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Empirical scaling laws describe how test loss and other performance metrics depend on model size, dataset size, and compute. While such laws are consistent within specific regimes, apparently distinct scaling behaviors have been reported…

Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

This research investigates a novel class of one-dimensional theories characterised by a distinctly defined infinite interaction range. We propose that such theories emerge naturally through a mesoscopic feedback mechanism. In this…

We derive an equilibrium statistical theory for the macroscopic description of a ferromagnetic material at positive finite temperatures. Our formulation describes the most-probable equilibrium macrostates that yield a coherent deterministic…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Many current applications in data science need rich model classes to adequately represent the statistics that may be driving the observations. But rich model classes may be too complex to admit estimators that converge to the truth with…

While hard-sphere models form the foundation of theoretical condensed matter physics, real systems often exhibit some degree of softness. We present a theoretical and numerical study of a class of nearly hard-sphere systems, generalized…

A basic issue in both teaching of and practice of statistics is the interplay between modelling assumptions and inference performance. The general message conveyed is that stronger assumptions lead to better statistical performance of the…

Researchers develop models to explain the unknowns. These models typically involve parameters that capture tangible quantities, the estimation of which is desired. Parameter identifiability investigates the recoverability of the unknown…

The use of emergent constraints to quantify uncertainty for key policy relevant quantities such as Equilibrium Climate Sensitivity (ECS) has become increasingly widespread in recent years. Many researchers, however, claim that emergent…

The structure of the equation of state $\omega$ could be very complicate in nature while a few linear models have been successful in cosmological predictions. Linear models are treated as leading approximation of a complete Taylor series in…

While supersymmetric extensions of the Standard Model can be fully described in terms of explicitly broken global supersymmetry, this description is only effective. Once related to spontaneous breaking in a more fundamental theory, the…

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the…

Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…

Many collective systems exist in nature far from equilibrium, ranging from cellular sheets up to flocks of birds. These systems reflect a form of active matter, whereby individual material components have internal energy. Under specific…

We present models in which the indeterministic feature of Quantum Mechanics is represented in the form of definite physical mechanisms. Our way is completely different from so-called hidden parameter models, namely, we start from a certain…

We work out an effective theory of accelerated expansion to describe general phenomena of inflation and acceleration (dark energy) in the Universe. Our aim is to determine from theoretical grounds, in a physically-motivated and model…

In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in…

The physics of matter in the condensed state is concerned with problems in which the number of constituent particles is vastly greater than can be easily comprehended. The inherent physical limitations of the human mind are fundamental and…

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…