Related papers: A Linear Programming Inequality with Applications …

In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…

Many quantitative properties of probabilistic programs can be characterized as least fixed points, but verifying their lower bounds remains a challenging problem. We present a new approach to lower-bound verification that exploits and…

This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…

Quantifying extra functions, herein referred to as outcome functions, over optimal solutions of an optimization problem can provide decision makers with additional information on a system. This bears more importance when the optimization…

Context: Software engineering has a problem in that when we empirically evaluate competing prediction systems we obtain conflicting results. Objective: To reduce the inconsistency amongst validation study results and provide a more formal…

We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…

For many common height functions, it is notoriously hard to compute the essential minimum. Nevertheless there are two classical methods, one giving lower bounds and the other giving upper bounds. In this paper, we show that the two methods…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.

We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat…

Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…

In the past years, deep learning models have been successfully applied in several cognitive tasks. Originally inspired by neuroscience, these models are specific examples of differentiable programs. In this paper we define and motivate…

As an intrinsic and fundamental property of big data, data heterogeneity exists in a variety of real-world applications, such as precision medicine, autonomous driving, financial applications, etc. For machine learning algorithms, the…

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…

In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at…

The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate…

Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…

Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…

Artificial Intelligence has gained a lot of traction in the recent years, with machine learning notably starting to see more applications across a varied range of fields. One specific machine learning application that is of interest to us…

Use of an error correction code in a given transmission channel can be regarded as the statistical experiment. Therefore, powerful results from the theory of comparison of experiments can be applied to compare the performances of different…