Related papers: A Non-Triviality Certificate for Scalars and its a…
Usually standard algorithms employ a loss where each error is the mere absolute difference between the true value and the prediction, in case of a regression task. In the present, we introduce several error weighting schemes that are a…
NLCertify is a software package for handling formal certification of nonlinear inequalities involving transcendental multivariate functions. The tool exploits sparse semialgebraic optimization techniques with approximation methods for…
Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper…
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
We introduce an efficient method for training the linear ranking support vector machine. The method combines cutting plane optimization with red-black tree based approach to subgradient calculations, and has O(m*s+m*log(m)) time complexity,…
We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their gradient ideals. We remove the two structural assumptions…
The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while…
We propose new methods for Support Vector Machines (SVMs) using tree architecture for multi-class classi- fication. In each node of the tree, we select an appropriate binary classifier using entropy and generalization error estimation, then…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
We consider the problem of certifying lower bounds for real-valued multivariate transcendental functions. The functions we are dealing with are nonlinear and involve semialgebraic operations as well as some transcendental functions like…
Systems of random linear equations may or may not have solutions with all components being non-negative. The question is, e.g., of relevance when the unknowns are concentrations or population sizes. In the present paper we show that if such…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
This paper deals with the comparison of several stationary processes with unequal sample sizes. We provide a detailed theoretical framework on the testing problem for equality of spectral densities in the bivariate case, after which the…
We consider a homogeneous system of linear equations of the form $A_\alpha^{\otimes N} {\bf x} = 0$ arising from the distinguishability of two quantum operations by $N$ uses in parallel, where the coefficient matrix $A_\alpha$ depends on a…
We introduce a randomized algorithm for computing the minimal-norm solution to an underdetermined system of linear equations. Given an arbitrary full-rank m x n matrix A with m<n, any m x 1 vector b, and any positive real number epsilon…
Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs.…
This paper gives a new algorithm for sampling tree-weighted partitions of a large class of planar graphs. Formally, the tree-weighted distribution on $k$-partitions of a graph weights $k$-partitions proportional to the product of the number…