[London] (No. 7 Weymouth Street, Portland Place) : Published as the Act directs ... by R. Duppa, Jan.y 1st 1802.

London (Pater Noster Row) : G.G. & J. Robinson, Nov.r 1st 1798.

Amsterdam : Uitgegeven by Frans Buffa en Zonen, [between 1843 and 1845]

Amsterdam : Uitgegeven by Frans Buffa en Zonen, [between 1843 and 1845]

London : James Nisbet & Co., MDCCCLXXX [1880]

(Printed in Austria)

[Paris] : [publisher not identified], 1782.

Only so money hockey options on that odd beast of a machine.

Wednesday's collection of links.

Thursday's collection of links.

Friday's collection of links.

There have been so many great hockey images taken by photographers. We choose our top three shots ranging from Stanley Cup celebations to iconic moments.

Learning how to decode words is essential to becoming a reader. But research shows that building a strong vocabulary and knowledge-base is crucial as well.

[London?], [1993?]

London : Stacy Bias, 2019.

Philippines

Stuttgart : In Kommission: Wissenschaftliche Verlagsgesellschaft, 2019.

Stuttgart : In Kommission: Wissenschaftliche Verlagsgesellschaft mbH, 2019.

Rockville, Maryland : National Institute on Drug Abuse, 1984.

Rockville, Maryland : National Institute on Drug Abuse, 1986.

Rockville, Maryland : National Institute on Drug Abuse, 1991.

Rockville, Maryland : National Institute on Drug Abuse, 1984.

Rockville, Maryland : National Institute on Drug Abuse, 1981.

Rockville, Maryland : National Institute on Drug Abuse, 1980.

Rockville, Maryland : National Institute on Drug Abuse, 1979.

Springfield, Virginia : National Technical Information Service, 1974.

York : York Consulting, 2001.

Sabrina Ionescu is the Naismith Trophy Player of the Year, concluding her illustrious Oregon career with one of the major postseason women's basketball awards. As the only player in college basketball history with 2,000 career points (2,562), 1,000 assists (1,091) and 1,000 rebounds (1,040) and the NCAA all-time leader with 26 triple-doubles, Ionescu has continued to rack up player of the year honors for her remarkable senior season.

Emanuel Ben-David, Bala Rajaratnam.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 580--604.

Abstract:
The Wishart distribution defined on the open cone of positive-definite matrices plays a central role in multivariate analysis and multivariate distribution theory. Its domain of parameters is often referred to as the Gindikin set. In recent years, varieties of useful extensions of the Wishart distribution have been proposed in the literature for the purposes of studying Markov random fields and graphical models. In particular, generalizations of the Wishart distribution, referred to as Type I and Type II (graphical) Wishart distributions introduced by Letac and Massam in Annals of Statistics (2007) play important roles in both frequentist and Bayesian inference for Gaussian graphical models. These distributions have been especially useful in high-dimensional settings due to the flexibility offered by their multiple-shape parameters. Concerning Type I and Type II Wishart distributions, a conjecture of Letac and Massam concerns the domain of multiple-shape parameters of these distributions. The conjecture also has implications for the existence of Bayes estimators corresponding to these high dimensional priors. The conjecture, which was first posed in the Annals of Statistics, has now been an open problem for about 10 years. In this paper, we give a necessary condition for the Letac and Massam conjecture to hold. More precisely, we prove that if the Letac and Massam conjecture holds on a decomposable graph, then no two separators of the graph can be nested within each other. For this, we analyze Type I and Type II Wishart distributions on appropriate Markov equivalent perfect DAG models and succeed in deriving the aforementioned necessary condition. This condition in particular identifies a class of counterexamples to the conjecture.

Emilio Porcu, Rachid Senoussi, Enner Mendoza, Moreno Bevilacqua.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 890--916.

Abstract:
The paper considers reduction problems and deformation approaches for nonstationary covariance functions on the $(d-1)$-dimensional spheres, $mathbb{S}^{d-1}$, embedded in the $d$-dimensional Euclidean space. Given a covariance function $C$ on $mathbb{S}^{d-1}$, we chase a pair $(R,Psi)$, for a function $R:[-1,+1] o mathbb{R}$ and a smooth bijection $Psi$, such that $C$ can be reduced to a geodesically isotropic one: $C(mathbf{x},mathbf{y})=R(langle Psi (mathbf{x}),Psi (mathbf{y}) angle )$, with $langle cdot ,cdot angle $ denoting the dot product. The problem finds motivation in recent statistical literature devoted to the analysis of global phenomena, defined typically over the sphere of $mathbb{R}^{3}$. The application domains considered in the manuscript makes the problem mathematically challenging. We show the uniqueness of the representation in the reduction problem. Then, under some regularity assumptions, we provide an inversion formula to recover the bijection $Psi$, when it exists, for a given $C$. We also give sufficient conditions for reducibility.

