Miracle-dz/UniFAR-FTUs huggingface dataset:
Inertial Block Mirror Descent Method for Non-Convex Non-Smooth Optimization

In this paper, we propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. We use the general framework of Bregman distance functions to compute the proximal maps. Our methods not only allow using two different extrapolation points to evaluate gradients and adding the inertial force, but also take advantage of randomly picking the block of variables to update. Moreover, our methods do not require a restarting step, and as such, it is not a monotonically decreasing method. To prove the convergence of the whole generated sequence to a critical point, we modify the convergence proof recipe of Bolte, Sabach and Teboulle (Proximal alternating linearized minimization for non-convex and non-smooth problems, Math.\@ Prog. 146(1):459--494, 2014), and combine it with auxiliary functions. We deploy the proposed methods to solve non-negative matrix factorization (NMF) and show that they compete favourably with the state-of-the-art NMF algorithms.
Marginal and Conditional Multiple Inference in Linear Mixed Models

In spite of its high practical relevance, multiple inference in linear mixed models has hardly been addressed so far. Such inference is interesting for population parameters (marginal) as well as about cluster specific ones (conditional). This work introduces a general framework for multiple inference in linear mixed models for the latter. Consistent simultaneous confidence sets for cluster specific parameters are constructed. Furthermore, it is shown that, while these simultaneous conditional confidence sets are feasible, remarkably, corresponding marginal confidence sets are also asymptotically valid for conditional inference. Testing linear hypotheses and multiple comparisons by Tukey's method are considered too. Our inference tools are based on standard quantiles and require no re-sampling techniques. All findings are validated in simulations, and illustrated along a study on Spanish income data.
Approximation of Wasserstein distance with Transshipment

An algorithm for approximating the p-Wasserstein distance between histograms defined on unstructured discrete grids is presented. It is based on the computation of a barycenter constrained to be supported on a low dimensional subspace, which corresponds to a transshipment problem. A multi-scale strategy is also considered. The method provides sparse transport matrices and can be applied to large scale and non structured data.
Asymptotic Theory of Eigenvectors for Large Random Matrices

Characterizing the exact asymptotic distributions of high-dimensional eigenvectors for large structured random matrices poses important challenges yet can provide useful insights into a range of applications. To this end, in this paper we introduce a general framework of asymptotic theory of eigenvectors (ATE) for large structured symmetric random matrices with heterogeneous variances, and establish the asymptotic properties of the spiked eigenvectors and eigenvalues for the scenario of the generalized Wigner matrix noise, where the mean matrix is assumed to have the low-rank structure. Under some mild regularity conditions, we provide the asymptotic expansions for the spiked eigenvalues and show that they are asymptotically normal after some normalization. For the spiked eigenvectors, we establish novel asymptotic expansions for the general linear combination and further show that it is asymptotically normal after some normalization, where the weight vector can be arbitrary. We also provide a more general asymptotic theory for the spiked eigenvectors using the bilinear form. Simulation studies verify the validity of our new theoretical results. Our family of models encompasses many popularly used ones such as the stochastic block models with or without overlapping communities for network analysis and the topic models for text analysis, and our general theory can be exploited for statistical inference in these large-scale applications.
Fixed-Width Output Analysis for Markov Chain Monte Carlo

Markov chain Monte Carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages. A fundamental question is when sampling should stop; that is, at what point the ergodic averages are good estimates of the desired quantities. We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value. Hence calculating a Monte Carlo standard error is a critical step in assessing the simulation output. We consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We give sufficient conditions for the strong consistency of both methods and investigate their finite-sample properties in various examples.
An Empirical Study of Obsolete Answers on Stack Overflow

Stack Overflow accumulates an enormous amount of software engineering knowledge. However, as time passes, certain knowledge in answers may become obsolete. Such obsolete answers, if not identified or documented clearly, may mislead answer seekers and cause unexpected problems (e.g., using an out-dated security protocol). In this paper, we investigate how the knowledge in answers becomes obsolete and identify the characteristics of such obsolete answers. We find that: 1) More than half of the obsolete answers (58.4 percent) were probably already obsolete when they were first posted. 2) When an obsolete answer is observed, only a small proportion (20.5 percent) of such answers are ever updated. 3) Answers to questions in certain tags (e.g., node.js, ajax, android, and objective-c) are more likely to become obsolete. Our findings suggest that Stack Overflow should develop mechanisms to encourage the whole community to maintain answers (to avoid obsolete answers) and answer seekers are encouraged to carefully go through all information (e.g., comments) in answer threads.
An alternative to continuous univariate distributions supported on a bounded interval: The BMT distribution

