Related papers: Data fission: splitting a single data point
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
In object tracking and state estimation problems, ambiguous evidence such as imprecise measurements and the absence of detections can contain valuable information and thus be leveraged to further refine the probabilistic belief state. In…
Big data sets must be carefully partitioned into statistically similar data subsets that can be used as representative samples for big data analysis tasks. In this paper, we propose the random sample partition (RSP) data model to represent…
We observe $n$ independent pairs of random variables $(W_{i}, Y_{i})$, where the conditional distribution of $Y_{i}$ given $W_{i}=w_{i}$ follows a one-parameter exponential family with parameter $\bsg^{*}(w_{i})\in\R$. Our goal is to…
In the context of big data analysis, the divide-and-conquer methodology refers to a multiple-step process: first splitting a data set into several smaller ones; then analyzing each set separately; finally combining results from each…
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 a method to restore and to segment simultaneously images degraded by a known point spread function (PSF) and additive white noise. For this purpose, we propose a joint Bayesian estimation framework, where a family of…
Investigation of the underlying physics or biology from empirical data requires a quantifiable notion of similarity - when do two observed data sets indicate nearly identical generating processes, and when they do not. The discriminating…
The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF…
Generative adversarial networks constitute a powerful approach to generative modeling. While generated samples often are indistinguishable from real data, there is no guarantee that they will follow the true data distribution. For…
We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts…
The goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a…
The split feasibility problem is to find an element in the intersection of a closed set $C$ and the linear preimage of another closed set $D$, assuming the projections onto $C$ and $D$ are easy to compute. This class of problems arises…
Given data drawn from an unknown distribution, $D$, to what extent is it possible to ``amplify'' this dataset and output an even larger set of samples that appear to have been drawn from $D$? We formalize this question as follows: an…
We study the problem of learning to choose from m discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive…
Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…
Modern statistical analysis often encounters datasets with large sizes. For these datasets, conventional estimation methods can hardly be used immediately because practitioners often suffer from limited computational resources. In most…
Given a dataset consisting of a single realization of a network, we consider conducting inference on a parameter selected from the data. In particular, we focus on the setting where the parameter of interest is a linear combination of the…