Graph learning from data is a canonical problem that has received substantial attention in the literature. Learning a structured graph is essential for interpretability and identification of the relationships among data. In general, learning a graph with a specific structure is an NP-hard combinatorial problem and thus designing a general tractable algorithm is challenging. Some useful structured graphs include connected, sparse, multi-component, bipartite, and regular graphs. In this paper, we introduce a unified framework for structured graph learning that combines Gaussian graphical model and spectral graph theory. We propose to convert combinatorial structural constraints into spectral constraints on graph matrices and develop an optimization framework based on block majorization-minimization to solve structured graph learning problem. The proposed algorithms are provably convergent and practically amenable for a number of graph based applications such as data clustering. Extensive numerical experiments with both synthetic and real data sets illustrate the effectiveness of the proposed algorithms. An open source R package containing the code for all the experiments is available at https://CRAN.R-project.org/package=spectralGraphTopology.

We study the identity testing problem in the context of spin systems or undirected graphical models, where it takes the following form: given the parameter specification of the model $M$ and a sampling oracle for the distribution $mu_{M^*}$ of an unknown model $M^*$, can we efficiently determine if the two models $M$ and $M^*$ are the same? We consider identity testing for both soft-constraint and hard-constraint systems. In particular, we prove hardness results in two prototypical cases, the Ising model and proper colorings, and explore whether identity testing is any easier than structure learning. For the ferromagnetic (attractive) Ising model, Daskalakis et al. (2018) presented a polynomial-time algorithm for identity testing. We prove hardness results in the antiferromagnetic (repulsive) setting in the same regime of parameters where structure learning is known to require a super-polynomial number of samples. Specifically, for $n$-vertex graphs of maximum degree $d$, we prove that if $|eta| d = omega(log{n})$ (where $eta$ is the inverse temperature parameter), then there is no polynomial running time identity testing algorithm unless $RP=NP$. In the hard-constraint setting, we present hardness results for identity testing for proper colorings. Our results are based on the presumed hardness of #BIS, the problem of (approximately) counting independent sets in bipartite graphs.

This paper considers a Bayesian approach to graph-based semi-supervised learning. We show that if the graph parameters are suitably scaled, the graph-posteriors converge to a continuum limit as the size of the unlabeled data set grows. This consistency result has profound algorithmic implications: we prove that when consistency holds, carefully designed Markov chain Monte Carlo algorithms have a uniform spectral gap, independent of the number of unlabeled inputs. Numerical experiments illustrate and complement the theory.

Consider an unknown smooth function $f: [0,1]^d ightarrow mathbb{R}$, and assume we are given $n$ noisy mod 1 samples of $f$, i.e., $y_i = (f(x_i) + eta_i) mod 1$, for $x_i in [0,1]^d$, where $eta_i$ denotes the noise. Given the samples $(x_i,y_i)_{i=1}^{n}$, our goal is to recover smooth, robust estimates of the clean samples $f(x_i) mod 1$. We formulate a natural approach for solving this problem, which works with angular embeddings of the noisy mod 1 samples over the unit circle, inspired by the angular synchronization framework. This amounts to solving a smoothness regularized least-squares problem -- a quadratically constrained quadratic program (QCQP) -- where the variables are constrained to lie on the unit circle. Our proposed approach is based on solving its relaxation, which is a trust-region sub-problem and hence solvable efficiently. We provide theoretical guarantees demonstrating its robustness to noise for adversarial, as well as random Gaussian and Bernoulli noise models. To the best of our knowledge, these are the first such theoretical results for this problem. We demonstrate the robustness and efficiency of our proposed approach via extensive numerical simulations on synthetic data, along with a simple least-squares based solution for the unwrapping stage, that recovers the original samples of $f$ (up to a global shift). It is shown to perform well at high levels of noise, when taking as input the denoised modulo $1$ samples. Finally, we also consider two other approaches for denoising the modulo 1 samples that leverage tools from Riemannian optimization on manifolds, including a Burer-Monteiro approach for a semidefinite programming relaxation of our formulation. For the two-dimensional version of the problem, which has applications in synthetic aperture radar interferometry (InSAR), we are able to solve instances of real-world data with a million sample points in under 10 seconds, on a personal laptop.

