相关论文: The Xerographic Distribution: Scientific Reasoning…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…
In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
A model is presented for the origin of the large scale structure of the universe and their Mass-Radius scaling law; a fractal power law, $M \propto R^D$, with dimension $D=2$, most significantly. The physics is conventional, orthodox, but…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
The development of science and technology has progressively demonstrated the ability of humankind to understand and manipulate the physical world, and it has also shown some fundamental limitations to predictability of physical events. This…
We consider the properties of an ensemble of universes as function of size, where size is defined in terms of the asymptotic value of the Hubble constant (or, equivalently, the value of the cosmological constant). We assume that standard…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
One signature of an expanding universe is the time-variation of the cosmological abundances of its different components. For example, a radiation-dominated universe inevitably gives way to a matter-dominated universe, and critical moments…
Inspired by Christopher Alexanders conception of the world - space is not lifeless or neutral but a living structure involving far more small things than large ones a topological representation has been previously developed to characterize…
The probabilities of point events in space 3 + 1 obey an equation of Dirac type. Masses, moments, energies, spins, etc. are the parameters of the probability distribution of such events. The terms and equations of quark-gluon theories turn…
The large-scale structure in cosmology is highly non-Gaussian at late times and small length scales, making it difficult to describe analytically. Parameter inference, data reconstruction, and data generation tasks in cosmology are greatly…
From the standpoint of theoretical physics we can treat Newtonian cosmology as a problem in nonlinear dynamics. The attempt to average the density, in search of a method of making contact between theory and observation, is replaced by the…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with…
We consider a model of selective prediction, where the prediction algorithm is given a data sequence in an online fashion and asked to predict a pre-specified statistic of the upcoming data points. The algorithm is allowed to choose when to…
Imagine being shown $N$ samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless we have some prior notions about what to…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…