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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.

François Bachoc, David Preinerstorfer, Lukas Steinberger.

Source: The Annals of Statistics, Volume 48, Number 1, 440--463.

Abstract:
We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. ( Ann. Statist. 41 (2013) 802–837). In particular, the candidate models used can be misspecified, the target of inference is model-specific, and coverage is guaranteed for any data-driven model selection procedure. After developing a general theory, we apply our methods to practically important situations where the candidate set of models, from which a working model is selected, consists of fixed design homoskedastic or heteroskedastic linear models, or of binary regression models with general link functions. In an extensive simulation study, we find that the proposed confidence intervals perform remarkably well, even when compared to existing methods that are tailored only for specific model selection procedures.

Steffen Grønneberg, Benjamin Holcblat.

Source: The Annals of Statistics, Volume 47, Number 6, 3216--3243.

Abstract:
We establish general and versatile results regarding the limit behavior of the partial-sum process of ARMAX residuals. Illustrations include ARMA with seasonal dummies, misspecified ARMAX models with autocorrelated errors, nonlinear ARMAX models, ARMA with a structural break, a wide range of ARMAX models with infinite-variance errors, weak GARCH models and the consistency of kernel estimation of the density of ARMAX errors. Our results identify the limit distributions, and provide a general algorithm to obtain pivot statistics for CUSUM tests.

Javier Cárcamo, Antonio Cuevas, Luis-Alberto Rodríguez.

Source: Bernoulli, Volume 26, Number 3, 2143--2175.

Abstract:
We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and the amplitude of a function. The (usually non-linear) derivatives of these maps adopt simple expressions under suitable assumptions on the underlying space. As an application, we improve and extend to the multidimensional case the results in Raghavachari ( Ann. Statist. 1 (1973) 67–73) regarding the limiting distributions of Kolmogorov–Smirnov type statistics under the alternative hypothesis. Similar results are obtained for analogous statistics associated with copulas. We additionally solve an open problem about the Berk–Jones statistic proposed by Jager and Wellner (In A Festschrift for Herman Rubin (2004) 319–331 IMS). Finally, the asymptotic distribution of maximum mean discrepancies over Donsker classes of functions is derived.

O. Collier, L. Comminges, A.B. Tsybakov.

Source: Bernoulli, Volume 26, Number 3, 1989--2020.

Abstract:
We study the problem of estimation of $N_{gamma }( heta )=sum_{i=1}^{d}| heta _{i}|^{gamma }$ for $gamma >0$ and of the $ell _{gamma }$-norm of $ heta $ for $gamma ge 1$ based on the observations $y_{i}= heta _{i}+varepsilon xi _{i}$, $i=1,ldots,d$, where $ heta =( heta _{1},dots , heta _{d})$ are unknown parameters, $varepsilon >0$ is known, and $xi _{i}$ are i.i.d. standard normal random variables. We find the non-asymptotic minimax rate for estimation of these functionals on the class of $s$-sparse vectors $ heta $ and we propose estimators achieving this rate.

Martin Kolb, Mladen Savov.

Source: Bernoulli, Volume 26, Number 2, 1453--1472.

Abstract:
We derive a criterium for the almost sure finiteness of perpetual integrals of Lévy processes for a class of real functions including all continuous functions and for general one-dimensional Lévy processes that drifts to plus infinity. This generalizes previous work of Döring and Kyprianou, who considered Lévy processes having a local time, leaving the general case as an open problem. It turns out, that the criterium in the general situation simplifies significantly in the situation, where the process has a local time, but we also demonstrate that in general our criterium can not be reduced. This answers an open problem posed in ( J. Theoret. Probab. 29 (2016) 1192–1198).

U.S. Chief Justice John Roberts on Friday put a temporary hold on the disclosure to a Democratic-led House of Representatives committee of grand jury material redacted from former Special Counsel Robert Mueller's report on Russian interference in the 2016 election. The U.S. Court of Appeals for the District of Columbia Circuit ruled in March that the materials had to be disclosed to the House Judiciary Committee and refused to put that decision on hold. The appeals court said the materials had to be handed over by May 11 if the Supreme Court did not intervene.

