Miracle-dz/UniFAR-FTUs huggingface dataset:
Adaptive Transmission in Cellular Networks: Fixed-Rate Codes With Power Control Versus Physical Layer Rateless Codes

Adaptive transmission schemes are a crucial aspect of radio design for future wireless networks. This paper studies the performance of two classes of adaptive transmission schemes in cellular downlink. One class is based on physical layer rateless codes with constant transmit power and the other uses fixed-rate codes in conjunction with power adaptation. Using a simple stochastic geometry model for the cellular downlink, the focus is to compare the adaptivity of fixed-rate codes with power adaptation to that of physical layer rateless codes only. The performance of both the rateless and fixed-rate coded adaptive transmission schemes are compared by evaluating the typical user success probability and rate achievable with the two schemes. Based on both the theoretical analysis and simulation results, it is clearly shown that the fixed-rate codes require power control to maintain good performance, whereas the physical layer rateless codes with constant power can still provide robust performance.
Implicit ridge regularization provided by the minimum-norm least squares estimator when $n\ll p$

A conventional wisdom in statistical learning is that large models require strong regularization to prevent overﬁtting. This rule has been recently challenged by deep neural networks: despite being expressive enough to ﬁt any training set perfectly, they still generalize well. Here we show that the same is true for linear regression in the under-determined n (cid:28) p situation, provided that one uses the minimum-norm estimator. The case of linear model with least squares loss allows full and exact mathematical analysis. We prove that augmenting a model with many random covariates with small constant variance and using minimum-norm estimator is asymptotically equivalent to adding the ridge penalty. Using toy example simulations as well as real-life high-dimensional data sets, we demonstrate that explicit ridge penalty often fails to provide any improvement over this implicit ridge regularization. In this regime, minimum-norm estimator achieves zero training error but nevertheless has low expected error.
Bayes factor testing of equality and order constraints on measures of association in social research

ABSTRACT Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses with equality and/or order constraints on these measures of association. In this paper a Bayes factor test is proposed for testing multiple hypotheses with constraints on the measures of association between ordinal and/or continuous variables, possibly after correcting for certain covariates. This test can be used to obtain a direct answer to the research question how much evidence there is in the data for a social science theory relative to competing theories. The stand-alone software package ‘BCT’ allows users to apply the methodology in an easy manner. The methodology will also be available in the R package ‘BFpack’. An empirical application from leisure studies about the associations between life, leisure and relationship satisfaction and an application about the differences about egalitarian justice beliefs across countries are used to illustrate the methodology.
Combine Statistical Thinking With Scientific Practice: A Protocol of a Bayesian Thesis Project For Undergraduate Students.

Current developments in the statistics community suggest that modern statistics education should be structured holistically, i.e., by allowing students to work with real data and answer concrete statistical questions, but also by educating them about alternative statistical frameworks, such as Bayesian statistics. In this article, we describe how we incorporated such a holistic structure in a Bayesian thesis project on ordered binomial probabilities. The project was targeted at undergraduate students in psychology with basic knowledge in Bayesian statistics and programming, but no formal mathematical training. The thesis project aimed to (1) convey the basic mathematical concepts of Bayesian inference, (2) let students experience the entire empirical cycle including the collection, analysis, and interpretation of data, and (3) teach students open science practices.
From Variational to Deterministic Autoencoders

Variational Autoencoders (VAEs) provide a theoretically-backed and popular framework for deep generative models. However, learning a VAE from data poses still unanswered theoretical questions and considerable practical challenges. In this work, we propose an alternative framework for generative modeling that is simpler, easier to train, and deterministic, yet has many of the advantages of VAEs. We observe that sampling a stochastic encoder in a Gaussian VAE can be interpreted as simply injecting noise into the input of a deterministic decoder. We investigate how substituting this kind of stochasticity, with other explicit and implicit regularization schemes, can lead to an equally smooth and meaningful latent space without forcing it to conform to an arbitrarily chosen prior. To retrieve a generative mechanism to sample new data, we introduce an ex-post density estimation step that can be readily applied also to existing VAEs, improving their sample quality. We show, in a rigorous empirical study, that the proposed regularized deterministic autoencoders are able to generate samples that are comparable to, or better than, those of VAEs and more powerful alternatives when applied to images as well as to structured data such as molecules. \footnote{An implementation is available at: \url{this https URL}}
Estimating cluster-level local average treatment effects in cluster randomised trials with non-adherence

