We study a variant of the widely popular, fast and often used family of community detection procedures referred to as label propagation algorithms. These mechanisms also exhibit many parallels with models of opinion exchange dynamics and consensus mechanisms in distributed computing. Initially, given a network, each vertex starts with a random label in the interval $[0,1]$. Then, in each round of the algorithm, every vertex switches its label to the majority label in its neighborhood (including its own label). At the first round, ties are broken towards smaller labels, while at each of the next rounds, ties are broken uniformly at random. We investigate the performance of this algorithm on the binomial random graph $\mathcal{G}(n,p)$. We show that for $np \ge n^{5/8+\varepsilon}$, the algorithm terminates with a single label a.a.s. (which was previously known only for $np\ge n^{3/4+\varepsilon}$). Moreover, we show that if $np\gg n^{2/3}$, a.a.s.\ this label is the smallest one, whereas if $n^{5/8+\varepsilon}\le np\ll n^{2/3}$, the surviving label is a.a.s. not the smallest one.
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Personalized recommendations form an important part of today's internet ecosystem, helping artists and creators to reach interested users, and helping users to discover new and engaging content. However, many users today are skeptical of platforms that personalize recommendations, in part due to historically careless treatment of personal data and data privacy. Now, businesses that rely on personalized recommendations are entering a new paradigm, where many of their systems must be overhauled to be privacy-first. In this article, we propose an algorithm for personalized recommendations that facilitates both precise and differentially-private measurement. We consider advertising as an example application, and conduct offline experiments to quantify how the proposed privacy-preserving algorithm affects key metrics related to user experience, advertiser value, and platform revenue compared to the extremes of both (private) non-personalized and non-private, personalized implementations.
In the present study we have used a set of methods and metrics to build a graph of relative neural connections in a hippocampus of a rodent. A set of graphs was built on top of time-sequenced data and analyzed in terms of dynamics of a connection genesis. The analysis has shown that during the process of a rodent exploring a novel environment, the relations between neurons constantly change which indicates that globally memory is constantly updated even for known areas of space. Even if some neurons gain cognitive specialization, the global network though remains relatively stable. Additionally we suggest a set of methods for building a graph of cognitive neural network.
Aiming for a mixbiotic society that combines freedom and solidarity among people with diverse values, I focused on nonviolent communication (NVC) that enables compassionate giving in various situations of social division and conflict, and tried a generative AI for it. Specifically, ChatGPT was used in place of the traditional certified trainer to test the possibility of mediating (modifying) input sentences in four processes: observation, feelings, needs, and requests. The results indicate that there is potential for the application of generative AI, although not yet at a practical level. Suggested improvement guidelines included adding model responses, relearning revised responses, specifying appropriate terminology for each process, and re-asking for required information. The use of generative AI will be useful initially to assist certified trainers, to prepare for and review events and workshops, and in the future to support consensus building and cooperative behavior in digital democracy, platform cooperatives, and cyber-human social co-operating systems. It is hoped that the widespread use of NVC mediation using generative AI will lead to the early realization of a mixbiotic society.
This note presents a refined local approximation for the logarithm of the ratio between the negative multinomial probability mass function and a multivariate normal density, both having the same mean-covariance structure. This approximation, which is derived using Stirling's formula and a meticulous treatment of Taylor expansions, yields an upper bound on the Hellinger distance between the jittered negative multinomial distribution and the corresponding multivariate normal distribution. Upper bounds on the Le Cam distance between negative multinomial and multivariate normal experiments ensue.
Partially linear additive models generalize linear ones since they model the relation between a response variable and covariates by assuming that some covariates have a linear relation with the response but each of the others enter through unknown univariate smooth functions. The harmful effect of outliers either in the residuals or in the covariates involved in the linear component has been described in the situation of partially linear models, that is, when only one nonparametric component is involved in the model. When dealing with additive components, the problem of providing reliable estimators when atypical data arise, is of practical importance motivating the need of robust procedures. Hence, we propose a family of robust estimators for partially linear additive models by combining $B-$splines with robust linear regression estimators. We obtain consistency results, rates of convergence and asymptotic normality for the linear components, under mild assumptions. A Monte Carlo study is carried out to compare the performance of the robust proposal with its classical counterpart under different models and contamination schemes. The numerical experiments show the advantage of the proposed methodology for finite samples. We also illustrate the usefulness of the proposed approach on a real data set.
A population-averaged additive subdistribution hazards model is proposed to assess the marginal effects of covariates on the cumulative incidence function and to analyze correlated failure time data subject to competing risks. This approach extends the population-averaged additive hazards model by accommodating potentially dependent censoring due to competing events other than the event of interest. Assuming an independent working correlation structure, an estimating equations approach is outlined to estimate the regression coefficients and a new sandwich variance estimator is proposed. The proposed sandwich variance estimator accounts for both the correlations between failure times and between the censoring times, and is robust to misspecification of the unknown dependency structure within each cluster. We further develop goodness-of-fit tests to assess the adequacy of the additive structure of the subdistribution hazards for the overall model and each covariate. Simulation studies are conducted to investigate the performance of the proposed methods in finite samples. We illustrate our methods using data from the STrategies to Reduce Injuries and Develop confidence in Elders (STRIDE) trial.
Penalized $M-$estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized $M-$estimators when the dimension $p$ grows to infinity with the sample size $n$. Specifically, we obtain consistency and rates of convergence results, for some choices of the penalty function. Moreover, we prove that these estimators consistently select variables with probability tending to 1 and derive their asymptotic distribution.
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed estimator dominates the classical maximum likelihood estimator under the quadratic risk. The estimating procedure is applied to special cases of distributions. The numerical simulations results are given.
Occupancy models are frequently used by ecologists to quantify spatial variation in species distributions while accounting for observational biases in the collection of detection-nondetection data. However, the common assumption that a single set of regression coefficients can adequately explain species-environment relationships is often unrealistic, especially across large spatial domains. Here we develop single-species (i.e., univariate) and multi-species (i.e., multivariate) spatially-varying coefficient (SVC) occupancy models to account for spatially-varying species-environment relationships. We employ Nearest Neighbor Gaussian Processes and Polya-Gamma data augmentation in a hierarchical Bayesian framework to yield computationally efficient Gibbs samplers, which we implement in the spOccupancy R package. For multi-species models, we use spatial factor dimension reduction to efficiently model datasets with large numbers of species (e.g., > 10). The hierarchical Bayesian framework readily enables generation of posterior predictive maps of the SVCs, with fully propagated uncertainty. We apply our SVC models to quantify spatial variability in the relationships between maximum breeding season temperature and occurrence probability of 21 grassland bird species across the U.S. Jointly modeling species generally outperformed single-species models, which all revealed substantial spatial variability in species occurrence relationships with maximum temperatures. Our models are particularly relevant for quantifying species-environment relationships using detection-nondetection data from large-scale monitoring programs, which are becoming increasingly prevalent for answering macroscale ecological questions regarding wildlife responses to global change.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
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