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Pavel N. Krivitsky

Publications and source records attributed to Pavel N. Krivitsky.

At least 19 recordsLinked to original sources

Multiview graph dual-attention deep learning and contrastive learning for multi-criteria recommender systems

Recommender systems leveraging deep learning models have been crucial for assisting users in selecting items aligned with their preferences and interests. However, a significant challenge persists in single-criteria recommender systems, which often overlook the diverse attributes of items that have been addressed by Multi-Criteria Recommender Systems (MCRS). Shared embedding vector for multi-criteria item ratings but have struggled to capture the nuanced relationships between users and items based on specific criteria. In this study, we present a novel representation for Multi-Criteria Recommender Systems (MCRS) based on a multi-edge bipartite graph, where each edge represents one criterion rating of items by users, and Multiview Dual Graph Attention Networks (MDGAT). Employing MDGAT is beneficial and important for adequately considering all relations between users and items, given the presence of both local (criterion-based) and global (multi-criteria) relations. Additionally, we define anchor points in each view based on similarity and employ local and global contrastive learning to distinguish between positive and negative samples across each view and the entire graph. We evaluate our method on two real-world datasets and assess its performance based on item rating predictions. The results demonstrate that our method achieves higher accuracy compared to the baseline method for predicting item ratings on the same datasets. MDGAT effectively capture the local and global impact of neighbours and the similarity between nodes.

cs.IR↗

Balance Correlations, Agentic Zeros, and Networks: The Structure of 192 Years of War and Peace

Social network extensions of Heider's balance theory have not always been consistent. Structural balance theory primarily focuses on graph partitioning, thereby assuming, homogeneity in balance-driven behavior of nodes. We present a general model and formal notation that permit testing such behavioral assumptions. Specifically, we formulate statements as a comparison of two conditional probabilities of a tie, $Ego\stackrel{q}{\text{-}}Alter$, first conditional on 2-paths $Ego\, \stackrel{r}{\text{-}}\,X\,\stackrel{s}{\text{-}}\,Alter$, and second conditional on all others, $\neg (Ego\,\stackrel{r}{\text{-}}\,X\,\stackrel{s}{\text{-}}\,Alter)$. The key here is that $q$, $r$ and $s$ represent indices of relations in a set of mutually exclusive and exhaustive relations (their sum produces a complete graph). This relaxes the assumption of a signed graph dichotomy. Here we identify neutral as distinct from negative and positive ties. Descriptive statistics measuring the difference in conditional probabilities, or the prevalence for any stipulated balance configuration, are given by the point bi-serial correlations of relation $q$ with the count of $2$-paths (through relations $r$ and $s$). Two major advantages are: direct comparison, even if network sizes and densities differ, and evaluation of specific (un)balance behaviors. We apply this approach on a data set with friendly vs hostile relations between countries from 1816 to 2007. We find strong evidence for one of the four classic Heiderian balance theory predictions, and virtually no evidence in support of the unbalanced predictions. However, we do find stable and surprising evidence that the neutral ties are important in balancing the relations among nations. Results further suggest that prevalence of balance driven behavior varies over time, and that other triadic motivated behaviors prevail among countries in certain eras.

physics.soc-ph↗

A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks

The last two decades have seen considerable progress in foundational aspects of statistical network analysis, but the path from theory to application is not straightforward. Two large, heterogeneous samples of small networks of within-household contacts in Belgium were collected using two different but complementary sampling designs: one smaller but with all contacts in each household observed, the other larger and more representative but recording contacts of only one person per household. We wish to combine their strengths to learn the social forces that shape household contact formation and facilitate simulation for prediction of disease spread, while generalising to the population of households in the region. To accomplish this, we describe a flexible framework for specifying multi-network models in the exponential family class and identify the requirements for inference and prediction under this framework to be consistent, identifiable, and generalisable, even when data are incomplete; explore how these requirements may be violated in practice; and develop a suite of quantitative and graphical diagnostics for detecting violations and suggesting improvements to candidate models. We report on the effects of network size, geography, and household roles on household contact patterns (activity, heterogeneity in activity, and triadic closure).

stat.ME↗

Revisiting Bayesian Autoencoders with MCMC

Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent deep learning methods have been used to enhance autoencoders, the need to provide robust uncertainty quantification remains a challenge. This has been addressed with variational autoencoders so far. Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling has faced several limitations for large models; however, recent advances in parallel computing and advanced proposal schemes have opened routes less traveled. This paper presents Bayesian autoencoders powered by MCMC sampling implemented using parallel computing and Langevin-gradient proposal distribution. The results indicate that the proposed Bayesian autoencoder provides similar performance accuracy when compared to related methods in the literature. Furthermore, it provides uncertainty quantification in the reduced data representation. This motivates further applications of the Bayesian autoencoder framework for other deep learning models.