The bombastic military parade through Moscow's Red Square on Saturday was slated to be the spectacle of the year on the Kremlin's calendar. Standing with Chinese leader Xi Jinping and French President Emmanuel Macron, President Vladimir Putin would have overseen a 90-minute procession of Russia's military might, showcasing 15,000 troops and the latest hardware. Now, military jets will roar over an eerily quiet Moscow, spurting red, white and blue smoke to mark 75 years since the defeat of Nazi Germany.

The ongoing investigation of the fatal shooting in Brunswick, Georgia, will also look at a neighbor of suspects Gregory and Travis McMichael who recorded video of the incident, authorities said.

Fangzheng Xie, Yanxun Xu.

Source: Bayesian Analysis, Volume 15, Number 1, 159--186.

Abstract:
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal contraction rate of the full posterior distribution up to a logarithmic factor by estimating metric entropies of certain function classes. Under the assumption that the degree of the polynomials is larger than the unknown smoothness level of the true function, the posterior contraction behavior can adapt to this smoothness level provided an upper bound is known. We also provide a frequentist sieve maximum likelihood estimator with a near-optimal convergence rate. We further investigate the application of the kernel mixture of polynomials to partial linear models and obtain both the near-optimal rate of contraction for the nonparametric component and the Bernstein-von Mises limit (i.e., asymptotic normality) of the parametric component. The proposed method is illustrated with numerical examples and shows superior performance in terms of computational efficiency, accuracy, and uncertainty quantification compared to the local polynomial regression, DiceKriging, and the robust Gaussian stochastic process.

L. F. South, A. N. Pettitt, C. C. Drovandi.

Source: Bayesian Analysis, Volume 14, Number 3, 773--796.

Abstract:
Sequential Monte Carlo (SMC) methods for sampling from the posterior of static Bayesian models are flexible, parallelisable and capable of handling complex targets. However, it is common practice to adopt a Markov chain Monte Carlo (MCMC) kernel with a multivariate normal random walk (RW) proposal in the move step, which can be both inefficient and detrimental for exploring challenging posterior distributions. We develop new SMC methods with independent proposals which allow recycling of all candidates generated in the SMC process and are embarrassingly parallelisable. A novel evidence estimator that is easily computed from the output of our independent SMC is proposed. Our independent proposals are constructed via flexible copula-type models calibrated with the population of SMC particles. We demonstrate through several examples that more precise estimates of posterior expectations and the marginal likelihood can be obtained using fewer likelihood evaluations than the more standard RW approach.

Georg Lindgren.

Source: Statistical Science, Volume 34, Number 1, 100--128.

Abstract:
We describe and compare how methods based on the classical Rice’s formula for the expected number, and higher moments, of level crossings by a Gaussian process stand up to contemporary numerical methods to accurately deal with crossing related characteristics of the sample paths. We illustrate the relative merits in accuracy and computing time of the Rice moment methods and the exact numerical method, developed since the late 1990s, on three groups of distribution problems, the maximum over a finite interval and the waiting time to first crossing, the length of excursions over a level, and the joint period/amplitude of oscillations. We also treat the notoriously difficult problem of dependence between successive zero crossing distances. The exact solution has been known since at least 2000, but it has remained largely unnoticed outside the ocean science community. Extensive simulation studies illustrate the accuracy of the numerical methods. As a historical introduction an attempt is made to illustrate the relation between Rice’s original formulation and arguments and the exact numerical methods.

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Sebastian Onasch
Apr 15, 2020; 40:3186-3202
Systems/Circuits

Georg S. Kranz
Nov 12, 2014; 34:15466-15475
Systems/Circuits

Does your customer relationship management strategy have what it takes to reach Generation Y? It's estimated that by 2021, an additional $394 billion in revenue could be gained from artificial intelligence adoption in CRM activities in the U.S. As companies grow and technology evolves at a faster-than-ever pace, collecting, storing and providing data is becoming a bigger and bigger task.

