Faced with a growing economic crisis, many European Union member states are clamoring for the introduction of so-called corona bonds. Just like it was in the euro crisis, though, Germany is opposed. In the end, Berlin may not have a choice. By DER SPIEGEL Staff

Police discovered firefighter Lenzell Ross, 28, snoozing in his parked Tesla on the side of the Belt Parkway near Shore Parkway in Lindenwood about 2:30 a.m., authorities said.

Friends played touch football and shared sweaty exercise equipment while others kept their distance from others

Suspect Donte West, 28, broke into a side door of the shoe store on Pitkin Ave. near Bristol St. in Brownsville about 8:45 a.m. Saturday and loaded up a Chevy Trailblazer with more than three dozen pairs of sneakers and nearly 40 baseball caps as cops arrived, police said.

Frederick Scheinin, 29, of Sunnyside, Queens, allegedly chatted for months with a federal agent posing as a minor, and now faces charges in Manhattan federal court of attempting to entice a minor and attempting to produce child pornography.

Robert Soto, 33, showed up drunk to his ex-lover’s Morrisania apartment some time before midnight Thursday and got into an argument with the woman. As she tried to escort him out, Soto bashed her head into a metal door, cops said.

Doctors caring for the sickest COVID-19 patients are trying new ways to attack the coronavirus. One theory is that they have blood clots in their lungs.

The author, most recently, of "Interior Chinatown" opts for "Independence Day," a slew of inspiring novels, "Thor: Ragnarok" and "Ozark."

Keeping him in office prevents the left from destroying America with their socialistic ideology, a letter to the editor says.

Until we have a vaccine, the road to opening is through a health care system which can handle the infection, a letter to the editor says.

An anonymous reader quotes a report from Bloomberg: Syed Shah usually buys and sells stocks and currencies through his Interactive Brokers account, but he couldn't resist trying his hand at some oil trading on April 20, the day prices plunged below zero for the first time ever. The day trader, working from his house in a Toronto suburb, figured he couldn't lose as he spent $2,400 snapping up crude at $3.30 a barrel, and then 50 cents. Then came what looked like the deal of a lifetime: buying 212 futures contracts on West Texas Intermediate for an astonishing penny each. What he didn't know was oil's first trip into negative pricing had broken Interactive Brokers Group Inc. Its software couldn't cope with that pesky minus sign, even though it was always technically possible -- though this was an outlandish idea before the pandemic -- for the crude market to go upside down. Crude was actually around negative $3.70 a barrel when Shah's screen had it at 1 cent. Interactive Brokers never displayed a subzero price to him as oil kept diving to end the day at minus $37.63 a barrel. At midnight, Shah got the devastating news: he owed Interactive Brokers $9 million. He'd started the day with $77,000 in his account. To be clear, investors who were long those oil contracts had a brutal day, regardless of what brokerage they had their account in. What set Interactive Brokers apart, though, is that its customers were flying blind, unable to see that prices had turned negative, or in other cases locked into their investments and blocked from trading. Compounding the problem, and a big reason why Shah lost an unbelievable amount in a few hours, is that the negative numbers also blew up the model Interactive Brokers used to calculate the amount of margin -- aka collateral -- that customers needed to secure their accounts. "It's a $113 million mistake on our part," said Thomas Peterffy, the chairman and founder of Interactive Brokers, in an interview Wednesday. Customers will be made whole, Peterffy said. "We will rebate from our own funds to our customers who were locked in with a long position during the time the price was negative any losses they suffered below zero."

Read more of this story at Slashdot.

Dave & Buster's is bringing its restaurant and entertainment complex to Greenwood in April, and the company plans to hire for more than 230 positions.

A show billed as "The Adventures of Kesha and Macklemore" resembles a summer popcorn movie at Ruoff Home Mortgage Music Center.

Until we have a vaccine, the road to opening is through a health care system which can handle the infection, a letter to the editor says.

