Related papers: The Generalized Pignistic Transformation
Generalized probabilistic theories (GPT) provide a general framework that includes classical and quantum theories. It is described by a cone $C$ and its dual $C^*$. We show that whether some one-way communication complexity problems can be…
Understanding why deep neural networks (DNNs) fail to generalize to unseen samples remains a long-standing challenge. Existing studies mainly examine changes in externally observable factors such as data, representations, or outputs, yet…
Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…
We study a mini-batch diversification scheme for stochastic gradient descent (SGD). While classical SGD relies on uniformly sampling data points to form a mini-batch, we propose a non-uniform sampling scheme based on the Determinantal Point…
The AGM theory of belief revision has become an important paradigm for investigating rational belief changes. Unfortunately, researchers working in this paradigm have restricted much of their attention to rather simple representations of…
Based on Pontryagin Maximum Principle (PMP), this paper establishes a generalized PMP aiming at control system with with extra input/output terms. The paper details the adaptive target and gives a proof of the generalized theorem.…
Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful connections between them have rarely been…
In this paper, we generalize the basic notions and results of Dempster-Shafer theory from predicates to formal concepts. Results include the representation of conceptual belief functions as inner measures of suitable probability functions,…
To foster the verifiability and testability of Deep Neural Networks (DNN), an increasing number of methods for test case generation techniques are being developed. When confronted with testing DNN models, the user can apply any existing…
The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…
The standard regression tree method applied to observations within clusters poses both methodological and implementation challenges. Effectively leveraging these data requires methods that account for both individual-level and sample-level…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
Dempster-Shafer evidence theory is an efficient mathematical tool to deal with uncertain information. In that theory, basic probability assignment (BPA) is the basic element for the expression and inference of uncertainty. Decision-making…
This paper extends the concept of generalized polarization tensors (GPTs), which was previously defined for inclusions with homogeneous conductivities, to inhomogeneous conductivity inclusions. We begin by giving two slightly different but…
Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple…
Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…