Related papers: Probabilistic divide-and-conquer: deterministic se…
In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of…
When split conformal prediction operates in batch mode with exchangeable data, we determine the exact distribution of the empirical coverage of prediction sets produced for a finite batch of future observables, as well as the exact…
Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For…
Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…
The strategy of divide-and-combine (DC) has been widely used in the area of big data. Bias-correction is crucial in the DC procedure for validly aggregating the locally biased estimators, especial for the case when the number of batches of…
Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
We address the problem of approximating the moments of the solution, $\boldsymbol{X}(t)$, of an It\^o stochastic differential equation (SDE) with drift and a diffusion terms over a time-grid $t_0, t_1, \ldots, t_n$. In particular, we assume…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…
Masked diffusion models (MDMs) generate text by iteratively selecting positions to unmask and then predicting tokens at those positions. Yet MDMs lack proper likelihood evaluation: the evidence lower bound (ELBO) is not only a loose bound…
We consider the problem of learning a discrete distribution in the presence of an $\epsilon$ fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, $p$, and each data source…
Split conformal prediction (CP) is arguably the most popular CP method for uncertainty quantification, enjoying both academic interest and widespread deployment. However, the original theoretical analysis of split CP makes the crucial…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk…
A novel decomposition scheme to solve parametric non-convex programs as they arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of a fixed number of alternating proximal gradient steps and a dual update per time…
In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…
The issues of bias-correction and robustness are crucial in the strategy of divide-and-conquer (DC), especially for asymmetric nonparametric models with massive data. It is known that quantile-based methods can achieve the robustness, but…
Let $L$ be a linear differential operator acting on functions defined over an open set $\mathcal{D}\subset \mathbb{R}^d$. In this article, we characterize the measurable second order random fields $U = (U(x))_{x\in\mathcal{D}}$ whose sample…