Qiyang Han, Tengyao Wang, Sabyasachi Chatterjee, Richard J. Samworth.

Source: The Annals of Statistics, Volume 47, Number 5, 2440--2471.

Abstract:
We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^{d}$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that the estimator achieves the minimax rate of order $n^{-min{2/(d+2),1/d}}$ in the empirical $L_{2}$ loss, up to polylogarithmic factors. Further, we prove a sharp oracle inequality, which reveals in particular that when the true regression function is piecewise constant on $k$ hyperrectangles, the least squares estimator enjoys a faster, adaptive rate of convergence of $(k/n)^{min(1,2/d)}$, again up to polylogarithmic factors. Previous results are confined to the case $dleq2$. Finally, we establish corresponding bounds (which are new even in the case $d=2$) in the more challenging random design setting. There are two surprising features of these results: first, they demonstrate that it is possible for a global empirical risk minimisation procedure to be rate optimal up to polylogarithmic factors even when the corresponding entropy integral for the function class diverges rapidly; second, they indicate that the adaptation rate for shape-constrained estimators can be strictly worse than the parametric rate.

Joshua Cape, Minh Tang, Carey E. Priebe.

Source: The Annals of Statistics, Volume 47, Number 5, 2405--2439.

Abstract:
The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric structure of singular values and singular vectors. This paper provides a novel collection of technical and theoretical tools for studying the geometry of singular subspaces using the two-to-infinity norm. Motivated by preliminary deterministic Procrustes analysis, we consider a general matrix perturbation setting in which we derive a new Procrustean matrix decomposition. Together with flexible machinery developed for the two-to-infinity norm, this allows us to conduct a refined analysis of the induced perturbation geometry with respect to the underlying singular vectors even in the presence of singular value multiplicity. Our analysis yields singular vector entrywise perturbation bounds for a range of popular matrix noise models, each of which has a meaningful associated statistical inference task. In addition, we demonstrate how the two-to-infinity norm is the preferred norm in certain statistical settings. Specific applications discussed in this paper include covariance estimation, singular subspace recovery, and multiple graph inference. Both our Procrustean matrix decomposition and the technical machinery developed for the two-to-infinity norm may be of independent interest.

Benedikt Bauer, Michael Kohler.

Source: The Annals of Statistics, Volume 47, Number 4, 2261--2285.

Abstract:
Assuming that a smoothness condition and a suitable restriction on the structure of the regression function hold, it is shown that least squares estimates based on multilayer feedforward neural networks are able to circumvent the curse of dimensionality in nonparametric regression. The proof is based on new approximation results concerning multilayer feedforward neural networks with bounded weights and a bounded number of hidden neurons. The estimates are compared with various other approaches by using simulated data.

Ivan Nourdin, Giovanni Peccati, Stéphane Seuret.

Source: Bernoulli, Volume 26, Number 3, 1619--1634.

Abstract:
We describe the size of the sets of sojourn times $E_{gamma }={tgeq 0:|B_{t}|leq t^{gamma }}$ associated with a fractional Brownian motion $B$ in terms of various large scale dimensions.

Denis Talay, Milica Tomašević.

Source: Bernoulli, Volume 26, Number 2, 1323--1353.

Abstract:
In this paper, we analyze a stochastic interpretation of the one-dimensional parabolic–parabolic Keller–Segel system without cut-off. It involves an original type of McKean–Vlasov interaction kernel. At the particle level, each particle interacts with all the past of each other particle by means of a time integrated functional involving a singular kernel. At the mean-field level studied here, the McKean–Vlasov limit process interacts with all the past time marginals of its probability distribution in a similarly singular way. We prove that the parabolic–parabolic Keller–Segel system in the whole Euclidean space and the corresponding McKean–Vlasov stochastic differential equation are well-posed for any values of the parameters of the model.

Binyan Jiang, Ziqi Chen, Chenlei Leng.

Source: Bernoulli, Volume 26, Number 2, 1234--1268.

