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.

Trang Quynh Nguyen, Elizabeth A. Stuart.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 518--520.

Francisco J. R. Ruiz, Susan Athey, David M. Blei.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 1--27.

Abstract:
We develop SHOPPER, a sequential probabilistic model of shopping data. SHOPPER uses interpretable components to model the forces that drive how a customer chooses products; in particular, we designed SHOPPER to capture how items interact with other items. We develop an efficient posterior inference algorithm to estimate these forces from large-scale data, and we analyze a large dataset from a major chain grocery store. We are interested in answering counterfactual queries about changes in prices. We found that SHOPPER provides accurate predictions even under price interventions, and that it helps identify complementary and substitutable pairs of products.

Jason Xu, Samson Koelle, Peter Guttorp, Chuanfeng Wu, Cynthia Dunbar, Janis L. Abkowitz, Vladimir N. Minin.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2091--2119.

Abstract:
Single-cell lineage tracking strategies enabled by recent experimental technologies have produced significant insights into cell fate decisions, but lack the quantitative framework necessary for rigorous statistical analysis of mechanistic models describing cell division and differentiation. In this paper, we develop such a framework with corresponding moment-based parameter estimation techniques for continuous-time, multi-type branching processes. Such processes provide a probabilistic model of how cells divide and differentiate, and we apply our method to study hematopoiesis , the mechanism of blood cell production. We derive closed-form expressions for higher moments in a general class of such models. These analytical results allow us to efficiently estimate parameters of much richer statistical models of hematopoiesis than those used in previous statistical studies. To our knowledge, the method provides the first rate inference procedure for fitting such models to time series data generated from cellular barcoding experiments. After validating the methodology in simulation studies, we apply our estimator to hematopoietic lineage tracking data from rhesus macaques. Our analysis provides a more complete understanding of cell fate decisions during hematopoiesis in nonhuman primates, which may be more relevant to human biology and clinical strategies than previous findings from murine studies. For example, in addition to previously estimated hematopoietic stem cell self-renewal rate, we are able to estimate fate decision probabilities and to compare structurally distinct models of hematopoiesis using cross validation. These estimates of fate decision probabilities and our model selection results should help biologists compare competing hypotheses about how progenitor cells differentiate. The methodology is transferrable to a large class of stochastic compartmental and multi-type branching models, commonly used in studies of cancer progression, epidemiology and many other fields.

Johann Gagnon-Bartsch, Yotam Shem-Tov.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1464--1483.

Abstract:
The gold standard for identifying causal relationships is a randomized controlled experiment. In many applications in the social sciences and medicine, the researcher does not control the assignment mechanism and instead may rely upon natural experiments or matching methods as a substitute to experimental randomization. The standard testable implication of random assignment is covariate balance between the treated and control units. Covariate balance is commonly used to validate the claim of as good as random assignment. We propose a new nonparametric test of covariate balance. Our Classification Permutation Test (CPT) is based on a combination of classification methods (e.g., random forests) with Fisherian permutation inference. We revisit four real data examples and present Monte Carlo power simulations to demonstrate the applicability of the CPT relative to other nonparametric tests of equality of multivariate distributions.

Sarat B. Moka, Dirk P. Kroese.

Source: Bernoulli, Volume 26, Number 3, 2082--2104.

Abstract:
We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo, Jerrum and Liu (In STOC’17 – Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) 342–355 ACM). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and area-interaction processes, with a finite interaction range. For an interaction range $2r$ of the target process, the proposed algorithm can generate a perfect sample with $O(log(1/r))$ expected running time complexity, provided that the intensity of the points is not too high and $Theta(1/r^{d})$ parallel processor units are available.

Elena Issoglio, Francesco Russo.

Source: Bernoulli, Volume 26, Number 1, 728--766.

Abstract:
In this paper, we investigate BSDEs where the driver contains a distributional term (in the sense of generalised functions) and derive general Feynman–Kac formulae related to these BSDEs. We introduce an integral operator to give sense to the equation and then we show the existence of a strong solution employing results on a related PDE. Due to the irregularity of the driver, the $Y$-component of a couple $(Y,Z)$ solving the BSDE is not necessarily a semimartingale but a weak Dirichlet process.

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 $1$.

For millions of Americans, working at home isn't an option. NBC News identified seven occupations in which employees are at especially high risk of COVID-19.

Muteb Alharthi, Theodore Kypraios, Philip D. O’Neill.

Source: Bayesian Analysis, Volume 14, Number 3, 927--956.