Non-adherence to assigned treatment is a common issue in cluster randomised trials. In these settings, the efficacy estimand may also be of interest. Many methodological contributions in recent years have advocated using instrumental variables to identify and estimate the local average treatment effect. However, the clustered nature of randomisation in cluster randomised trials adds to the complexity of such analyses. In this paper, we show that the local average treatment effect can be estimated via two-stage least squares regression using cluster-level summaries of the outcome and treatment received under certain assumptions. We propose the use of baseline variables to adjust the cluster-level summaries before performing two-stage least squares in order to improve efficiency. Implementation needs to account for the reduced sample size, as well as the possible heteroscedasticity, to obtain valid inferences. Simulations are used to assess the performance of two-stage least squares of cluster-level summaries under cluster-level or individual-level non-adherence, with and without weighting and robust standard errors. The impact of adjusting for baseline covariates and of appropriate degrees of freedom correction for inference is also explored. The methods are then illustrated by re-analysing a cluster randomised trial carried out in a specific UK primary care setting. Two-stage least squares estimation using cluster-level summaries provides estimates with small to negligible bias and coverage close to nominal level, provided the appropriate small sample degrees of freedom correction and robust standard errors are used for inference.
Adaptive circular deconvolution by model selection under unknown error distribution

We consider a circular deconvolution problem, where the density f of a circular random variable X has to be estimated nonparametrically based on an iid. sample from a noisy observation Y of X. The additive measurement error is supposed to be independent of X. The objective of this paper is the construction of a fully data-driven estimation procedure when the error density φ is unknown. However, we suppose that in addition to the iid. sample from Y , we have at our disposal an additional iid. sample independently drawn from the error distribution. First, we develop a minimax theory in terms of both sample sizes. However, the proposed orthogonal series estimator requires an optimal choice of a dimension parameter depending on certain characteristics of f and φ, which are not known in practice. The main issue addressed in our work is the adaptive choice of this dimension parameter using a model selection approach. In a first step, we develop a penalized minimum contrast estimator supposing the degree of ill-posedness of the underlying inverse problem to be known, which amounts to assuming partial knowledge of the error distribution. We show that this data-driven estimator can attain the lower risk bound up to a constant in both sample sizes n and m over a wide range of density classes covering in particular ordinary and super smooth densities. Finally, by randomizing the penalty and the collection of models, we modify the estimator such that it does not require any prior knowledge of the error distribution anymore. Even when dispensing with any hypotheses on φ,this fully data-driven estimator still preserves minimax optimality in almost the same cases as the partially adaptive estimator.
Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models

Abstract High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this article, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression settings. A test statistic for testing the global null hypothesis is constructed using a generalized low-dimensional projection for bias correction and its asymptotic null distribution is derived. A lower bound for the global testing is established, which shows that the proposed test is asymptotically minimax optimal over some sparsity range. For testing the individual coefficients simultaneously, multiple testing procedures are proposed and shown to control the false discovery rate and falsely discovered variables asymptotically. Simulation studies are carried out to examine the numerical performance of the proposed tests and their superiority over existing methods. The testing procedures are also illustrated by analyzing a dataset of a metabolomics study that investigates the association between fecal metabolites and pediatric Crohn’s disease and the effects of treatment on such associations. Supplementary materials for this article are available online.
An Efficient Pseudo-likelihood Method for Sparse Binary Pairwise Markov Network Estimation

The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic regression problem. In this way, many insights and optimization procedures for sparse logistic regression can be applied to the learning of discrete Markov networks. Specifically, we use the coordinate descent algorithm for generalized linear models with convex penalties, combined with strong screening rules, to solve the pseudo-likelihood problem with $L_1$ regularization. Therefore a substantial speedup without losing any accuracy can be achieved. Furthermore, this method is more stable than the node-wise logistic regression approach on unbalanced high-dimensional data when penalized by small regularization parameters. Thorough numerical experiments on simulated data and real world data demonstrate the advantages of the proposed method.
A simple recipe for making accurate parametric inference in finite sample