Abstract:
High-dimensional data that evolve dynamically feature predominantly in the modern data era. As a partial response to this, recent years have seen increasing emphasis to address the dimensionality challenge. However, the non-static nature of these datasets is largely ignored. This paper addresses both challenges by proposing a novel yet simple dynamic linear programming discriminant (DLPD) rule for binary classification. Different from the usual static linear discriminant analysis, the new method is able to capture the changing distributions of the underlying populations by modeling their means and covariances as smooth functions of covariates of interest. Under an approximate sparse condition, we show that the conditional misclassification rate of the DLPD rule converges to the Bayes risk in probability uniformly over the range of the variables used for modeling the dynamics, when the dimensionality is allowed to grow exponentially with the sample size. The minimax lower bound of the estimation of the Bayes risk is also established, implying that the misclassification rate of our proposed rule is minimax-rate optimal. The promising performance of the DLPD rule is illustrated via extensive simulation studies and the analysis of a breast cancer dataset.

Peggy Cénac, Basile de Loynes, Yoann Offret, Arnaud Rousselle.

Source: Bernoulli, Volume 26, Number 2, 858--892.

Abstract:
The recurrence and transience of persistent random walks built from variable length Markov chains are investigated. It turns out that these stochastic processes can be seen as Lévy walks for which the persistence times depend on some internal Markov chain: they admit Markov random walk skeletons. A recurrence versus transience dichotomy is highlighted. Assuming the positive recurrence of the driving chain, a sufficient Fourier criterion for the recurrence, close to the usual Chung–Fuchs one, is given and a series criterion is derived. The key tool is the Nagaev–Guivarc’h method. Finally, we focus on particular two-dimensional persistent random walks, including directionally reinforced random walks, for which necessary and sufficient Fourier and series criteria are obtained. Inspired by ( Adv. Math. 208 (2007) 680–698), we produce a genuine counterexample to the conjecture of ( Adv. Math. 117 (1996) 239–252). As for the one-dimensional case studied in ( J. Theoret. Probab. 31 (2018) 232–243), it is easier for a persistent random walk than its skeleton to be recurrent. However, such examples are much more difficult to exhibit in the higher dimensional context. These results are based on a surprisingly novel – to our knowledge – upper bound for the Lévy concentration function associated with symmetric distributions.

Keisuke Yano, Kengo Kato.

Source: Bernoulli, Volume 26, Number 1, 616--641.

Abstract:
In this paper, we study frequentist coverage errors of Bayesian credible sets for an approximately linear regression model with (moderately) high dimensional regressors, where the dimension of the regressors may increase with but is smaller than the sample size. Specifically, we consider quasi-Bayesian inference on the slope vector under the quasi-likelihood with Gaussian error distribution. Under this setup, we derive finite sample bounds on frequentist coverage errors of Bayesian credible rectangles. Derivation of those bounds builds on a novel Berry–Esseen type bound on quasi-posterior distributions and recent results on high-dimensional CLT on hyperrectangles. We use this general result to quantify coverage errors of Castillo–Nickl and $L^{infty}$-credible bands for Gaussian white noise models, linear inverse problems, and (possibly non-Gaussian) nonparametric regression models. In particular, we show that Bayesian credible bands for those nonparametric models have coverage errors decaying polynomially fast in the sample size, implying advantages of Bayesian credible bands over confidence bands based on extreme value theory.

Zhuang Ma, Xiaodong Li.

Source: Bernoulli, Volume 26, Number 1, 432--470.

Abstract:
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by the recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose two losses based on the principal angles between the model spaces spanned by the sample canonical variates and their population correspondents, respectively. We further characterize the non-asymptotic error bounds for the estimation risks under the proposed error metrics, which reveal how the performance of sample CCA depends adaptively on key quantities including the dimensions, the sample size, the condition number of the covariance matrices and particularly the population canonical correlation coefficients. The optimality of our uniform upper bounds is also justified by lower-bound analysis based on stringent and localized parameter spaces. To the best of our knowledge, for the first time our paper separates $p_{1}$ and $p_{2}$ for the first order term in the upper bounds without assuming the residual correlations are zeros. More significantly, our paper derives $(1-lambda_{k}^{2})(1-lambda_{k+1}^{2})/(lambda_{k}-lambda_{k+1})^{2}$ for the first time in the non-asymptotic CCA estimation convergence rates, which is essential to understand the behavior of CCA when the leading canonical correlation coefficients are close to $1$.

