Pierre Lairez
J. Amer. Math. Soc. 33 (2019), 487-526.
Abstract, references and article information

A. G. Sergeev and Kh. A. Khachatryan
Trans. Moscow Math. Soc. 80 (2020), 95-111.
Abstract, references and article information

S. A. Kashchenko
Trans. Moscow Math. Soc. 80 (2020), 53-71.
Abstract, references and article information

Votes are cast by the full membership in each house of Congress, but much of the important maneuvering occurs in committees. Graph theory and linear algebra are two mathematics subjects that have revealed a level of organization in Congress groups of committees above the known levels of subcommittees and committees. The result is based on strong connections between certain committees that can be detected by examining their memberships, but which were virtually unknown until uncovered by mathematical analysis. Mathematics has also been applied to individual congressional voting records. Each legislator.s record is represented in a matrix whose larger dimension is the number of votes cast (which in a House term is approximately 1000). Using eigenvalues and eigenvectors, researchers have shown that the entire collection of votes for a particular Congress can be approximated very well by a two-dimensional space. Thus, for example, in almost all cases the success or failure of a bill can be predicted from information derived from two coordinates. Consequently it turns out that some of the values important in Washington are, in fact, eigenvalues. For More Information: Porter, Mason A; Mucha, Peter J.; Newman, M. E. J.; and Warmbrand, Casey M., A Network Analysis of Committees in the United States House of Representatives, Proceedings of the National Academy of Sciences, Vol. 102 [2005], No. 20, pp. 7057-7062.

When did you last see a glow worm? Most likely, quite some time ago. Depending on how young you are, you may have never seen one at all. Those light-emitting insects, Wordsworth's "earthborn stars", have been declining in the UK for decades. That means that scientists now see them in fewer places, and even in those pockets where conditions are right for them, there are fewer of them to be found.

Ning Zhang, Jia Wu and Liwei Zhang
Math. Comp. 89 (2020), 1867-1894.
Abstract, references and article information

Côme Huré, Huyên Pham and Xavier Warin
Math. Comp. 89 (2020), 1547-1579.
Abstract, references and article information

Kamen G. Ivanov and Pencho Petrushev
Trans. Amer. Math. Soc. 373 (2020), 3117-3176.
Abstract, references and article information

Yu. V. Kozachenko and I. V. Rozora
Theor. Probability and Math. Statist. 99 (2020), 113-124.
Abstract, references and article information

A. Seesanea and I. E. Verbitsky
St. Petersburg Math. J. 31 (2020), 557-572.
Abstract, references and article information

S.-S. Byun, D. K. Palagachev and L. G. Softova
St. Petersburg Math. J. 31 (2020), 401-419.
Abstract, references and article information

Mohamed Jleli, Bessem Samet and Philippe Souplet
Proc. Amer. Math. Soc. 148 (2020), 2579-2593.
Abstract, references and article information

Michiya Mori
Proc. Amer. Math. Soc. 148 (2020), 2477-2485.
Abstract, references and article information

VOLUME 289 (2014) PAGES 30635–30644This article has been withdrawn by Guangnan Chen, Dongkyoo Park, Francis A. Cucinotta, David S. Yu, Xingming Deng, William S. Dynan, Paul W. Doetsch, and Ya Wang. Hongyan Wang, Xiang Wang, Xiangming Zhang, and Xiaobing Tang could not be reached. The last two lanes of the actin immunoblot in Fig. 1A were reused in the last two lanes of the actin immunoblot in Fig. 1C. In Fig. 2A, the γ-H2AX and the merge with DAPI images for no IR treatment do not match. In Fig. 3A, lanes 3 and 4 of the γ-H2AX immunoblot were reused in lanes 7 and 8, and lanes 5 and 6 of the H2A immunoblot were reused in lanes 7 and 8. In Fig. 3B, lanes 5 and 6 of the H2A immunoblot were reused in lanes 7 and 8. In Fig. 3C, lanes 5 and 6 of the γ-H2AX immunoblot were reused in lanes 7 and 8. Additionally, lanes 1 and 2 of the H2A immunoblot were reused in lanes 3 and 4. In Fig. 3D, lanes 1 and 2 of the Mre11 immunoblot from lysates were reused in lanes 4 and 5. In the γ-H2AX immunoblot, lane 3 was reused in lane 7, and lane 4 was reused in lanes 6 and 8. Also in the H2A immunoblot, lanes 1 and 2 were reused in lanes 3 and 4. In Fig. 4B, lanes 2 and 6 of the Mre11 immunoblot from Ogg1−/− cells are the same. In the Ape1...

