Related papers: Distance function of D numbers
We present a Gibbs sampler for the Dempster-Shafer (DS) approach to statistical inference for Categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
This paper proposes using a method named Double Score Matching (DSM) to do mass-imputation and presents an application to make inferences with a nonprobability sample. DSM is a $k$-Nearest Neighbors algorithm that uses two balance scores…
We revisit the fundamental problem of learning with distribution shift, in which a learner is given labeled samples from training distribution $D$, unlabeled samples from test distribution $D'$ and is asked to output a classifier with low…
Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a much higher computational burden. A lot of work has been done to reduce the time complexity of information…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
We study the problem of distinguishing between two symmetric probability distributions over $n$ bits by observing $k$ bits of a sample, subject to the constraint that all $k-1$-wise marginal distributions of the two distributions are…
It is well-known since the seventies of last century that Depth First Search (DFS) can be used to compute strongly connected components [RE. Tarjan. SIAM Journal on Computing, 1972] and Breadth First Search (BFS) can be used to compute…
This paper relates parameter distance to gradient breakdown for a broad class of nonlinear compositional functions. The analysis leads to a new distance function called deep relative trust and a descent lemma for neural networks. Since the…
In this work, we use the Belief Function Theory which extends the probabilistic framework in order to provide uncertainty bounds to different categories of crowd density estimators. Our method allows us to compare the multi-scale…
Multi-sensor data fusion technology plays an important role in real applications. Because of the flexibility and effectiveness in modelling and processing the uncertain information regardless of prior probabilities, Dempster-Shafer evidence…
The $L^k$-Wasserstein distance $\mathbb{W}_k (k\ge 1)$ and the probability distance $\mathbb{W}_\psi$ induced by a concave function $\psi$, are estimated between different diffusion processes with singular coefficients. As applications, the…
This paper deals with maximization of classical $f$-divergence between the distributions of a measurement outputs of a given pair of quantum states. $f$-divergence $D_{f}$ between the probability density functions $p_{1}$ and $p_{2}$ over a…
A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…
This paper describes a natural framework for rules, based on belief functions, which includes a repre- sentation of numerical rules, default rules and rules allowing and rules not allowing contraposition. In particular it justifies the use…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modelling. Existing methods for uncertainty modelling face a fundamental…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are…