Related papers: Median of Means Sampling for the Keister Function
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
Determinantal points processes are a promising but relatively under-developed tool in machine learning and statistical modelling, being the canonical statistical example of distributions with repulsion. While their mathematical formulation…
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…
An easy-to-implement form of the Metropolis Algorithm is described which, unlike most standard techniques, is well suited to sampling from multi-modal distributions on spaces with moderate numbers of dimensions (order ten) in environments…
In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why…
Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating…
We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…
We study the power of uniform sampling for $k$-Median in various metric spaces. We relate the query complexity for approximating $k$-Median, to a key parameter of the dataset, called the balancedness $\beta \in (0, 1]$ (with $1$ being…
Researchers increasingly use meta-analysis to synthesize the results of several studies in order to estimate a common effect. When the outcome variable is continuous, standard meta-analytic approaches assume that the primary studies report…
Randomized quasi-Monte Carlo (RQMC) sampling can bring orders of magnitude reduction in variance compared to plain Monte Carlo (MC) sampling. The extent of the efficiency gain varies from problem to problem and can be hard to predict. This…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
We study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synthesized to an output signal. We show how to approximate such…
Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency,…
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…
The classical approaches to numerically integrating a function $f$ are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate $f$ and have error $O(\sigma(f)/\sqrt{n})$, where $\sigma(f)$ is the…
We consider the problem of estimating the density of a random variable $X$ that can be sampled exactly by Monte Carlo (MC). We investigate the effectiveness of replacing MC by randomized quasi Monte Carlo (RQMC) or by stratified sampling…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
The $k$-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to…
We motive and calculate Newton--Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that…
For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries…