Related papers: Le cam theory on the comparison of statistical mod…
We investigate statistical inference across time scales. We take as toy model the estimation of the intensity of a discretely observed compound Poisson process with symmetric Bernoulli jumps. We have data at different time scales:…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
We begin with an interpretation of the L1-distance between two power spectral densities and then, following an analogous rationale, we develop a natural metric for quantifying distance between respective covariance matrices.
Statistical models often assume that data are generated near a structured, smooth, or low-dimensional set. A common approach is to use Bayesian latent variable models, in which each observation is associated with a latent coordinate on the…
The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…
Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…
Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in…
We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information…
Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…
We consider the problem of computing L1-distances between every pair ofcprobability densities from a given family. We point out that the technique of Cauchy random projections (Indyk'06) in this context turns into stochastic integrals with…
Parallel texts (bitexts) have properties that distinguish them from other kinds of parallel data. First, most words translate to only one other word. Second, bitext correspondence is noisy. This article presents methods for biasing…
We use white Gaussian noise as a test signal for single-mode and multimode transmission links and estimate the link capacity based on a calculation of mutual information. We also extract the complex amplitude channel estimations and…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
The general problem of performance advantage obtainable by the use of nonclassical transmitted states over classical ones is considered. Attention is focused on the situation where system loss is significant and additive Gaussian noise may…
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
The paper discusses a test for the hypothesis that a random sample comes from the Cauchy distribution. The test statistics is derived from a characterization and is based on the characteristic function. Properties of the test are discussed…
We consider the famous Rasch model, which is applied to psychometric surveys when n persons under test answer m questions. The score is given by a realization of a random binary (n,m)-matrix. Its (j,k)th component indicates whether or not…