A practical joke gone too far caused a St Mary resident, Byron Wilson, to burst into tears after he received a phone call from one of his mischievous friends telling him that he may be a carrier of the novel coronavirus. "A dead mi dead right...

The road back from Tommy John surgery is often long and tedious, but Giants right-hander Johnny Cueto has a notable milestone approaching.

An Australian man who scored a lottery jackpot of nearly $800,000 said he bought his ticket by mistake while attempting to play a different drawing.

At least two people died and more than a dozen were hurt Friday when a moderate earthquake struck in Iran's northern city of Damavand, near Tehran.

The Air Force and Marines have both reported engaging in training maneuvers in the East and South China Sea in recent weeks amid escalating tensions in the region.

Average fuel prices in the United States started the week at $2.26 per gallon, showing little change from the last month or last week, and may remain flat.

Oil prices were near flat early Thursday in what was seen as a pause after gains in the two previous sessions, as traders considered geopolitical developments.

Nearly 5,000 workers in 115 meat processing workers across 19 states have been diagnosed with COVID-19, according to figures released Friday by the U.S. Centers for Disease Control and Prevention.

The United States economy shed more than 20 million jobs last month, the greatest month-to-month decline in history, the Labor Department said Friday in its monthly employment analysis.

Eight states have passed laws requiring students to pass some version of a civics test so far in 2015.

Wayne Sanstead, who has been North Dakota's state schools superintendent for nearly three decades, has decided not to run for an eighth term this fall.

Dozens of Colorado school districts are asking voters next month for more funding for education through bond issues, mill levy overrides, or renewal of a city sales tax.

Democrat Gavin Newsom, who takes office Jan. 7, plans to expand full-day kindergarten and child-care offerings in the state, according to media reports.

Montana Superintendent Elsie Arntzen offers practical advice to schools that could open as early as May 7, even as she says "how they open schools and how learning takes place is up to them."

A new study says that problems surrounding child-care hurt Georgia parents economically in many ways including in turned down promotions and having to cut back on work and school hours.

In Kodiak, Alaska, a school district with deep ties to the U.S. Coast Guard has been walloped by the government shutdown with hundreds of families going without paychecks. And news of a deal to temporarily reopen the government was doing little to allay the community's anxieties.

David Azriel, Armin Schwartzman.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 174--206.

Abstract:
In this work we study estimation of signals when the number of parameters is much larger than the number of observations. A large body of literature assumes for these kind of problems a sparse structure where most of the parameters are zero or close to zero. When this assumption does not hold, one can focus on low-dimensional functions of the parameter vector. In this work we study one-dimensional linear projections. Specifically, in the context of high-dimensional linear regression, the parameter of interest is ${oldsymbol{eta}}$ and we study estimation of $mathbf{a}^{T}{oldsymbol{eta}}$. We show that $mathbf{a}^{T}hat{oldsymbol{eta}}$, where $hat{oldsymbol{eta}}$ is the least squares estimator, using pseudo-inverse when $p>n$, is minimax and admissible. Thus, for linear projections no regularization or shrinkage is needed. This estimator is easy to analyze and confidence intervals can be constructed. We study a high-dimensional dataset from brain imaging where it is shown that the signal is weak, non-sparse and significantly different from zero.

Ryoya Oda, Hirokazu Yanagihara.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1386--1412.

Abstract:
We put forward a variable selection method for selecting explanatory variables in a normality-assumed multivariate linear regression. It is cumbersome to calculate variable selection criteria for all subsets of explanatory variables when the number of explanatory variables is large. Therefore, we propose a fast and consistent variable selection method based on a generalized $C_{p}$ criterion. The consistency of the method is provided by a high-dimensional asymptotic framework such that the sample size and the sum of the dimensions of response vectors and explanatory vectors divided by the sample size tend to infinity and some positive constant which are less than one, respectively. Through numerical simulations, it is shown that the proposed method has a high probability of selecting the true subset of explanatory variables and is fast under a moderate sample size even when the number of dimensions is large.