• Facebook has been in negotiations for months to lease over 700,000 square feet at the Farley Building on Manhattan's West Side. 
• Office leasing activity in the city has plummeted, giving the blockbuster deal even more importance as a sign of life in a suddenly lethargic market.
• The coronavirus has spurred a deep downturn in the economy that is already being felt in the city's commercial real-estate market, prompting a big slowdown in leasing activity.  
• The rapid expansion of tech in recent years has propelled the city's office market. Real estate execs say that Facebook's big deal is a key barometer. 
• The crisis also raises questions whether tenants will ever occupy office space the same way as companies and their workforces around the world grow familiar with remote work. 
• Click here for more BI Prime stories.

Leasing activity in New York City's multi-billion-dollar commercial office market has dropped precipitously as the coronavirus has battered the market and raised questions of when — and even if — tenants can return to the workplace in a post-Covid world.

Amid the growing concerns the crisis will smother what had been robust demand for office space, eyes in the city's real estate industry have turned to a pending blockbuster deal on the West Side that could offer a signal of confidence to the market.

Facebook is in talks to take over 700,000 square feet of space in the Farley Building, a block-long property across Eighth Avenue from Penn Station.

"If that deal happens, then this market will be just fine," said Peter Riguardi, the New York area chairman and president of JLL. "If the deal happens but it's renegotiated, it will be fine, but it will be a trend that every tenant can follow. And if it doesn't happen, I would be very concerned about the market."

Read More: Inside the drama over control of the iconic Chrysler Building: A real-estate tycoon and a prestigious college are renegotiating a critical $150 million deal.

Facebook's NYC real-estate footprint

Last year, Facebook signed on for 1.5 million square feet in the Hudson Yards mega-development just west of the Farley Building, taking space in three new office towers at the project.

For months the $600 billion Silicon Valley-based social media giant has been in negotiations for even more space at the nearby Farley Building, whose interior landlord Vornado Realty Trust is redeveloping to include newly built office and retail space.

Vornado had originally expected to complete the deal with Facebook in early March, according to a source familiar with the negotiations. The talks have continued on as the virus pandemic has brought commerce and social life to a virtual halt. The source expected the lease, which will commit Facebook to pay hundreds of millions of dollars in rent for the space over the life of the lease, to soon be completed.

In a conference call with investors and analysts on Tuesday to discuss Vornado's first-quarter earnings, the company's CEO Steve Roth also hinted that the Facebook deal was still on track.

"There's another large tenant that has been rumored to be that we've been in dialogue with," Roth said, not directly naming the company. "That conversation is going forward aggressively and hopefully maybe even almost complete."

Rapid growth in Big Tech leasing before coronavirus

Recent real-estate decisions by Facebook and other tech companies have worried real-estate executives that they may reconsider their footprint after years of dramatic growth. Facebook on Thursday revealed that the bulk of its over 40,000-person workforce will be asked to work remotely for the remainder of the year, a timeline that appears to show the company is using caution in returning to its footprint.

Read More: Neiman Marcus just filed for bankruptcy, and it could mark a major blow to NYC's glitzy Hudson Yards — one of the most expensive mega-malls in US history. Here's why.

Real-estate executives have expressed concern that tenants may become accustomed to offloading a portion or even the bulk of their workforce to a remote-working model, leading them to drastically reduce their office commitments.

At a minimum, the economic upheaval has appeared to spur a newfound sense of caution in tech companies that have grown rapidly in recent years. Alphabet called off negotiations to expand its San Francisco offices by over 2 million square feet in recent weeks, according to a report from The Information.  

Tech has been a big driver of demand for office space

In recent years the tech industry had become one of the most voracious takers of space in the city, helping to push up commercial rents and spur the construction of new office space.

In 2019, tech firms accounted for 24.5% of the 31.6 million square feet of leasing activity in Manhattan, eclipsing the financial industry as the city's biggest space-taking sector for the first time, according to data from the real estate services and brokerage firm CBRE.

In 2010 tech leasing comprised just 4% of the 24.2 million square feet that was leased in the Manhattan market that year, CBRE said.

"Nothing has buoyed the confidence of landlords more in recent years than tech tenants," said Sacha Zarba, a leasing executive at CBRE who specializes in working with tech firms. "It didn't matter where your building was. If it was attractive to tech, you would stand a good chance to lease your space. If that industry retrenches a bit, it removes a big driver of demand."

The Manhattan office market has slowed rapidly in recent weeks as the virus crisis has battered the economy and shut down daily life.

