Related papers: A Kernel Mean Embedding Approach to Reducing Conse…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…
The consistency of a learning method is usually established under the assumption that the observations are a realization of an independent and identically distributed (i.i.d.) or mixing process. Yet, kernel methods such as support vector…
Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…
In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…
Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…
We study a class of sampled stochastic optimization problems, where the underlying state process has diffusive dynamics of the mean-field type. We establish the existence of optimal relaxed controls when the sample set has finite size. The…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features.We present theoretical properties of this method and show that it is uniformly consistent in finding the…
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…
Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…
Leveraging the kernel trick in both the input and output spaces, surrogate kernel methods are a flexible and theoretically grounded solution to structured output prediction. If they provide state-of-the-art performance on complex data sets…
As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…
We explore the performance of sample average approximation in comparison with several other methods for stochastic optimization when there is information available on the underlying true probability distribution. The methods we evaluate are…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing…
We study channel simulation and distributed matching, two fundamental problems with several applications to machine learning, using a recently introduced generalization of the standard rejection sampling (RS) algorithm known as Ensemble…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…