We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving noise and reward feedback. Our main theoretical result provides an explicit bound on the sample or evaluation complexity: we show that these methods are guaranteed to converge to within any pre-specified tolerance of the optimal policy with a number of zero-order evaluations that is an explicit polynomial of the error tolerance, dimension, and curvature properties of the problem. Our analysis reveals some interesting differences between the settings of additive driving noise and random initialization, as well as the settings of one-point and two-point reward feedback. Our theory is corroborated by simulations of derivative-free methods in application to these systems. Along the way, we derive convergence rates for stochastic zero-order optimization algorithms when applied to a certain class of non-convex problems.

We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, the inferred causal relationships among the observed variables are often wrong. Under faithfulness assumption, we propose a method to check whether there exists a causal path between any two observed variables. From this information, we can obtain the causal order among the observed variables. The next question is whether the causal effects can be uniquely identified as well. We show that causal effects among observed variables cannot be identified uniquely under mere assumptions of faithfulness and non-Gaussianity of exogenous noises. However, we are able to propose an efficient method that identifies the set of all possible causal effects that are compatible with the observational data. We present additional structural conditions on the causal graph under which causal effects among observed variables can be determined uniquely. Furthermore, we provide necessary and sufficient graphical conditions for unique identification of the number of variables in the system. Experiments on synthetic data and real-world data show the effectiveness of our proposed algorithm for learning causal models.

The success of Deep Learning and its potential use in many safety-critical applicationshas motivated research on formal verification of Neural Network (NN) models. In thiscontext, verification involves proving or disproving that an NN model satisfies certaininput-output properties. Despite the reputation of learned NN models as black boxes,and the theoretical hardness of proving useful properties about them, researchers havebeen successful in verifying some classes of models by exploiting their piecewise linearstructure and taking insights from formal methods such as Satisifiability Modulo Theory.However, these methods are still far from scaling to realistic neural networks. To facilitateprogress on this crucial area, we exploit the Mixed Integer Linear Programming (MIP) formulation of verification to propose a family of algorithms based on Branch-and-Bound (BaB). We show that our family contains previous verification methods as special cases.With the help of the BaB framework, we make three key contributions. Firstly, we identifynew methods that combine the strengths of multiple existing approaches, accomplishingsignificant performance improvements over previous state of the art. Secondly, we introducean effective branching strategy on ReLU non-linearities. This branching strategy allows usto efficiently and successfully deal with high input dimensional problems with convolutionalnetwork architecture, on which previous methods fail frequently. Finally, we proposecomprehensive test data sets and benchmarks which includes a collection of previouslyreleased testcases. We use the data sets to conduct a thorough experimental comparison ofexisting and new algorithms and to provide an inclusive analysis of the factors impactingthe hardness of verification problems.

Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly, Yvik Swan.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 394--413.

Abstract:
In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as linear combinations of (not necessarily independent) gamma distributed random variables. The connection with Malliavin calculus for random variables in the second Wiener chaos is detailed. An application to McKay Type I random variables is also outlined.

Flávio B. Gonçalves, Marcos O. Prates, Victor Hugo Lachos.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 51--70.

Abstract:
In this paper, we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture corresponds to one possible model within the symmetrical class of normal independent distributions. Naturally, the Gaussian model is one of the possibilities. This allows for a simultaneous analysis based on the posterior probability of each model. Inference is performed via Markov chain Monte Carlo—a Gibbs sampler with Metropolis–Hastings steps for a class of parameters. Simulated examples highlight the advantages of this approach compared to a segregated analysis based on arbitrarily chosen model selection criteria. Examples with real data are presented and an extension to censored linear regression is introduced and discussed.

Francisco Cribari-Neto, Rodney V. Fonseca.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 329--355.

