arXiv subjects

Elizaveta Levina

Publications and source records attributed to Elizaveta Levina.

At least 19 recordsLinked to original sources

arXiv2026

Conformal Prediction for Dyadic Regression Under Complex Missingness

We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms. At the theoretical level, we develop general technical tools for establishing finite-sample validity of conformal prediction under distributional invariance conditions weaker than exchangeability. A key result handles the case where the sample itself is a random subset of the index set, a setting not covered by existing theory. In addition, we propose conformal prediction procedures for jointly exchangeable arrays, including full conformal, split conformal, a row-column approach exploiting similarities within rows and columns, and a selective conformal procedure achieving mask-conditional validity. For missing elements, we establish asymptotic validity of a weighted conformal procedure under a nonparametric graphon model for the missingness mechanism. We further establish conditional validity results for both continuous and discrete responses; to the best of our knowledge, this is the first formal proof of asymptotic conditional validity for weighted conformal prediction under a missing-not-at-random assumption. The proposed methods are illustrated on synthetic and real network data.

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arXiv2026

Interpretable Network-assisted Random Forest+

Machine learning algorithms often assume that training samples are independent. When data points are connected by a network, the induced dependency between samples is both a challenge, reducing effective sample size, and an opportunity to improve prediction by leveraging information from network neighbors. Multiple methods taking advantage of this opportunity are available, but many, including graph neural networks, are not easily interpretable, limiting their usefulness for understanding how models make predictions. Others, such as network-assisted linear regression, are interpretable but often yield worse prediction performance. We bridge this gap by proposing a family of flexible network-assisted models built upon a generalization of random forests (RF+), which achieves highly-competitive prediction accuracy and can be understood through intrinsic interpretability measures, derived directly from the model parameters and structure. In particular, we develop a suite of interpretation tools that enable researchers to both identify important features that drive model predictions and quantify the importance of the network contribution to prediction. Importantly, we provide global and local feature importances as well as sample influence measures to assess the impact of individual observations. This suite of tools broadens the scope and applicability of network-assisted machine learning for high-impact problems where interpretability and transparency are essential.

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arXiv2026

Heterogeneous Treatment Effects under Network Interference: A Nonparametric Approach Based on Node Connectivity

In network settings, interference between units makes causal inference more challenging as outcomes may depend on the treatments received by others in the network. Typical estimands in network settings focus on treatment effects aggregated across individuals in the population. We propose a framework for estimating node-wise counterfactual means, allowing for more granular insights into the impact of network structure on treatment effect heterogeneity. We develop a doubly robust and non-parametric estimation procedure, KECENI (Kernel Estimator of Causal Effect under Network Interference), which offers consistency and asymptotic normality under network dependence. The utility of this method is demonstrated through an application to microfinance data, revealing the impact of network characteristics on treatment effects.

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arXiv2026

Mesoscale two-sample testing for networks

Networks arise naturally in many scientific fields as a representation of pairwise connections. Statistical network analysis has most often considered a single large network, but it is common in a number of applications to observe multiple networks on a shared node set. When these networks are grouped by case-control status or another categorical covariate, the classical statistical question of two-sample comparison arises. In this work, we address the problem of testing for statistically significant differences in a given arbitrary subset of connections. This general framework allows an analyst to focus on a single node, a specific region of interest, or compare whole networks. Our ability to conduct ``mesoscale'' testing on a meaningful group of edges is particularly relevant for applications such as neuroimaging and distinguishes our approach from prior work, which tends to focus either on a single node or the whole network. In this mesoscale setting, we develop statistically sound projection-based tests for two-sample comparison in both weighted and binary edge networks. The key to our approach is to leverage network information from outside the set of interest to learn informative low-rank projections which leads to more powerful tests.

