Related papers: Optimal Classification for Functional Data
In the framework of supervised classification (discrimination) for functional data, it is shown that the optimal classification rule can be explicitly obtained for a class of Gaussian processes with "triangular" covariance functions. This…
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…
Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…
High-dimensional classification is a fundamentally important research problem in high-dimensional data analysis. In this paper, we derive a nonasymptotic rate for the minimax excess misclassification risk when feature dimension…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
We establish minimax convergence rates for classification of functional data and for nonparametric regression with functional design variables. The optimal rates are of logarithmic type under smoothness constraints on the functional density…
In the past two decades we have seen the popularity of neural networks increase in conjunction with their classification accuracy. Parallel to this, we have also witnessed how fragile the very same prediction models are: tiny perturbations…
We consider the binary supervised classification problem with the Gaussian functional model introduced in [7]. Taking advantage of the Gaussian structure, we design a natural plug-in classifier and derive a family of upper bounds on its…
We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…
While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether…
Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these…
Most classification models can be considered as the process of matching templates. However, when intra-class uncertainty/variability is not considered, especially for datasets containing unbalanced classes, this may lead to classification…
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…
To detect differences between the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. In this paper we apply the…
We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…
In recent years, there has been considerable innovation in the world of predictive methodologies. This is evident by the relative domination of machine learning approaches in various classification competitions. While these algorithms have…
We investigate the availability of approaching perfect classification on functional data with finite samples. The seminal work (Delaigle and Hall (2012)) showed that perfect classification for functional data is easier to achieve than for…
Data driven classification that relies on neural networks is based on optimization criteria that involve some form of distance between the output of the network and the desired label. Using the same mathematical analysis, for a multitude of…
In this paper, we propose a data based transformation for infinite-dimensional Gaussian processes and derive its limit theorem. For a classification problem, this transformation induces complete separation among the associated Gaussian…
Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data…