Abstract:
The log-linear Birnbaum–Saunders model has been widely used in empirical applications. We introduce an extension of this model based on a recently proposed version of the Birnbaum–Saunders distribution which is more flexible than the standard Birnbaum–Saunders law since its density may assume both unimodal and bimodal shapes. We show how to perform point estimation, interval estimation and hypothesis testing inferences on the parameters that index the regression model we propose. We also present a number of diagnostic tools, such as residual analysis, local influence, generalized leverage, generalized Cook’s distance and model misspecification tests. We investigate the usefulness of model selection criteria and the accuracy of prediction intervals for the proposed model. Results of Monte Carlo simulations are presented. Finally, we also present and discuss an empirical application.

Alain Desgagné, Philippe Gagnon.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 205--221.

Abstract:
Whole robustness is a nice property to have for statistical models. It implies that the impact of outliers gradually vanishes as they approach plus or minus infinity. So far, the Bayesian literature provides results that ensure whole robustness for the location-scale model. In this paper, we make two contributions. First, we generalise the results to attain whole robustness in simple linear regression through the origin, which is a necessary step towards results for general linear regression models. We allow the variance of the error term to depend on the explanatory variable. This flexibility leads to the second contribution: we provide a simple Bayesian approach to robustly estimate finite population means and ratios. The strategy to attain whole robustness is simple since it lies in replacing the traditional normal assumption on the error term by a super heavy-tailed distribution assumption. As a result, users can estimate the parameters as usual, using the posterior distribution.

An R package for computing the all-subsets regression problem is presented. The proposed algorithms are based on computational strategies recently developed. A novel algorithm for the best-subset regression problem selects subset models based on a predetermined criterion. The package user can choose from exact and from approximation algorithms. The core of the package is written in C++ and provides an efficient implementation of all the underlying numerical computations. A case study and benchmark results illustrate the usage and the computational efficiency of the package.

According to data released by Power to Decide, an estimated 369,960 New Jersey women of reproductive age (13-44) in need of publicly funded contraception live in counties impacted by the...

(PRWeb April 09, 2020)

Read the full story at https://www.prweb.com/releases/domestic_gag_rule_reduces_contraceptive_access_for_nearly_370_000_women_living_in_new_jersey/prweb17040987.htm

Edgar Dobriban, William Leeb, Amit Singer.

Source: The Annals of Statistics, Volume 48, Number 1, 491--513.

Abstract:
We consider the linearly transformed spiked model , where the observations $Y_{i}$ are noisy linear transforms of unobserved signals of interest $X_{i}$: egin{equation*}Y_{i}=A_{i}X_{i}+varepsilon_{i},end{equation*} for $i=1,ldots ,n$. The transform matrices $A_{i}$ are also observed. We model the unobserved signals (or regression coefficients) $X_{i}$ as vectors lying on an unknown low-dimensional space. Given only $Y_{i}$ and $A_{i}$ how should we predict or recover their values? The naive approach of performing regression for each observation separately is inaccurate due to the large noise level. Instead, we develop optimal methods for predicting $X_{i}$ by “borrowing strength” across the different samples. Our linear empirical Bayes methods scale to large datasets and rely on weak moment assumptions. We show that this model has wide-ranging applications in signal processing, deconvolution, cryo-electron microscopy, and missing data with noise. For missing data, we show in simulations that our methods are more robust to noise and to unequal sampling than well-known matrix completion methods.

Vladimir Koltchinskii, Matthias Löffler, Richard Nickl.

Source: The Annals of Statistics, Volume 48, Number 1, 464--490.

Abstract:
We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_{1},dots,X_{n}$ in a separable Hilbert space $mathbb{H}$ with unknown covariance operator $Sigma $. The complexity of the problem is characterized by its effective rank $mathbf{r}(Sigma):=frac{operatorname{tr}(Sigma)}{|Sigma |}$, where $mathrm{tr}(Sigma)$ denotes the trace of $Sigma $ and $|Sigma|$ denotes its operator norm. We develop a method of bias reduction in the problem of estimation of linear functionals of eigenvectors of $Sigma $. Under the assumption that $mathbf{r}(Sigma)=o(n)$, we establish the asymptotic normality and asymptotic properties of the risk of the resulting estimators and prove matching minimax lower bounds, showing their semiparametric optimality.