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Distributed learning provides an attractive framework for scaling the learning task by sharing the computational load over multiple nodes in a network. Here, we investigate the performance of distributed learning for large-scale linear…

In a recent paper published in this journal [J. Phys. A: Math. Theor. 42 (2009) 495004] we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power \alpha of their distance…

The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple…

In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…

We introduce a multiple criteria Bayesian preference learning framework incorporating behavioral cues for decision aiding. The framework integrates pairwise comparisons, response time, and attention duration to deepen insights into…

Many researchers have identified distribution shift as a likely contributor to the reproducibility crisis in behavioral and biomedical sciences. The idea is that if treatment effects vary across individual characteristics and experimental…

Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence…

Evolutionary game theory has been an important tool for describing economic and social behaviour for decades. Approximate mean value equations describing the time evolution of strategy concentrations can be derived from the players'…

Aligning large language models (LLMs) to human preferences typically relies on aggregating pooled feedback into a single reward model. However, this standard approach assumes that all labelers share the same underlying preferences, ignoring…

For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles…

Penalized B-splines are routinely used in additive models to describe smooth changes in a response with quantitative covariates. It is typically done through the conditional mean in the exponential family using generalized additive models…

The brain anticipates future events using internal models that specify not only what will occur, but also when it will occur and with what probability. We refer to this joint specification of identity, timing, and likelihood as a complete…

Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the…

In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal…

Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Contextual and selection effects tend to produce extreme values in the tails of rank-ordered distributions…

Rule representations significantly influence the search capabilities and decision boundaries within the search space of Learning Classifier Systems (LCSs), a family of rule-based machine learning systems that evolve interpretable models…

In behavioral and psychiatric research, data consisting of a per-subject proportion of "successes" and "failures" over a finite number of trials often arise. This kind of clustered binary data are usually non-normally distributed, which can…

Despite recent progress in time-series foundation models, challenges persist in improving representation learning and adapting to diverse downstream tasks. We introduce a General Time-series Model (GTM), which advances representation…

In his 1986 book, Aitchison explains that compositional data is regularly mishandled in statistical analyses, a pattern that continues to this day. The Dirichlet Type I distribution is a multivariate distribution commonly used to model a…

This paper considers the issue of modeling fractional data observed in the interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model…