Related papers: On the complexity of PAC learning in Hilbert space…
In this paper, we study linearly constrained optimization problems (LCP). After applying Hadamard parametrization, the feasible set of the parametrized problem (LCPH) becomes an algebraic variety, with conducive geometric properties which…
The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…
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…
The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
Convex algebras, also called (semi)convex sets, are at the heart of modelling probabilistic systems including probabilistic automata. Abstractly, they are the Eilenberg-Moore algebras of the finitely supported distribution monad.…
Learning binary representations of instances and classes is a classical problem with several high potential applications. In modern settings, the compression of high-dimensional neural representations to low-dimensional binary codes is a…
The problem of classifying high-dimensional shapes in real-world data grows in complexity as the dimension of the space increases. For the case of identifying convex shapes of different geometries, a new classification framework has…
In this paper, we study the problem of hyperspectral pixel classification based on the recently proposed architectures for compressive whisk-broom hyperspectral imagers without the need to reconstruct the complete data cube. A clear…
We consider the long-standing question of finding a parameter of a class of probability distributions that characterizes its PAC learnability. We provide a rather surprising answer - no such parameter exists. Our techniques allow us to show…
This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…
The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously considered generalizations: while previous research was…
Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…
Piecewise linear vector optimization problems in a locally convex Hausdorff topological vector spaces setting are considered in this paper. The efficient solution set of these problems are shown to be the unions of finitely many semi-closed…
In this paper convex optimization techniques are employed for convex optimization problems in infinite dimensional Hilbert spaces. A first order optimality condition is given. Let $f : \mathbb{R}^{n}\rightarrow \mathbb{R}$ and let $x\in…
We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…