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arXiv2026

Latent space models for grouped multiplex networks

Complex multilayer network datasets have become ubiquitous in various applications, including neuroscience, social sciences, economics, and genetics. Notable examples include brain connectivity networks collected across multiple patients or trade networks between countries collected across multiple goods. Existing statistical approaches to such data typically focus on modeling the structure shared by all networks; some go further by accounting for individual, layer-specific variation. However, real-world multilayer networks often exhibit additional patterns shared only within certain subsets of layers, which can represent treatment and control groups, or patients grouped by a specific trait. Identifying these group-level structures can uncover systematic differences between groups of networks and influence many downstream tasks, such as testing and low-dimensional visualization. To address this gap, we introduce the GroupMultiNeSS model, which enables the simultaneous extraction of shared, group-specific, and individual latent structures from a sample of networks on a shared node set. For this model, we establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions as long as there is sufficient separation between the shared, group-specific, and individual latent subspaces. We compare the model with MultiNeSS and other models for multiplex networks in various synthetic scenarios and observe an apparent improvement in the modeling accuracy when the group component is accounted for. Experiment with the Parkinson's disease brain connectivity dataset demonstrates the superiority of GroupMultiNeSS in highlighting node-level insights on biological differences between the treatment and control patient groups.

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arXiv2025

Flexible Modeling of Information Diffusion on Networks with Statistical Guarantees

Modeling information spread through a network is one of the key problems of network analysis, with applications in a wide array of areas such as marketing and public health. Most approaches assume that the spread is governed by some probabilistic diffusion model, often parameterized by the strength of connections between network members (edge weights), highlighting the need for methods that can accurately estimate them. Multiple prior works suggest such estimators for particular diffusion models; however, most of them lack a rigorous statistical analysis that would establish the asymptotic properties of the estimator and allow for uncertainty quantification. In this paper, we develop a likelihood-based approach to estimate edge weights from the observed information diffusion paths under the proposed General Linear Threshold (GLT) model, a broad class of discrete-time information diffusion models that includes both the well-known linear threshold (LT) and independent cascade (IC) models. We first derive necessary and sufficient conditions that make the edge weights identifiable under this model. Then, we derive a finite sample error bound for the estimator and demonstrate that it is asymptotically normal under mild conditions. We conclude by studying the GLT model in the context of the Influence Maximization (IM) problem, that is, the task of selecting a subset of $k$ nodes to start the diffusion, so that the average information spread is maximized. Extensive experiments on synthetic and real-world networks demonstrate that the flexibility of the proposed class of GLT models, coupled with the proposed estimation and inference framework for its parameters, can significantly improve estimation of spread from a given subset of nodes, prediction of node activation, and the quality of the IM problem solutions.

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arXiv2024

Latent process models for functional network data

Network data are often sampled with auxiliary information or collected through the observation of a complex system over time, leading to multiple network snapshots indexed by a continuous variable. Many methods in statistical network analysis are traditionally designed for a single network, and can be applied to an aggregated network in this setting, but that approach can miss important functional structure. Here we develop an approach to estimating the expected network explicitly as a function of a continuous index, be it time or another indexing variable. We parameterize the network expectation through low dimensional latent processes, whose components we represent with a fixed, finite-dimensional functional basis. We derive a gradient descent estimation algorithm, establish theoretical guarantees for recovery of the low dimensional structure, compare our method to competitors, and apply it to a data set of international political interactions over time, showing our proposed method to adapt well to data, outperform competitors, and provide interpretable and meaningful results.

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arXiv2023

Predicting Responses from Weighted Networks with Node Covariates in an Application to Neuroimaging

We consider the setting where many networks are observed on a common node set, and each observation comprises edge weights of a network, covariates observed at each node, and an overall response. The goal is to use the edge weights and node covariates to predict the response while identifying an interpretable set of predictive features. Our motivating application is neuroimaging, where edge weights encode functional connectivity measured between brain regions, node covariates encode task activations at each brain region, and the response is disease status or score on a behavioral task. We propose an approach that constructs feature groups based on assumed community structure (naturally occurring in neuroimaging applications). We propose two feature grouping schemes that incorporate both edge weights and node covariates, and we derive algorithms for optimization using an overlapping group LASSO penalty. Empirical results on synthetic data show that our method, relative to competing approaches, has similar or improved prediction error along with superior support recovery, enabling a more interpretable and potentially more accurate understanding of the underlying process. We also apply the method to neuroimaging data from the Human Connectome Project. Our approach is widely applicable in neuroimaging where interpretability is highly desired.

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arXiv2023

Computational Inference for Directions in Canonical Correlation Analysis

Canonical Correlation Analysis (CCA) is a method for analyzing pairs of random vectors; it learns a sequence of paired linear transformations such that the resultant canonical variates are maximally correlated within pairs while uncorrelated across pairs. CCA outputs both canonical correlations as well as the canonical directions which define the transformations. While inference for canonical correlations is well developed, conducting inference for canonical directions is more challenging and not well-studied, but is key to interpretability. We propose a computational bootstrap method (combootcca) for inference on CCA directions. We conduct thorough simulation studies that range from simple and well-controlled to complex but realistic and validate the statistical properties of combootcca while comparing it to several competitors. We also apply the combootcca method to a brain imaging dataset and discover linked patterns in brain connectivity and behavioral scores.