In this paper, we introduce the BMT distribution as an unimodal alternative to continuous univariate distributions supported on a bounded interval. The ideas behind the mathematical formulation of this new distribution come from computer aid geometric design, specifically from Bezier curves. First, we review general properties of a distribution given by parametric equations and extend the definition of a Bezier distribution. Then, after proposing the BMT cumulative distribution function, we derive its probability density function and a closed-form expression for quantile function, median, interquartile range, mode, and moments. The domain change from [0,1] to [c,d] is mentioned. Estimation of parameters is approached by the methods of maximum likelihood and maximum product of spacing. We test the numerical estimation procedures using some simulated data. Usefulness and flexibility of the new distribution are illustrated in three real data sets. The BMT distribution has a significant potential to estimate domain parameters and to model data outside the scope of the beta or similar distributions.
Uniformity-independent minimum degree conditions for perfect matchings in hypergraphs

In this note, we prove that there exists a universal constant $c=\frac{43}{50}$ such that for every $k\in \mathbb{N}$ and every $d<k/2$, every $k$-uniform hypergraph on $n$ vertices and with minimum $d$-degree at least $(c+o_n(1))\binom{n-d}{k-d}$ contains a perfect matching. This is the first such bound which is independent of $k$, and therefore, improves all previously known bounds when $k$ is large. Our approach is based on combining the seminal work of Alon et al. with known bounds on a conjectured probabilistic inequality due to Feige.
Concentration-based confidence intervals for U-statistics.

Concentration inequalities have become increasingly popular in machine learning, probability, and statistical research. Using concentration inequalities, one can construct confidence intervals (CIs) for many quantities of interest. Unfortunately, many of these CIs require the knowledge of population variances, which are generally unknown, making these CIs impractical for numerical application. However, recent results regarding the simultaneous bounding of the probabilities of quantities of interest and their variances have permitted the construction of empirical CIs, where variances are replaced by their sample estimators. Among these new results are two-sided empirical CIs for U-statistics, which are useful for the construction of CIs for a rich class of parameters. In this article, we derive a number of new one-sided empirical CIs for U-statistics and their variances. We show that our one-sided CIs can be used to construct tighter two-sided CIs for U-statistics, than those currently reported. We also demonstrate how our CIs can be used to construct new empirical CIs for the mean, which provide tighter bounds than currently known CIs for the same number of observations, under various settings.
On minimax nonparametric estimation of signal in Gaussian noise

For the problem of nonparametric estimation of signal in Gaussian noise we point out the strong asymptotically minimax estimators on maxisets for linear estimators (see \cite{ker93,rio}). It turns out that the order of rates of convergence of Pinsker estimator on this maxisets is worse than the order of rates of convergence for the class of linear estimators considered on this maxisets. We show that balls in Sobolev spaces are maxisets for Pinsker estimators.
Primordial Gravitational Waves in the Cosmic Bubble Chamber

We explore the effect of relic gravitational waves on the primordial phase change from the quark-gluon plasma into the low density hadron gas that occurred approximately $10^{-5}$s after the beginning. We show that the gravitational wave, through doing work on the fluid, modulates the local volumes, causing a pressure modulation which either suppresses or boosts the bubble cavitation rate. The boosted rate is significant, implying that the phase transition could have occurred earlier than if this interaction is not considered.
Cyber-Social Systems: Modeling, Inference, and Optimal Design

This paper models the cyber-social system as a cyber-network of agents monitoring states of individuals in a social network. The state of each individual is represented by a social node, and the interactions among individuals are represented by a social link. In the cyber-network, each node represents an agent, and the links represent information sharing among agents. The agents make an observation of social states and perform distributed inference. In this direction, the contribution of this paper is threefold: First, a novel distributed inference protocol is proposed that makes no assumption on the rank of the underlying social system. This is significant as most protocols in the literature only work on full-rank systems. Second, a novel agent classification is developed, where it is shown that the connectivity requirement of the cyber-network differs for each type. This is particularly important in finding the minimal number of observations and minimal connectivity of the cyber-network as the next contribution. Third, the cost-optimal design of the cyber-network constraint with distributed observability is addressed. This problem is subdivided into sensing cost optimization and networking cost optimization, where both are claimed to be NP-hard. We solve both the problems for certain types of social networks and find polynomial-order solutions.
Statistical inference for time-varying ARCH processes