Human ventral temporal cortex (VTC) is critical for visual recognition. It is thought that this ability is supported by large-scale patterns of activity across VTC that contain information about visual categories. However, it is unknown how category representations in VTC are organized at the submillimeter scale and across cortical depths. To fill this gap in knowledge, we measured BOLD responses in medial and lateral VTC to images spanning 10 categories from five domains (written characters, bodies, faces, places, and objects) at an ultra-high spatial resolution of 0.8 mm using 7 Tesla fMRI in both male and female participants. Representations in lateral VTC were organized most strongly at the general level of domains (e.g., places), whereas medial VTC was also organized at the level of specific categories (e.g., corridors and houses within the domain of places). In both lateral and medial VTC, domain-level and category-level structure decreased with cortical depth, and downsampling our data to standard resolution (2.4 mm) did not reverse differences in representations between lateral and medial VTC. The functional diversity of representations across VTC partitions may allow downstream regions to read out information in a flexible manner according to task demands. These results bridge an important gap between electrophysiological recordings in single neurons at the micron scale in nonhuman primates and standard-resolution fMRI in humans by elucidating distributed responses at the submillimeter scale with ultra-high-resolution fMRI in humans.

SIGNIFICANCE STATEMENT Visual recognition is a fundamental ability supported by human ventral temporal cortex (VTC). However, the nature of fine-scale, submillimeter distributed representations in VTC is unknown. Using ultra-high-resolution fMRI of human VTC, we found differential distributed visual representations across lateral and medial VTC. Domain representations (e.g., faces, bodies, places, characters) were most salient in lateral VTC, whereas category representations (e.g., corridors/houses within the domain of places) were equally salient in medial VTC. These results bridge an important gap between electrophysiological recordings in single neurons at a micron scale and fMRI measurements at a millimeter scale.

Neurons and circuits each with a distinct balance of intrinsic and synaptic conductances can generate similar behavior but sometimes respond very differently to perturbation. Examining a large family of circuit models with non-identical neurons and synapses underlying rhythmic behavior, we analyzed the circuits' response to modifications in single and multiple intrinsic conductances in the individual neurons. To summarize these changes over the entire range of perturbed parameters, we quantified circuit output by defining a global stability measure. Using this measure, we identified specific subsets of conductances that when perturbed generate similar behavior in diverse individuals of the population. Our unbiased clustering analysis enabled us to quantify circuit stability when simultaneously perturbing multiple conductances as a nonlinear combination of single conductance perturbations. This revealed surprising conductance combinations that can predict the response to specific perturbations, even when the remaining intrinsic and synaptic conductances are unknown. Therefore, our approach can expose hidden variability in the balance of intrinsic and synaptic conductances of the same neurons across different versions of the same circuit solely from the circuit response to perturbations. Developed for a specific family of model circuits, our quantitative approach to characterizing high-dimensional degenerate systems provides a conceptual and analytic framework to guide future theoretical and experimental studies on degeneracy and robustness.

SIGNIFICANCE STATEMENT Neural circuits can generate nearly identical behavior despite neuronal and synaptic parameters varying several-fold between individual instantiations. Yet, when these parameters are perturbed through channel deletions and mutations or environmental disturbances, seemingly identical circuits can respond very differently. What distinguishes inconsequential perturbations that barely alter circuit behavior from disruptive perturbations that drastically disturb circuit output remains unclear. Focusing on a family of rhythmic circuits, we propose a computational approach to reveal hidden variability in the intrinsic and synaptic conductances in seemingly identical circuits based solely on circuit output to different perturbations. We uncover specific conductance combinations that work similarly to maintain stability and predict the effect of changing multiple conductances simultaneously, which often results from neuromodulation or injury.

The action potential (AP) waveform controls the opening of voltage-gated calcium channels and contributes to the driving force for calcium ion flux that triggers neurotransmission at presynaptic nerve terminals. Although the frog neuromuscular junction (NMJ) has long been a model synapse for the study of neurotransmission, its presynaptic AP waveform has never been directly studied, and thus the AP waveform shape and propagation through this long presynaptic nerve terminal are unknown. Using a fast voltage-sensitive dye, we have imaged the AP waveform from the presynaptic terminal of male and female frog NMJs and shown that the AP is very brief in duration and actively propagated along the entire length of the terminal. Furthermore, based on measured AP waveforms at different regions along the length of the nerve terminal, we show that the terminal is divided into three distinct electrical regions: A beginning region immediately after the last node of Ranvier where the AP is broadest, a middle region with a relatively consistent AP duration, and an end region near the tip of nerve terminal branches where the AP is briefer. We hypothesize that these measured changes in the AP waveform along the length of the motor nerve terminal may explain the proximal-distal gradient in transmitter release previously reported at the frog NMJ.

