Related papers: Deterministic and Probabilistic Error Bounds for F…
Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to…
In this work, we study the generalization capability of algorithms from an information-theoretic perspective. It has been shown that the expected generalization error of an algorithm is bounded from above by a function of the relative…
We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper…
We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be…
This note introduce three Bayesian style Multi-armed bandit algorithms: Information-directed sampling, Thompson Sampling and Generalized Thompson Sampling. The goal is to give an intuitive explanation for these three algorithms and their…
In this paper, we improve the usual relative error bound for the computation of x^n through iterated multiplications by x in binary floating-point arithmetic. The obtained error bound is only slightly better than the usual one, but it is…
This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…
Many canonical machine learning problems boil down to a convex optimization problem with a finite sum structure. However, whereas much progress has been made in developing faster algorithms for this setting, the inherent limitations of…
We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…
A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these…
This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…
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…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
We study fine-grained error bounds for differentially private algorithms for counting under continual observation. Our main insight is that the matrix mechanism when using lower-triangular matrices can be used in the continual observation…
Using the Moore--Penrose pseudoinverse, this work generalizes the gradient approximation technique called centred simplex gradient to allow sample sets containing any number of points. This approximation technique is called the…
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 provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…
In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…
Probabilistic model checking computes probabilities and expected values related to designated behaviours of interest in Markov models. As a formal verification approach, it is applied to critical systems; thus we trust that probabilistic…