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arXiv2023

Selective Inference for Sparse Multitask Regression with Applications in Neuroimaging

Multi-task learning is frequently used to model a set of related response variables from the same set of features, improving predictive performance and modeling accuracy relative to methods that handle each response variable separately. Despite the potential of multi-task learning to yield more powerful inference than single-task alternatives, prior work in this area has largely omitted uncertainty quantification. Our focus in this paper is a common multi-task problem in neuroimaging, where the goal is to understand the relationship between multiple cognitive task scores (or other subject-level assessments) and brain connectome data collected from imaging. We propose a framework for selective inference to address this problem, with the flexibility to: (i) jointly identify the relevant covariates for each task through a sparsity-inducing penalty, and (ii) conduct valid inference in a model based on the estimated sparsity structure. Our framework offers a new conditional procedure for inference, based on a refinement of the selection event that yields a tractable selection-adjusted likelihood. This gives an approximate system of estimating equations for maximum likelihood inference, solvable via a single convex optimization problem, and enables us to efficiently form confidence intervals with approximately the correct coverage. Applied to both simulated data and data from the Adolescent Brain Cognitive Development (ABCD) study, our selective inference methods yield tighter confidence intervals than commonly used alternatives, such as data splitting. We also demonstrate through simulations that multi-task learning with selective inference can more accurately recover true signals than single-task methods.

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arXiv2023

Fair Information Spread on Social Networks with Community Structure

Information spread through social networks is ubiquitous. Influence maximiza- tion (IM) algorithms aim to identify individuals who will generate the greatest spread through the social network if provided with information, and have been largely devel- oped with marketing in mind. In social networks with community structure, which are very common, IM algorithms focused solely on maximizing spread may yield signifi- cant disparities in information coverage between communities, which is problematic in settings such as public health messaging. While some IM algorithms aim to remedy disparity in information coverage using node attributes, none use the empirical com- munity structure within the network itself, which may be beneficial since communities directly affect the spread of information. Further, the use of empirical network struc- ture allows us to leverage community detection techniques, making it possible to run fair-aware algorithms when there are no relevant node attributes available, or when node attributes do not accurately capture network community structure. In contrast to other fair IM algorithms, this work relies on fitting a model to the social network which is then used to determine a seed allocation strategy for optimal fair information spread. We develop an algorithm to determine optimal seed allocations for expected fair coverage, defined through maximum entropy, provide some theoretical guarantees under appropriate conditions, and demonstrate its empirical accuracy on both simu- lated and real networks. Because this algorithm relies on a fitted network model and not on the network directly, it is well-suited for partially observed and noisy social networks.

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arXiv2023

A pseudo-likelihood approach to community detection in weighted networks

Community structure is common in many real networks, with nodes clustered in groups sharing the same connections patterns. While many community detection methods have been developed for networks with binary edges, few of them are applicable to networks with weighted edges, which are common in practice. We propose a pseudo-likelihood community estimation algorithm derived under the weighted stochastic block model for networks with normally distributed edge weights, extending the pseudo-likelihood algorithm for binary networks, which offers some of the best combinations of accuracy and computational efficiency. We prove that the estimates obtained by the proposed method are consistent under the assumption of homogeneous networks, a weighted analogue of the planted partition model, and show that they work well in practice for both homogeneous and heterogeneous networks. We illustrate the method on simulated networks and on a fMRI dataset, where edge weights represent connectivity between brain regions and are expected to be close to normal in distribution by construction.

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arXiv2023

Conformal Prediction for Network-Assisted Regression

An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics. While standard regression methods that make use of both types of covariates may be used for prediction, statistical inference is complicated by the fact that the nodal summary statistics are often dependent in complex ways. We show that under a mild joint exchangeability assumption, a network analog of conformal prediction achieves finite sample validity for a wide range of network covariates. We also show that a form of asymptotic conditional validity is achievable. The methods are illustrated on both simulated networks and a citation network dataset.