About 844,000 square feet of space was leased in Manhattan in April, according to CBRE, 64% lower than the five-year monthly average. In the first four months of the year, nearly seven million square feet was leased, a decline of 30% for the same period a year ago. 

So far, however, there are signs that tech continues to snap up space.

After scuttling plans to develop a 25,000 person second headquarters space in Long Island City last year, Amazon purchased 424 Fifth Avenue, a former flagship department store for Lord & Taylor, for nearly $1 billion in March. That property totals about 660,000 square feet. Late last year, before the pandemic hit U.S. shores but had flared in China, Amazon also leased 335,000 square feet at 410 Tenth Avenue.

The commitments of major tech companies absorb millions of square feet in the city, but they also help fuel a larger ecosystem of tenants that occupies an even larger footprint. That means that a decrease in the real estate of just a few big tech players could be multiplied across the market as smaller players in the sector follow suit.

"Those big tech firms do a fantastic job of training and credentialing tech talent on the city," said Matt Harrigan, a co-founder of Company, a space incubator at 335 Madison Avenue that provides offices and community for both startups and more established tech firms. "Google and Facebook spin off talent who start or join other tech ventures that take space. That's what's so important about having the large presence of those companies here."

Have a tip? Contact Daniel Geiger at dgeiger@businessinsider.com or via encrypted messaging app Signal at +1 (646) 352-2884, or Twitter DM at @dangeiger79. You can also contact Business Insider securely via SecureDrop.

SEE ALSO: What to expect when you're back in the office: 7 real-estate experts break down what the transition will look like, and why the workplace may never be the same

SEE ALSO: Major tenants are delaying big leases in NYC as they re-think their office space needs for the post-coronavirus world

SEE ALSO: As WeWork and flex-space rivals stumble, 18 million square feet of space in NYC is at risk. Here's what that means for the real-estate market.

SEE ALSO: BI Prime Edit in Viking Neiman Marcus just filed for bankruptcy, and it could mark a major blow to NYC's glitzy Hudson Yards — one of the most expensive mega-malls in US history. Here's why.

Join the conversation about this story »

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Many of the changes are simply worse for the economy.

The online gambling ring allegedly used an offshore website to help book $32 million in illegal sports wagers placed by more than 2,000 bettors in the United States.

The following article, Busted! Late-Night Hack Comedian, Jimmy Kimmel Is Forced To Apologize For Sharing Highly Edited Video Of VP Pence To Make Him Look Bad, was first published on 100PercentFedUp.com.

Last night, Jimmy Kimmel, host of the low-rated, late-night Jimmy Kimmel Show, shared a deceptively edited video clip of Vice President Pence delivering PPE to a nursing home. Today, liberal activist Matt McDermott tweeted the videotaped segment on VP Pence that was edited to make the vice president look like he was faking a delivery […]

Continue reading: Busted! Late-Night Hack Comedian, Jimmy Kimmel Is Forced To Apologize For Sharing Highly Edited Video Of VP Pence To Make Him Look Bad ...

Adriaan Sticker
Apr 22, 2020; 0:RA119.001624v1-mcp.RA119.001624
Research

The presentation of peptides on class I human leukocyte antigen (HLA-I) molecules plays a central role in immune recognition of infected or malignant cells. In cancer, non-self HLA-I ligands can arise from many different alterations, including non-synonymous mutations, gene fusion, cancer-specific alternative mRNA splicing or aberrant post-translational modifications. Identifying HLA-I ligands remains a challenging task that requires either heavy experimental work for in vivo identification or optimized bioinformatics tools for accurate predictions. To date, no HLA-I ligand predictor includes post-translational modifications. To fill this gap, we curated phosphorylated HLA-I ligands from several immunopeptidomics studies (including six newly measured samples) covering 72 HLA-I alleles and retrieved a total of 2,066 unique phosphorylated peptides. We then expanded our motif deconvolution tool to identify precise binding motifs of phosphorylated HLA-I ligands. Our results reveal a clear enrichment of phosphorylated peptides among HLA-C ligands and demonstrate a prevalent role of both HLA-I motifs and kinase motifs on the presentation of phosphorylated peptides. These data further enabled us to develop and validate the first predictor of interactions between HLA-I molecules and phosphorylated peptides.

Label-Free Quantitative mass spectrometry based workflows for differential expression (DE) analysis of proteins impose important challenges on the data analysis due to peptide-specific effects and context dependent missingness of peptide intensities. Peptide-based workflows, like MSqRob, test for DE directly from peptide intensities and outperform summarization methods which first aggregate MS1 peptide intensities to protein intensities before DE analysis. However, these methods are computationally expensive, often hard to understand for the non-specialised end-user, and do not provide protein summaries, which are important for visualisation or downstream processing. In this work, we therefore evaluate state-of-the-art summarization strategies using a benchmark spike-in dataset and discuss why and when these fail compared to the state-of-the-art peptide based model, MSqRob. Based on this evaluation, we propose a novel summarization strategy, MSqRobSum, which estimates MSqRob’s model parameters in a two-stage procedure circumventing the drawbacks of peptide-based workflows. MSqRobSum maintains MSqRob’s superior performance, while providing useful protein expression summaries for plotting and downstream analysis. Summarising peptide to protein intensities considerably reduces the computational complexity, the memory footprint and the model complexity, and makes it easier to disseminate DE inferred on protein summaries. Moreover, MSqRobSum provides a highly modular analysis framework, which provides researchers with full flexibility to develop data analysis workflows tailored towards their specific applications.

HE Hohmeier
Mar 1, 2000; 49:424-430
Articles

[Rome?] : [publisher not identified], [1807?]

[The Netherlands] : [Romeyn de Hooghe?], [1678?]

We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensional clusters in high-dimensional space, in the presence of a large number of high-dimensional outliers. By combining these results with spectral clustering with respect to LLPD, we provide conditions under which the Laplacian eigengap statistic correctly determines the number of clusters for a large class of data sets, and prove guarantees on the labeling accuracy of the proposed algorithm. Our methods are quite general and provide performance guarantees for spectral clustering with any ultrametric. We also introduce an efficient, easy to implement approximation algorithm for the LLPD based on a multiscale analysis of adjacency graphs, which allows for the runtime of LLPD spectral clustering to be quasilinear in the number of data points.

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 consider the standard model of distributed optimization of a sum of functions $F(mathbf z) = sum_{i=1}^n f_i(mathbf z)$, where node $i$ in a network holds the function $f_i(mathbf z)$. We allow for a harsh network model characterized by asynchronous updates, message delays, unpredictable message losses, and directed communication among nodes. In this setting, we analyze a modification of the Gradient-Push method for distributed optimization, assuming that (i) node $i$ is capable of generating gradients of its function $f_i(mathbf z)$ corrupted by zero-mean bounded-support additive noise at each step, (ii) $F(mathbf z)$ is strongly convex, and (iii) each $f_i(mathbf z)$ has Lipschitz gradients. We show that our proposed method asymptotically performs as well as the best bounds on centralized gradient descent that takes steps in the direction of the sum of the noisy gradients of all the functions $f_1(mathbf z), ldots, f_n(mathbf z)$ at each step.

This work is concerned with the non-negative rank-1 robust principal component analysis (RPCA), where the goal is to recover the dominant non-negative principal components of a data matrix precisely, where a number of measurements could be grossly corrupted with sparse and arbitrary large noise. Most of the known techniques for solving the RPCA rely on convex relaxation methods by lifting the problem to a higher dimension, which significantly increase the number of variables. As an alternative, the well-known Burer-Monteiro approach can be used to cast the RPCA as a non-convex and non-smooth $ell_1$ optimization problem with a significantly smaller number of variables. In this work, we show that the low-dimensional formulation of the symmetric and asymmetric positive rank-1 RPCA based on the Burer-Monteiro approach has benign landscape, i.e., 1) it does not have any spurious local solution, 2) has a unique global solution, and 3) its unique global solution coincides with the true components. An implication of this result is that simple local search algorithms are guaranteed to achieve a zero global optimality gap when directly applied to the low-dimensional formulation. Furthermore, we provide strong deterministic and probabilistic guarantees for the exact recovery of the true principal components. In particular, it is shown that a constant fraction of the measurements could be grossly corrupted and yet they would not create any spurious local solution.