The algorithmic principle of the bootstrap method is quite simple: reiterate the mechanism that produces an estimator on pseudo-samples. But when it comes to estimators that are numerically complicated to obtain, the bootstrap is less attractive to use due to the numerical burden. If one estimator is hard to find, reiterating compounds this issue. Paraphrasing Emile in the French comedy La Cite de la Peur: we can implement the bootstrap when the estimator is simple to obtain or we can compute a numerically complex point estimator, but it is too computationally cumbersome to do both.
Matrix Linear Discriminant Analysis

Abstract We propose a novel linear discriminant analysis (LDA) approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional LDA and the ordinary least squares, we consider an efficient nuclear norm penalized regression that encourages a low-rank structure. Theoretical properties including a nonasymptotic risk bound and a rank consistency result are established. Simulation studies and an application to electroencephalography data show the superior performance of the proposed method over the existing approaches.
Non-Gaussian Observations in Nonlinear Compressed Sensing via Stein Discrepancies

Performance guarantees for compression in nonlinear models under non-Gaussian observations can be achieved through the use of distributional characteristics that are sensitive to the distance to normality, and which in particular return the value of zero under Gaussian or linear sensing. The use of these characteristics, or discrepancies, improves some previous results in this area by relaxing conditions and tightening performance bounds. In addition, these characteristics are tractable to compute when Gaussian sensing is corrupted by either additive errors or mixing.
Generalized Sparse Additive Models

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of observations and features. We prove minimax optimal convergence bounds for this class under a weak compatibility condition. In addition, we characterize the rate of convergence when this compatibility condition is not met. Finally, we also show that the optimal penalty parameters for structure and sparsity penalties in our framework are linked, allowing cross-validation to be conducted over only a single tuning parameter. We complement our theoretical results with empirical studies comparing some existing methods within this framework.
A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters

In this paper, we consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the support points of the barycenter are pre-specified, this problem can be modeled as a linear program (LP) whose problem size can be extremely large. To handle this large-scale LP, we analyse the structure of its dual problem, which is conceivably more tractable and can be reformulated as a well-structured convex problem with 3 kinds of block variables and a coupling linear equality constraint. We then adapt a symmetric Gauss-Seidel based alternating direction method of multipliers (sGS-ADMM) to solve the resulting dual problem and establish its global convergence and global linear convergence rate. As a critical component for efficient computation, we also show how all the subproblems involved can be solved exactly and efficiently. This makes our method suitable for computing a Wasserstein barycenter on a large dataset, without introducing an entropy regularization term as is commonly practiced. In addition, our sGS-ADMM can be used as a subroutine in an alternating minimization method to compute a barycenter when its support points are not pre-specified. Numerical results on synthetic datasets and image datasets demonstrate that our method is highly competitive for solving large-scale problems, in comparison to two existing representative methods and the commercial software Gurobi.
A unified approach for solving sequential selection problems

In this paper we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as well as random problem horizons. The proposed framework is based on a reduction of the original selection problem to one of optimal stopping for a sequence of judiciously constructed independent random variables. We demonstrate that our approach allows exact and efficient computation of optimal policies and various performance metrics thereof for a variety of sequential selection problems, several of which have not been solved to date.
Monotone least squares and isotonic quantiles

We consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n)$ such that, conditional on the $X_i$, the $Y_i$ are independent random variables with distribution functions $F_{X_i}$, where $(F_x)_x$ is an unknown family of distribution functions. Under the sole assumption that $x \mapsto F_x$ is isotonic with respect to stochastic order, one can estimate $(F_x)_x$ in two ways: (i) For any fixed $y$ one estimates the antitonic function $x \mapsto F_x(y)$ via nonparametric monotone least squares, replacing the responses $Y_i$ with the indicators $1_{[Y_i \le y]}$. (ii) For any fixed $\beta \in (0,1)$ one estimates the isotonic quantile function $x \mapsto F_x^{-1}(\beta)$ via a nonparametric version of regression quantiles. We show that these two approaches are closely related, with (i) being more flexible than (ii). Then, under mild regularity conditions, we establish rates of convergence for the resulting estimators $\hat{F}_x(y)$ and $\hat{F}_x^{-1}(\beta)$, uniformly over $(x,y)$ and $(x,\beta)$ in certain rectangles as well as uniformly in $y$ or $\beta$ for a fixed $x$.
Incremental Learning with Unlabeled Data in the Wild

