33,944 research outputs found
Exchangeable Variable Models
A sequence of random variables is exchangeable if its joint distribution is
invariant under variable permutations. We introduce exchangeable variable
models (EVMs) as a novel class of probabilistic models whose basic building
blocks are partially exchangeable sequences, a generalization of exchangeable
sequences. We prove that a family of tractable EVMs is optimal under zero-one
loss for a large class of functions, including parity and threshold functions,
and strictly subsumes existing tractable independence-based model families.
Extensive experiments show that EVMs outperform state of the art classifiers
such as SVMs and probabilistic models which are solely based on independence
assumptions.Comment: ICML 201
Nonparametric estimation of non-exchangeable latent-variable models
We propose a two-step method to nonparametrically estimate multivariate models in which the observed outcomes are independent conditional on a discrete latent variable. Applications include microeconometric models with unobserved types of agents, regime-switching models, and models with misclassification error. In the first step, we estimate weights that transform moments of the marginal distribution of the data into moments of the conditional distribution of the data for given values of the latent variable. In the second step, these conditional moments are estimated as weighted sample averages. We illustrate the method by estimating a model of wages with unobserved heterogeneity on PSID data
Nonparametric estimation of non-exchangeable latent-variable models
We propose a two-step method to nonparametrically estimate multivariate models in which the observed outcomes are independent conditional on a discrete latent variable. Applications include microeconometric models with unobserved types of agents, regime-switching models, and models with misclassification error. In the first step, we estimate weights that transform moments of the marginal distribution of the data into moments of the conditional distribution of the data for given values of the latent variable. In the second step, these conditional moments are estimated as weighted sample averages. We illustrate the method by estimating a model of wages with unobserved heterogeneity on PSID data
Regression of binary network data with exchangeable latent errors
Undirected, binary network data consist of indicators of symmetric relations
between pairs of actors. Regression models of such data allow for the
estimation of effects of exogenous covariates on the network and for prediction
of unobserved data. Ideally, estimators of the regression parameters should
account for the inherent dependencies among relations in the network that
involve the same actor. To account for such dependencies, researchers have
developed a host of latent variable network models, however, estimation of many
latent variable network models is computationally onerous and which model is
best to base inference upon may not be clear. We propose the Probit
Exchangeable (PX) Model for undirected binary network data that is based on an
assumption of exchangeability, which is common to many of the latent variable
network models in the literature. The PX model can represent the second moments
of any exchangeable network model, yet specifies no particular parametric
model. We present an algorithm for obtaining the maximum likelihood estimator
of the PX model, as well as a modified version of the algorithm that is
extremely computationally efficient and provides an approximate estimator.
Using simulation studies, we demonstrate the improvement in estimation of
regression coefficients of the proposed model over existing latent variable
network models. In an analysis of purchases of politically-aligned books, we
demonstrate political polarization in purchase behavior and show that the
proposed estimator significantly reduces runtime relative to estimators of
latent variable network models while maintaining predictive performance
Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference
Exchangeability is a central notion in statistics and probability theory. The
assumption that an infinite sequence of data points is exchangeable is at the
core of Bayesian statistics. However, finite exchangeability as a statistical
property that renders probabilistic inference tractable is less
well-understood. We develop a theory of finite exchangeability and its relation
to tractable probabilistic inference. The theory is complementary to that of
independence and conditional independence. We show that tractable inference in
probabilistic models with high treewidth and millions of variables can be
understood using the notion of finite (partial) exchangeability. We also show
that existing lifted inference algorithms implicitly utilize a combination of
conditional independence and partial exchangeability.Comment: In Proceedings of the 28th AAAI Conference on Artificial Intelligenc
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