Saralees Nadarajah, Yuancheng Si.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 183--187.

Abstract:
Da Paz, Balakrishnan and Bazan [Braz. J. Probab. Stat. 33 (2019), 455–479] introduced the L-logistic distribution, studied its properties including estimation issues and illustrated a data application. This note derives a closed form expression for moment properties of the distribution. Some computational issues are discussed.

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.

Rosineide F. da Paz, Narayanaswamy Balakrishnan, Jorge Luis Bazán.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 455--479.

Abstract:
Tadikamalla and Johnson [ Biometrika 69 (1982) 461–465] developed the $L_{B}$ distribution to variables with bounded support by considering a transformation of the standard Logistic distribution. In this manuscript, a convenient parametrization of this distribution is proposed in order to develop regression models. This distribution, referred to here as L-Logistic distribution, provides great flexibility and includes the uniform distribution as a particular case. Several properties of this distribution are studied, and a Bayesian approach is adopted for the parameter estimation. Simulation studies, considering prior sensitivity analysis, recovery of parameters and comparison of algorithms, and robustness to outliers are all discussed showing that the results are insensitive to the choice of priors, efficiency of the algorithm MCMC adopted, and robustness of the model when compared with the beta distribution. Applications to estimate the vulnerability to poverty and to explain the anxiety are performed. The results to applications show that the L-Logistic regression models provide a better fit than the corresponding beta regression models.

Emilia Athayde, Assis Azevedo, Michelli Barros, Víctor Leiva.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 301--328.

Abstract:
The Birnbaum–Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas.

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.

Area under ROC curve (AUC) is a widely used performance measure for classification models. We propose two new distributionally robust AUC maximization models (DR-AUC) that rely on the Kantorovich metric and approximate the AUC with the hinge loss function. We consider the two cases with respectively fixed and variable support for the worst-case distribution. We use duality theory to reformulate the DR-AUC models and derive tractable convex optimization problems. The numerical experiments show that the proposed DR-AUC models -- benchmarked with the standard deterministic AUC and the support vector machine models - perform better in general and in particular improve the worst-case out-of-sample performance over the majority of the considered datasets, thereby showing their robustness. The results are particularly encouraging since our numerical experiments are conducted with training sets of small size which have been known to be conducive to low out-of-sample performance.

This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some of covariates. The target is a marginal location parameter which is given through an $M-$functional. To obtain robust Fisher--consistent estimators, properly defined marginal distribution function estimators are considered. These estimators avoid the bias due to missing values by assuming a missing at random condition. Three methods are considered to estimate the marginal distribution function which allows to obtain the $M-$location of interest: the well-known inverse probability weighting, a convolution--based method that makes use of the regression model and an augmented inverse probability weighting procedure that prevents against misspecification. The robust proposed estimators and the classical ones are compared through a numerical study under different missing models including clean and contaminated samples. We illustrate the estimators behaviour under a nonlinear model. A real data set is also analysed.

In causal settings, such as instrumental variable settings, it is well known that estimators based on ordinary least squares (OLS) can yield biased and non-consistent estimates of the causal parameters. This is partially overcome by two-stage least squares (TSLS) estimators. These are, under weak assumptions, consistent but do not have desirable finite sample properties: in many models, for example, they do not have finite moments. The set of K-class estimators can be seen as a non-linear interpolation between OLS and TSLS and are known to have improved finite sample properties. Recently, in causal discovery, invariance properties such as the moment criterion which TSLS estimators leverage have been exploited for causal structure learning: e.g., in cases, where the causal parameter is not identifiable, some structure of the non-zero components may be identified, and coverage guarantees are available. Subsequently, anchor regression has been proposed to trade-off invariance and predictability. The resulting estimator is shown to have optimal predictive performance under bounded shift interventions. In this paper, we show that the concepts of anchor regression and K-class estimators are closely related. Establishing this connection comes with two benefits: (1) It enables us to prove robustness properties for existing K-class estimators when considering distributional shifts. And, (2), we propose a novel estimator in instrumental variable settings by minimizing the mean squared prediction error subject to the constraint that the estimator lies in an asymptotically valid confidence region of the causal parameter. We call this estimator PULSE (p-uncorrelated least squares estimator) and show that it can be computed efficiently, even though the underlying optimization problem is non-convex. We further prove that it is consistent.