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arXiv2022

Graph-aware Modeling of Brain Connectivity Networks

Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain, and edges representing the strength of connectivity between these locations. One challenge in analyzing such data is that inference at the individual edge level is not particularly biologically meaningful; interpretation is more useful at the level of so-called functional regions, or groups of nodes and connections between them; this is often called "graph-aware" inference in the neuroimaging literature. However, pooling over functional regions leads to significant loss of information and lower accuracy. Another challenge is correlation among edge weights within a subject, which makes inference based on independence assumptions unreliable. We address both these challenges with a linear mixed effects model, which accounts for functional regions and for edge dependence, while still modeling individual edge weights to avoid loss of information. The model allows for comparing two populations, such as patients and healthy controls, both at the functional regions level and at individual edge level, leading to biologically meaningful interpretations. We fit this model to a resting state fMRI data on schizophrenics and healthy controls, obtaining interpretable results consistent with the schizophrenia literature.

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arXiv2022

Network resampling for estimating uncertainty

With network data becoming ubiquitous in many applications, many models and algorithms for network analysis have been proposed. Yet methods for providing uncertainty estimates in addition to point estimates of network parameters are much less common. While bootstrap and other resampling procedures have been an effective general tool for estimating uncertainty from i.i.d. samples, adapting them to networks is highly nontrivial. In this work, we study three different network resampling procedures for uncertainty estimation, and propose a general algorithm to construct confidence intervals for network parameters through network resampling. We also propose an algorithm for selecting the sampling fraction, which has a substantial effect on performance. We find that, unsurprisingly, no one procedure is empirically best for all tasks, but that selecting an appropriate sampling fraction substantially improves performance in many cases. We illustrate this on simulated networks and on Facebook data.

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arXiv2021

Bootstrapping Networks with Latent Space Structure

A core problem in statistical network analysis is to develop network analogues of classical techniques. The problem of bootstrapping network data stands out as especially challenging, since typically one observes only a single network, rather than a sample. Here we propose two methods for obtaining bootstrap samples for networks drawn from latent space models. The first method generates bootstrap replicates of network statistics that can be represented as U-statistics in the latent positions, and avoids actually constructing new bootstrapped networks. The second method generates bootstrap replicates of whole networks, and thus can be used for bootstrapping any network function. Commonly studied network quantities that can be represented as U-statistics include many popular summaries, such as average degree and subgraph counts, but other equally popular summaries, such as the clustering coefficient, are not expressible as U-statistics and thus require the second bootstrap method. Under the assumption of a random dot product graph, a type of latent space network model, we show consistency of the proposed bootstrap methods. We give motivating examples throughout and demonstrate the effectiveness of our methods on synthetic data.

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arXiv2021

Matrix Means and a Novel High-Dimensional Shrinkage Phenomenon

Many statistical settings call for estimating a population parameter, most typically the population mean, based on a sample of matrices. The most natural estimate of the population mean is the arithmetic mean, but there are many other matrix means that may behave differently, especially in high dimensions. Here we consider the matrix harmonic mean as an alternative to the arithmetic matrix mean. We show that in certain high-dimensional regimes, the harmonic mean yields an improvement over the arithmetic mean in estimation error as measured by the operator norm. Counter-intuitively, studying the asymptotic behavior of these two matrix means in a spiked covariance estimation problem, we find that this improvement in operator norm error does not imply better recovery of the leading eigenvector. We also show that a Rao-Blackwellized version of the harmonic mean is equivalent to a linear shrinkage estimator studied previously in the high-dimensional covariance estimation literature, while applying a similar Rao-Blackwellization to regularized sample covariance matrices yields a novel nonlinear shrinkage estimator. Simulations complement the theoretical results, illustrating the conditions under which the harmonic matrix mean yields an empirically better estimate.

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arXiv2021

Latent space models for multiplex networks with shared structure

Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex network structures, which are becoming increasingly common in practice. Here we propose a new latent space model for multiplex networks: multiple, heterogeneous networks observed on a shared node set. Multiplex networks can represent a network sample with shared node labels, a network evolving over time, or a network with multiple types of edges. The key feature of our model is that it learns from data how much of the network structure is shared between layers and pools information across layers as appropriate. We establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions as long as there is sufficient separation between the shared and the individual latent subspaces. We compare the model to competing methods in the literature on simulated networks and on a multiplex network describing the worldwide trade of agricultural products.

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