Related papers: Maximum Principles for Matrix-Valued Analytic Func…
Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore classical methods, like dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that by using…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial…
Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the…
We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and sufficient conditions for this singular value functional…
Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we…
This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue…
Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our primary goal is to establish central limit theorems for these functionals when mixed estimators are employed. Our study is relevant to the…
We characterize the optimal reward functions (scoring rules) that incentivize an agent to acquire information and report it truthfully to the principal. The optimal scoring rules let the agent make a simple binary bet in single-dimensional…
Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…
We investigate the set-theoretic strength of several maximality principles that play an important role in the study of modal and intuitionistic logics. We focus on the well-known Fine and Esakia maximality principles, present two…
A necessary maximum principle is proved for optimal controls of stochastic systems driven by multidimensional Teugel's martingales. The multidimensional Teugel's martingales are constructed by orthogonalizing the multidimensional L\'{e}vy…
In this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin's maximum principle from optimal control theory for the Loewner equation in several complex…
For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
This work advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite…
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. The valuations are classified in terms of their behaviour with…
We characterize the infimum of a matrix norm of a square matrix A induced by an absolute norm, over the fields of real and complex numbers. Usually this infimum is greater than the spectral radius of A. If A is sign equivalent to a…