In this paper the class of ARCH(oo) models is generalized to the nonstationary class of ARCH(oo) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation "locally stationary ARCH(oo) process. " The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p < oo) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.
Baryon density extraction and isotropy analysis of Cosmic Microwave Background using a multilayer perceptron

The discovery of cosmic microwave background (CMB) was a paradigm shift in the study and fundamental understanding of the early universe and also the Big Bang phenomenon. Cosmic microwave background is one of the richest and intriguing sources of information available to cosmologists. Although there are some well established statistical methods for the analysis of CMB, here we explore the use of deep learning in this respect. We correlate the baryon density obtained from the power spectrum of CMB temperature maps with the corresponding map and form the dataset for training the neural network model. We analyze the accuracy with which the model is able to predict the results from a relatively abstract dataset considering the fact that CMB is a Gaussian random field. CMB is anisotropic due to temperature fluctuations at small scales but on a larger scale CMB is considered isotropic, here we analyze the isotropy of CMB by training the model with CMB maps centered at different galactic coordinates and compare the predictions of neural network models.
The limits of distribution-free conditional predictive inference

We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal coverage guarantees, where predictive coverage holds on average over all possible test points, but this is not sufficient for many practical applications where we would like to know that our predictions are valid for a given individual, not merely on average over a population. On the other hand, exact conditional inference guarantees are known to be impossible without imposing assumptions on the underlying distribution. In this work, we aim to explore the space in between these two and examine what types of relaxations of the conditional coverage property would alleviate some of the practical concerns with marginal coverage guarantees while still being possible to achieve in a distribution-free setting.
The physical parameters of neuronal cargo transport regulated by autoinhibition of kinesin UNC-104

In this review, we focus on the kinesin-3 family molecular motor protein UNC-104 and its regulatory protein ARL-8. UNC-104, originally identified in Caenorhabditis elegans (C. elegans), has a primary role transporting synaptic vesicle precursors (SVPs). Although in vitro single-molecule experiments have been performed to primarily investigate the kinesin motor domain, these have not addressed the in vivo reality of the existence of regulatory proteins, such as ARL-8, that control kinesin attachment to/detachment from cargo vesicles, which is essential to the overall transport efficiency of cargo vesicles. To quantitatively understand the role of the regulatory protein, we review the in vivo physical parameters of UNC-104-mediated SVP transport, including force, velocity, run length and run time, derived from wild-type and arl-8-deletion mutant C. elegans. Our future aim is to facilitate the construction of a consensus physical model to connect SVP transport with pathologies related to deficient synapse construction caused by the deficient UNC-104 regulation. We hope that the physical parameters of SVP transport summarized in this review become a useful guide for the development of such model.
Semi-parametric estimation of the hazard function in a model with covariate measurement error

We consider a model where the failure hazard function, conditional on a time- independent covariate Z is given by R(t,� 0 |Z) = �γ0(t)fβ0(Z), with � 0 = (� 0 , 0 ) ⊤ 2 R m+p . The baseline hazard function �γ0 and relative risk fβ0 belong both to parametric families. The covariate Z is measured with an error through an additive error model U = Z + " where " is a random variable, independent from Z, with known density fe. We observe a n-sample (Xi,Di,Ui), i = 1,. ,n, where Xi is the minimum between the failure time and the censoring time, and Di is the censoring indicator. We aim at estimating � 0 in presence of the unknown density g of the covariate Z using the observations (Xi,Di,Ui), i = 1,. ,n. Our estimation procedure based on least squares criterion provide two estimators of � 0 . The first one is obtained by minimizing an estimation of the least squares criterion where g is estimated by density deconvolution. We give upper bounds for its risk that depend on the smoothness properties of fe and fβ(z) as a function of z. We derive from this construction sufficient conditions that ensure the p n-consistency. The second estimator is constructed under conditions ensuring that the least squares criterion can be directly estimated with the parametric rate. We propose a deep study of examples considering various type of relative risks fβ and various types of error density fe. We show in particular that in the Cox model and in the excess risk model, the estimators are p n-consistent and asymptotically Gaussian estimators of � 0 whatever is fe. Abstract. Considerons un modelerisque instantane modelise par la relation R(t,� 0 |Z) = �γ0(t)fβ0(Z), ou � 0 = (� 0 , 0 ) ⊤ 2 R m+p . Le risque de base �γ0 et la fonction de risque
Spatial modeling of trends in crime over time in Philadelphia

