Related papers: Optimal link prediction with matrix logistic regre…
We consider a latent space model for random graphs where a node $i$ is associated to a random latent point $X_i$ on the Euclidean unit ball. The probability that an edge exists between two nodes is determined by a ``link'' function, which…
Bipartite networks provide a major insight into the organisation of many real-world systems. One of the most relevant issues encountered when modelling a bipartite network is that of facing the information shortage concerning intra-layer…
Risk classification plays an important role in many regulations and standards. However, a general method that provides an optimal classification has not been proposed yet. Also, the criteria of optimality are not defined in these…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…
Evaluation of link prediction methods is a hard task in very large complex networks because of the inhibitive computational cost. By setting a lower bound of the number of common neighbors (CN), we propose a new framework to efficiently and…
Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including…
Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…
Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…
We compare different selection criteria to choose the number of latent states of a multivariate latent Markov model for longitudinal data. This model is based on an underlying Markov chain to represent the evolution of a latent…
Real-time network traffic forecasting is crucial for network management and early resource allocation. Existing network traffic forecasting approaches operate under the assumption that the network traffic data is fully observed. However, in…
We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…
Denoising Diffusion Probabilistic Models (DDPMs) represent a contemporary class of generative models with exceptional qualities in both synthesis and maximizing the data likelihood. These models work by traversing a forward Markov Chain…
Prediction algorithms typically assume the training data are independent samples, but in many modern applications samples come from individuals connected by a network. For example, in adolescent health studies of risk-taking behaviors,…
A common data analysis task is the reduced-rank regression problem: $$\min_{\textrm{rank-}k \ X} \|AX-B\|,$$ where $A \in \mathbb{R}^{n \times c}$ and $B \in \mathbb{R}^{n \times d}$ are given large matrices and $\|\cdot\|$ is some norm.…
Community detection is one of the most important problems in network analysis. Among many algorithms proposed for this task, methods based on statistical inference are of particular interest: they are mathematically sound and were shown to…
We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…
The short-term forecasting of real-time locational marginal price (LMP) and network congestion is considered from a system operator perspective. A new probabilistic forecasting technique is proposed based on a multiparametric programming…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
Link prediction plays an important role in network analysis and applications. Recently, approaches for link prediction have evolved from traditional similarity-based algorithms into embedding-based algorithms. However, most existing…
In this note, we consider using a link function that has heavier tails than the usual exponential link function. We construct efficient Gibbs algorithms for Poisson and Multinomial models based on this link function by introducing gamma and…