Related papers: Error rate control for classification rules in mul…
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…
We consider a class of learning problem of point estimation for modeling high-dimensional nonlinear functions, whose learning dynamics is guided by model training dataset, while the estimated parameter in due course provides an acceptable…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed…
Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
Simultaneous statistical inference has been a cornerstone in the statistics methodology literature because of its fundamental theory and paramount applications. The mainstream multiple testing literature has traditionally considered two…
Classification tasks in machine learning involving more than two classes are known by the name of "multi-class classification". Performance indicators are very useful when the aim is to evaluate and compare different classification models…
We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…
Multi-label classification (MLC) is a supervised learning problem in which, contrary to standard multiclass classification, an instance can be associated with several class labels simultaneously. In this chapter, we advocate a rule-based…
Within the machine learning community, the widely-used uniform convergence framework has been used to answer the question of how complex, over-parameterized models can generalize well to new data. This approach bounds the test error of the…
Many important tasks of large-scale recommender systems can be naturally cast as testing multiple linear forms for noisy matrix completion. These problems, however, present unique challenges because of the subtle bias-and-variance tradeoff…
Multivariate statistics are often available as well as necessary in hypothesis tests. We study how to use such statistics to control not only false discovery rate (FDR) but also positive FDR (pFDR) with good power. We show that FDR can be…
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…
We consider the problem of selecting an optimal subset of information sources for a hypothesis testing/classification task where the goal is to identify the true state of the world from a finite set of hypotheses, based on finite…
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…
In multiclass classification, the goal is to learn how to predict a random label $Y$, valued in $\mathcal{Y}=\{1,\; \ldots,\; K \}$ with $K\geq 3$, based upon observing a r.v. $X$, taking its values in $\mathbb{R}^q$ with $q\geq 1$ say, by…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There…
Calibrating a multiclass predictor, that outputs a distribution over labels, is particularly challenging due to the exponential number of possible prediction values. In this work, we propose a new definition of calibration error that…