cs.LG↗

ergm 4: Computational Improvements

The ergm package supports the statistical analysis and simulation of network data. It anchors the statnet suite of packages for network analysis in R introduced in a special issue in Journal of Statistical Software in 2008. This article provides an overview of the performance improvements in the 2021 release of ergm version 4. These include performance enhancements to the Markov chain Monte Carlo and maximum likelihood estimation algorithms as well as broader and faster searching for networks with certain target statistics using simulated annealing.

stat.CO↗

ergm 4: New features

The ergm package supports the statistical analysis and simulation of network data. It anchors the statnet suite of packages for network analysis in R introduced in a special issue in Journal of Statistical Software in 2008. This article provides an overview of the new functionality in the 2021 release of ergm version 4. These include more flexible handling of nodal covariates, term operators that extend and simplify model specification, new models for networks with valued edges, improved handling of constraints on the sample space of networks, and estimation with missing edge data. We also identify the new packages in the statnet suite that extend ergm's functionality to other network data types and structural features and the robust set of online resources that support the statnet development process and applications.

stat.CO↗

Modeling of Dynamic Networks based on Egocentric Data with Durational Information

Modeling of dynamic networks -- networks that evolve over time -- has manifold applications in many fields. In epidemiology in particular, there is a need for data-driven modeling of human sexual relationship networks for the purpose of modeling and simulation of the spread of sexually transmitted disease. Dynamic network data about such networks are extremely difficult to collect, however, and much more readily available are egocentrically sampled data of a network at a single time point, with some attendant information about the sexual history of respondents. Krivitsky and Handcock (2014) proposed a Separable Temporal ERGM (STERGM) framework, which facilitates separable modeling of the tie duration distributions and the structural dynamics of tie formation. In this work, we apply this modeling framework to this problem, by studying the long-run properties of STERGM processes, developing methods for fitting STERGMs to egocentrically sampled data, and extending the network size adjustment method of Krivitsky, Handcock, and Morris (2011) to dynamic models.

stat.ME↗

Modeling Tie Duration in ERGM-Based Dynamic Network Models

Krivitsky and Handcock (2014) proposed a Separable Temporal ERGM (STERGM) framework for modeling social networks, which facilitates separable modeling of the tie duration distributions and the structural dynamics of tie formation. In this note, we explore the hazard structures achievable in this framework, with first- and higher-order Markov assumptions, and propose ways to model a variety of duration distributions in this framework.

cs.SI↗

Likelihood-based Inference for Exponential-Family Random Graph Models via Linear Programming

This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a particular approximation to the loglikelihood function for an exponential family model; in particular, we discuss the application to network models here. While the convex hull question may be solved via a simple linear program, this approach is not well known in the statistical literature. Furthermore, this article details several substantial improvements to the convex hull-testing algorithm currently implemented in the widely used 'ergm' package for network modeling.

stat.CO↗

Bayesian graph convolutional neural networks via tempered MCMC

Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be represented via graphs. These types of data are often found in health and medicine, social networks, and research data repositories. Graph convolutional neural networks have recently gained attention in the field of deep learning that takes advantage of graph-based data representation with automatic feature extraction via convolutions. Given the popularity of these methods in a wide range of applications, robust uncertainty quantification is vital. This remains a challenge for large models and unstructured datasets. Bayesian inference provides a principled approach to uncertainty quantification of model parameters for deep learning models. Although Bayesian inference has been used extensively elsewhere, its application to deep learning remains limited due to the computational requirements of the Markov Chain Monte Carlo (MCMC) methods. Recent advances in parallel computing and advanced proposal schemes in MCMC sampling methods has opened the path for Bayesian deep learning. In this paper, we present Bayesian graph convolutional neural networks that employ tempered MCMC sampling with Langevin-gradient proposal distribution implemented via parallel computing. Our results show that the proposed method can provide accuracy similar to advanced optimisers while providing uncertainty quantification for key benchmark problems.

cs.LG↗

Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios

Exponential-family Random Graph Models (ERGMs) constitute a large statistical framework for modeling sparse and dense random graphs, short- and long-tailed degree distributions, covariates, and a wide range of complex dependencies. Special cases of ERGMs are generalized linear models (GLMs), Bernoulli random graphs, $β$-models, $p_1$-models, and models related to Markov random fields in spatial statistics and other areas of statistics. While widely used in practice, questions have been raised about the theoretical properties of ERGMs. These include concerns that some ERGMs are near-degenerate and that many ERGMs are non-projective. To address them, careful attention must be paid to model specifications and their underlying assumptions, and in which inferential settings models are employed. As we discuss, near-degeneracy can affect simplistic ERGMs lacking structure, but well-posed ERGMs with additional structure can be well-behaved. Likewise, lack of projectivity can affect non-likelihood-based inference, but likelihood-based inference does not require projectivity. Here, we review well-posed ERGMs along with likelihood-based inference. We first clarify the core statistical notions of "sample" and "population" in the ERGM framework, and separate the process that generates the population graph from the observation process. We then review likelihood-based inference in finite-, super-, and infinite-population scenarios. We conclude with consistency results, and an application to human brain networks

stat.ME↗

A note on the role of projectivity in likelihood-based inference for random graph models

