap(v)∈ℕ for each node v∈V, the CapMDS problem asks for a subset S⊆V of minimal cardinality, such that every network node not in S is covered by at least one neighbor in S, and every node v∈S covers at most cap(v) of its neighbors. We prove that in general graphs and even with uniform capacities, the problem is inherently non-local, i.e., every distributed algorithm achieving a non-trivial approximation ratio must have a time complexity that essentially grows linearly with the network diameter. On the other hand, if for some parameter e>0, capacities can be violated by a factor of 1+e, CapMDS becomes much more local. Particularly, based on a novel distributed randomized rounding technique, we present a distributed bi-criteria algorithm that achieves an O(log Δ)-approximation in time O(log 3 n+log (n) e), where n and Δ denote the number of nodes and the maximal degree in G, respectively. Finally, we prove that in geometric network graphs typically arising in wireless settings, the uniform problem can be approximated within a constant factor in logarithmic time, whereas the non-uniform problem remains entirely non-local. We consider the CEO problem for non-regular source distributions (such as uniform or truncated Gaussian). A group of agents observe independently corrupted versions of data and transmit coded versions over rate-limited links to a CEO. The CEO then estimates the underlying data based on the received coded observations. Agents are not allowed to convene before transmitting their observations. This formulation is motivated by the practical problem of a firm’s CEO estimating (non-regular) beliefs about a sequence of events, before acting on them. Agents’ observations are modeled as jointly distributed with the underlying data through a given conditional probability density function. We study the asymptotic behavior of the minimum achievable mean squared error distortion at the CEO in the limit when the number of agents @math and the sum rate @math tend to infinity. We establish a @math convergence of the distortion, an intermediate regime of performance between the exponential behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and the @math behavior in Gaussian CEO problems [Viswanathan and Berger (1997)]. Achievability is proved by a layered architecture with scalar quantization, distributed entropy coding, and midrange estimation. The converse is proved using the Bayesian Chazan–Zakai–Ziv bound. We want to deduce, from a sequence of noisy two-dimensional images of a scene of several rigid bodies moving independently in three dimensions, the number of bodies and the grouping of given feature points in the images to the bodies. Prior processing is assumed to have identified features or points common to all frames and the images are assumed to be created by orthographic projection (i.e., perspective effects are minimal). We describe a computationally inexpensive algorithm that can determine which points or features belong to which rigid body using the fact that, with exact observations in orthographic projection, points on a single body lie in a three or less dimensional linear manifold of frame space. If there are enough observations and independent motions, these manifolds can be viewed as a set linearly independent, four or less dimensional subspaces. We show that the row echelon canonical form provides direct information on the grouping of points to these subspaces. Treatment of the noise is the most difficult part of the problem. This paper uses a statistical approach to estimate the grouping of points to subspaces in the presence of noise by computing which partition has the maximum likelihood. The input data is assumed to be contaminated with independent Gaussian noise. The algorithm can base its estimates on a user-supplied standard deviation of the noise, or it can estimate the noise from the data. The algorithm can also be used to estimate the probability of a user-specified partition so that the hypothesis can be combined with others using Bayesian statistics. Power consumption is a key factor in modern ICT infrastructure, especially in the expanding world of High Performance Computing, Cloud Computing and Big Data. Such consumption is bound to become an even greater issue as supercomputers are envisioned to enter the Exascale by 2020, granted that they obtain an order of magnitude energy efficiency gain. An important component in many strategies devised to decrease energy usage is "power capping", i.e., the possibility to constrain the system power consumption within certain power budget. In this paper we propose two novel approaches for power capped workload dispatching and we demonstrate them on a real-life high-performance machine: the Eurora supercomputer hosted at CINECA computing center in Bologna. Power capping is a feature not included in the commercial Portable Batch System PBS dispatcher currently in use on Eurora. The first method is based on a heuristic technique while the second one relies on a hybrid strategy which combines a CP and a heuristic approach. Both systems are evaluated and compared on simulated job traces.