Current explanation techniques towards a transparent Convolutional Neural Network (CNN) mainly focuses on building connections between the human-understandable input features with models' prediction, overlooking an alternative representation of the input, the frequency components decomposition. In this work, we present an analysis of the connection between the distribution of frequency components in the input dataset and the reasoning process the model learns from the data. We further provide quantification analysis about the contribution of different frequency components toward the model's prediction. We show that the vulnerability of the model against tiny distortions is a result of the model is relying on the high-frequency features, the target features of the adversarial (black and white-box) attackers, to make the prediction. We further show that if the model develops stronger association between the low-frequency component with true labels, the model is more robust, which is the explanation of why adversarially trained models are more robust against tiny distortions.

John Goes, Gilad Lerman, Boaz Nadler.

Source: The Annals of Statistics, Volume 48, Number 1, 86--110.

Abstract:
Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental task in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Toward bridging this gap, in this work we consider estimating a sparse shape matrix from $n$ samples following a possibly heavy-tailed elliptical distribution. We propose estimators based on thresholding either Tyler’s M-estimator or its regularized variant. We prove that in the joint limit as the dimension $p$ and the sample size $n$ tend to infinity with $p/n ogamma>0$, our estimators are minimax rate optimal. Results on simulated data support our theoretical analysis.

Gabriela V. Cohen Freue, David Kepplinger, Matías Salibián-Barrera, Ezequiel Smucler.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2065--2090.

Abstract:
In large-scale quantitative proteomic studies, scientists measure the abundance of thousands of proteins from the human proteome in search of novel biomarkers for a given disease. Penalized regression estimators can be used to identify potential biomarkers among a large set of molecular features measured. Yet, the performance and statistical properties of these estimators depend on the loss and penalty functions used to define them. Motivated by a real plasma proteomic biomarkers study, we propose a new class of penalized robust estimators based on the elastic net penalty, which can be tuned to keep groups of correlated variables together in the selected model and maintain robustness against possible outliers. We also propose an efficient algorithm to compute our robust penalized estimators and derive a data-driven method to select the penalty term. Our robust penalized estimators have very good robustness properties and are also consistent under certain regularity conditions. Numerical results show that our robust estimators compare favorably to other robust penalized estimators. Using our proposed methodology for the analysis of the proteomics data, we identify new potentially relevant biomarkers of cardiac allograft vasculopathy that are not found with nonrobust alternatives. The selected model is validated in a new set of 52 test samples and achieves an area under the receiver operating characteristic (AUC) of 0.85.

Chao Gao.

Source: Bernoulli, Volume 26, Number 2, 1139--1170.

Abstract:
This paper studies robust regression in the settings of Huber’s $epsilon$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of $epsilon$-contamination models for various regression problems including nonparametric regression, sparse linear regression, reduced rank regression, etc. We also discuss a general notion of depth function for linear operators that has potential applications in robust functional linear regression.

Nhat Ho, XuanLong Nguyen, Ya’acov Ritov.

Source: Bernoulli, Volume 26, Number 2, 828--857.

Abstract:
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we empirically believe our data are generated from and use these kernels to fit our models. Nevertheless, as long as the chosen kernel and the true kernel are different, statistical inference of mixing measure under this setting will be highly unstable. To overcome this challenge, we propose flexible and efficient robust estimators of the mixing measure in these models, which are inspired by the idea of minimum Hellinger distance estimator, model selection criteria, and superefficiency phenomenon. We demonstrate that our estimators consistently recover the true number of components and achieve the optimal convergence rates of parameter estimation under both the well- and misspecified kernel settings for any fixed bandwidth. These desirable asymptotic properties are illustrated via careful simulation studies with both synthetic and real data.

Stanislav Minsker, Xiaohan Wei.

Source: Bernoulli, Volume 26, Number 1, 694--727.

