Related papers: A simple universal algorithm for high-dimensional …
In this paper, we study an efficient algorithm for constructing point sets underlying quasi-Monte Carlo integration rules for weighted Korobov classes. The algorithm presented is a reduced fast component-by-component digit-by-digit…
A pure state of fixed Hamming weight is a superposition of computational basis states such that each bitstring in the superposition has the same number of ones. Given a Hilbert space of the form $\mathcal{H} = (\mathbb{C}_2)^{\otimes n}$,…
Bayesian Optimization (BO) has shown significant success in tackling expensive low-dimensional black-box optimization problems. Many optimization problems of interest are high-dimensional, and scaling BO to such settings remains an…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Quasi-Monte Carlo algorithms are studied for designing discrete approximations of two-stage linear stochastic programs. Their integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error…
This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of Dimensional complexity in algorithmic…
In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…
In this paper, we propose a novel algorithm for function approximation in a weighted Korobov space based on shifted rank-1 lattice rules. To mitigate aliasing errors inherent in lattice-based Fourier coefficient estimation, we employ…
We consider the problem of global optimization with noisy zeroth order oracles - a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
Bayesian optimization has recently emerged as a popular method for the sample-efficient optimization of expensive black-box functions. However, the application to high-dimensional problems with several thousand observations remains…
We consider the problem of identifying universal low-dimensional features from high-dimensional data for inference tasks in settings involving learning. For such problems, we introduce natural notions of universality and we show a local…
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
We study the multivariate integration problem for periodic functions from the weighted Korobov space in the randomized setting. We introduce a new randomized rank-1 lattice rule with a randomly chosen number of points, which avoids the need…
Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
Scaling Bayesian optimization to high dimensions is challenging task as the global optimization of high-dimensional acquisition function can be expensive and often infeasible. Existing methods depend either on limited active variables or…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
Metric learning aims at finding a suitable distance metric over the input space, to improve the performance of distance-based learning algorithms. In high-dimensional settings, it can also serve as dimensionality reduction by imposing a…