SIGNIFICANCE STATEMENT The AP waveform plays an essential role in determining the behavior of neurotransmission at the presynaptic terminal. Although the frog NMJ is a model synapse for the study of synaptic transmission, there are many unknowns centered around the shape and propagation of its presynaptic AP waveform. Here, we demonstrate that the presynaptic terminal of the frog NMJ has a very brief AP waveform and that the motor nerve terminal contains three distinct electrical regions. We propose that the changes in the AP waveform as it propagates along the terminal can explain the proximal-distal gradient in transmitter release seen in electrophysiological studies.

Behavior can be guided by neuronal activity in visual, auditory, or somatosensory cerebral cortex, depending on task requirements. In contrast to this flexible access of cortical signals, several observations suggest that behaviors depend more on neurons in later areas of visual cortex than those in earlier areas, although neurons in earlier areas would provide more reliable signals for many tasks. We recorded from neurons in different levels of visual cortex of 2 male rhesus monkeys while the animals did a visual discrimination task and examined trial-to-trial correlations between neuronal and behavioral responses. These correlations became stronger in primary visual cortex as neuronal signals in that area became more reliable relative to the other areas. The results suggest that the mechanisms that read signals from cortex might access any cortical area depending on the relative value of those signals for the task at hand.

SIGNIFICANCE STATEMENT Information is encoded by the action potentials of neurons in various cortical areas in a hierarchical manner such that increasingly complex stimulus features are encoded in successive stages. The brain must extract information from the response of appropriate neurons to drive optimal behavior. A widely held view of this decoding process is that the brain relies on the output of later cortical areas to make decisions, although neurons in earlier areas can provide more reliable signals. We examined correlations between perceptual decisions and the responses of neurons in different levels of monkey visual cortex. The results suggest that the brain may access signals in any cortical area depending on the relative value of those signals for the task at hand.

Basic facts The world contains an estimated 1 400 million cubic km of water. Only 0.003% of this vast amount, about 45 000 cubic km, are what is called “fresh water resources” - water that theoretically can be used for drinking, hygiene, agriculture and industry. But not all of this water is accessible. For example, seasonal flooding makes water extremely difficult [...]

Biodiversity may sound complicated, but it’s a fairly simple concept: the existence of many different types of plants and animals makes the world a healthier and more productive place. A mix of genetics, species and habitats allows Earth’s ecosystems to keep up with challenges like population growth and climate change. Biodiversity is important to us because it plays a crucial [...]

Four years into the 2030 Agenda, there is still a large gap in data to understand where the world stands in achieving its shared goals, the SDGs. To support [...]

The Library Street Collective's "We All Rise" coloring book features drawings by around 30 contemporary artists

A sweeping new study of 101 mammal species found that females live, on average, 18.6 percent longer than their male counterparts

A recent excavation located the first physical evidence of the capital of the Maya kingdom of Sak Tz'i', founded in 750 B.C.

A rare cache of aquatic animal remains suggests that like early humans, Neanderthals were exploiting marine resources

Select Andrew Lloyd Webber productions will stream on YouTube for 48 hours at a time

With many zoos and aquariums closed to the public, keepers let animals roam empty hallways to meet their neighbors

Doctors and nurses are attaching smiling photos of themselves to the outside of their protective gear to maintain connections with patients

New research reveals the ancient symbiotic relationship behind geosmin, the chemical compound responsible for the scent of fresh rain

Coyotes, bears and more are enjoying areas usually reserved for crowds of human visitors

Funeral parlors' enterprising staff offered burial packages to suit every social strata and budget

Find the capital cities, working from a list of state names

The projects are helping Australia's drought-stricken rural towns find new life as outdoor art galleries

The American Geriatrics Society annually honors researchers, clinicians, educators, and emerging health professionals who have made outstanding contributions to high-quality, person-centered care for older people.

We need to recognize any signposts leading up and out.

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