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Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large…
We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…
Two types of recurrence sets are introduced for inverse semigroup partial actions in topological spaces. We explore their connections with similar notions for related types of imperfect symmetries (prefix inverse semigroup expansions,…
In this paper we propose a numerical scheme for the class of backward doubly stochastic (BDSDEs) with possible path-dependent terminal values. We prove that our scheme converge in the strong $L^2$-sense and derive its rate of convergence.…
A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving…
Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…
The distribution of reversible programs tends to a limit as their size increases. For problems with a Hamming distance fitness function the limiting distribution is binomial with an exponentially small chance (but non~zero) chance of…
A common lens to theoretically study neural net architectures is to analyze the functions they can approximate. However, constructions from approximation theory may be unrealistic and therefore less meaningful. For example, a common…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
We study the problem of approximating an unknown function $f:\mathbb{R}\to\mathbb{R}$ by a degree-$d$ polynomial using as few function evaluations as possible, where error is measured with respect to a probability distribution $\mu$.…
Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation…
Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
We propose a novel dictionary learning add-on for existing approximation algorithms for spherical inverse problems such as the downward continuation of the gravitational potential. The Inverse Problem Matching Pursuit (IPMP) algorithms…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the…
In this work we relate the deterministic complexity of factoring polynomials (over finite fields) to certain combinatorial objects we call m-schemes. We extend the known conditional deterministic subexponential time polynomial factoring…
We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…