Abstract:
We consider the problem of model choice for stochastic epidemic models given partial observation of a disease outbreak through time. Our main focus is on the use of Bayes factors. Although Bayes factors have appeared in the epidemic modelling literature before, they can be hard to compute and little attention has been given to fundamental questions concerning their utility. In this paper we derive analytic expressions for Bayes factors given complete observation through time, which suggest practical guidelines for model choice problems. We adapt the power posterior method for computing Bayes factors so as to account for missing data and apply this approach to partially observed epidemics. For comparison, we also explore the use of a deviance information criterion for missing data scenarios. The methods are illustrated via examples involving both simulated and real data.

Pantelis Samartsidis, Shaun R. Seaman, Anne M. Presanis, Matthew Hickman, Daniela De Angelis.

Source: Statistical Science, Volume 34, Number 3, 486--503.

Abstract:
Researchers are often challenged with assessing the impact of an intervention on an outcome of interest in situations where the intervention is nonrandomised, the intervention is only applied to one or few units, the intervention is binary, and outcome measurements are available at multiple time points. In this paper, we review existing methods for causal inference in these situations. We detail the assumptions underlying each method, emphasize connections between the different approaches and provide guidelines regarding their practical implementation. Several open problems are identified thus highlighting the need for future research.

A guide to the tech gadgets even your hard-to-shop-for friends and family members will love.

Here’s where you can snag their Alo Yoga Moto leggings for less.

The chic sneaks are part of Zappos' massive Cyber Monday sale.

Keep your feet comfy and your wallet fat.

Once you try them, you’ll never want to wear anything else

Randy L. Buckner
Feb 11, 2009; 29:1860-1873
Neurobiology of Disease

Adaptive coding of stimuli is well documented in perception, where it supports efficient encoding over a broad range of possible percepts. Recently, a similar neural mechanism has been reported also in value-based decision, where it allows optimal encoding of vast ranges of values in PFC: neuronal response to value depends on the choice context (relative coding), rather than being invariant across contexts (absolute coding). Additionally, value learning is sensitive to the amount of feedback information: providing complete feedback (both obtained and forgone outcomes) instead of partial feedback (only obtained outcome) improves learning. However, it is unclear whether relative coding occurs in all PFC regions and how it is affected by feedback information. We systematically investigated univariate and multivariate feedback encoding in various mPFC regions and compared three modes of neural coding: absolute, partially-adaptive and fully-adaptive.

Twenty-eight human participants (both sexes) performed a learning task while undergoing fMRI scanning. On each trial, they chose between two symbols associated with a certain outcome. Then, the decision outcome was revealed. Notably, in one-half of the trials participants received partial feedback, whereas in the other half they got complete feedback. We used univariate and multivariate analysis to explore value encoding in different feedback conditions.

We found that both obtained and forgone outcomes were encoded in mPFC, but with opposite sign in its ventral and dorsal subdivisions. Moreover, we showed that increasing feedback information induced a switch from absolute to relative coding. Our results suggest that complete feedback information enhances context-dependent outcome encoding.

SIGNIFICANCE STATEMENT This study offers a systematic investigation of the effect of the amount of feedback information (partial vs complete) on univariate and multivariate outcome value encoding, within multiple regions in mPFC and cingulate cortex that are critical for value-based decisions and behavioral adaptation. Moreover, we provide the first comparison of three possible models of neural coding (i.e., absolute, partially-adaptive, and fully-adaptive coding) of value signal in these regions, by using commensurable measures of prediction accuracy. Taken together, our results help build a more comprehensive picture of how the human brain encodes and processes outcome value. In particular, our results suggest that simultaneous presentation of obtained and foregone outcomes promotes relative value representation.

Theoretical models and experimental evidence have suggested that connections from the dentate gyrus (DG) to CA3 play important roles in representing orthogonal information (i.e., pattern separation) in the hippocampus. However, the effects of eliminating the DG on neural firing patterns in the CA3 have rarely been tested in a goal-directed memory task that requires both the DG and CA3. In this study, selective lesions in the DG were made using colchicine in male Long–Evans rats, and single units from the CA3 were recorded as the rats performed visual scene memory tasks. The original scenes used in training were altered during testing by blurring to varying degrees or by using visual masks, resulting in maximal recruitment of the DG–CA3 circuits. Compared with controls, the performance of rats with DG lesions was particularly impaired when blurred scenes were used in the task. In addition, the firing rate modulation associated with visual scenes in these rats was significantly reduced in the single units recorded from the CA3 when ambiguous scenes were presented, largely because DG-deprived CA3 cells did not show stepwise, categorical rate changes across varying degrees of scene ambiguity compared with controls. These findings suggest that the DG plays key roles not only during the acquisition of scene memories but also during retrieval when modified visual scenes are processed in conjunction with the CA3 by making the CA3 network respond orthogonally to ambiguous scenes.

SIGNIFICANCE STATEMENT Despite the behavioral evidence supporting the role of the dentate gyrus in pattern separation in the hippocampus, the underlying neural mechanisms are largely unknown. By recording single units from the CA3 in DG-lesioned rats performing a visual scene memory task, we report that the scene-related modulation of neural firing was significantly reduced in the DG-lesion rats compared with controls, especially when the original scene stimuli were ambiguously altered. Our findings suggest that the dentate gyrus plays an essential role during memory retrieval and performs a critical computation to make categorical rate modulation occur in the CA3 between different scenes, especially when ambiguity is present in the environment.

Bombing ground targets from the air is tricky and not always accurate. But a new type of bomb creates an unimaginable level of destruction

After 85 years, officials plan to remove the old, undetonated bombs that were part of a 1935 plan to divert lava flow on Mauna Loa

The impact that created Pluto’s 'heart' may have rippled through its ocean and damaged its rear

The crustaceans' guts pulverize plastics into tiny bits that can be consumed by even smaller creatures at the base of the ocean food chain

The snazzy search is part of the telescope’s 30th anniversary celebration

An abstract aerial view of a sand dune at sunset at Imperial Sand Dunes, Glamis, California.

Darin Isaac was elected on Wednesday as the new chief of the Selkirk First Nation in Yukon. Isaac also held the position for two terms from 2005 to 2011. He has also served as a councillor for three terms.

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We assess the dynamics of volatility spillovers among global systemically important banks (G-SIBs). We measure spillovers using vector-autoregressive models of range volatility of the equity prices of G-SIBs, together with machine learning methods. We then compare the size of these spillovers with the degree of systemic importance measured by the Basel Committee on Banking Supervision's G-SIB bucket designations.

Fifty thousand jobs were lost in Nova Scotia in April, reflecting the devastating economic impact of the first full month of public health orders to prevent the spread of COVID-19.

About one in 12 Manitoba jobs disappeared during the first two months of the COVID-19 pandemic, according to Statistics Canada's latest monthly survey of Canadian employment.

Shopify has unveiled an app that lets users discover local businesses, receive relevant product recommendations from their favorite brands, check out effortlessly, and track all their online orders. It can gather and track orders automatically, but it also works without auto-tracking. Consumers can get a customized feed with deals, trending items and recommendations from their favorite stores.

P.E.I. had the lowest unemployment rate in the country in April, but behind that seemingly strong showing are hiding problems in the labour market.

The soil is ready to be tilled and seeds wait to be planted at community gardens across Ottawa after the province reversed a decision declaring them off limits during the COVID-19 pandemic.

More than 1,000 people looking for work in the tech industry are signed up for a virtual job fair on Thursday afternoon.

Taking mom out for Mother's Day brunch is a tradition for many. But with people staying home and restaurants closed except for delivery or pick-up, this year's Mother's Day will be a little bit different. Food columnist Andrew Coppolino looks at options.

Saskatchewan's unemployment rate soared in April due to the COVID-19 economic shutdown but an economist says it's not likely to get much worse.

Approximately one out of every seven Ontarians who were working before the coronavirus pandemic hit the province have now lost their jobs, according to Statistics Canada's latest national labour survey.

As truckers move vital supplies such as food, hand sanitizer and ventilators during the COVID-19 pandemic, they're pleading with governments to allow more truck stops to reopen so they can get meals, showers and rest. Social media groups and individual businesses are doing their part to thank truckers.

Veteran forward Kelly Babstock signed with the new Toronto franchise of the National Women's Hockey League on Saturday. The two-time all-star has 27 goals and 60 points in 65 games over four seasons.

Former Montreal Canadiens enforcer Georges Laraque's biggest challenge is trying to breathe clearly as he fights COVID-19 at a Montreal hospital. "The nights are the worst. I have fevers a couple times a night. I have to get up and take pills."

Curbside pickups offer a bit of hope after months of being shuttered by COVID-19, but while retailers are happy to start getting back to business some are raising questions of fairness and access to opportunity.

Billions for oil, nothing for nurses and teachers.

Wink customers will soon have to pay a monthly subscription fee to access any of the smart home hardware that they have purchased.

The screenwriter says his new movie is not a biopic. So true. The film simply doesn’t understand its subject.

The number of Americans filing for unemployment benefits topped 3 million for a seventh straight week, signaling little relief in sight for the economy since the coronavirus began closing restaurants, factories and offices from coast to coast in mid-March.