相关论文: The Generalized Pignistic Transformation

Gaussian process tomography (GPT) is a method used for obtaining real-time tomographic reconstructions of the plasma emissivity profile in a tokamak, given some model for the underlying physical processes involved. GPT can also be used,…

Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…

What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We…

The reparameterization trick has become one of the most useful tools in the field of variational inference. However, the reparameterization trick is based on the standardization transformation which restricts the scope of application of…

The generalized belief propagation (GBP), introduced by Yedidia et al., is an extension of the belief propagation (BP) algorithm, which is widely used in different problems involved in calculating exact or approximate marginals of…

Probability metrics have become an indispensable part of modern statistics and machine learning, and they play a quintessential role in various applications, including statistical hypothesis testing and generative modeling. However, in a…

Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…

In this paper, we present a decision support system based on belief functions and the pignistic transformation. The system is an integration of an evidential system for belief function propagation and a valuation-based system for Bayesian…

There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…

Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often…

This paper proposes a methodology for generating and perturbing detailed derivations of equations at scale, aided by a symbolic engine, to evaluate the generalisability of Transformers to out-of-distribution mathematical reasoning problems.…

Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained…

Geometric complexity theory (GCT) is an approach to the $P$ vs. $NP$ and related problems. A high level overview of this research plan and the results obtained so far was presented in a series of three lectures in the Institute of Advanced…

The Generative Pre-trained Transformer (GPT) represents a notable breakthrough in the domain of natural language processing, which is propelling us toward the development of machines that can understand and communicate using language in a…

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how…

Symbolic regression is the task of identifying a mathematical expression that best fits a provided dataset of input and output values. Due to the richness of the space of mathematical expressions, symbolic regression is generally a…

We present the Generalized Policy Gradient (GPG) Theorem, specifically designed for Transformer-based policies. Notably, we demonstrate that both standard Policy Gradient Theorem and GRPO emerge as special cases within our GPG framework.…

Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…