Xiucai Ding.

Source: Bernoulli, Volume 26, Number 1, 387--417.

Abstract:
We consider the recovery of a low rank $M imes N$ matrix $S$ from its noisy observation $ ilde{S}$ in the high dimensional framework when $M$ is comparable to $N$. We propose two efficient estimators for $S$ under two different regimes. Our analysis relies on the local asymptotics of the eigenstructure of large dimensional rectangular matrices with finite rank perturbation. We derive the convergent limits and rates for the singular values and vectors for such matrices.

Xuan Cao, Kshitij Khare, Malay Ghosh.

Source: Bayesian Analysis, Volume 15, Number 1, 241--262.

Abstract:
The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an important tuning parameter which reflects the dispersion of the non-local prior density around zero, and implicitly determines the size of the regression coefficients that will be shrunk to zero. Current approaches treat the scale parameter as given, and suggest choices based on prior coverage/asymptotic considerations. In this paper, we consider the fully Bayesian approach introduced in (Wu, 2016) with the pMOM non-local prior and an appropriate Inverse-Gamma prior on the tuning parameter to analyze the underlying theoretical property. Under standard regularity assumptions, we establish strong model selection consistency in a high-dimensional setting, where $p$ is allowed to increase at a polynomial rate with $n$ or even at a sub-exponential rate with $n$ . Through simulation studies, we demonstrate that our model selection procedure can outperform other Bayesian methods which treat the scale parameter as given, and commonly used penalized likelihood methods, in a range of simulation settings.

Gemma E. Moran, Veronika Ročková, Edward I. George.

Source: Bayesian Analysis, Volume 14, Number 4, 1091--1119.

Abstract:
Consider the problem of high dimensional variable selection for the Gaussian linear model when the unknown error variance is also of interest. In this paper, we show that the use of conjugate shrinkage priors for Bayesian variable selection can have detrimental consequences for such variance estimation. Such priors are often motivated by the invariance argument of Jeffreys (1961). Revisiting this work, however, we highlight a caveat that Jeffreys himself noticed; namely that biased estimators can result from inducing dependence between parameters a priori . In a similar way, we show that conjugate priors for linear regression, which induce prior dependence, can lead to such underestimation in the Bayesian high-dimensional regression setting. Following Jeffreys, we recommend as a remedy to treat regression coefficients and the error variance as independent a priori . Using such an independence prior framework, we extend the Spike-and-Slab Lasso of Ročková and George (2018) to the unknown variance case. This extended procedure outperforms both the fixed variance approach and alternative penalized likelihood methods on simulated data. On the protein activity dataset of Clyde and Parmigiani (1998), the Spike-and-Slab Lasso with unknown variance achieves lower cross-validation error than alternative penalized likelihood methods, demonstrating the gains in predictive accuracy afforded by simultaneous error variance estimation. The unknown variance implementation of the Spike-and-Slab Lasso is provided in the publicly available R package SSLASSO (Ročková and Moran, 2017).

Joseph Antonelli, Giovanni Parmigiani, Francesca Dominici.

Source: Bayesian Analysis, Volume 14, Number 3, 825--848.

Abstract:
In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders ( $p$ ) is larger than the number of observations ( $n$ ), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable $X_{j}$ is strongly associated with the treatment $T$ but weakly with the outcome $Y$ , the coefficient $eta_{j}$ will be shrunk towards zero thus leading to confounding bias. Under the assumption of a linear model for the outcome and sparsity, we propose continuous spike and slab priors on the regression coefficients $eta_{j}$ corresponding to the potential confounders $X_{j}$ . Specifically, we introduce a prior distribution that does not heavily shrink to zero the coefficients ( $eta_{j}$ s) of the $X_{j}$ s that are strongly associated with $T$ but weakly associated with $Y$ . We compare our proposed approach to several state of the art methods proposed in the literature. Our proposed approach has the following features: 1) it reduces confounding bias in high dimensional settings; 2) it shrinks towards zero coefficients of instrumental variables; and 3) it achieves good coverages even in small sample sizes. We apply our approach to the National Health and Nutrition Examination Survey (NHANES) data to estimate the causal effects of persistent pesticide exposure on triglyceride levels.

