Related papers: Information Splitting for Big Data Analytics
Suppose we observe a random vector $X$ from some distribution $P$ in a known family with unknown parameters. We ask the following question: when is it possible to split $X$ into two parts $f(X)$ and $g(X)$ such that neither part is…
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
In non-linear estimations, it is common to assess sampling uncertainty by bootstrap inference. For complex models, this can be computationally intensive. This paper combines optimization with resampling: turning stochastic optimization into…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
In the context of the usual calibration model, we consider the case in which the independent variable is unobservable, but a pre-fixed value on its surrogate is available. Thus, considering controlled variables and assuming that the…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
The planning and design of future experiments rely heavily on forecasting to assess the potential scientific value provided by a hypothetical set of measurements. The Fisher information matrix, due to its convenient properties and low…
The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…
Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…
This paper introduces a method for efficiently approximating the inverse of the Fisher information matrix, a crucial step in achieving effective variational Bayes inference. A notable aspect of our approach is the avoidance of analytically…
Assessing sampling uncertainty in extremum estimation can be challenging when the asymptotic variance is not analytically tractable. Bootstrap inference offers a feasible solution but can be computationally costly especially when the model…
Learning Ising or Potts models from data has become an important topic in statistical physics and computational biology, with applications to predictions of structural contacts in proteins and other areas of biological data analysis. The…
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…
In the traditional object recognition pipeline, descriptors are densely sampled over an image, pooled into a high dimensional non-linear representation and then passed to a classifier. In recent years, Fisher Vectors have proven empirically…
A machine that learns a task from observations must encounter and process uncertainty and novelty, especially when it is to maintain performance when observing new information and to select the hypothesis that best fits the current…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…