相关论文: Average sensitivity and noise sensitivity of polyn…

The empirical evidence indicates that stochastic optimization with heavy-tailed gradient noise is more appropriate to characterize the training of machine learning models than that with standard bounded gradient variance noise. Most…

We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…

In the study of stochastic PDEs with colored, non-trace class space-time noise, one frequently encounters Gaussian series of the form $$g \sum_{n\geq 1} \gamma_n \mu_n f_n, $$ where $(\gamma_n)_{n}$ is a sequence of standard independent…

We investigate the effect of noise on Random Boolean Networks. Noise is implemented as a probability $p$ that a node does not obey its deterministic update rule. We define two order parameters, the long-time average of the Hamming distance…

Advances in neural architecture search, as well as explainability and interpretability of connectionist architectures, have been reported in the recent literature. However, our understanding of how to design Bayesian Deep Learning (BDL)…

We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…

A Boolean function $f:\{0,1\}^n \to \{0,1\}$ is said to be noise sensitive if inserting a small random error in its argument makes the value of the function almost unpredictable. Benjamini, Kalai and Schramm showed that if the sum of…

We study functions on the infinite-dimensional Hamming cube $\{-1,1\}^\infty$, in particular Boolean functions into $\{-1,1\}$, generalising results on analysis of Boolean functions on $\{-1,1\}^n$ for $n\in\mathbb{N}$. The notion of noise…

We study a natural complexity measure of Boolean functions known as the rational degree. Denoted $\textrm{rdeg}(f)$, it is the minimal degree of a rational function that is equal to $f$ on the Boolean hypercube. For total functions $f$, it…

Machine learning models trained by different optimization algorithms under different data distributions can exhibit distinct generalization behaviors. In this paper, we analyze the generalization of models trained by noisy iterative…

We determine a fundamental upper bound on the performance of any adaptive protocol for discrimination or estimation of a channel which has an unknown parameter encoded in the state of its environment. Since our approach relies on the…

We introduce the notion of classical fractional query algorithms, which generalize decision trees in the average-case setting, and can potentially perform better than them. We show that the limiting run-time complexity of a natural class of…

We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy…

This paper, the fourth part of a series of papers on the arithmetic average (AA) density fusion approach and its application for target tracking, addresses the intricate challenge of distributed heterogeneous multisensor multitarget…

We introduce a new tensor norm, the average spectrum norm, to study sample complexity of tensor completion problems based on the canonical polyadic decomposition (CPD). Properties of the average spectrum norm and its dual norm are…

Recent work has shown the surprising power of low-degree sandwiching polynomial approximators in the context of challenging learning settings such as learning with distribution shift, testable learning, and learning with contamination. A…

We establish maximal concentration bounds for the iterates generated by stochastic approximation algorithms with general step sizes, where the noise has a finite-state Markovian component plus a Martingale-difference component. When the…

The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation stating that arbitrarily long quantum computations can be performed with a polylogarithmic overhead provided the noise level is below a…

What kinds of functions are learnable from their satisfying assignments? Motivated by this simple question, we extend the framework of De, Diakonikolas, and Servedio [DDS15], which studied the learnability of probability distributions over…

We consider the problem of testing whether an unknown Boolean function $f$ is monotone versus $\epsilon$-far from every monotone function. The two main results of this paper are a new lower bound and a new algorithm for this well-studied…