KM Harris
Jul 1, 1992; 12:2685-2705
Articles

Fiona Doetsch
Jul 1, 1997; 17:5046-5061
Articles

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Verification of a USB4 router design is not just about USB4 but also about the inclusion of the three other major protocols namely, USB3, DisplayPort (DP), and PCI Express (PCIe). These protocols can be simultaneously tunneled through a USB4 router. Put in simple terms, such tunneling involves the conversion of the respective native USB3, DP, or PCIe protocol traffic into the USB4 transport layer packets, which are tunneled through a USB4 fabric, and converted back into the respective original native protocol traffic.

It may sound simple but is perhaps not.

There are several aspects in a router that come into picture to carry out this task of conversion of native protocol traffic, route it to the intended destination, and then convert it back to the original form. Some of those are the USB3, DP and PCIe protocol adapters, transport mechanism using routing, flow control, paths, path set-up and teardown, control and configuration, configuration spaces.

That is not all. There are core USB4 specific logical layer intricacies as well, which carry out the tasks of ensuring that all the USB4 ports and links are working as desired to provide up to 40Gbps speed and that the USB4 traffic flows through out the fabric in the intended way. These bring on the table features like High Speed link, ordered sets, lane initialization, lane adapter state machine, low power, lane bonding, RS-FEC, side band channel, sleep and wake, error checking.

All of these put together give rise to a very large verification space against which a USB4 router design should be verified. If we were to break down this space it can be broadly put in the following major dimensions,

• Protocol Adapter Layer
  • USB3 tunneling
  • DP tunneling
  • PCIe tunneling
• Host Interface Adapter Layer
• Transport Layer
  • Flow control
  • Routing
  • Paths
• Configuration layer and control packet protocol
• Configuration spaces
• Logical Layer

The independent verification of these dimensions is not all that would qualify the design as verified. They have to be verified in various combinations of each other too. Overall, all the parts of a USB4 router system need to be working together coherently.

For example, the following diagram depicts the various layers that a USB4 router may comprise of,

A USB4 router or a domain of routers does not work on its own. There is a Connection Manager per domain, which is a software-based entity managing a domain. A router provides the various capabilities for a Connection Manager to carry out its responsibilities of managing a domain.

It would not be an exaggeration to say that the spectrum of verification of a USB4 router ranges from the very minute details of logical layer to the system-level like multiple dependencies as the whole USB4 system is brought up layer by layer, step-by-step.

Cadence has a mature Verification IP solution that can help in the verification of USB4 designs. Cadence has taken an active part in the working group that defined the USB4 specification and has created a comprehensive Verification IP that is being used by multiple members in the last two years.

If you plan to have a USB4 compatible design, you can reduce the risk of adopting a new technology by using our proven and mature USB4 Verification IP. Please contact your Cadence local account team for more details and to get connected.

This working paper proposes flood footprint and accountability to coordinate risk management projects through appropriate spatial planning at river basin scale.

With the opening of its Luxury Audio Studio, HARMAN is building on the success of its Experience Store in Munich and creating a whole new dimension of experiential excellence. Dedicated to the Art of Listening, the new Luxury Studio celebrates and...

Mechanical heterogeneity of a sedimentary sequence exerts a primary control on the geometry of fault zones and the proportion of offset accommodated by folding. The Wildensbuch Fault Zone in the Swiss Molasse Basin, with a maximum throw of 40 m, intersects a Mesozoic section containing a thick (120 m) clay-dominated unit (Opalinus Clay) over- and underlain by more competent limestone units. Interpretation of a 3D seismic reflection survey indicates that the fault zone formed by upward propagation of an east–west-trending basement structure, through the Mesozoic section, in response to NE–SW Miocene extension. This configuration formed an array of left-stepping normal fault segments above and below the Opalinus Clay. In cross-section a broad monoclinal fold is observed in the Opalinus Clay. Folding, however, is not ubiquitous and occurs in the Opalinus Clay where fault segments above and below are oblique to one another; where they are parallel the fault passes through the Opalinus Clay with little folding. These observations demonstrate that, even in strongly heterogeneous sequences, here a four-fold difference in both Young's modulus and cohesion between layers, the occurrence of folding may depend on the local relationship between fault geometry and applied stress field rather than rheological properties alone.

