Related papers: D-optimal designs for the Mitscherlich non-linear …
Optimal experimental design is an essential subfield of statistics that maximizes the chances of experimental success. The D- and A-optimal design is a very challenging problem in the field of optimal design, namely minimizing the…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
We investigate the possibility of extending some results of Pazman and Pronzato (2014) to a larger set of optimality criteria. Namely, in a linear regression model the problem of computing D-, A-, E_k-optimal designs, of combining these…
We study reinforcement learning (RL) with linear function approximation. For episodic time-inhomogeneous linear Markov decision processes (linear MDPs) whose transition probability can be parameterized as a linear function of a given…
We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. These are functions $f$ that may be represented as the difference $\phi_1 - \phi_2$ for a choice of…
This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…
We propose a method that would allow for a rigorous statistical analysis of neural responses to natural stimuli, which are non-Gaussian and exhibit strong correlations. We have in mind a model in which neurons are selective for a small…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…
We consider the optimal experimental design problem of allocating subjects to treatment or control when subjects participate in multiple, separate controlled experiments within a short time-frame and subject covariate information is…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…
In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective…
This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
Experimental designs that are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values.…
In this work, an adaptive time-stepping Milstein method is constructed for stochastic differential equations with piecewise continuous arguments (SDEPCAs), where the drift is one-sided Lipschitz continuous and the diffusion does not impose…
The problem of measuring the best linear approximation of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by…
We consider a stochastic linear bandit model in which the available actions correspond to arbitrary context vectors whose associated rewards follow a non-stationary linear regression model. In this setting, the unknown regression parameter…
Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…