Related papers: Pr{\'e}diction optimale pour un mod{\`e}le ordinal…

Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…

We introduce a causal modeling framework that captures the input-output behavior of predictive models (e.g., machine learning models). The framework enables us to identify features that directly cause the predictions, which has broad…

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

The Loewner framework for model order reduction is applied to the class of infinite-dimension systems. The transfer function of such systems is irrational (as opposed to linear systems, whose transfer function is rational) and can be…

Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional…

This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…

This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…

We present results on the estimation and evaluation of success probabilities for ordinal optimisation over uncountable sets (such as subsets of $\mathbb{R}^{d}$). Our formulation invokes an assumption of a Gaussian copula model, and we show…

For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…

Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…

This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the…

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate,…

We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our…

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…

We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality…