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We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on…
Nonlinearity and endogeneity are prevalent challenges in causal analysis using observational data. This paper proposes an inference procedure for a nonlinear and endogenous marginal effect function, defined as the derivative of the…
Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…
Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely…
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that…
This paper studies the causal representation learning problem when the latent causal variables are observed indirectly through an unknown linear transformation. The objectives are: (i) recovering the unknown linear transformation (up to…
A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate…
In this work we investigate the generic properties of a stochastic linear model in the regime of high-dimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both…
We consider the problem of predicting a response variable from a set of covariates on a data set that differs in distribution from the training data. Causal parameters are optimal in terms of predictive accuracy if in the new distribution…
The article investigates an algorithm for identifying an unknown constant parameter for a scalar regression model using a nonlinear operator that allows us to obtain a new regression equation (with an expanded number of unknown parameters)…
This paper studies point identification of the distribution of the coefficients in some random coefficients models with exogenous regressors when their support is a proper subset, possibly discrete but countable. We exhibit trade-offs…
Machine-learning techniques are evolving into a subsidiary tool for studying phase transitions in many-body systems. However, most studies are tied to situations involving only one phase transition and one order parameter. Systems that…
We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a $\beta$-mixing time…
We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identifiability, and show that the means and the variances and covariances of the random coefficients…
We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
This paper explores the identification and estimation of nonseparable panel data models. We show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable, the conditional…
Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
A comprehensive methodology for inference in vector autoregressions (VARs) using sign and other structural restrictions is developed. The reduced-form VAR disturbances are driven by a few common factors and structural identification…