Related papers: Optimal functional supervised classification with …
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…
The problem of supervised classification (or discrimination) with functional data is considered, with a special interest on the popular k-nearest neighbors (k-NN) classifier. First, relying on a recent result by Cerou and Guyader (2006), we…
A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…
The recent success of neural networks in pattern recognition and classification problems suggests that neural networks possess qualities distinct from other more classical classifiers such as SVMs or boosting classifiers. This paper studies…
We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this…
We examine the supervised learning problem in its continuous setting and give a general optimality condition through techniques of functional analysis and the calculus of variations. This enables us to solve the optimality condition for the…
Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…
Performing optimal Bayesian design for discriminating between competing models is computationally intensive as it involves estimating posterior model probabilities for thousands of simulated datasets. This issue is compounded further when…
When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop…
The problem of obtaining optimal projections for performing discriminant analysis with Gaussian class densities is studied. Unlike in most existing approaches to the problem, the focus of the optimisation is on the multinomial likelihood…
In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…
We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…
The k-nearest-neighbour procedure is a well-known deterministic method used in supervised classification. This paper proposes a reassessment of this approach as a statistical technique derived from a proper probabilistic model; in…
We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution…
We focus on the supervised binary classification problem, which consists in guessing the label $Y$ associated to a co-variate $X \in \R^d$, given a set of $n$ independent and identically distributed co-variates and associated labels…
The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
In sequential hypothesis testing, Generalized Binary Search (GBS) greedily chooses the test with the highest information gain at each step. It is known that GBS obtains the gold standard query cost of $O(\log n)$ for problems satisfying the…