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We introduce beta diffusion, a novel generative modeling method that integrates demasking and denoising to generate data within bounded ranges. Using scaled and shifted beta distributions, beta diffusion utilizes multiplicative transitions…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
Gaussian belief propagation (GBP) is a recursive computation method that is widely used in inference for computing marginal distributions efficiently. Depending on how the factorization of the underlying joint Gaussian distribution is…
Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, which is often viewed as a remedy for potential model…
Deep neural networks often suffer the data distribution shift between training and testing, and the batch statistics are observed to reflect the shift. In this paper, targeting of alleviating distribution shift in test time, we revisit the…
A Wright function based framework is proposed to combine and extend several distribution families. The $\alpha$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution…
Response times collected in computerised assessments provide information about the underlying response process and may exhibit within-person variation over the course of a test. We propose a latent variable model for log response times that…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
In this paper, we introduce the flexible interpretable gamma (FIG) distribution which has been derived by Weibullisation of the body-tail generalised normal distribution. The parameters of the FIG have been verified graphically and…
The paper describes the global limiting behavior of Gaussian beta ensembles where the parameter $\beta$ is allowed to vary with the matrix size $n$. In particular, we show that as $n \to \infty$ with $n\beta \to \infty$, the empirical…
The Gradient Boosted Tree (GBT) algorithm is one of the most popular machine learning algorithms used in production, for tasks that include Click-Through Rate (CTR) prediction and learning-to-rank. To deal with the massive datasets…
In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…
Statistical methodology for the design and analysis of clinical Phase II dose response studies, with related software implementation, are well developed for the case of a normally distributed, homoscedastic response considered for a single…
We study the probability distribution of the value of geometric Brownian motion at the stochastic observation time. It is known that the exponentially distributed observation time yields the distribution called the double Pareto…
The homogeneous cooling state (HCS) of a granular gas described by the inelastic Boltzmann equation is reconsidered. As usual, particles are taken as inelastic hard disks or spheres, but now the coefficient of normal restitution $\alpha$ is…
Neural networks often make predictions relying on the spurious correlations from the datasets rather than the intrinsic properties of the task of interest, facing sharp degradation on out-of-distribution (OOD) test data. Existing de-bias…
The primary visual cortex processes a large amount of visual information, however, due to its large receptive fields, when multiple stimuli fall within one receptive field, there are computational problems. To solve this problem, the visual…
This work introduces a novel approach for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are jointly…
We propose new analytical tools for describing growth-rate distributions generated by stationary time-series. Our analysis shows how deviations from normality are not pathological behaviour, as suggested by some traditional views, but…
In many practical reinforcement learning tasks, feedback is only provided at the end of a long horizon, leading to sparse and delayed rewards. Existing reward redistribution methods typically assume that per-step rewards are independent,…