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Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Accuracy-driven computation is a strategy widely used in exact-decisions number types for robust geometric algorithms. This work provides an overview on the usage of error bounds in accuracy-driven computation, compares different approaches…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
Given a combinatorial decomposition for a counting problem, we resort to the simple scheme of approximating large numbers by floating-point representations in order to obtain efficient Fully Polynomial Time Approximation Schemes (FPTASes)…
We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…
While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced. Thus, interpretability…
The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems Ax = b, where A is a symmetric positive definite matrix. Rather than computing residuals directly, it updates…
Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
This paper provides a bound on the number of numeric operations (fixed or floating point) that can safely be performed before accuracy is lost. This work has important implications for control systems with safety-critical software, as these…
Smoothed online combinatorial optimization considers a learner who repeatedly chooses a combinatorial decision to minimize an unknown changing cost function with a penalty on switching decisions in consecutive rounds. We study smoothed…
The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…
We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…
The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point…
In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
In compressive sensing, one important parameter that characterizes the various greedy recovery algorithms is the iteration bound which provides the maximum number of iterations by which the algorithm is guaranteed to converge. In this…
This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multi-armed bandit problems. The algorithm, also known as Thompson Sampling,…
We consider distributed statistical optimization in one-shot setting, where there are $m$ machines each observing $n$ i.i.d. samples. Based on its observed samples, each machine sends a $B$-bit-long message to a server. The server then…