Deep neural networks are known to suffer from catastrophic forgetting in class-incremental learning, where the performance on previous tasks drastically degrades when learning a new task. To alleviate this effect, we propose to leverage a continuous and large stream of unlabeled data in the wild. In particular, to leverage such transient external data effectively, we design a novel class-incremental learning scheme with (a) a new distillation loss, termed global distillation, (b) a learning strategy to avoid overfitting to the most recent task, and (c) a sampling strategy for the desired external data. Our experimental results on various datasets, including CIFAR and ImageNet, demonstrate the superiority of the proposed methods over prior methods, particularly when a stream of unlabeled data is accessible: we achieve up to 9.3% of relative performance improvement compared to the state-of-the-art method.
Double shrunken selection operator

ABSTRACT The least absolute shrinkage and selection operator (LASSO) is a prominent estimator which selects significant (under some sense) features and kills insignificant ones. Indeed the LASSO shrinks features larger than a noise level to zero. In this article, we force LASSO to be shrunken more by proposing a Stein-type shrinkage estimator emanating from the LASSO, namely the Stein-type LASSO. The newly proposed estimator proposes good performance in risk sense numerically. Variants of this estimator have smaller relative MSE and prediction error, compared to the LASSO, in the analysis of prostate cancer dataset.
Simplified Energy Landscape for Modularity Using Total Variation

Networks capture pairwise interactions between entities and are frequently used in applications such as social networks, food networks, and protein interaction networks, to name a few. Communities, cohesive groups of nodes, often form in these applications, and identifying them gives insight into the overall organization of the network. One common quality function used to identify community structure is modularity. In Hu et al. [SIAM J. App. Math., 73(6), 2013], it was shown that modularity optimization is equivalent to minimizing a particular nonconvex total variation (TV) based functional over a discrete domain. They solve this problem, assuming the number of communities is known, using a Merriman, Bence, Osher (MBO) scheme. We show that modularity optimization is equivalent to minimizing a convex TV-based functional over a discrete domain, again, assuming the number of communities is known. Furthermore, we show that modularity has no convex relaxation satisfying certain natural conditions. We therefore, find a manageable non-convex approximation using a Ginzburg Landau functional, which provably converges to the correct energy in the limit of a certain parameter. We then derive an MBO algorithm with fewer hand-tuned parameters than in Hu et al. and which is 7 times faster at solving the associated diffusion equation due to the fact that the underlying discretization is unconditionally stable. Our numerical tests include a hyperspectral video whose associated graph has 2.9x10^7 edges, which is roughly 37 times larger than was handled in the paper of Hu et al.
Scalable Optimization-Based Sampling on Function Space

Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw samples from an approximate posterior distribution. "Correcting" these samples, either by Metropolization or importance sampling, enables characterization of the original posterior distribution. This paper focuses on the scalability of RTO to problems with high- or infinite-dimensional parameters. We introduce a new subspace acceleration strategy that makes the computational complexity of RTO scale linearly with the parameter dimension. This subspace perspective suggests a natural extension of RTO to a function space setting. We thus formalize a function space version of RTO and establish sufficient conditions for it to produce a valid Metropolis-Hastings proposal, yielding dimension-independent sampling performance. Numerical examples corroborate the dimension-independence of RTO and demonstrate sampling performance that is also robust to small observational noise.
A Generalized Publication Bias Model

Scargle (2000) has discussed Rosenthal and Rubin's (1978) fail-safe number” (FSN) method for estimating the number of unpublished studies in meta-analysis. He concluded that this FSN cannot possibly be correct because a central assumption the authors used conflicts with the very definition of publication bias. While this point has been made by others before (Darlington, 1980; Elsahoff, 1978; lyengar & Greenhouse, 1988; Thomas, 1985), Scargle showed, by way of a simple 2-parameter model, how far off Rosenthal and Rubin's estimate can be in practice. However, his results relied on the assumption that the decision variable is normally distributed with zero mean. In this case the ratio of unpublished to published papers is large only in a tiny region of the parameter plane. Building on these results, we now show that (1) replacing densities with probability masses greatly simplifies Scargle's derivations and permits an explicit statement of the relation between the probability a of Type I errors and the step-size β; (2) this result does not require any distribution assumptions; (3) the distinction between 1-sided and 2-sided rejection regions becomes immaterial; (4) this distribution-free approach leads to an immediate generalization to partitions involving more than two intervals, and thus covers more general selection functions.