Related papers: Decision-theoretic rough sets based on time-depend…

We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we…

We consider a random process as a solution of stochastic differential equations with dependence of the coefficients on small parameter $\varepsilon$ and we suppose that the drift coefficients of these equations are unbounded on the…

We present a practical scheme for performing error estimates for Density Functional Theory calculations. The approach which is based on ideas from Bayesian statistics involves creating an ensemble of exchange-correlation functionals by…

Coreset of a given dataset and loss function is usually a small weighed set that approximates this loss for every query from a given set of queries. Coresets have shown to be very useful in many applications. However, coresets construction…

This brief note clarifies that, in Generator Matching (which subsumes a large family of flow matching and diffusion models over continuous, manifold, and discrete spaces), both the Bregman divergence loss and the linear parameterization of…

Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality. Making predictions on these time series has become a critical challenge due…

The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is…

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…

Many applications require the ability to judge uncertainty of time-series forecasts. Uncertainty is often specified as point-wise error bars around a mean or median forecast. Due to temporal dependencies, such a method obscures some…

Scheduling policies for real-time systems exhibit threshold behavior that is related to the utilization of the task set they schedule, and in some cases this threshold is sharp. For the rate monotonic scheduling policy, we show that…

A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition $z_0 \in \mathcal{Z}$ and (b) transition function $f: (\mathcal{Z}, \mathcal{T}) \to \mathcal{Z}$ often…

Attribute reduction is one of the most important topics in rough set theory. Heuristic attribute reduction algorithms have been presented to solve the attribute reduction problem. It is generally known that fitness functions play a key role…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy intervals. The membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the…

We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

The relation between rate distortion function (RDF) and Bayesian filtering theory is discussed. The relation is established by imposing a causal or realizability constraint on the reconstruction conditional distribution of the RDF, leading…