A common approach to modeling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter communities; negative curvature induces repulsion. We consistently estimate manifold type, dimension, and curvature from simply connected, complete Riemannian manifolds of constant curvature. We represent the graph as a noisy distance matrix based on the ties between cliques, then develop hypothesis tests to determine whether the observed distances could plausibly be embedded isometrically in each of the candidate geometries. We apply our approach to data-sets from economics and neuroscience.
A Monte Carlo simulation was used to determine which assumptions for ordered categorical data, continuity vs. discrete categories, most frequently identifies the underlying factor structure when a response variable has five ordered categories. The impact of infrequently endorsed response categories was also examined, a condition that has not been fully explored. The typical method for overcoming infrequently endorsed categories in applied research is to collapse response options with adjacent categories resulting in less response categories that are endorsed more frequently, but this approach …
A latent bandit problem is one in which the learning agent knows the arm reward distributions conditioned on an unknown discrete latent state. The primary goal of the agent is to identify the latent state, after which it can act optimally. This setting is a natural midpoint between online and offline learning---complex models can be learned offline with the agent identifying latent state online---of practical relevance in, say, recommender systems. In this work, we propose general algorithms for this setting, based on both upper confidence bounds (UCBs) and Thompson sampling. Our methods are c…
We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations.
Assume that cause-effect relationships between variables can be described as a directed acyclic graph and the corresponding linear structural equation model.We consider the identification problem of total effects in the presence of latent variables and selection bias between a treatment variable and a response variable. Pearl and his colleagues provided the back door criterion, the front door criterion (Pearl, 2000) and the conditional instrumental variable method (Brito and Pearl, 2002) as identifiability criteria for total effects in the presence of latent variables, but not in the presence …
Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations wh…
Identifying Direct Causal Effects in Latent Factor Models by Accounting for Unidentified Parents
German Aerospace Center (DLR), Institute of Data Science（德国航空航天中心数据科学研究所）；Technische Universität Berlin（柏林工业大学）；Institute of Mathematics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院数学研究所）；Institute of Computer Science, University of Potsdam（波茨坦大学计算机研究所）；Department of Mathematics, TUM School of Computation, Information and Technology, Technical University of Munich（慕尼黑工业大学计算、信息与技术学院数学系）；Munich Center for Machine Learning（慕尼黑机器学习中心）
Identifying the causal structure of systems with multiple dynamic elements is critical to several scientific disciplines. The conventional approach is to conduct statistical tests of causality, for example with Granger Causality, between observed signals that are selected a priori. Here it is posited that, in many systems, the causal relations are embedded in a latent space that is expressed in the observed data as a linear mixture. A technique for blindly identifying the latent sources is presented: the observations are projected into pairs of components -- driving and driven -- to maximize t…
Latent or unobserved phenomena pose a significant difficulty in data analysis as they induce complicated and confounding dependencies among a collection of observed variables. Factor analysis is a prominent multivariate statistical modeling approach that addresses this challenge by identifying the effects of (a small number of) latent variables on a set of observed variables. However, the latent variables in a factor model are purely mathematical objects that are derived from the observed phenomena, and they do not have any interpretation associated to them. A natural approach for attributing …
The application of Bayesian networks (BNs) to cognitive assessment and intelligent tutoring systems poses new challenges for model construction. When cognitive task analyses suggest constructing a BN with several latent variables, empirical model criticism of the latent structure becomes both critical and complex. This paper introduces a methodology for criticizing models both globally (a BN in its entirety) and locally (observable nodes), and explores its value in identifying several kinds of misfit: node errors, edge errors, state errors, and prior probability errors in the latent structure.…
The Graduate University for Advanced Studies（综合研究大学院大学）；The Institute of Statistical Mathematics（统计数学研究所）
As an important problem in causal inference, we discuss the identification and estimation of treatment effects (TEs) under limited overlap; that is, when subjects with certain features belong to a single treatment group. We use a latent variable to model a prognostic score which is widely used in biostatistics and sufficient for TEs; i.e., we build a generative prognostic model. We prove that the latent variable recovers a prognostic score, and the model identifies individualized treatment effects. The model is then learned as β-Intact-VAE--a new type of variational autoencoder (VAE). We deriv…
When searching for gene pathways leading to specific disease outcomes, additional information on gene characteristics is often available that may facilitate to differentiate genes related to the disease from irrelevant background when connections involving both types of genes are observed and their relationships to the disease are unknown. We propose method to single out irrelevant background genes with the help of auxiliary information through a logistic regression, and cluster relevant genes into cohesive groups using the adjacency matrix. Expectation-maximization algorithm is modified to ma…
We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to capture relevant dynamic features. We present a new technique for identifying the emergence or disappearance of distinct subpopulations of vertices. In this formulation, a network is observed over time, with attributed edges appearing at random times. At unknown time points, subgroups of vertices may exhibit a change in behavior. Such changes may take the form of …
Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as \emph{wombling} boundaries, occur in geographic space in the form of rivers in a flood plain, roads, mountains or plateaus or other topograph…