We propose graph-dependent implicit regularisation strategies for synchronised distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity, and smoothness, we establish statistical learning rates that retain, up to logarithmic terms, single-machine serial statistical guarantees through implicit regularisation (step size tuning and early stopping) with appropriate dependence on the graph topology. Our approach avoids the need for explicit regularisation in decentralised learning problems, such as adding constraints to the empirical risk minimisation rule. Particularly for distributed methods, the use of implicit regularisation allows the algorithm to remain simple, without projections or dual methods. To prove our results, we establish graph-independent generalisation bounds for Distributed SGD that match the single-machine serial SGD setting (using algorithmic stability), and we establish graph-dependent optimisation bounds that are of independent interest. We present numerical experiments to show that the qualitative nature of the upper bounds we derive can be representative of real behaviours.

We consider the skill rating problem for multiplayer games, that is how to infer player skills from game outcomes in multiplayer games. We formulate the problem as a minimization problem $arg min_{s} s^T Delta s$ where $Delta$ is a positive semidefinite matrix and $s$ a real-valued function, of which some entries are the skill values to be inferred and other entries are constrained by the game outcomes. We leverage graph-based semi-supervised learning (SSL) algorithms for this problem. We apply our algorithms on several data sets of multiplayer games and obtain very promising results compared to Elo Duelling (see Elo, 1978) and TrueSkill (see Herbrich et al., 2006).. As we leverage graph-based SSL algorithms and because games can be seen as relations between sets of players, we then generalize the approach. For this aim, we introduce a new finite model, called hypernode graph, defined to be a set of weighted binary relations between sets of nodes. We define Laplacians of hypernode graphs. Then, we show that the skill rating problem for multiplayer games can be formulated as $arg min_{s} s^T Delta s$ where $Delta$ is the Laplacian of a hypernode graph constructed from a set of games. From a fundamental perspective, we show that hypernode graph Laplacians are symmetric positive semidefinite matrices with constant functions in their null space. We show that problems on hypernode graphs can not be solved with graph constructions and graph kernels. We relate hypernode graphs to signed graphs showing that positive relations between groups can lead to negative relations between individuals.

Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial step for reducing the dimension of the feature space. We employ model assisted clustering, in which the clusters contain features that are similar to the same unobserved latent variable. Two different cluster-based Gaussian graphical models are considered: the latent variable graph, corresponding to the graphical model associated with the unobserved latent variables, and the cluster-average graph, corresponding to the vector of features averaged over clusters. Our study reveals that likelihood based inference for the latent graph, not analyzed previously, is analytically intractable. Our main contribution is the development and analysis of alternative estimation and inference strategies, for the precision matrix of an unobservable latent vector Z. We replace the likelihood of the data by an appropriate class of empirical risk functions, that can be specialized to the latent graphical model and to the simpler, but under-analyzed, cluster-average graphical model. The estimators thus derived can be used for inference on the graph structure, for instance on edge strength or pattern recovery. Inference is based on the asymptotic limits of the entry-wise estimates of the precision matrices associated with the conditional independence graphs under consideration. While taking the uncertainty induced by the clustering step into account, we establish Berry-Esseen central limit theorems for the proposed estimators. It is noteworthy that, although the clusters are estimated adaptively from the data, the central limit theorems regarding the entries of the estimated graphs are proved under the same conditions one would use if the clusters were known in advance. As an illustration of the usage of these newly developed inferential tools, we show that they can be reliably used for recovery of the sparsity pattern of the graphs we study, under FDR control, which is verified via simulation studies and an fMRI data analysis. These experimental results confirm the theoretically established difference between the two graph structures. Furthermore, the data analysis suggests that the latent variable graph, corresponding to the unobserved cluster centers, can help provide more insight into the understanding of the brain connectivity networks relative to the simpler, average-based, graph.