Understanding the relationship between change in crime over time and the geography of urban areas is an important problem for urban planning. Accurate estimation of changing crime rates throughout a city would aid law enforcement as well as enable studies of the association between crime and the built environment. Bayesian modeling is a promising direction since areal data, such as trends in crime counts over time, require principled sharing of information to address spatial autocorrelation between proximal neighborhoods. We develop several Bayesian approaches to spatial sharing between neighborhoods. We apply our methodology to estimate changes in crime throughout Philadelphia over the 2006-15 period, while also incorporating spatially-varying economic and demographic predictors. We find that the local shrinkage imposed by a conditional autoregressive model has substantial benefits in terms of out-of-sample predictive accuracy of crime. We also explore the possibility of spatial discontinuities between neighborhoods that could represent natural barriers or aspects of the built environment.
Schwinger scattering of twisted neutrons by nuclei

Thanks to J.~Schwinger, the process of elastic scattering of neutrons by nuclei is known to depend on the interference between a nuclear amplitude and an electromagnetic one for small scattering angles, resulting in spin asymmetries of a cross section or in polarization of the scattered neutrons. While this interference depends on the neutron's {\it transverse} polarization and on {\it an imaginary part} of the nuclear amplitude, this conclusion holds only for the incident plane-wave neutrons with a definite momentum. Here we show that this scattering is altered when the twisted neutrons, recently obtained experimentally, are used instead -- that is, neutrons with an orbital angular momentum. For bulk targets, the angular distributions of the scattered neutrons get modified, while scattering of a superposition of states with the different angular momenta also reveals dependence on the longitudinal polarization. For well-localized targets, the observables develop a dependence on the neutron's {\it helicity} and on {\it a real part} of the nuclear amplitude, providing full access to its phase already in the Born approximation. We argue that the corresponding spin asymmetries are measurable at existing neutron facilities. Thus, scattering of the twisted neutrons by nuclei can provide means for quantum tomography of the neutron states and become a useful tool for hadronic studies, low-energy nuclear physics, tests of fundamental symmetries, and neutron optics.
Bayesian Graphical Compositional Regression for Microbiome Data

Abstract An important task in microbiome studies is to test the existence of and give characterization to differences in the microbiome composition across groups of samples. Important challenges of this problem include the large within-group heterogeneities among samples and the existence of potential confounding variables that, when ignored, increase the chance of false discoveries and reduce the power for identifying true differences. We propose a probabilistic framework to overcome these issues by combining three ideas: (i) a phylogenetic tree-based decomposition of the cross-group comparison problem into a series of local tests, (ii) a graphical model that links the local tests to allow information sharing across taxa, and (iii) a Bayesian testing strategy that incorporates covariates and integrates out the within-group variation, avoiding potentially unstable point estimates. With the proposed method, we analyze the American Gut data to compare the gut microbiome composition of groups of participants with different dietary habits. Our analysis shows that (i) the frequency of consuming fruit, seafood, vegetable, and whole grain are closely related to the gut microbiome composition and (ii) the conclusion of the analysis can change drastically when different sets of relevant covariates are adjusted, indicating the necessity of carefully selecting and including possible confounders in the analysis when comparing microbiome compositions with data from observational studies. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
Some Experimental Results of Relieving Discomfort in Virtual Reality by Disturbing Feedback Loop in Human Brain

Recently, great progress has been made in virtual reality(VR) research and application. However, virtual reality faces a big problem since its appearance, i.e. discomfort (nausea, stomach awareness, etc). Discomfort can be relieved by increasing hardware (sensor, cpu and display) speed. But this will increase cost. This paper gives another low cost solution. The phenomenon of cybersickness is explained with the control theory: discomfort arises if feedback scene differs from expectation, so it can be relieved by disturbing feedback loop in human brain. A hardware platform is build to test this explanation. The VR display on a Samsung S6 is blurred while head movement is detected. The effect is evaluated by comparing responses to the Simulated Sickness Questionnaire (SSQ) between a control and experimental condition. Experimental results show that the new method can ease discomfort remarkably with little extra cost. As a result, VR may be used more widely in teaching (like foreign language, medicine). It's also reasonable to expect likewise merits in other VR applications.
An interval-valued GARCH model for range-measured return processes

Range-measured return contains more information than the traditional scalar-valued return. In this paper, we propose to model the [low, high] price range as a random interval and suggest an interval-valued GARCH (Int-GARCH) model for the corresponding range-measured return process. Under the general framework of random sets, the model properties are investigated. Parameters are estimated by the maximum likelihood method, and the asymptotic properties are established. Empirical application to stocks and financial indices data sets suggests that our Int-GARCH model overall outperforms the traditional GARCH for both in-sample estimation and out-of-sample prediction of volatility.