Related papers: Regularized Estimation and Testing for High-Dimens…
As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse…
We consider the multivariate max-linear regression problem where the model parameters $\boldsymbol{\beta}_{1},\dotsc,\boldsymbol{\beta}_{k}\in\mathbb{R}^{p}$ need to be estimated from $n$ independent samples of the (noisy) observations $y =…
We address the component-based regularisation of a multivariate Generalized Linear Mixed Model (GLMM). A set of random responses Y is modelled by a GLMM, using a set X of explanatory variables, a set T of additional covariates, and random…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
We develop an approximate formula for evaluating a cross-validation estimator of predictive likelihood for multinomial logistic regression regularized by an $\ell_1$-norm. This allows us to avoid repeated optimizations required for…
Complex systems, such as brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often challenging. We propose using a…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
Granger causality (GC) is often considered not an actual form of causality. Still, it is arguably the most widely used method to assess the predictability of a time series from another one. Granger causality has been widely used in many…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expressions and genetic variants can both be…
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…
We document regime-dependent predictive structure between equity factors using 35 years of Fama-French data (1990-2024). We find that Value (HML) Granger-causes Size (SMB) during crisis regimes (p < 1e-4, 9-day lag) but not during normal…
In the Bayesian reinforcement learning (RL) setting, a prior distribution over the unknown problem parameters -- the rewards and transitions -- is assumed, and a policy that optimizes the (posterior) expected return is sought. A common…
Granger causality, a popular method for determining causal influence between stochastic processes, is most commonly estimated via linear autoregressive modeling. However, this approach has a serious drawback: if the process being modeled…
Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically…
This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…