Abstract:
Let $Y$ be a $d$-dimensional random vector with unknown mean $mu $ and covariance matrix $Sigma $. This paper is motivated by the problem of designing an estimator of $Sigma $ that admits exponential deviation bounds in the operator norm under minimal assumptions on the underlying distribution, such as existence of only 4th moments of the coordinates of $Y$. To address this problem, we propose robust modifications of the operator-valued U-statistics, obtain non-asymptotic guarantees for their performance, and demonstrate the implications of these results to the covariance estimation problem under various structural assumptions.

Eduard Belitser, Nurzhan Nurushev.

Source: Bernoulli, Volume 26, Number 1, 191--225.

Abstract:
In the general signal$+$noise (allowing non-normal, non-independent observations) model, we construct an empirical Bayes posterior which we then use for uncertainty quantification for the unknown, possibly sparse, signal. We introduce a novel excessive bias restriction (EBR) condition, which gives rise to a new slicing of the entire space that is suitable for uncertainty quantification. Under EBR and some mild exchangeable exponential moment condition on the noise, we establish the local (oracle) optimality of the proposed confidence ball. Without EBR, we propose another confidence ball of full coverage, but its radius contains an additional $sigma n^{1/4}$-term. In passing, we also get the local optimal results for estimation , posterior contraction problems, and the problem of weak recovery of sparsity structure . Adaptive minimax results (also for the estimation and posterior contraction problems) over various sparsity classes follow from our local results.

While President Donald Trump traveled to the battleground state of Arizona this week, his Democratic opponent for the White House, Joe Biden, campaigned from his basement as he has done throughout the coronavirus pandemic. The freeze on in-person campaigning during the outbreak has had an upside for Biden, giving the former vice president more time to court donors and shielding him from on-the-trail gaffes. "I personally would like to see him out more because he's in his element when he's meeting people," said Tom Sacks-Wilner, a fundraiser for Biden who is on the campaign's finance committee.

Philippe Gagnon, Alain Desgagné, Mylène Bédard.

Source: Bayesian Analysis, Volume 15, Number 2, 389--414.

Abstract:
Linear regression is ubiquitous in statistical analysis. It is well understood that conflicting sources of information may contaminate the inference when the classical normality of errors is assumed. The contamination caused by the light normal tails follows from an undesirable effect: the posterior concentrates in an area in between the different sources with a large enough scaling to incorporate them all. The theory of conflict resolution in Bayesian statistics (O’Hagan and Pericchi (2012)) recommends to address this problem by limiting the impact of outliers to obtain conclusions consistent with the bulk of the data. In this paper, we propose a model with super heavy-tailed errors to achieve this. We prove that it is wholly robust, meaning that the impact of outliers gradually vanishes as they move further and further away from the general trend. The super heavy-tailed density is similar to the normal outside of the tails, which gives rise to an efficient estimation procedure. In addition, estimates are easily computed. This is highlighted via a detailed user guide, where all steps are explained through a simulated case study. The performance is shown using simulation. All required code is given.

Andrea Cremaschi, Raffaele Argiento, Katherine Shoemaker, Christine Peterson, Marina Vannucci.

Source: Bayesian Analysis, Volume 14, Number 4, 1271--1301.

Abstract:
Gaussian graphical models are useful tools for exploring network structures in multivariate normal data. In this paper we are interested in situations where data show departures from Gaussianity, therefore requiring alternative modeling distributions. The multivariate $t$ -distribution, obtained by dividing each component of the data vector by a gamma random variable, is a straightforward generalization to accommodate deviations from normality such as heavy tails. Since different groups of variables may be contaminated to a different extent, Finegold and Drton (2014) introduced the Dirichlet $t$ -distribution, where the divisors are clustered using a Dirichlet process. In this work, we consider a more general class of nonparametric distributions as the prior on the divisor terms, namely the class of normalized completely random measures (NormCRMs). To improve the effectiveness of the clustering, we propose modeling the dependence among the divisors through a nonparametric hierarchical structure, which allows for the sharing of parameters across the samples in the data set. This desirable feature enables us to cluster together different components of multivariate data in a parsimonious way. We demonstrate through simulations that this approach provides accurate graphical model inference, and apply it to a case study examining the dependence structure in radiomics data derived from The Cancer Imaging Atlas.