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In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

As the amount and complexity of available data increases, the need for robust statistical learning becomes more pressing. To enhance resilience against model misspecification, the generalized posterior inference method adjusts the…

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…

We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the…

Inferential challenges that arise when data are censored have been extensively studied under the classical frameworks. In this paper, we provide an alternative generalized inferential model approach whose output is a data-dependent…

Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack of theory to support the…

Regression methods for interval-valued data have been increasingly studied in recent years. As most of the existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and therefore…

Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

The availability of multidimensional economic datasets has grown significantly in recent years. An example is bilateral trade values across goods among countries, comprising three dimensions -- importing countries, exporting countries, and…

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

For the conditional mean function of panel count model with time-varying coefficients, we propose to use local kernel regression method for estimation. Partial log-likelihood with local polynomial is formed for estimation. Under some…

A new forecasting method based on the concept of the profile predictive the likelihood function is proposed for discrete-valued processes. In particular, generalized autoregressive and moving average (GARMA) models for Poisson distributed…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact…

We construct a general stochastic process and prove weak convergence results. It is scaled in space and through the parameters of its distribution. We show that our simplified scaling is equivalent to time scaling used frequently. The…

We study the theoretical properties of the fused lasso procedure originally proposed by \cite{tibshirani2005sparsity} in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be…

A new multivariate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step…

We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…

In this paper we propose a new time-varying econometric model, called Time-Varying Poisson AutoRegressive with eXogenous covariates (TV-PARX), suited to model and forecast time series of counts. {We show that the score-driven framework is…