Related papers: Fast rates for noisy clustering
We study high-probability convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. In the proposed scenario, the model is updated in an online fashion, as new information is observed, without storing any…
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than $n^{-1/2}$. The work on this subject has suggested…
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy…
We study statistical and computational limits of clustering when the means of the centres are sparse and their dimension is possibly much larger than the sample size. Our theoretical analysis focuses on the model $X_i = z_i \theta +…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and…
We consider the prediction error of linear regression with L1 regularization when the number of covariates p is large relative to the sample size n. When the model is k-sparse and well-specified, and restricted isometry or similar…
We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a…
Motivated by the need of observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems with noisy output that consists of the…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to…
We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed…
A challenge in developing machine learning regression models is that it is difficult to know whether maximal performance has been reached on a particular dataset, or whether further model improvement is possible. In biology this problem is…
Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…
We consider the problem of clustering a graph $G$ into two communities by observing a subset of the vertex correlations. Specifically, we consider the inverse problem with observed variables $Y=B_G x \oplus Z$, where $B_G$ is the incidence…
The ODE method has been a workhorse for algorithm design and analysis since the introduction of the stochastic approximation. It is now understood that convergence theory amounts to establishing robustness of Euler approximations for ODEs,…
The performance measure of an algorithm is a crucial part of its analysis. The performance can be determined by the study on the convergence rate of the algorithm in question. It is necessary to study some (hopefully convergent) sequence…
We consider estimation of the common probability density $f$ of i.i.d. random variables $X_i$ that are observed with an additive i.i.d. noise. We assume that the unknown density $f$ belongs to a class $\mathcal{A}$ of densities whose…
We revisit the problem of empirical risk minimziation (ERM) with differential privacy. We show that noisy AdaGrad, given appropriate knowledge and conditions on the subspace from which gradients can be drawn, achieves a regret comparable to…
We consider the problem of minimizing a given $n$-variate polynomial $f$ over the hypercube $[-1,1]^n$. An idea introduced by Lasserre, is to find a probability distribution on $[-1,1]^n$ with polynomial density function $h$ (of given…