The problem of accurately measuring the similarity between graphs is at the core of many applications in a variety of disciplines. Graph kernels have recently emerged as a promising approach to this problem. There are now many kernels, each focusing on different structural aspects of graphs. Here, we present GraKeL, a library that unifies several graph kernels into a common framework. The library is written in Python and adheres to the scikit-learn interface. It is simple to use and can be naturally combined with scikit-learn's modules to build a complete machine learning pipeline for tasks such as graph classification and clustering. The code is BSD licensed and is available at: https://github.com/ysig/GraKeL.

A new strategy for probabilistic graphical modeling is developed that draws parallels to community detection analysis. The method jointly estimates an undirected graph and homogeneous communities of nodes. The structure of the communities is taken into account when estimating the graph and at the same time, the structure of the graph is accounted for when estimating communities of nodes. The procedure uses a joint group graphical lasso approach with community detection-based grouping, such that some groups of edges co-occur in the estimated graph. The grouping structure is unknown and is estimated based on community detection algorithms. Theoretical derivations regarding graph convergence and sparsistency, as well as accuracy of community recovery are included, while the method's empirical performance is illustrated in an fMRI context, as well as with simulated examples.

Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static graphs. However, many applications involve evolving graphs. This introduces important challenges for learning and inference since nodes, attributes, and edges change over time. In this survey, we review the recent advances in representation learning for dynamic graphs, including dynamic knowledge graphs. We describe existing models from an encoder-decoder perspective, categorize these encoders and decoders based on the techniques they employ, and analyze the approaches in each category. We also review several prominent applications and widely used datasets and highlight directions for future research.

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that the observations are independent and identically distributed. At the same time, observations connected by a network are becoming increasingly common, and tend to violate these assumptions. Here we develop a Gaussian graphical model for observations connected by a network with potentially different mean vectors, varying smoothly over the network. We propose an efficient estimation algorithm and demonstrate its effectiveness on both simulated and real data, obtaining meaningful and interpretable results on a statistics coauthorship network. We also prove that our method estimates both the inverse covariance matrix and the corresponding graph structure correctly under the assumption of network “cohesion”, which refers to the empirically observed phenomenon of network neighbors sharing similar traits.

Kazuki Okamura.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 586--637.

Abstract:
We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected graph and the trace of the simple random walk on the same graph. We investigate asymptotics for the number of vertices of the enlargement of the trace of the walk until a fixed time, when the time tends to infinity. This process is more highly self-interacting than the range of random walk, which yields difficulties. We show a law of large numbers on vertex-transitive transient graphs. We compare the process on a vertex-transitive graph with the process on a finitely modified graph of the original vertex-transitive graph and show their behaviors are similar. We show that the process fluctuates almost surely on a certain non-vertex-transitive graph. On the two-dimensional integer lattice, by investigating the size of the boundary of the trace, we give an estimate for variances of the process implying a law of large numbers. We give an example of a graph with unbounded degrees on which the process behaves in a singular manner. As by-products, some results for the range and the boundary, which will be of independent interest, are obtained.

Oleksandr Sverdlov, Weng Kee Wong, Yevgen Ryeznik.

Source: Statistics Surveys, Volume 8, 2--44.

Abstract:
Adaptive clinical trials are becoming increasingly popular research designs for clinical investigation. Adaptive designs are particularly useful in phase I cancer studies where clinical data are scant and the goals are to assess the drug dose-toxicity profile and to determine the maximum tolerated dose while minimizing the number of study patients treated at suboptimal dose levels. In the current work we give an overview of adaptive design methods for phase I cancer trials. We find that modern statistical literature is replete with novel adaptive designs that have clearly defined objectives and established statistical properties, and are shown to outperform conventional dose finding methods such as the 3+3 design, both in terms of statistical efficiency and in terms of minimizing the number of patients treated at highly toxic or nonefficacious doses. We discuss statistical, logistical, and regulatory aspects of these designs and present some links to non-commercial statistical software for implementing these methods in practice.

Jeffrey Picka

Source: Statist. Surv., Volume 6, 74--112.

Abstract:
This paper gives an overview of statistical inference for disordered sphere packing processes. These processes are used extensively in physics and engineering in order to represent the internal structure of composite materials, packed bed reactors, and powders at rest, and are used as initial arrangements of grains in the study of avalanches and other problems involving powders in motion. Packing processes are spatial processes which are neither stationary nor ergodic. Classical spatial statistical models and procedures cannot be applied to these processes, but alternative models and procedures can be developed based on ideas from statistical physics. Most of the development of models and statistics for sphere packings has been undertaken by scientists and engineers. This review summarizes their results from an inferential perspective.