There is widespread confusion about the role of projectivity in likelihood-based inference for random graph models. The confusion is rooted in claims that projectivity, a form of marginalizability, may be necessary for likelihood-based inference and consistency of maximum likelihood estimators. We show that likelihood-based superpopulation inference is not affected by lack of projectivity and that projectivity is not a necessary condition for consistency of maximum likelihood estimators.

math.ST↗

Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models

Motivated by a real-life problem of sharing social network data that contain sensitive personal information, we propose a novel approach to release and analyze synthetic graphs in order to protect privacy of individual relationships captured by the social network while maintaining the validity of statistical results. A case study using a version of the Enron e-mail corpus dataset demonstrates the application and usefulness of the proposed techniques in solving the challenging problem of maintaining privacy \emph{and} supporting open access to network data to ensure reproducibility of existing studies and discovering new scientific insights that can be obtained by analyzing such data. We use a simple yet effective randomized response mechanism to generate synthetic networks under $ε$-edge differential privacy, and then use likelihood based inference for missing data and Markov chain Monte Carlo techniques to fit exponential-family random graph models to the generated synthetic networks.

stat.CO↗

On the Question of Effective Sample Size in Network Modeling: An Asymptotic Inquiry

The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this area to date by researchers from various disciplines, however, there remain many questions of a decidedly foundational nature - natural analogues of standard questions already posed and addressed in more classical areas of statistics - that have yet to even be posed, much less addressed. Here we raise and consider one such question in connection with network modeling. Specifically, we ask, "Given an observed network, what is the sample size?" Using simple, illustrative examples from the class of exponential random graph models, we show that the answer to this question can very much depend on basic properties of the networks expected under the model, as the number of vertices $n_V$ in the network grows. In particular, adopting the (asymptotic) scaling of the variance of the maximum likelihood parameter estimates as a notion of effective sample size ($n_{\mathrm{eff}}$), we show that when modeling the overall propensity to have ties and the propensity to reciprocate ties, whether the networks are sparse or not under the model (i.e., having a constant or an increasing number of ties per vertex, respectively) is sufficient to yield an order of magnitude difference in $n_{\mathrm{eff}}$, from $O(n_V)$ to $O(n^2_V)$. In addition, we report simulation study results that suggest similar properties for models for triadic (friend-of-a-friend) effects. We then explore some practical implications of this result, using both simulation and data on food-sharing from Lamalera, Indonesia.

math.ST↗

Capturing Multivariate Spatial Dependence: Model, Estimate and then Predict

Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction between these two dependencies that is the focus of Genton and Kleiber's paper under discussion. We see the problem of ensuring that any multivariate spatial covariance matrix is nonnegative definite as important, but we also see it as a means to an end. That "end" is solving the scientific problem of predicting a multivariate field. [arXiv:1507.08017].

stat.ME↗

Exponential-Family Random Graph Models for Rank-Order Relational Data

Rank-order relational data, in which each actor ranks the others according to some criterion, often arise from sociometric measurements of judgment (e.g., self-reported interpersonal interaction) or preference (e.g., relative liking). We propose a class of exponential-family models for rank-order relational data and derive a new class of sufficient statistics for such data, which assume no more than within-subject ordinal properties. Application of MCMC MLE to this family allows us to estimate effects for a variety of plausible mechanisms governing rank structure in cross-sectional context, and to model the evolution of such structures over time. We apply this framework to model the evolution of relative liking judgments in an acquaintance process, and to model recall of relative volume of interpersonal interaction among members of a technology education program.

stat.ME↗

A Separable Model for Dynamic Networks

Models of dynamic networks --- networks that evolve over time --- have manifold applications. We develop a discrete-time generative model for social network evolution that inherits the richness and flexibility of the class of exponential-family random graph models. The model --- a Separable Temporal ERGM (STERGM) --- facilitates separable modeling of the tie duration distributions and the structural dynamics of tie formation. We develop likelihood-based inference for the model, and provide computational algorithms for maximum likelihood estimation. We illustrate the interpretability of the model in analyzing a longitudinal network of friendship ties within a school.

stat.ME↗