Asja Guzman, Rachel C. Avard, Alexander J. Devanny, Oh Sang Kweon, and Laura J. Kaufman

The study of cancer cell invasion in 3D environments in vitro has revealed a variety of invasive modes, including amoeboid migration, characterized by primarily round cells that invade in a protease- and adhesion-independent manner. Here, we delineate a contractility-dependent migratory mode of primarily round breast cancer cells that is associated with extensive integrin-mediated extracellular matrix (ECM) reorganization that occurs at membrane blebs, with bleb necks sites of integrin clustering and integrin-dependent ECM alignment. We show that the spatiotemporal distribution of blebs and their utilization for ECM reorganization is mediated by functional β1 integrin receptors and other components of focal adhesions. Taken together, the work presented here characterizes a migratory mode of primarily round cancer cells in complex 3D environments and reveals a fundamentally new function for membrane blebs in cancer cell invasion.

For most of Doom Eternal‘s demonic foes, the best they can expect is to make a nice corpse. A particularly pleasing splash of gore on the Doom Slayer’s boot. But for those lucky few that manage to take down our man in green, a special reward will soon be in store. Doom Eternal’s first major […]

We return from a weekend off to discuss good games, bad games, old games, and new games that aren’t out yet! Anna Marie hosts as we tackle TGS, the continued flood of holiday releases, and numerous site features.

Congress and the Trump administration are beginning to pull together the components of a fourth COVID-19 emergency supplemental. The first package included initial emergency funding to bolster foreign assistance programs. In the third package, while containing critical funding for the safety of our diplomatic and development workers, less than half of 1 percent of the…

Congress and the Trump administration are beginning to pull together the components of a fourth COVID-19 emergency supplemental. The first package included initial emergency funding to bolster foreign assistance programs. In the third package, while containing critical funding for the safety of our diplomatic and development workers, less than half of 1 percent of the…

These pre-assembled pieces of furniture can fold completely flat, and when needed, are opened up into three-dimensional functionality.

Atmospheric glazes of color and hand-shaped clay leaves and tree trunks adorn these beautiful ceramic pieces.

This paper examines the role of businesses in the tax system. In addition to being taxed directly, businesses act as withholding agents and remitters of tax on behalf of others. Yet the share of tax revenue that businesses remit to governments outside of direct tax liabilities is under-studied.

Thailand has made remarkable socio-economic progress over the past several decades. Even so, rising prosperity has not been shared equally across the country. Today, Thailand strives to pursue a development path to benefit all, seeking to reinvigorate economic transformation and reduce multifaceted inequalities in the face of a rapidly ageing population and technological change.

Mark Cavendish has been left out of the Dimension Data team that will compete in this year's Tour de France. It is the first time in 13 years that the British rider will not compete in France.

Earlier this week news broke that Dimension Data's team principal, Doug Ryder, ignored the recommendation by performance boss Rolf Aldag to include Cavendish in line-up.

Team Dimension Data head of performance Rolf Aldag has made clear he will stay with the team for the remainder of the Tour de France as the row over Mark Cavendish's non-selection rumbled on.

The pandemic wave, similarly, will be with us for the foreseeable future before it diminishes. But depending on the location and the policies in place, it will exhibit variegated dimensions and dynamics traveling through time and space.

Singapore : Springer, c2019.

Cham : Springer, 2019.

[S.l.] : SPRINGER NATURE, 2019.

Cham : Springer, 2019.

Cham : Birkhäuser, [2019]

Barker Library - TA357.D45 2013

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Over Dimensional Cargo