Related papers: On the Observability of Gaussian Models using Disc…
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…
A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
We establish a novel criterion for comparing the performance of two densities, $g_1$ and $g_2$, within the context of corrupted data. Utilizing this criterion, we propose an algorithm to construct a density estimator within a star-shaped…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility…
In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability…
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
This paper is concerned with a characterization of the observability for a continuous-time hidden Markov model where the state evolves as a general continuous-time Markov process and the observation process is modeled as nonlinear function…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a…
This paper presents a new approach to the detection of discontinuities in the n-th derivative of observational data. This is achieved by performing two polynomial approximations at each interstitial point. The polynomials are coupled by…
We propose a discrete approach for approximating solutions to the prescribed Gaussian curvature problem in two-dimensional manifolds, based on the notion of discrete conformality. Our approach provides an efficient numerical method to…