Related papers: SILVar: Single Index Latent Variable Models
Reliably characterizing the full conditional distribution of a multivariate response variable given a set of covariates is crucial for trustworthy decision-making. However, misspecified or miscalibrated multivariate models may yield a poor…
Bayesian Additive Regression Trees (BART) is a flexible machine learning algorithm capable of capturing nonlinearities between an outcome and covariates and interaction among covariates. We extend BART to a semiparametric regression…
Vector autoregressive (VAR) models are widely used in multivariate time series analysis for describing the short-time dynamics of the data. The reduced-rank VAR models are of particular interest when dealing with high-dimensional and highly…
A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued…
The vector autoregressive (VAR) model is a powerful tool in modeling complex time series and has been exploited in many fields. However, fitting high dimensional VAR model poses some unique challenges: On one hand, the dimensionality,…
Modern network data analysis often involves analyzing network structures alongside covariate features to gain deeper insights into underlying patterns. However, traditional covariate-assisted statistical network models may not adequately…
This paper analyzes a new regularized learning scheme for high dimensional partially linear support vector machine. The proposed approach consists of an empirical risk and the Lasso-type penalty for linear part, as well as the standard…
Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to…
We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model…
We present a latent variable model for predicting the relationship between a pair of text sequences. Unlike previous auto-encoding--based approaches that consider each sequence separately, our proposed framework utilizes both sequences…
Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. Variational methods are commonly used for inference; however, the exact likelihood of…
Models with a large number of latent variables are often used to fully utilize the information in big or complex data. However, they can be difficult to estimate using standard approaches, and variational inference methods are a popular…
In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
When a missing process depends on the missing values themselves, it needs to be explicitly modelled and taken into account while doing likelihood-based inference. We present an approach for building and fitting deep latent variable models…
This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
Researchers now routinely use AI or other machine learning methods to estimate latent variables of economic interest, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating…
In practice, there often exist unobserved variables, also termed hidden variables, associated with both the response and covariates. Existing works in the literature mostly focus on linear regression with hidden variables. However, when the…
This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise in industrial organization and labor economics settings where data are collected using an input-based sampling…