Related papers: Online monotone density estimation and log-optimal…
Given a sequence of $n$ independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing…
We consider kernel smoothed Grenander-type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate $n^{2/5}$ and that the limit distribution at a fixed…
We consider the problem of estimating piecewise regular functions in an online setting, i.e., the data arrive sequentially and at any round our task is to predict the value of the true function at the next revealed point using the available…
One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function…
We establish limit theory for the Grenander estimator of a monotone density near zero. In particular we consider the situation when the true density $f_0$ is unbounded at zero, with different rates of growth to infinity. In the course of…
Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…
Conformal prediction provides a principled framework for uncertainty quantification with finite-sample coverage guarantees. While recent work has extended conformal prediction to online and sequential settings, existing methods typically…
Conformal prediction equips machine learning models with a reasonable notion of uncertainty quantification without making strong distributional assumptions. It wraps around any prediction model and converts point predictions into set…
We consider the problem of converting offline estimators into an online predictor or estimator with small extra regret. Formally this is the problem of merging a collection of probability measures over strings of length 1,2,3,... into a…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
Longitudinal network consists of a sequence of temporal edges among multiple nodes, where the temporal edges are observed in real time. It has become ubiquitous with the rise of online social platform and e-commerce, but largely…
We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret…
We study the problem of prediction with expert advice when the number of experts in question may be extremely large or even infinite. We devise an algorithm that obtains a tight regret bound of $\widetilde{O}(\epsilon T + N + \sqrt{NT})$,…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
We propose a general framework for studying adaptive regret bounds in the online learning framework, including model selection bounds and data-dependent bounds. Given a data- or model-dependent bound we ask, "Does there exist some algorithm…
The problem of estimation of density functionals like entropy and mutual information has received much attention in the statistics and information theory communities. A large class of estimators of functionals of the probability density…
This paper proposes a new family of algorithms for the online optimisation of composite objectives. The algorithms can be interpreted as the combination of the exponentiated gradient and $p$-norm algorithm. Combined with algorithmic ideas…
We study online estimation in latent-variable models by recasting the problem as tracking a moving empirical equilibrium. Standard online EM and stochastic approximation analyses primarily study convergence toward the population parameter…
Due to the drastic gap in complexity between sequential and batch statistical learning, recent work has studied a smoothed sequential learning setting, where Nature is constrained to select contexts with density bounded by 1/{\sigma} with…
We consider the problem of \textit{online sparse linear approximation}, where one predicts the best sparse approximation of a sequence of measurements in terms of linear combination of columns of a given measurement matrix. Such online…