相关论文: Universally optimal crossover designs under subjec…

Dropout, a simple and effective way to train deep neural networks, has led to a number of impressive empirical successes and spawned many recent theoretical investigations. However, the gap between dropout's training and inference phases,…

Deep learning models learn to fit training data while they are highly expected to generalize well to testing data. Most works aim at finding such models by creatively designing architectures and fine-tuning parameters. To adapt to…

Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…

Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue.…

A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in…

Optimal designs for generalized linear models require a prior knowledge of the regression parameters. At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without…

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…

We study a problem of best-effort adaptation motivated by several applications and considerations, which consists of determining an accurate predictor for a target domain, for which a moderate amount of labeled samples are available, while…

An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…

A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…

Optimum experimental design theory has recently been extended for parameter estimation in copula models. However, the choice of the correct dependence structure still requires wider analyses. In this work the issue of copula selection is…

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a…

Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an…

In this letter we summarize some recent theoretical work on the design of collectives, i.e., of systems containing many agents, each of which can be viewed as trying to maximize an associated private utility, where there is also a world…

This article makes no claim to originality, other than, perhaps, the simple statement here called the {\it Abstract Maximum Principle}. Actually, the whole contents are strongly based on some H. Sussmann's and coauthors' papers, in which,…

This paper shows that dropout training in Generalized Linear Models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric…

Understanding generalization is crucial to confidently engineer and deploy machine learning models, especially when deployment implies a shift in the data domain. For such domain adaptation problems, we seek generalization bounds which are…

A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…

We consider the best-choice problem for independent (not necessarily iid) observations $X_1, \cdots, X_n$ with the aim of selecting the sample minimum. We show that in this full generality the monotone case of optimal stopping holds and the…

It is impossible today to pretend that the practice of machine learning is always compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how…